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Nuclear engineering is the engineering discipline concerned with designing and applying systems that utilize the energy released by nuclear processes. The most prominent application of nuclear engineering is the generation of electricity. Worldwide, some 440 nuclear reactors in 32 countries generate 10 percent of the world's energy through nuclear fission. In the future, it is expected that nuclear fusion will add another nuclear means of generating energy. Both reactions make use of the nuclear binding energy released when atomic nucleons are either separated (fission) or brought together (fusion). The energy available is given by the binding energy curve, and the amount generated is much greater than that generated through chemical reactions. Fission of 1 gram of uranium yields as much energy as burning 3 tons of coal or 600 gallons of fuel oil, without adding carbon dioxide to the atmosphere. == History == Nuclear engineering was born in 1938, with the discovery of nuclear fission. The first artificial nuclear reactor, CP-1, was designed by a team of physicists who were concerned that Nazi Germany might also be seeking to build a bomb based on nuclear fission. (The earliest known nuclear reaction on Earth occurred naturally, 1.7 billion years ago, in Oklo, Gabon, Africa.) The second artificial nuclear reactor, the X-10 Graphite Reactor, was also a part of the Manhattan Project, as were the plutonium-producing reactors of the Hanford Engineer Works. The first nuclear reactor to generate electricity was Experimental Breeder Reactor I (EBR-I), which did so near Arco, Idaho, in 1951. EBR-I was a standalone facility, not connected to a grid, but a later Idaho research reactor in the BORAX series did briefly supply power to the town of Arco in 1955. The first commercial nuclear power plant, built to be connected to an electrical grid, is the Obninsk Nuclear Power Plant, which began operation in 1954. The second is the Shippingport Atomic Power Station, which produced electricity in 1957. For a chronology, from the discovery of uranium to the current era, see Outline History of Nuclear Energy or History of Nuclear Power. Also see History of Nuclear Engineering Part 1: Radioactivity, Part 2: Building the Bomb, and Part 3: Atoms for Peace. See List of Commercial Nuclear Reactors for a comprehensive listing of nuclear power reactors and IAEA Power Reactor Information System (PRIS) for worldwide and country-level statistics on nuclear power generation. == Sub-disciplines == Nuclear engineers work in such areas as the following: Nuclear reactor design, which has evolved from the Generation I, proof-of concept, reactors of the 1950s and 1960s, to Generation II, Generation III, and Generation IV concepts Thermal hydraulics and heat transfer. In a typical nuclear power plant, heat generates steam that drives a steam turbine and a generator that produces electricity Materials science as it relates to nuclear power applications Managing the nuclear fuel cycle, in which fissile material is obtained, formed into fuel, removed when depleted, and safely stored or reprocessed Nuclear propulsion, mainly for military naval vessels, but there have been concepts for aircraft and missiles. Nuclear power has been used in space since the 1960s Plasma physics, which is integral to the development of fusion power Weapons development and management Generation of radionuclides, which have applications in industry, medicine, and many other areas Nuclear waste management Health physics Nuclear medicine and Medical Physics Health and safety Instrumentation and control engineering Process engineering Project Management Quality engineering Reactor operations Nuclear security (detection of clandestine nuclear materials) Nuclear engineering even has a role in criminal investigation, and agriculture. Many chemical, electrical and mechanical and other types of engineers also work in the nuclear industry, as do many scientists and support staff. In the U.S., nearly 100,000 people directly work in the nuclear industry. Including secondary sector jobs, the number of people supported by the U.S. nuclear industry is 475,000. == Employment == In the United States, nuclear engineers are employed as follows: Electric power generation 25% Federal government 18% Scientific research and development 15% Engineering services 5% Manufacturing 10% Other areas 27% Worldwide, job prospects for nuclear engineers are likely best in those countries that are active in or exploring nuclear technologies: == Education == Organizations that provide study and training in nuclear engineering include the following: == Organizations == American Nuclear Society Asian Network for Education in Nuclear Technology (ANENT) https://www.iaea.org/services/networks/anent Canadian Nuclear Association Chinese Nuclear Society International Atomic Energy Agency International Energy Agency (IEA) Japan Atomic Industrial Forum (JAIF) Korea Nuclear Energy Agency (KNEA) Latin American Network for Education in Nuclear Technology (LANENT) https://www.iaea.org/services/networks/lanent Minerals Council of Australia Nucleareurope Nuclear Institute Nuclear Energy Institute (NEI) Nuclear Industry Association of South Africa (NIASA) Nuclear Technology Education Consortion https://www.ntec.ac.uk/ OECD Nuclear Energy Agency (NEA) Regional Network for Education and Training in Nuclear Technology (STAR-NET) https://www.iaea.org/services/networks/star-net World Nuclear Association World Nuclear Transport Institute == See also == == References == == Further reading == Ash, Milton, "Nuclear reactor kinetics", McGraw-Hill, (1965) Cravens, Gwyneth. Power to Save the World (2007) Gowing, Margaret. Britain and Atomic Energy, 1939–1945 (1964). Gowing, Margaret, and Lorna Arnold. Independence and Deterrence: Britain and Atomic Energy, Vol. I: Policy Making, 1945–52; Vol. II: Policy Execution, 1945–52 (London, 1974) Johnston, Sean F. "Creating a Canadian Profession: The Nuclear Engineer, 1940–68," Canadian Journal of History, Winter 2009, Vol. 44 Issue 3, pp 435–466 Johnston, Sean F. "Implanting a discipline: the academic trajectory of nuclear engineering in the USA and UK," Minerva, 47 (2009), pp. 51–73 == External links == Electric Generation from Commercial Nuclear Power Hacettepe University Department of Nuclear Engineering Nuclear Engineering International magazine Nuclear Safety Info Resources Nuclear Science and Engineering technical journal Science and Technology of Nuclear Installation Open-Access Journal
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https://en.wikipedia.org/wiki/Nuclear_engineering
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Process engineering is a field of study focused on the development and optimization of industrial processes. It consists of the understanding and application of the fundamental principles and laws of nature to allow humans to transform raw material and energy into products that are useful to society, at an industrial level. By taking advantage of the driving forces of nature such as pressure, temperature and concentration gradients, as well as the law of conservation of mass, process engineers can develop methods to synthesize and purify large quantities of desired chemical products. Process engineering focuses on the design, operation, control, optimization and intensification of chemical, physical, and biological processes. Their work involves analyzing the chemical makeup of various ingredients and determining how they might react with one another. A process engineer can specialize in a number of areas, including the following: Agriculture processing Food and dairy production Beer and whiskey production Cosmetics production Pharmaceutical production Petrochemical manufacturing Mineral processing Printed circuit board production == Overview == Process engineering involves the utilization of multiple tools and methods. Depending on the exact nature of the system, processes need to be simulated and modeled using mathematics and computer science. Processes where phase change and phase equilibria are relevant require analysis using the principles and laws of thermodynamics to quantify changes in energy and efficiency. In contrast, processes that focus on the flow of material and energy as they approach equilibria are best analyzed using the disciplines of fluid mechanics and transport phenomena. Disciplines within the field of mechanics need to be applied in the presence of fluids or porous and dispersed media. Materials engineering principles also need to be applied, when relevant. Manufacturing in the field of process engineering involves an implementation of process synthesis steps. Regardless of the exact tools required, process engineering is then formatted through the use of a process flow diagram (PFD) where material flow paths, storage equipment (such as tanks and silos), transformations (such as distillation columns, receiver/head tanks, mixing, separations, pumping, etc.) and flowrates are specified, as well as a list of all pipes and conveyors and their contents, material properties such as density, viscosity, particle-size distribution, flowrates, pressures, temperatures, and materials of construction for the piping and unit operations. The process flow diagram is then used to develop a piping and instrumentation diagram (P&ID) which graphically displays the actual process occurring. P&ID are meant to be more complex and specific than a PFD. They represent a less muddled approach to the design. The P&ID is then used as a basis of design for developing the "system operation guide" or "functional design specification" which outlines the operation of the process. It guides the process through operation of machinery, safety in design, programming and effective communication between engineers. From the P&ID, a proposed layout (general arrangement) of the process can be shown from an overhead view (plot plan) and a side view (elevation), and other engineering disciplines are involved such as civil engineers for site work (earth moving), foundation design, concrete slab design work, structural steel to support the equipment, etc. All previous work is directed toward defining the scope of the project, then developing a cost estimate to get the design installed, and a schedule to communicate the timing needs for engineering, procurement, fabrication, installation, commissioning, startup, and ongoing production of the process. Depending on needed accuracy of the cost estimate and schedule that is required, several iterations of designs are generally provided to customers or stakeholders who feed back their requirements. The process engineer incorporates these additional instructions (scope revisions) into the overall design and additional cost estimates, and schedules are developed for funding approval. Following funding approval, the project is executed via project management. == Principal areas of focus in process engineering == Process engineering activities can be divided into the following disciplines: Process design: synthesis of energy recovery networks, synthesis of distillation systems (azeotropic), synthesis of reactor networks, hierarchical decomposition flowsheets, superstructure optimization, design multiproduct batch plants, design of the production reactors for the production of plutonium, design of nuclear submarines. Process control: model predictive control, controllability measures, robust control, nonlinear control, statistical process control, process monitoring, thermodynamics-based control, denoted by three essential items, a collection of measurements, method of taking measurements, and a system of controlling the desired measurement. Process operations: scheduling process networks, multiperiod planning and optimization, data reconciliation, real-time optimization, flexibility measures, fault diagnosis. Supporting tools: sequential modular simulation, equation-based process simulation, AI/expert systems, large-scale nonlinear programming (NLP), optimization of differential algebraic equations (DAEs), mixed-integer nonlinear programming (MINLP), global optimization, optimization under uncertainty, and quality function deployment (QFD). Process Economics: This includes using simulation software such as ASPEN, Super-Pro to find out the break even point, net present value, marginal sales, marginal cost, return on investment of the industrial plant after the analysis of the heat and mass transfer of the plant. Process Data Analytics: Applying data analytics and machine learning methods for process manufacturing problems. == History of process engineering == Various chemical techniques have been used in industrial processes since time immemorial. However, it wasn't until the advent of thermodynamics and the law of conservation of mass in the 1780s that process engineering was properly developed and implemented as its own discipline. The set of knowledge that is now known as process engineering was then forged out of trial and error throughout the industrial revolution. The term process, as it relates to industry and production, dates back to the 18th century. During this time period, demands for various products began to drastically increase, and process engineers were required to optimize the process in which these products were created. By 1980, the concept of process engineering emerged from the fact that chemical engineering techniques and practices were being used in a variety of industries. By this time, process engineering had been defined as "the set of knowledge necessary to design, analyze, develop, construct, and operate, in an optimal way, the processes in which the material changes". By the end of the 20th century, process engineering had expanded from chemical engineering-based technologies to other applications, including metallurgical engineering, agricultural engineering, and product engineering. == See also == == References == == External links == Advanced Process Engineering at Cranfield University (Cranfield, UK) Sargent Centre for Process Systems Engineering (Imperial) Process Systems Engineering at Cornell University (Ithaca, New York) Department of Process Engineering at Stellenbosch University Process Research and Intelligent Systems Modeling (PRISM) group at BYU Process Systems Engineering at CMU Process Systems Engineering Laboratory at RWTH Aachen The Process Systems Engineering Laboratory (MIT) Process Engineering Consulting at Canada
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Manufacturing engineering or production engineering is a branch of professional engineering that shares many common concepts and ideas with other fields of engineering such as mechanical, chemical, electrical, and industrial engineering. Manufacturing engineering requires the ability to plan the practices of manufacturing; to research and to develop tools, processes, machines, and equipment; and to integrate the facilities and systems for producing quality products with the optimum expenditure of capital. The manufacturing or production engineer's primary focus is to turn raw material into an updated or new product in the most effective, efficient & economic way possible. An example would be a company uses computer integrated technology in order for them to produce their product so that it is faster and uses less human labor. == Overview == Manufacturing Engineering is based on core industrial engineering and mechanical engineering skills, adding important elements from mechatronics, commerce, economics, and business management. This field also deals with the integration of different facilities and systems for producing quality products (with optimal expenditure) by applying the principles of physics and the results of manufacturing systems studies, such as the following: Manufacturing engineers develop and create physical artifacts, production processes, and technology. It is a very broad area which includes the design and development of products. Manufacturing engineering is considered to be a subdiscipline of industrial engineering/systems engineering and has very strong overlaps with mechanical engineering. Manufacturing engineers' success or failure directly impacts the advancement of technology and the spread of innovation. This field of manufacturing engineering emerged from the tool and die discipline in the early 20th century. It expanded greatly from the 1960s when industrialized countries introduced factories with: 1. Numerical control machine tools and automated systems of production. 2. Advanced statistical methods of quality control: These factories were pioneered by the American electrical engineer William Edwards Deming, who was initially ignored by his home country. The same methods of quality control later turned Japanese factories into world leaders in cost-effectiveness and production quality. 3. Industrial robots on the factory floor, introduced in the late 1970s: These computer-controlled welding arms and grippers could perform simple tasks such as attaching a car door quickly and flawlessly 24 hours a day. This cut costs and improved production speed. == History == The history of manufacturing engineering can be traced to factories in the mid-19th century USA and 18th century UK. Although large home production sites and workshops were established in China, ancient Rome, and the Middle East, the Venice Arsenal provides one of the first examples of a factory in the modern sense of the word. Founded in 1104 in the Republic of Venice several hundred years before the Industrial Revolution, this factory mass-produced ships on assembly lines using manufactured parts. The Venice Arsenal apparently produced nearly one ship every day and, at its height, employed 16,000 people. Many historians regard Matthew Boulton's Soho Manufactory (established in 1761 in Birmingham) as the first modern factory. Similar claims can be made for John Lombe's silk mill in Derby (1721), or Richard Arkwright's Cromford Mill (1771). The Cromford Mill was purpose-built to accommodate the equipment it held and to take the material through the various manufacturing processes. One historian, Jack Weatherford, contends that the first factory was in Potosí. The Potosi factory took advantage of the abundant silver that was mined nearby and processed silver ingot slugs into coins. British colonies in the 19th century built factories simply as buildings where a large number of workers gathered to perform hand labor, usually in textile production. This proved more efficient for the administration and distribution of materials to individual workers than earlier methods of manufacturing, such as cottage industries or the putting-out system. Cotton mills used inventions such as the steam engine and the power loom to pioneer the industrial factories of the 19th century, where precision machine tools and replaceable parts allowed greater efficiency and less waste. This experience formed the basis for the later studies of manufacturing engineering. Between 1820 and 1850, non-mechanized factories supplanted traditional artisan shops as the predominant form of manufacturing institution. Henry Ford further revolutionized the factory concept and thus manufacturing engineering in the early 20th century with the innovation of mass production. Highly specialized workers situated alongside a series of rolling ramps would build up a product such as (in Ford's case) an automobile. This concept dramatically decreased production costs for virtually all manufactured goods and brought about the age of consumerism. === Modern developments === Modern manufacturing engineering studies include all intermediate processes required for the production and integration of a product's components. Some industries, such as semiconductor and steel manufacturers use the term "fabrication" for these processes. Automation is used in different processes of manufacturing such as machining and welding. Automated manufacturing refers to the application of automation to produce goods in a factory. The main advantages of automated manufacturing for the manufacturing process are realized with effective implementation of automation and include higher consistency and quality, reduction of lead times, simplification of production, reduced handling, improved workflow, and improved worker morale. Robotics is the application of mechatronics and automation to create robots, which are often used in manufacturing to perform tasks that are dangerous, unpleasant, or repetitive. These robots may be of any shape and size, but all are preprogrammed and interact physically with the world. To create a robot, an engineer typically employs kinematics (to determine the robot's range of motion) and mechanics (to determine the stresses within the robot). Robots are used extensively in manufacturing engineering. Robots allow businesses to save money on labor, perform tasks that are either too dangerous or too precise for humans to perform economically, and ensure better quality. Many companies employ assembly lines of robots, and some factories are so robotized that they can run by themselves. Outside the factory, robots have been employed in bomb disposal, space exploration, and many other fields. Robots are also sold for various residential applications. == Education == === Manufacturing Engineers === Manufacturing Engineers focus on the design, development, and operation of integrated systems of production to obtain high quality & economically competitive products. These systems may include material handling equipment, machine tools, robots, or even computers or networks of computers. === Certification Programs === Manufacturing engineers possess an associate's or bachelor's degree in engineering with a major in manufacturing engineering. The length of study for such a degree is usually two to five years followed by five more years of professional practice to qualify as a professional engineer. Working as a manufacturing engineering technologist involves a more applications-oriented qualification path. Academic degrees for manufacturing engineers are usually the Associate or Bachelor of Engineering, [BE] or [BEng], and the Associate or Bachelor of Science, [BS] or [BSc]. For manufacturing technologists the required degrees are Associate or Bachelor of Technology [B.TECH] or Associate or Bachelor of Applied Science [BASc] in Manufacturing, depending upon the university. Master's degrees in engineering manufacturing include Master of Engineering [ME] or [MEng] in Manufacturing, Master of Science [M.Sc] in Manufacturing Management, Master of Science [M.Sc] in Industrial and Production Management, and Master of Science [M.Sc] as well as Master of Engineering [ME] in Design, which is a subdiscipline of manufacturing. Doctoral [PhD] or [DEng] level courses in manufacturing are also available depending on the university. The undergraduate degree curriculum generally includes courses in physics, mathematics, computer science, project management, and specific topics in mechanical and manufacturing engineering. Initially, such topics cover most, if not all, of the subdisciplines of manufacturing engineering. Students then choose to specialize in one or more subdisciplines towards the end of their degree work. === Syllabus === The Foundational Curriculum for a Bachelor's Degree in Manufacturing Engineering or Production Engineering includes below mentioned syllabus. This syllabus is closely related to Industrial Engineering and Mechanical Engineering, but it differs by placing more emphasis on Manufacturing Science or Production Science. It includes the following areas: Mathematics (Calculus, Differential Equations, Statistics and Linear Algebra) Mechanics (Statics & Dynamics) Solid Mechanics Fluid Mechanics Materials Science Strength of Materials Fluid Dynamics Hydraulics Pneumatics HVAC (Heating, Ventilation & Air Conditioning) Heat Transfer Applied Thermodynamics Energy Conversion Instrumentation and Measurement Engineering Drawing (Drafting) & Engineering Design Engineering Graphics Mechanism Design including Kinematics and Dynamics Manufacturing Processes Mechatronics Circuit Analysis Lean Manufacturing Automation Reverse Engineering Quality Control CAD (Computer Aided Design) CAM (Computer Aided Manufacturing) Project Management A degree in Manufacturing Engineering typically differs from Mechanical Engineering in only a few specialized classes. Mechanical Engineering degrees focus more on the product design process and on complex products which requires more mathematical expertise. == Manufacturing engineering certification == Certification and licensure: In some countries, "professional engineer" is the term for registered or licensed engineers who are permitted to offer their professional services directly to the public. Professional Engineer, abbreviated (PE - USA) or (PEng - Canada), is the designation for licensure in North America. To qualify for this license, a candidate needs a bachelor's degree from an ABET-recognized university in the USA, a passing score on a state examination, and four years of work experience usually gained via a structured internship. In the USA, more recent graduates have the option of dividing this licensure process into two segments. The Fundamentals of Engineering (FE) exam is often taken immediately after graduation and the Principles and Practice of Engineering exam is taken after four years of working in a chosen engineering field. Society of Manufacturing Engineers (SME) certification (USA): The SME administers qualifications specifically for the manufacturing industry. These are not degree level qualifications and are not recognized at the professional engineering level. The following discussion deals with qualifications in the USA only. Qualified candidates for the Certified Manufacturing Technologist Certificate (CMfgT) must pass a three-hour, 130-question multiple-choice exam. The exam covers math, manufacturing processes, manufacturing management, automation, and related subjects. Additionally, a candidate must have at least four years of combined education and manufacturing-related work experience. Certified Manufacturing Engineer (CMfgE) is an engineering qualification administered by the Society of Manufacturing Engineers, Dearborn, Michigan, USA. Candidates qualifying for a Certified Manufacturing Engineer credential must pass a four-hour, 180-question multiple-choice exam which covers more in-depth topics than the CMfgT exam. CMfgE candidates must also have eight years of combined education and manufacturing-related work experience, with a minimum of four years of work experience. Certified Engineering Manager (CEM). The Certified Engineering Manager Certificate is also designed for engineers with eight years of combined education and manufacturing experience. The test is four hours long and has 160 multiple-choice questions. The CEM certification exam covers business processes, teamwork, responsibility, and other management-related categories. == Modern tools == Many manufacturing companies, especially those in industrialized nations, have begun to incorporate computer-aided engineering (CAE) programs into their existing design and analysis processes, including 2D and 3D solid modeling computer-aided design (CAD). This method has many benefits, including easier and more exhaustive visualization of products, the ability to create virtual assemblies of parts, and ease of use in designing mating interfaces and tolerances. Other CAE programs commonly used by product manufacturers include product life cycle management (PLM) tools and analysis tools used to perform complex simulations. Analysis tools may be used to predict product response to expected loads, including fatigue life and manufacturability. These tools include finite element analysis (FEA), computational fluid dynamics (CFD), and computer-aided manufacturing (CAM). Using CAE programs, a mechanical design team can quickly and cheaply iterate the design process to develop a product that better meets cost, performance, and other constraints. No physical prototype need be created until the design nears completion, allowing hundreds or thousands of designs to be evaluated, instead of relatively few. In addition, CAE analysis programs can model complicated physical phenomena which cannot be solved by hand, such as viscoelasticity, complex contact between mating parts, or non-Newtonian flows. Just as manufacturing engineering is linked with other disciplines, such as mechatronics, multidisciplinary design optimization (MDO) is also being used with other CAE programs to automate and improve the iterative design process. MDO tools wrap around existing CAE processes, allowing product evaluation to continue even after the analyst goes home for the day. They also utilize sophisticated optimization algorithms to more intelligently explore possible designs, often finding better, innovative solutions to difficult multidisciplinary design problems. On the business side of manufacturing engineering, enterprise resource planning (ERP) tools can overlap with PLM tools and use connector programs with CAD tools to share drawings, sync revisions, and be the master for certain data used in the other modern tools above, like part numbers and descriptions. == Manufacturing Engineering around the world == Manufacturing engineering is an extremely important discipline worldwide. It goes by different names in different countries. In the United States and the continental European Union it is commonly known as Industrial Engineering and in the United Kingdom and Australia it is called Manufacturing Engineering. == Subdisciplines == === Mechanics === Mechanics, in the most general sense, is the study of forces and their effects on matter. Typically, engineering mechanics is used to analyze and predict the acceleration and deformation (both elastic and plastic) of objects under known forces (also called loads) or stresses. Subdisciplines of mechanics include: Statics, the study of non-moving bodies under known loads Dynamics (or kinetics), the study of how forces affect moving bodies Mechanics of materials, the study of how different materials deform under various types of stress Fluid mechanics, the study of how fluids react to forces Continuum mechanics, a method of applying mechanics that assumes that objects are continuous (rather than discrete) If the engineering project were to design a vehicle, statics might be employed to design the frame of the vehicle to evaluate where the stresses will be most intense. Dynamics might be used when designing the car's engine to evaluate the forces in the pistons and cams as the engine cycles. Mechanics of materials might be used to choose appropriate materials for the manufacture of the frame and engine. Fluid mechanics might be used to design a ventilation system for the vehicle or to design the intake system for the engine. === Kinematics === Kinematics is the study of the motion of bodies (objects) and systems (groups of objects), while ignoring the forces that cause the motion. The movement of a crane and the oscillations of a piston in an engine are both simple kinematic systems. The crane is a type of open kinematic chain, while the piston is part of a closed four-bar linkage. Engineers typically use kinematics in the design and analysis of mechanisms. Kinematics can be used to find the possible range of motion for a given mechanism, or, working in reverse, can be used to design a mechanism that has a desired range of motion. === Drafting === Drafting or technical drawing is the means by which manufacturers create instructions for manufacturing parts. A technical drawing can be a computer model or hand-drawn schematic showing all the dimensions necessary to manufacture a part, as well as assembly notes, a list of required materials, and other pertinent information. A U.S engineer or skilled worker who creates technical drawings may be referred to as a drafter or draftsman. Drafting has historically been a two-dimensional process, but computer-aided design (CAD) programs now allow the designer to create in three dimensions. Instructions for manufacturing a part must be fed to the necessary machinery, either manually, through programmed instructions, or through the use of a computer-aided manufacturing (CAM) or combined CAD/CAM program. Optionally, an engineer may also manually manufacture a part using the technical drawings, but this is becoming an increasing rarity with the advent of computer numerically controlled (CNC) manufacturing. Engineers primarily manufacture parts manually in the areas of applied spray coatings, finishes, and other processes that cannot economically or practically be done by a machine. Drafting is used in nearly every subdiscipline of mechanical and manufacturing engineering, and by many other branches of engineering and architecture. Three-dimensional models created using CAD software are also commonly used in finite element analysis (FEA) and computational fluid dynamics (CFD). === Machine tools and metal fabrication === Machine tools employ some sort of tool that does the cutting or shaping. All machine tools have some means of constraining the workpiece and providing a guided movement of the parts of the machine. Metal fabrication is the building of metal structures by cutting, bending, and assembling processes. === Computer Integrated Manufacturing === Computer-integrated manufacturing (CIM) is the manufacturing approach of using computers to control the entire production process. Computer-integrated manufacturing is used in automotive, aviation, space, and ship building industries. === Mechatronics === Mechatronics is an engineering discipline that deals with the convergence of electrical, mechanical and manufacturing systems. Such combined systems are known as electromechanical systems and are widespread. Examples include automated manufacturing systems, heating, ventilation and air-conditioning systems, and various aircraft and automobile subsystems. The term mechatronics is typically used to refer to macroscopic systems, but futurists have predicted the emergence of very small electromechanical devices. Already such small devices, known as Microelectromechanical systems (MEMS), are used in automobiles to initiate the deployment of airbags, in digital projectors to create sharper images, and in inkjet printers to create nozzles for high-definition printing. In the future, it is hoped that such devices will be used in tiny implantable medical devices and to improve optical communication. === Textile engineering === Textile engineering courses deal with the application of scientific and engineering principles to the design and control of all aspects of fiber, textile, and apparel processes, products, and machinery. These include natural and man-made materials, interaction of materials with machines, safety and health, energy conservation, and waste and pollution control. Additionally, students are given experience in plant design and layout, machine and wet process design and improvement, and designing and creating textile products. Throughout the textile engineering curriculum, students take classes from other engineering and disciplines including: mechanical, chemical, materials and industrial engineering. === Advanced composite materials === Advanced composite materials (engineering) (ACMs) are also known as advanced polymer matrix composites. These are generally characterized or determined by unusually high strength fibres with unusually high stiffness, or modulus of elasticity characteristics, compared to other materials, while bound together by weaker matrices. Advanced composite materials have broad, proven applications, in the aircraft, aerospace, and sports equipment sectors. Even more specifically ACMs are very attractive for aircraft and aerospace structural parts. Manufacturing ACMs is a multibillion-dollar industry worldwide. Composite products range from skateboards to components of the space shuttle. The industry can be generally divided into two basic segments, industrial composites and advanced composites. == Employment == Manufacturing engineering is just one facet of the engineering manufacturing industry. Manufacturing engineers enjoy improving the production process from start to finish. They have the ability to keep the whole production process in mind as they focus on a particular portion of the process. Successful students in manufacturing engineering degree programs are inspired by the notion of starting with a natural resource, such as a block of wood, and ending with a usable, valuable product, such as a desk, produced efficiently and economically. Manufacturing engineers are closely connected with engineering and industrial design efforts. Examples of major companies that employ manufacturing engineers in the United States include General Motors Corporation, Ford Motor Company, Chrysler, Boeing, Gates Corporation and Pfizer. Examples in Europe include Airbus, Daimler, BMW, Fiat, Navistar International, and Michelin Tyre. Industries where manufacturing engineers are generally employed include: Aerospace industry Automotive industry Chemical industry Computer industry Engineering management Food processing industry Garment industry Industrial engineering Mechanical engineering Pharmaceutical industry Process engineering Pulp and paper industry Systems engineering Toy industry == Frontiers of research == === Flexible manufacturing systems === A flexible manufacturing system (FMS) is a manufacturing system in which there is some amount of flexibility that allows the system to react to changes, whether predicted or unpredicted. This flexibility is generally considered to fall into two categories, both of which have numerous subcategories. The first category, machine flexibility, covers the system's ability to be changed to produce new product types and the ability to change the order of operations executed on a part. The second category, called routing flexibility, consists of the ability to use multiple machines to perform the same operation on a part, as well as the system's ability to absorb large-scale changes, such as in volume, capacity, or capability. Most FMS systems comprise three main systems. The work machines, which are often automated CNC machines, are connected by a material handling system to optimize parts flow, and to a central control computer, which controls material movements and machine flow. The main advantages of an FMS is its high flexibility in managing manufacturing resources like time and effort in order to manufacture a new product. The best application of an FMS is found in the production of small sets of products from a mass production. === Computer integrated manufacturing === Computer-integrated manufacturing (CIM) in engineering is a method of manufacturing in which the entire production process is controlled by computer. Traditionally separated process methods are joined through a computer by CIM. This integration allows the processes to exchange information and to initiate actions. Through this integration, manufacturing can be faster and less error-prone, although the main advantage is the ability to create automated manufacturing processes. Typically CIM relies on closed-loop control processes based on real-time input from sensors. It is also known as flexible design and manufacturing. === Friction stir welding === Friction stir welding was discovered in 1991 by The Welding Institute (TWI). This innovative steady state (non-fusion) welding technique joins previously un-weldable materials, including several aluminum alloys. It may play an important role in the future construction of airplanes, potentially replacing rivets. Current uses of this technology to date include: welding the seams of the aluminum main space shuttle external tank, the Orion Crew Vehicle test article, Boeing Delta II and Delta IV Expendable Launch Vehicles and the SpaceX Falcon 1 rocket; armor plating for amphibious assault ships; and welding the wings and fuselage panels of the new Eclipse 500 aircraft from Eclipse Aviation, among an increasingly growing range of uses. Other areas of research are Product Design, MEMS (Micro-Electro-Mechanical Systems), Lean Manufacturing, Intelligent Manufacturing Systems, Green Manufacturing, Precision Engineering, Smart Materials, etc. == See also == == Notes == == External links == Institute of Manufacturing - UK Georgia Tech Manufacturing Institute [1] Application note "Yield Learning Flow Provides Faster Production Ramp"
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Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems that use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the latter half of the 19th century after the commercialization of the electric telegraph, the telephone, and electrical power generation, distribution, and use. Electrical engineering is divided into a wide range of different fields, including computer engineering, systems engineering, power engineering, telecommunications, radio-frequency engineering, signal processing, instrumentation, photovoltaic cells, electronics, and optics and photonics. Many of these disciplines overlap with other engineering branches, spanning a huge number of specializations including hardware engineering, power electronics, electromagnetics and waves, microwave engineering, nanotechnology, electrochemistry, renewable energies, mechatronics/control, and electrical materials science. Electrical engineers typically hold a degree in electrical engineering, electronic or electrical and electronic engineering. Practicing engineers may have professional certification and be members of a professional body or an international standards organization. These include the International Electrotechnical Commission (IEC), the National Society of Professional Engineers (NSPE), the Institute of Electrical and Electronics Engineers (IEEE) and the Institution of Engineering and Technology (IET, formerly the IEE). Electrical engineers work in a very wide range of industries and the skills required are likewise variable. These range from circuit theory to the management skills of a project manager. The tools and equipment that an individual engineer may need are similarly variable, ranging from a simple voltmeter to sophisticated design and manufacturing software. == History == Electricity has been a subject of scientific interest since at least the early 17th century. William Gilbert was a prominent early electrical scientist, and was the first to draw a clear distinction between magnetism and static electricity. He is credited with establishing the term "electricity". He also designed the versorium: a device that detects the presence of statically charged objects. In 1762 Swedish professor Johan Wilcke invented a device later named electrophorus that produced a static electric charge. By 1800 Alessandro Volta had developed the voltaic pile, a forerunner of the electric battery. === 19th century === In the 19th century, research into the subject started to intensify. Notable developments in this century include the work of Hans Christian Ørsted, who discovered in 1820 that an electric current produces a magnetic field that will deflect a compass needle; of William Sturgeon, who in 1825 invented the electromagnet; of Joseph Henry and Edward Davy, who invented the electrical relay in 1835; of Georg Ohm, who in 1827 quantified the relationship between the electric current and potential difference in a conductor; of Michael Faraday, the discoverer of electromagnetic induction in 1831; and of James Clerk Maxwell, who in 1873 published a unified theory of electricity and magnetism in his treatise Electricity and Magnetism. In 1782, Georges-Louis Le Sage developed and presented in Berlin probably the world's first form of electric telegraphy, using 24 different wires, one for each letter of the alphabet. This telegraph connected two rooms. It was an electrostatic telegraph that moved gold leaf through electrical conduction. In 1795, Francisco Salva Campillo proposed an electrostatic telegraph system. Between 1803 and 1804, he worked on electrical telegraphy, and in 1804, he presented his report at the Royal Academy of Natural Sciences and Arts of Barcelona. Salva's electrolyte telegraph system was very innovative though it was greatly influenced by and based upon two discoveries made in Europe in 1800—Alessandro Volta's electric battery for generating an electric current and William Nicholson and Anthony Carlyle's electrolysis of water. Electrical telegraphy may be considered the first example of electrical engineering. Electrical engineering became a profession in the later 19th century. Practitioners had created a global electric telegraph network, and the first professional electrical engineering institutions were founded in the UK and the US to support the new discipline. Francis Ronalds created an electric telegraph system in 1816 and documented his vision of how the world could be transformed by electricity. Over 50 years later, he joined the new Society of Telegraph Engineers (soon to be renamed the Institution of Electrical Engineers) where he was regarded by other members as the first of their cohort. By the end of the 19th century, the world had been forever changed by the rapid communication made possible by the engineering development of land-lines, submarine cables, and, from about 1890, wireless telegraphy. Practical applications and advances in such fields created an increasing need for standardized units of measure. They led to the international standardization of the units volt, ampere, coulomb, ohm, farad, and henry. This was achieved at an international conference in Chicago in 1893. The publication of these standards formed the basis of future advances in standardization in various industries, and in many countries, the definitions were immediately recognized in relevant legislation. During these years, the study of electricity was largely considered to be a subfield of physics since early electrical technology was considered electromechanical in nature. The Technische Universität Darmstadt founded the world's first department of electrical engineering in 1882 and introduced the first-degree course in electrical engineering in 1883. The first electrical engineering degree program in the United States was started at Massachusetts Institute of Technology (MIT) in the physics department under Professor Charles Cross, though it was Cornell University to produce the world's first electrical engineering graduates in 1885. The first course in electrical engineering was taught in 1883 in Cornell's Sibley College of Mechanical Engineering and Mechanic Arts. In about 1885, Cornell President Andrew Dickson White established the first Department of Electrical Engineering in the United States. In the same year, University College London founded the first chair of electrical engineering in Great Britain. Professor Mendell P. Weinbach at University of Missouri established the electrical engineering department in 1886. Afterwards, universities and institutes of technology gradually started to offer electrical engineering programs to their students all over the world. During these decades the use of electrical engineering increased dramatically. In 1882, Thomas Edison switched on the world's first large-scale electric power network that provided 110 volts—direct current (DC)—to 59 customers on Manhattan Island in New York City. In 1884, Sir Charles Parsons invented the steam turbine allowing for more efficient electric power generation. Alternating current, with its ability to transmit power more efficiently over long distances via the use of transformers, developed rapidly in the 1880s and 1890s with transformer designs by Károly Zipernowsky, Ottó Bláthy and Miksa Déri (later called ZBD transformers), Lucien Gaulard, John Dixon Gibbs and William Stanley Jr. Practical AC motor designs including induction motors were independently invented by Galileo Ferraris and Nikola Tesla and further developed into a practical three-phase form by Mikhail Dolivo-Dobrovolsky and Charles Eugene Lancelot Brown. Charles Steinmetz and Oliver Heaviside contributed to the theoretical basis of alternating current engineering. The spread in the use of AC set off in the United States what has been called the war of the currents between a George Westinghouse backed AC system and a Thomas Edison backed DC power system, with AC being adopted as the overall standard. === Early 20th century === During the development of radio, many scientists and inventors contributed to radio technology and electronics. The mathematical work of James Clerk Maxwell during the 1850s had shown the relationship of different forms of electromagnetic radiation including the possibility of invisible airborne waves (later called "radio waves"). In his classic physics experiments of 1888, Heinrich Hertz proved Maxwell's theory by transmitting radio waves with a spark-gap transmitter, and detected them by using simple electrical devices. Other physicists experimented with these new waves and in the process developed devices for transmitting and detecting them. In 1895, Guglielmo Marconi began work on a way to adapt the known methods of transmitting and detecting these "Hertzian waves" into a purpose-built commercial wireless telegraphic system. Early on, he sent wireless signals over a distance of one and a half miles. In December 1901, he sent wireless waves that were not affected by the curvature of the Earth. Marconi later transmitted the wireless signals across the Atlantic between Poldhu, Cornwall, and St. John's, Newfoundland, a distance of 2,100 miles (3,400 km). Millimetre wave communication was first investigated by Jagadish Chandra Bose during 1894–1896, when he reached an extremely high frequency of up to 60 GHz in his experiments. He also introduced the use of semiconductor junctions to detect radio waves, when he patented the radio crystal detector in 1901. In 1897, Karl Ferdinand Braun introduced the cathode-ray tube as part of an oscilloscope, a crucial enabling technology for electronic television. John Fleming invented the first radio tube, the diode, in 1904. Two years later, Robert von Lieben and Lee De Forest independently developed the amplifier tube, called the triode. In 1920, Albert Hull developed the magnetron which would eventually lead to the development of the microwave oven in 1946 by Percy Spencer. In 1934, the British military began to make strides toward radar (which also uses the magnetron) under the direction of Dr Wimperis, culminating in the operation of the first radar station at Bawdsey in August 1936. In 1941, Konrad Zuse presented the Z3, the world's first fully functional and programmable computer using electromechanical parts. In 1943, Tommy Flowers designed and built the Colossus, the world's first fully functional, electronic, digital and programmable computer. In 1946, the ENIAC (Electronic Numerical Integrator and Computer) of John Presper Eckert and John Mauchly followed, beginning the computing era. The arithmetic performance of these machines allowed engineers to develop completely new technologies and achieve new objectives. In 1948, Claude Shannon published "A Mathematical Theory of Communication" which mathematically describes the passage of information with uncertainty (electrical noise). === Solid-state electronics === The first working transistor was a point-contact transistor invented by John Bardeen and Walter Houser Brattain while working under William Shockley at the Bell Telephone Laboratories (BTL) in 1947. They then invented the bipolar junction transistor in 1948. While early junction transistors were relatively bulky devices that were difficult to manufacture on a mass-production basis, they opened the door for more compact devices. The first integrated circuits were the hybrid integrated circuit invented by Jack Kilby at Texas Instruments in 1958 and the monolithic integrated circuit chip invented by Robert Noyce at Fairchild Semiconductor in 1959. The MOSFET (metal–oxide–semiconductor field-effect transistor, or MOS transistor) was invented by Mohamed Atalla and Dawon Kahng at BTL in 1959. It was the first truly compact transistor that could be miniaturised and mass-produced for a wide range of uses. It revolutionized the electronics industry, becoming the most widely used electronic device in the world. The MOSFET made it possible to build high-density integrated circuit chips. The earliest experimental MOS IC chip to be fabricated was built by Fred Heiman and Steven Hofstein at RCA Laboratories in 1962. MOS technology enabled Moore's law, the doubling of transistors on an IC chip every two years, predicted by Gordon Moore in 1965. Silicon-gate MOS technology was developed by Federico Faggin at Fairchild in 1968. Since then, the MOSFET has been the basic building block of modern electronics. The mass-production of silicon MOSFETs and MOS integrated circuit chips, along with continuous MOSFET scaling miniaturization at an exponential pace (as predicted by Moore's law), has since led to revolutionary changes in technology, economy, culture and thinking. The Apollo program which culminated in landing astronauts on the Moon with Apollo 11 in 1969 was enabled by NASA's adoption of advances in semiconductor electronic technology, including MOSFETs in the Interplanetary Monitoring Platform (IMP) and silicon integrated circuit chips in the Apollo Guidance Computer (AGC). The development of MOS integrated circuit technology in the 1960s led to the invention of the microprocessor in the early 1970s. The first single-chip microprocessor was the Intel 4004, released in 1971. The Intel 4004 was designed and realized by Federico Faggin at Intel with his silicon-gate MOS technology, along with Intel's Marcian Hoff and Stanley Mazor and Busicom's Masatoshi Shima. The microprocessor led to the development of microcomputers and personal computers, and the microcomputer revolution. == Subfields == One of the properties of electricity is that it is very useful for energy transmission as well as for information transmission. These were also the first areas in which electrical engineering was developed. Today, electrical engineering has many subdisciplines, the most common of which are listed below. Although there are electrical engineers who focus exclusively on one of these subdisciplines, many deal with a combination of them. Sometimes, certain fields, such as electronic engineering and computer engineering, are considered disciplines in their own right. === Power and energy === Power & Energy engineering deals with the generation, transmission, and distribution of electricity as well as the design of a range of related devices. These include transformers, electric generators, electric motors, high voltage engineering, and power electronics. In many regions of the world, governments maintain an electrical network called a power grid that connects a variety of generators together with users of their energy. Users purchase electrical energy from the grid, avoiding the costly exercise of having to generate their own. Power engineers may work on the design and maintenance of the power grid as well as the power systems that connect to it. Such systems are called on-grid power systems and may supply the grid with additional power, draw power from the grid, or do both. Power engineers may also work on systems that do not connect to the grid, called off-grid power systems, which in some cases are preferable to on-grid systems. === Telecommunications === Telecommunications engineering focuses on the transmission of information across a communication channel such as a coax cable, optical fiber or free space. Transmissions across free space require information to be encoded in a carrier signal to shift the information to a carrier frequency suitable for transmission; this is known as modulation. Popular analog modulation techniques include amplitude modulation and frequency modulation. The choice of modulation affects the cost and performance of a system and these two factors must be balanced carefully by the engineer. Once the transmission characteristics of a system are determined, telecommunication engineers design the transmitters and receivers needed for such systems. These two are sometimes combined to form a two-way communication device known as a transceiver. A key consideration in the design of transmitters is their power consumption as this is closely related to their signal strength. Typically, if the power of the transmitted signal is insufficient once the signal arrives at the receiver's antenna(s), the information contained in the signal will be corrupted by noise, specifically static. === Control engineering === Control engineering focuses on the modeling of a diverse range of dynamic systems and the design of controllers that will cause these systems to behave in the desired manner. To implement such controllers, electronics control engineers may use electronic circuits, digital signal processors, microcontrollers, and programmable logic controllers (PLCs). Control engineering has a wide range of applications from the flight and propulsion systems of commercial airliners to the cruise control present in many modern automobiles. It also plays an important role in industrial automation. Control engineers often use feedback when designing control systems. For example, in an automobile with cruise control the vehicle's speed is continuously monitored and fed back to the system which adjusts the motor's power output accordingly. Where there is regular feedback, control theory can be used to determine how the system responds to such feedback. Control engineers also work in robotics to design autonomous systems using control algorithms which interpret sensory feedback to control actuators that move robots such as autonomous vehicles, autonomous drones and others used in a variety of industries. === Electronics === Electronic engineering involves the design and testing of electronic circuits that use the properties of components such as resistors, capacitors, inductors, diodes, and transistors to achieve a particular functionality. The tuned circuit, which allows the user of a radio to filter out all but a single station, is just one example of such a circuit. Another example to research is a pneumatic signal conditioner. Prior to the Second World War, the subject was commonly known as radio engineering and basically was restricted to aspects of communications and radar, commercial radio, and early television. Later, in post-war years, as consumer devices began to be developed, the field grew to include modern television, audio systems, computers, and microprocessors. In the mid-to-late 1950s, the term radio engineering gradually gave way to the name electronic engineering. Before the invention of the integrated circuit in 1959, electronic circuits were constructed from discrete components that could be manipulated by humans. These discrete circuits consumed much space and power and were limited in speed, although they are still common in some applications. By contrast, integrated circuits packed a large number—often millions—of tiny electrical components, mainly transistors, into a small chip around the size of a coin. This allowed for the powerful computers and other electronic devices we see today. === Microelectronics and nanoelectronics === Microelectronics engineering deals with the design and microfabrication of very small electronic circuit components for use in an integrated circuit or sometimes for use on their own as a general electronic component. The most common microelectronic components are semiconductor transistors, although all main electronic components (resistors, capacitors etc.) can be created at a microscopic level. Nanoelectronics is the further scaling of devices down to nanometer levels. Modern devices are already in the nanometer regime, with below 100 nm processing having been standard since around 2002. Microelectronic components are created by chemically fabricating wafers of semiconductors such as silicon (at higher frequencies, compound semiconductors like gallium arsenide and indium phosphide) to obtain the desired transport of electronic charge and control of current. The field of microelectronics involves a significant amount of chemistry and material science and requires the electronic engineer working in the field to have a very good working knowledge of the effects of quantum mechanics. === Signal processing === Signal processing deals with the analysis and manipulation of signals. Signals can be either analog, in which case the signal varies continuously according to the information, or digital, in which case the signal varies according to a series of discrete values representing the information. For analog signals, signal processing may involve the amplification and filtering of audio signals for audio equipment or the modulation and demodulation of signals for telecommunications. For digital signals, signal processing may involve the compression, error detection and error correction of digitally sampled signals. Signal processing is a very mathematically oriented and intensive area forming the core of digital signal processing and it is rapidly expanding with new applications in every field of electrical engineering such as communications, control, radar, audio engineering, broadcast engineering, power electronics, and biomedical engineering as many already existing analog systems are replaced with their digital counterparts. Analog signal processing is still important in the design of many control systems. DSP processor ICs are found in many types of modern electronic devices, such as digital television sets, radios, hi-fi audio equipment, mobile phones, multimedia players, camcorders and digital cameras, automobile control systems, noise cancelling headphones, digital spectrum analyzers, missile guidance systems, radar systems, and telematics systems. In such products, DSP may be responsible for noise reduction, speech recognition or synthesis, encoding or decoding digital media, wirelessly transmitting or receiving data, triangulating positions using GPS, and other kinds of image processing, video processing, audio processing, and speech processing. === Instrumentation === Instrumentation engineering deals with the design of devices to measure physical quantities such as pressure, flow, and temperature. The design of such instruments requires a good understanding of physics that often extends beyond electromagnetic theory. For example, flight instruments measure variables such as wind speed and altitude to enable pilots the control of aircraft analytically. Similarly, thermocouples use the Peltier-Seebeck effect to measure the temperature difference between two points. Often instrumentation is not used by itself, but instead as the sensors of larger electrical systems. For example, a thermocouple might be used to help ensure a furnace's temperature remains constant. For this reason, instrumentation engineering is often viewed as the counterpart of control. === Computers === Computer engineering deals with the design of computers and computer systems. This may involve the design of new hardware. Computer engineers may also work on a system's software. However, the design of complex software systems is often the domain of software engineering, which is usually considered a separate discipline. Desktop computers represent a tiny fraction of the devices a computer engineer might work on, as computer-like architectures are now found in a range of embedded devices including video game consoles and DVD players. Computer engineers are involved in many hardware and software aspects of computing. Robots are one of the applications of computer engineering. === Photonics and optics === Photonics and optics deals with the generation, transmission, amplification, modulation, detection, and analysis of electromagnetic radiation. The application of optics deals with design of optical instruments such as lenses, microscopes, telescopes, and other equipment that uses the properties of electromagnetic radiation. Other prominent applications of optics include electro-optical sensors and measurement systems, lasers, fiber-optic communication systems, and optical disc systems (e.g. CD and DVD). Photonics builds heavily on optical technology, supplemented with modern developments such as optoelectronics (mostly involving semiconductors), laser systems, optical amplifiers and novel materials (e.g. metamaterials). == Related disciplines == Mechatronics is an engineering discipline that deals with the convergence of electrical and mechanical systems. Such combined systems are known as electromechanical systems and have widespread adoption. Examples include automated manufacturing systems, heating, ventilation and air-conditioning systems, and various subsystems of aircraft and automobiles. Electronic systems design is the subject within electrical engineering that deals with the multi-disciplinary design issues of complex electrical and mechanical systems. The term mechatronics is typically used to refer to macroscopic systems but futurists have predicted the emergence of very small electromechanical devices. Already, such small devices, known as microelectromechanical systems (MEMS), are used in automobiles to tell airbags when to deploy, in digital projectors to create sharper images, and in inkjet printers to create nozzles for high definition printing. In the future it is hoped the devices will help build tiny implantable medical devices and improve optical communication. In aerospace engineering and robotics, an example is the most recent electric propulsion and ion propulsion. == Education == Electrical engineers typically possess an academic degree with a major in electrical engineering, electronics engineering, electrical engineering technology, or electrical and electronic engineering. The same fundamental principles are taught in all programs, though emphasis may vary according to title. The length of study for such a degree is usually four or five years and the completed degree may be designated as a Bachelor of Science in Electrical/Electronics Engineering Technology, Bachelor of Engineering, Bachelor of Science, Bachelor of Technology, or Bachelor of Applied Science, depending on the university. The bachelor's degree generally includes units covering physics, mathematics, computer science, project management, and a variety of topics in electrical engineering. Initially such topics cover most, if not all, of the subdisciplines of electrical engineering. At many schools, electronic engineering is included as part of an electrical award, sometimes explicitly, such as a Bachelor of Engineering (Electrical and Electronic), but in others, electrical and electronic engineering are both considered to be sufficiently broad and complex that separate degrees are offered. Some electrical engineers choose to study for a postgraduate degree such as a Master of Engineering/Master of Science (MEng/MSc), a Master of Engineering Management, a Doctor of Philosophy (PhD) in Engineering, an Engineering Doctorate (Eng.D.), or an Engineer's degree. The master's and engineer's degrees may consist of either research, coursework or a mixture of the two. The Doctor of Philosophy and Engineering Doctorate degrees consist of a significant research component and are often viewed as the entry point to academia. In the United Kingdom and some other European countries, Master of Engineering is often considered to be an undergraduate degree of slightly longer duration than the Bachelor of Engineering rather than a standalone postgraduate degree. == Professional practice == In most countries, a bachelor's degree in engineering represents the first step towards professional certification and the degree program itself is certified by a professional body. After completing a certified degree program the engineer must satisfy a range of requirements (including work experience requirements) before being certified. Once certified the engineer is designated the title of Professional Engineer (in the United States, Canada and South Africa), Chartered engineer or Incorporated Engineer (in India, Pakistan, the United Kingdom, Ireland and Zimbabwe), Chartered Professional Engineer (in Australia and New Zealand) or European Engineer (in much of the European Union). The advantages of licensure vary depending upon location. For example, in the United States and Canada "only a licensed engineer may seal engineering work for public and private clients". This requirement is enforced by state and provincial legislation such as Quebec's Engineers Act. In other countries, no such legislation exists. Practically all certifying bodies maintain a code of ethics that they expect all members to abide by or risk expulsion. In this way these organizations play an important role in maintaining ethical standards for the profession. Even in jurisdictions where certification has little or no legal bearing on work, engineers are subject to contract law. In cases where an engineer's work fails he or she may be subject to the tort of negligence and, in extreme cases, the charge of criminal negligence. An engineer's work must also comply with numerous other rules and regulations, such as building codes and legislation pertaining to environmental law. Professional bodies of note for electrical engineers include the Institute of Electrical and Electronics Engineers (IEEE) and the Institution of Engineering and Technology (IET). The IEEE claims to produce 30% of the world's literature in electrical engineering, has over 360,000 members worldwide and holds over 3,000 conferences annually. The IET publishes 21 journals, has a worldwide membership of over 150,000, and claims to be the largest professional engineering society in Europe. Obsolescence of technical skills is a serious concern for electrical engineers. Membership and participation in technical societies, regular reviews of periodicals in the field and a habit of continued learning are therefore essential to maintaining proficiency. An MIET(Member of the Institution of Engineering and Technology) is recognised in Europe as an Electrical and computer (technology) engineer. In Australia, Canada, and the United States, electrical engineers make up around 0.25% of the labor force. == Tools and work == From the Global Positioning System to electric power generation, electrical engineers have contributed to the development of a wide range of technologies. They design, develop, test, and supervise the deployment of electrical systems and electronic devices. For example, they may work on the design of telecommunications systems, the operation of electric power stations, the lighting and wiring of buildings, the design of household appliances, or the electrical control of industrial machinery. Fundamental to the discipline are the sciences of physics and mathematics as these help to obtain both a qualitative and quantitative description of how such systems will work. Today most engineering work involves the use of computers and it is commonplace to use computer-aided design programs when designing electrical systems. Nevertheless, the ability to sketch ideas is still invaluable for quickly communicating with others. Although most electrical engineers will understand basic circuit theory (that is, the interactions of elements such as resistors, capacitors, diodes, transistors, and inductors in a circuit), the theories employed by engineers generally depend upon the work they do. For example, quantum mechanics and solid state physics might be relevant to an engineer working on VLSI (the design of integrated circuits), but are largely irrelevant to engineers working with macroscopic electrical systems. Even circuit theory may not be relevant to a person designing telecommunications systems that use off-the-shelf components. Perhaps the most important technical skills for electrical engineers are reflected in university programs, which emphasize strong numerical skills, computer literacy, and the ability to understand the technical language and concepts that relate to electrical engineering. A wide range of instrumentation is used by electrical engineers. For simple control circuits and alarms, a basic multimeter measuring voltage, current, and resistance may suffice. Where time-varying signals need to be studied, the oscilloscope is also an ubiquitous instrument. In RF engineering and high-frequency telecommunications, spectrum analyzers and network analyzers are used. In some disciplines, safety can be a particular concern with instrumentation. For instance, medical electronics designers must take into account that much lower voltages than normal can be dangerous when electrodes are directly in contact with internal body fluids. Power transmission engineering also has great safety concerns due to the high voltages used; although voltmeters may in principle be similar to their low voltage equivalents, safety and calibration issues make them very different. Many disciplines of electrical engineering use tests specific to their discipline. Audio electronics engineers use audio test sets consisting of a signal generator and a meter, principally to measure level but also other parameters such as harmonic distortion and noise. Likewise, information technology have their own test sets, often specific to a particular data format, and the same is true of television broadcasting. For many engineers, technical work accounts for only a fraction of the work they do. A lot of time may also be spent on tasks such as discussing proposals with clients, preparing budgets and determining project schedules. Many senior engineers manage a team of technicians or other engineers and for this reason project management skills are important. Most engineering projects involve some form of documentation and strong written communication skills are therefore very important. The workplaces of engineers are just as varied as the types of work they do. Electrical engineers may be found in the pristine lab environment of a fabrication plant, on board a Naval ship, the offices of a consulting firm or on site at a mine. During their working life, electrical engineers may find themselves supervising a wide range of individuals including scientists, electricians, computer programmers, and other engineers. Electrical engineering has an intimate relationship with the physical sciences. For instance, the physicist Lord Kelvin played a major role in the engineering of the first transatlantic telegraph cable. Conversely, the engineer Oliver Heaviside produced major work on the mathematics of transmission on telegraph cables. Electrical engineers are often required on major science projects. For instance, large particle accelerators such as CERN need electrical engineers to deal with many aspects of the project including the power distribution, the instrumentation, and the manufacture and installation of the superconducting electromagnets. == See also == == Notes == == References == Bibliography Abramson, Albert (1955). Electronic Motion Pictures: A History of the Television Camera. University of California Press. Åström, K.J.; Murray, R.M. (2021). Feedback Systems: An Introduction for Scientists and Engineers, Second Edition. Princeton University Press. p. 108. ISBN 978-0-691-21347-7. Bayoumi, Magdy A.; Swartzlander, Earl E. Jr. (31 October 1994). VLSI Signal Processing Technology. Springer. ISBN 978-0-7923-9490-7. Bhushan, Bharat (1997). Micro/Nanotribology and Its Applications. Springer. ISBN 978-0-7923-4386-8. Bissell, Chris (25 July 1996). Control Engineering, 2nd Edition. CRC Press. ISBN 978-0-412-57710-9. Chandrasekhar, Thomas (1 December 2006). 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McDavid, Richard A.; Echaore-McDavid, Susan (1 January 2009). Career Opportunities in Engineering. Infobase Publishing. ISBN 978-1-4381-1070-7. Merhari, Lhadi (3 March 2009). Hybrid Nanocomposites for Nanotechnology: Electronic, Optical, Magnetic and Biomedical Applications. Springer. ISBN 978-0-387-30428-1. Mook, William Moyer (2008). The Mechanical Response of Common Nanoscale Contact Geometries. ISBN 978-0-549-46812-7. Naidu, S. M.; Kamaraju, V. (2009). High Voltage Engineering. Tata McGraw-Hill Education. ISBN 978-0-07-066928-4. Obaidat, Mohammad S.; Denko, Mieso; Woungang, Isaac (9 June 2011). Pervasive Computing and Networking. John Wiley & Sons. ISBN 978-1-119-97043-9. Rosenberg, Chaim M. (2008). America at the Fair: Chicago's 1893 World's Columbian Exposition. Arcadia Publishing. ISBN 978-0-7385-2521-1. Schmidt, Rüdiger, "The LHC accelerator and its challenges", in Kramer M.; Soler, F.J.P. (eds), Large Hadron Collider Phenomenology, pp. 217–250, CRC Press, 2004 ISBN 0-7503-0986-5. Severs, Jeffrey; Leise, Christopher (24 February 2011). Pynchon's Against the Day: A Corrupted Pilgrim's Guide. Lexington Books. ISBN 978-1-61149-065-7. Shetty, Devdas; Kolk, Richard (14 September 2010). Mechatronics System Design, SI Version. Cengage Learning. ISBN 978-1-133-16949-9. Smith, Brian W. (January 2007). Communication Structures. Thomas Telford. ISBN 978-0-7277-3400-6. Sullivan, Dennis M. (24 January 2012). Quantum Mechanics for Electrical Engineers. John Wiley & Sons. ISBN 978-0-470-87409-7. Taylor, Allan (2008). Energy Industry. Infobase Publishing. ISBN 978-1-4381-1069-1. Thompson, Marc (12 June 2006). Intuitive Analog Circuit Design. Newnes. ISBN 978-0-08-047875-3. Tobin, Paul (1 January 2007). PSpice for Digital Communications Engineering. Morgan & Claypool Publishers. ISBN 978-1-59829-162-9. Tunbridge, Paul (1992). Lord Kelvin, His Influence on Electrical Measurements and Units. IET. ISBN 978-0-86341-237-0. Tuzlukov, Vyacheslav (12 December 2010). Signal Processing Noise. CRC Press. ISBN 978-1-4200-4111-8. Walker, Denise (2007). Metals and Non-metals. Evans Brothers. ISBN 978-0-237-53003-7. Wildes, Karl L.; Lindgren, Nilo A. (1 January 1985). A Century of Electrical Engineering and Computer Science at MIT, 1882–1982. MIT Press. p. 19. ISBN 978-0-262-23119-0. Zhang, Yan; Hu, Honglin; Luo, Jijun (27 June 2007). Distributed Antenna Systems: Open Architecture for Future Wireless Communications. CRC Press. ISBN 978-1-4200-4289-4. == Further reading == Adhami, Reza; Meenen, Peter M.; Hite, Denis (2007). Fundamental Concepts in Electrical and Computer Engineering with Practical Design Problems. Universal-Publishers. ISBN 978-1-58112-971-7. Bober, William; Stevens, Andrew (27 August 2012). Numerical and Analytical Methods with MATLAB for Electrical Engineers. CRC Press. ISBN 978-1-4398-5429-7. Bobrow, Leonard S. (1996). Fundamentals of Electrical Engineering. Oxford University Press. ISBN 978-0-19-510509-4. Chen, Wai Kai (16 November 2004). The Electrical Engineering Handbook. Academic Press. ISBN 978-0-08-047748-0. Ciuprina, G.; Ioan, D. (30 May 2007). Scientific Computing in Electrical Engineering. Springer. ISBN 978-3-540-71980-9. Faria, J. A. Brandao (15 September 2008). Electromagnetic Foundations of Electrical Engineering. John Wiley & Sons. ISBN 978-0-470-69748-1. Jones, Lincoln D. (July 2004). Electrical Engineering: Problems and Solutions. Dearborn Trade Publishing. ISBN 978-1-4195-2131-7. Karalis, Edward (18 September 2003). 350 Solved Electrical Engineering Problems. Dearborn Trade Publishing. ISBN 978-0-7931-8511-5. Krawczyk, Andrzej; Wiak, S. (1 January 2002). Electromagnetic Fields in Electrical Engineering. IOS Press. ISBN 978-1-58603-232-6. Laplante, Phillip A. (31 December 1999). Comprehensive Dictionary of Electrical Engineering. Springer. ISBN 978-3-540-64835-2. Leon-Garcia, Alberto (2008). Probability, Statistics, and Random Processes for Electrical Engineering. Prentice Hall. ISBN 978-0-13-147122-1. Malaric, Roman (2011). Instrumentation and Measurement in Electrical Engineering. Universal-Publishers. ISBN 978-1-61233-500-1. Sahay, Kuldeep; Pathak, Shivendra (1 January 2006). Basic Concepts of Electrical Engineering. New Age International. ISBN 978-81-224-1836-1. Srinivas, Kn (1 January 2007). Basic Electrical Engineering. I. K. International Pvt Ltd. ISBN 978-81-89866-34-1. == External links == International Electrotechnical Commission (IEC) MIT OpenCourseWare Archived 26 January 2008 at the Wayback Machine in-depth look at Electrical Engineering – online courses with video lectures. IEEE Global History Network A wiki-based site with many resources about the history of IEEE, its members, their professions and electrical and informational technologies and sciences.
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Genetic engineering, also called genetic modification or genetic manipulation, is the modification and manipulation of an organism's genes using technology. It is a set of technologies used to change the genetic makeup of cells, including the transfer of genes within and across species boundaries to produce improved or novel organisms. New DNA is obtained by either isolating and copying the genetic material of interest using recombinant DNA methods or by artificially synthesising the DNA. A construct is usually created and used to insert this DNA into the host organism. The first recombinant DNA molecule was made by Paul Berg in 1972 by combining DNA from the monkey virus SV40 with the lambda virus. As well as inserting genes, the process can be used to remove, or "knock out", genes. The new DNA can be inserted randomly, or targeted to a specific part of the genome. An organism that is generated through genetic engineering is considered to be genetically modified (GM) and the resulting entity is a genetically modified organism (GMO). The first GMO was a bacterium generated by Herbert Boyer and Stanley Cohen in 1973. Rudolf Jaenisch created the first GM animal when he inserted foreign DNA into a mouse in 1974. The first company to focus on genetic engineering, Genentech, was founded in 1976 and started the production of human proteins. Genetically engineered human insulin was produced in 1978 and insulin-producing bacteria were commercialised in 1982. Genetically modified food has been sold since 1994, with the release of the Flavr Savr tomato. The Flavr Savr was engineered to have a longer shelf life, but most current GM crops are modified to increase resistance to insects and herbicides. GloFish, the first GMO designed as a pet, was sold in the United States in December 2003. In 2016 salmon modified with a growth hormone were sold. Genetic engineering has been applied in numerous fields including research, medicine, industrial biotechnology and agriculture. In research, GMOs are used to study gene function and expression through loss of function, gain of function, tracking and expression experiments. By knocking out genes responsible for certain conditions it is possible to create animal model organisms of human diseases. As well as producing hormones, vaccines and other drugs, genetic engineering has the potential to cure genetic diseases through gene therapy. Chinese hamster ovary (CHO) cells are used in industrial genetic engineering. Additionally mRNA vaccines are made through genetic engineering to prevent infections by viruses such as COVID-19. The same techniques that are used to produce drugs can also have industrial applications such as producing enzymes for laundry detergent, cheeses and other products. The rise of commercialised genetically modified crops has provided economic benefit to farmers in many different countries, but has also been the source of most of the controversy surrounding the technology. This has been present since its early use; the first field trials were destroyed by anti-GM activists. Although there is a scientific consensus that currently available food derived from GM crops poses no greater risk to human health than conventional food, critics consider GM food safety a leading concern. Gene flow, impact on non-target organisms, control of the food supply and intellectual property rights have also been raised as potential issues. These concerns have led to the development of a regulatory framework, which started in 1975. It has led to an international treaty, the Cartagena Protocol on Biosafety, that was adopted in 2000. Individual countries have developed their own regulatory systems regarding GMOs, with the most marked differences occurring between the United States and Europe. == Overview == Genetic engineering is a process that alters the genetic structure of an organism by either removing or introducing DNA, or modifying existing genetic material in situ. Unlike traditional animal and plant breeding, which involves doing multiple crosses and then selecting for the organism with the desired phenotype, genetic engineering takes the gene directly from one organism and delivers it to the other. This is much faster, can be used to insert any genes from any organism (even ones from different domains) and prevents other undesirable genes from also being added. Genetic engineering could potentially fix severe genetic disorders in humans by replacing the defective gene with a functioning one. It is an important tool in research that allows the function of specific genes to be studied. Drugs, vaccines and other products have been harvested from organisms engineered to produce them. Crops have been developed that aid food security by increasing yield, nutritional value and tolerance to environmental stresses. The DNA can be introduced directly into the host organism or into a cell that is then fused or hybridised with the host. This relies on recombinant nucleic acid techniques to form new combinations of heritable genetic material followed by the incorporation of that material either indirectly through a vector system or directly through micro-injection, macro-injection or micro-encapsulation. Genetic engineering does not normally include traditional breeding, in vitro fertilisation, induction of polyploidy, mutagenesis and cell fusion techniques that do not use recombinant nucleic acids or a genetically modified organism in the process. However, some broad definitions of genetic engineering include selective breeding. Cloning and stem cell research, although not considered genetic engineering, are closely related and genetic engineering can be used within them. Synthetic biology is an emerging discipline that takes genetic engineering a step further by introducing artificially synthesised material into an organism. Plants, animals or microorganisms that have been changed through genetic engineering are termed genetically modified organisms or GMOs. If genetic material from another species is added to the host, the resulting organism is called transgenic. If genetic material from the same species or a species that can naturally breed with the host is used the resulting organism is called cisgenic. If genetic engineering is used to remove genetic material from the target organism the resulting organism is termed a knockout organism. In Europe genetic modification is synonymous with genetic engineering while within the United States of America and Canada genetic modification can also be used to refer to more conventional breeding methods. == History == Humans have altered the genomes of species for thousands of years through selective breeding, or artificial selection: 1 : 1 as contrasted with natural selection. More recently, mutation breeding has used exposure to chemicals or radiation to produce a high frequency of random mutations, for selective breeding purposes. Genetic engineering as the direct manipulation of DNA by humans outside breeding and mutations has only existed since the 1970s. The term "genetic engineering" was coined by the Russian-born geneticist Nikolay Timofeev-Ressovsky in his 1934 paper "The Experimental Production of Mutations", published in the British journal Biological Reviews. Jack Williamson used the term in his science fiction novel Dragon's Island, published in 1951 – one year before DNA's role in heredity was confirmed by Alfred Hershey and Martha Chase, and two years before James Watson and Francis Crick showed that the DNA molecule has a double-helix structure – though the general concept of direct genetic manipulation was explored in rudimentary form in Stanley G. Weinbaum's 1936 science fiction story Proteus Island. In 1972, Paul Berg created the first recombinant DNA molecules by combining DNA from the monkey virus SV40 with that of the lambda virus. In 1973 Herbert Boyer and Stanley Cohen created the first transgenic organism by inserting antibiotic resistance genes into the plasmid of an Escherichia coli bacterium. A year later Rudolf Jaenisch created a transgenic mouse by introducing foreign DNA into its embryo, making it the world's first transgenic animal These achievements led to concerns in the scientific community about potential risks from genetic engineering, which were first discussed in depth at the Asilomar Conference in 1975. One of the main recommendations from this meeting was that government oversight of recombinant DNA research should be established until the technology was deemed safe. In 1976 Genentech, the first genetic engineering company, was founded by Herbert Boyer and Robert Swanson and a year later the company produced a human protein (somatostatin) in E. coli. Genentech announced the production of genetically engineered human insulin in 1978. In 1980, the U.S. Supreme Court in the Diamond v. Chakrabarty case ruled that genetically altered life could be patented. The insulin produced by bacteria was approved for release by the Food and Drug Administration (FDA) in 1982. In 1983, a biotech company, Advanced Genetic Sciences (AGS) applied for U.S. government authorisation to perform field tests with the ice-minus strain of Pseudomonas syringae to protect crops from frost, but environmental groups and protestors delayed the field tests for four years with legal challenges. In 1987, the ice-minus strain of P. syringae became the first genetically modified organism (GMO) to be released into the environment when a strawberry field and a potato field in California were sprayed with it. Both test fields were attacked by activist groups the night before the tests occurred: "The world's first trial site attracted the world's first field trasher". The first field trials of genetically engineered plants occurred in France and the US in 1986, tobacco plants were engineered to be resistant to herbicides. The People's Republic of China was the first country to commercialise transgenic plants, introducing a virus-resistant tobacco in 1992. In 1994 Calgene attained approval to commercially release the first genetically modified food, the Flavr Savr, a tomato engineered to have a longer shelf life. In 1994, the European Union approved tobacco engineered to be resistant to the herbicide bromoxynil, making it the first genetically engineered crop commercialised in Europe. In 1995, Bt potato was approved safe by the Environmental Protection Agency, after having been approved by the FDA, making it the first pesticide producing crop to be approved in the US. In 2009 11 transgenic crops were grown commercially in 25 countries, the largest of which by area grown were the US, Brazil, Argentina, India, Canada, China, Paraguay and South Africa. In 2010, scientists at the J. Craig Venter Institute created the first synthetic genome and inserted it into an empty bacterial cell. The resulting bacterium, named Mycoplasma laboratorium, could replicate and produce proteins. Four years later this was taken a step further when a bacterium was developed that replicated a plasmid containing a unique base pair, creating the first organism engineered to use an expanded genetic alphabet. In 2012, Jennifer Doudna and Emmanuelle Charpentier collaborated to develop the CRISPR/Cas9 system, a technique which can be used to easily and specifically alter the genome of almost any organism. == Process == Creating a GMO is a multi-step process. Genetic engineers must first choose what gene they wish to insert into the organism. This is driven by what the aim is for the resultant organism and is built on earlier research. Genetic screens can be carried out to determine potential genes and further tests then used to identify the best candidates. The development of microarrays, transcriptomics and genome sequencing has made it much easier to find suitable genes. Luck also plays its part; the Roundup Ready gene was discovered after scientists noticed a bacterium thriving in the presence of the herbicide. === Gene isolation and cloning === The next step is to isolate the candidate gene. The cell containing the gene is opened and the DNA is purified. The gene is separated by using restriction enzymes to cut the DNA into fragments or polymerase chain reaction (PCR) to amplify up the gene segment. These segments can then be extracted through gel electrophoresis. If the chosen gene or the donor organism's genome has been well studied it may already be accessible from a genetic library. If the DNA sequence is known, but no copies of the gene are available, it can also be artificially synthesised. Once isolated the gene is ligated into a plasmid that is then inserted into a bacterium. The plasmid is replicated when the bacteria divide, ensuring unlimited copies of the gene are available. The RK2 plasmid is notable for its ability to replicate in a wide variety of single-celled organisms, which makes it suitable as a genetic engineering tool. Before the gene is inserted into the target organism it must be combined with other genetic elements. These include a promoter and terminator region, which initiate and end transcription. A selectable marker gene is added, which in most cases confers antibiotic resistance, so researchers can easily determine which cells have been successfully transformed. The gene can also be modified at this stage for better expression or effectiveness. These manipulations are carried out using recombinant DNA techniques, such as restriction digests, ligations and molecular cloning. === Inserting DNA into the host genome === There are a number of techniques used to insert genetic material into the host genome. Some bacteria can naturally take up foreign DNA. This ability can be induced in other bacteria via stress (e.g. thermal or electric shock), which increases the cell membrane's permeability to DNA; up-taken DNA can either integrate with the genome or exist as extrachromosomal DNA. DNA is generally inserted into animal cells using microinjection, where it can be injected through the cell's nuclear envelope directly into the nucleus, or through the use of viral vectors. Plant genomes can be engineered by physical methods or by use of Agrobacterium for the delivery of sequences hosted in T-DNA binary vectors. In plants the DNA is often inserted using Agrobacterium-mediated transformation, taking advantage of the Agrobacteriums T-DNA sequence that allows natural insertion of genetic material into plant cells. Other methods include biolistics, where particles of gold or tungsten are coated with DNA and then shot into young plant cells, and electroporation, which involves using an electric shock to make the cell membrane permeable to plasmid DNA. As only a single cell is transformed with genetic material, the organism must be regenerated from that single cell. In plants this is accomplished through the use of tissue culture. In animals it is necessary to ensure that the inserted DNA is present in the embryonic stem cells. Bacteria consist of a single cell and reproduce clonally so regeneration is not necessary. Selectable markers are used to easily differentiate transformed from untransformed cells. These markers are usually present in the transgenic organism, although a number of strategies have been developed that can remove the selectable marker from the mature transgenic plant. Further testing using PCR, Southern hybridization, and DNA sequencing is conducted to confirm that an organism contains the new gene. These tests can also confirm the chromosomal location and copy number of the inserted gene. The presence of the gene does not guarantee it will be expressed at appropriate levels in the target tissue so methods that look for and measure the gene products (RNA and protein) are also used. These include northern hybridisation, quantitative RT-PCR, Western blot, immunofluorescence, ELISA and phenotypic analysis. The new genetic material can be inserted randomly within the host genome or targeted to a specific location. The technique of gene targeting uses homologous recombination to make desired changes to a specific endogenous gene. This tends to occur at a relatively low frequency in plants and animals and generally requires the use of selectable markers. The frequency of gene targeting can be greatly enhanced through genome editing. Genome editing uses artificially engineered nucleases that create specific double-stranded breaks at desired locations in the genome, and use the cell's endogenous mechanisms to repair the induced break by the natural processes of homologous recombination and nonhomologous end-joining. There are four families of engineered nucleases: meganucleases, zinc finger nucleases, transcription activator-like effector nucleases (TALENs), and the Cas9-guideRNA system (adapted from CRISPR). TALEN and CRISPR are the two most commonly used and each has its own advantages. TALENs have greater target specificity, while CRISPR is easier to design and more efficient. In addition to enhancing gene targeting, engineered nucleases can be used to introduce mutations at endogenous genes that generate a gene knockout. == Applications == Genetic engineering has applications in medicine, research, industry and agriculture and can be used on a wide range of plants, animals and microorganisms. Bacteria, the first organisms to be genetically modified, can have plasmid DNA inserted containing new genes that code for medicines or enzymes that process food and other substrates. Plants have been modified for insect protection, herbicide resistance, virus resistance, enhanced nutrition, tolerance to environmental pressures and the production of edible vaccines. Most commercialised GMOs are insect resistant or herbicide tolerant crop plants. Genetically modified animals have been used for research, model animals and the production of agricultural or pharmaceutical products. The genetically modified animals include animals with genes knocked out, increased susceptibility to disease, hormones for extra growth and the ability to express proteins in their milk. === Medicine === Genetic engineering has many applications to medicine that include the manufacturing of drugs, creation of model animals that mimic human conditions and gene therapy. One of the earliest uses of genetic engineering was to mass-produce human insulin in bacteria. This application has now been applied to human growth hormones, follicle stimulating hormones (for treating infertility), human albumin, monoclonal antibodies, antihemophilic factors, vaccines and many other drugs. Mouse hybridomas, cells fused together to create monoclonal antibodies, have been adapted through genetic engineering to create human monoclonal antibodies. Genetically engineered viruses are being developed that can still confer immunity, but lack the infectious sequences. Genetic engineering is also used to create animal models of human diseases. Genetically modified mice are the most common genetically engineered animal model. They have been used to study and model cancer (the oncomouse), obesity, heart disease, diabetes, arthritis, substance abuse, anxiety, aging and Parkinson disease. Potential cures can be tested against these mouse models. Gene therapy is the genetic engineering of humans, generally by replacing defective genes with effective ones. Clinical research using somatic gene therapy has been conducted with several diseases, including X-linked SCID, chronic lymphocytic leukemia (CLL), and Parkinson's disease. In 2012, Alipogene tiparvovec became the first gene therapy treatment to be approved for clinical use. In 2015 a virus was used to insert a healthy gene into the skin cells of a boy suffering from a rare skin disease, epidermolysis bullosa, in order to grow, and then graft healthy skin onto 80 percent of the boy's body which was affected by the illness. Germline gene therapy would result in any change being inheritable, which has raised concerns within the scientific community. In 2015, CRISPR was used to edit the DNA of non-viable human embryos, leading scientists of major world academies to call for a moratorium on inheritable human genome edits. There are also concerns that the technology could be used not just for treatment, but for enhancement, modification or alteration of a human beings' appearance, adaptability, intelligence, character or behavior. The distinction between cure and enhancement can also be difficult to establish. In November 2018, He Jiankui announced that he had edited the genomes of two human embryos, to attempt to disable the CCR5 gene, which codes for a receptor that HIV uses to enter cells. The work was widely condemned as unethical, dangerous, and premature. Currently, germline modification is banned in 40 countries. Scientists that do this type of research will often let embryos grow for a few days without allowing it to develop into a baby. Researchers are altering the genome of pigs to induce the growth of human organs, with the aim of increasing the success of pig to human organ transplantation. Scientists are creating "gene drives", changing the genomes of mosquitoes to make them immune to malaria, and then looking to spread the genetically altered mosquitoes throughout the mosquito population in the hopes of eliminating the disease. === Research === Genetic engineering is an important tool for natural scientists, with the creation of transgenic organisms one of the most important tools for analysis of gene function. Genes and other genetic information from a wide range of organisms can be inserted into bacteria for storage and modification, creating genetically modified bacteria in the process. Bacteria are cheap, easy to grow, clonal, multiply quickly, relatively easy to transform and can be stored at -80 °C almost indefinitely. Once a gene is isolated it can be stored inside the bacteria providing an unlimited supply for research. Organisms are genetically engineered to discover the functions of certain genes. This could be the effect on the phenotype of the organism, where the gene is expressed or what other genes it interacts with. These experiments generally involve loss of function, gain of function, tracking and expression. Loss of function experiments, such as in a gene knockout experiment, in which an organism is engineered to lack the activity of one or more genes. In a simple knockout a copy of the desired gene has been altered to make it non-functional. Embryonic stem cells incorporate the altered gene, which replaces the already present functional copy. These stem cells are injected into blastocysts, which are implanted into surrogate mothers. This allows the experimenter to analyse the defects caused by this mutation and thereby determine the role of particular genes. It is used especially frequently in developmental biology. When this is done by creating a library of genes with point mutations at every position in the area of interest, or even every position in the whole gene, this is called "scanning mutagenesis". The simplest method, and the first to be used, is "alanine scanning", where every position in turn is mutated to the unreactive amino acid alanine. Gain of function experiments, the logical counterpart of knockouts. These are sometimes performed in conjunction with knockout experiments to more finely establish the function of the desired gene. The process is much the same as that in knockout engineering, except that the construct is designed to increase the function of the gene, usually by providing extra copies of the gene or inducing synthesis of the protein more frequently. Gain of function is used to tell whether or not a protein is sufficient for a function, but does not always mean it is required, especially when dealing with genetic or functional redundancy. Tracking experiments, which seek to gain information about the localisation and interaction of the desired protein. One way to do this is to replace the wild-type gene with a 'fusion' gene, which is a juxtaposition of the wild-type gene with a reporting element such as green fluorescent protein (GFP) that will allow easy visualisation of the products of the genetic modification. While this is a useful technique, the manipulation can destroy the function of the gene, creating secondary effects and possibly calling into question the results of the experiment. More sophisticated techniques are now in development that can track protein products without mitigating their function, such as the addition of small sequences that will serve as binding motifs to monoclonal antibodies. Expression studies aim to discover where and when specific proteins are produced. In these experiments, the DNA sequence before the DNA that codes for a protein, known as a gene's promoter, is reintroduced into an organism with the protein coding region replaced by a reporter gene such as GFP or an enzyme that catalyses the production of a dye. Thus the time and place where a particular protein is produced can be observed. Expression studies can be taken a step further by altering the promoter to find which pieces are crucial for the proper expression of the gene and are actually bound by transcription factor proteins; this process is known as promoter bashing. === Industrial === Organisms can have their cells transformed with a gene coding for a useful protein, such as an enzyme, so that they will overexpress the desired protein. Mass quantities of the protein can then be manufactured by growing the transformed organism in bioreactor equipment using industrial fermentation, and then purifying the protein. Some genes do not work well in bacteria, so yeast, insect cells or mammalian cells can also be used. These techniques are used to produce medicines such as insulin, human growth hormone, and vaccines, supplements such as tryptophan, aid in the production of food (chymosin in cheese making) and fuels. Other applications with genetically engineered bacteria could involve making them perform tasks outside their natural cycle, such as making biofuels, cleaning up oil spills, carbon and other toxic waste and detecting arsenic in drinking water. Certain genetically modified microbes can also be used in biomining and bioremediation, due to their ability to extract heavy metals from their environment and incorporate them into compounds that are more easily recoverable. In materials science, a genetically modified virus has been used in a research laboratory as a scaffold for assembling a more environmentally friendly lithium-ion battery. Bacteria have also been engineered to function as sensors by expressing a fluorescent protein under certain environmental conditions. === Agriculture === One of the best-known and controversial applications of genetic engineering is the creation and use of genetically modified crops or genetically modified livestock to produce genetically modified food. Crops have been developed to increase production, increase tolerance to abiotic stresses, alter the composition of the food, or to produce novel products. The first crops to be released commercially on a large scale provided protection from insect pests or tolerance to herbicides. Fungal and virus resistant crops have also been developed or are in development. This makes the insect and weed management of crops easier and can indirectly increase crop yield. GM crops that directly improve yield by accelerating growth or making the plant more hardy (by improving salt, cold or drought tolerance) are also under development. In 2016 Salmon have been genetically modified with growth hormones to reach normal adult size much faster. GMOs have been developed that modify the quality of produce by increasing the nutritional value or providing more industrially useful qualities or quantities. The Amflora potato produces a more industrially useful blend of starches. Soybeans and canola have been genetically modified to produce more healthy oils. The first commercialised GM food was a tomato that had delayed ripening, increasing its shelf life. Plants and animals have been engineered to produce materials they do not normally make. Pharming uses crops and animals as bioreactors to produce vaccines, drug intermediates, or the drugs themselves; the useful product is purified from the harvest and then used in the standard pharmaceutical production process. Cows and goats have been engineered to express drugs and other proteins in their milk, and in 2009 the FDA approved a drug produced in goat milk. === Other applications === Genetic engineering has potential applications in conservation and natural area management. Gene transfer through viral vectors has been proposed as a means of controlling invasive species as well as vaccinating threatened fauna from disease. Transgenic trees have been suggested as a way to confer resistance to pathogens in wild populations. With the increasing risks of maladaptation in organisms as a result of climate change and other perturbations, facilitated adaptation through gene tweaking could be one solution to reducing extinction risks. Applications of genetic engineering in conservation are thus far mostly theoretical and have yet to be put into practice. Genetic engineering is also being used to create microbial art. Some bacteria have been genetically engineered to create black and white photographs. Novelty items such as lavender-colored carnations, blue roses, and glowing fish, have also been produced through genetic engineering. == Regulation == The regulation of genetic engineering concerns the approaches taken by governments to assess and manage the risks associated with the development and release of GMOs. The development of a regulatory framework began in 1975, at Asilomar, California. The Asilomar meeting recommended a set of voluntary guidelines regarding the use of recombinant technology. As the technology improved the US established a committee at the Office of Science and Technology, which assigned regulatory approval of GM food to the USDA, FDA and EPA. The Cartagena Protocol on Biosafety, an international treaty that governs the transfer, handling, and use of GMOs, was adopted on 29 January 2000. One hundred and fifty-seven countries are members of the Protocol, and many use it as a reference point for their own regulations. The legal and regulatory status of GM foods varies by country, with some nations banning or restricting them, and others permitting them with widely differing degrees of regulation. Some countries allow the import of GM food with authorisation, but either do not allow its cultivation (Russia, Norway, Israel) or have provisions for cultivation even though no GM products are yet produced (Japan, South Korea). Most countries that do not allow GMO cultivation do permit research. Some of the most marked differences occur between the US and Europe. The US policy focuses on the product (not the process), only looks at verifiable scientific risks and uses the concept of substantial equivalence. The European Union by contrast has possibly the most stringent GMO regulations in the world. All GMOs, along with irradiated food, are considered "new food" and subject to extensive, case-by-case, science-based food evaluation by the European Food Safety Authority. The criteria for authorisation fall in four broad categories: "safety", "freedom of choice", "labelling", and "traceability". The level of regulation in other countries that cultivate GMOs lie in between Europe and the United States. One of the key issues concerning regulators is whether GM products should be labeled. The European Commission says that mandatory labeling and traceability are needed to allow for informed choice, avoid potential false advertising and facilitate the withdrawal of products if adverse effects on health or the environment are discovered. The American Medical Association and the American Association for the Advancement of Science say that absent scientific evidence of harm even voluntary labeling is misleading and will falsely alarm consumers. Labeling of GMO products in the marketplace is required in 64 countries. Labeling can be mandatory up to a threshold GM content level (which varies between countries) or voluntary. In Canada and the US labeling of GM food is voluntary, while in Europe all food (including processed food) or feed which contains greater than 0.9% of approved GMOs must be labelled. == Controversy == Critics have objected to the use of genetic engineering on several grounds, including ethical, ecological and economic concerns. Many of these concerns involve GM crops and whether food produced from them is safe and what impact growing them will have on the environment. These controversies have led to litigation, international trade disputes, and protests, and to restrictive regulation of commercial products in some countries. Accusations that scientists are "playing God" and other religious issues have been ascribed to the technology from the beginning. Other ethical issues raised include the patenting of life, the use of intellectual property rights, the level of labeling on products, control of the food supply and the objectivity of the regulatory process. Although doubts have been raised, economically most studies have found growing GM crops to be beneficial to farmers. Gene flow between GM crops and compatible plants, along with increased use of selective herbicides, can increase the risk of "superweeds" developing. Other environmental concerns involve potential impacts on non-target organisms, including soil microbes, and an increase in secondary and resistant insect pests. Many of the environmental impacts regarding GM crops may take many years to be understood and are also evident in conventional agriculture practices. With the commercialisation of genetically modified fish there are concerns over what the environmental consequences will be if they escape. There are three main concerns over the safety of genetically modified food: whether they may provoke an allergic reaction; whether the genes could transfer from the food into human cells; and whether the genes not approved for human consumption could outcross to other crops. There is a scientific consensus that currently available food derived from GM crops poses no greater risk to human health than conventional food, but that each GM food needs to be tested on a case-by-case basis before introduction. Nonetheless, members of the public are less likely than scientists to perceive GM foods as safe. == In popular culture == Genetic engineering features in many science fiction stories. Frank Herbert's novel The White Plague describes the deliberate use of genetic engineering to create a pathogen which specifically kills women. Another of Herbert's creations, the Dune series of novels, uses genetic engineering to create the powerful Tleilaxu. Few films have informed audiences about genetic engineering, with the exception of the 1978 The Boys from Brazil and the 1993 Jurassic Park, both of which make use of a lesson, a demonstration, and a clip of scientific film. Genetic engineering methods are weakly represented in film; Michael Clark, writing for the Wellcome Trust, calls the portrayal of genetic engineering and biotechnology "seriously distorted" in films such as The 6th Day. In Clark's view, the biotechnology is typically "given fantastic but visually arresting forms" while the science is either relegated to the background or fictionalised to suit a young audience. == See also == Biological engineering Computational genomics Modifications (genetics) Mutagenesis (molecular biology technique) == References == == Further reading == == External links == GMO Safety - Information about research projects on the biological safety of genetically modified plants. GMO-compass, news on GMO en EU
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https://en.wikipedia.org/wiki/Genetic_engineering
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Regarding the civil engineering of shorelines, soft engineering is a shoreline management practice that uses sustainable ecological principles to restore shoreline stabilization and protect riparian habitats. Soft Shoreline Engineering (SSE) uses the strategic placement of organic materials such as vegetation, stones, sand, debris, and other structural materials to reduce erosion, enhance shoreline aesthetic, soften the land-water interface, and lower costs of ecological restoration. To differentiate Soft Shoreline Engineering from Hard Shoreline Engineering, Hard Shoreline Engineering tends to use steel sheet piling or concrete breakwalls to prevent danger and fortify shorelines. Generally, Hard Shoreline Engineering is used for navigational or industrial purposes. To contrast, Soft Shoreline Engineering emphasizes the application of ecological principles rather than compromising the engineered integrity of the shoreline. The opposite alternative is hard engineering. == Background == Hard shoreline engineering is the use of non-organic reinforcing materials, such as concrete, steel, and plastic to fortify shorelines, stop erosion, and protect urban development from flooding. However, as shoreline development among coastal cities increased dramatically, the detrimental ecological factors became apparent. Hard shoreline engineering was designed to accommodate human development along the coast, focusing on increasing efficiency in the commercial, navigational, and industrial sectors of the economy. In 2003, the global population living within 120 miles (190 km) of an ocean was 3 billion and is expected to double by the year 2025. These developments came at a high cost, destroying biological communities, isolating riparian habitats, altering the natural transport of sediment by disrupting wave action and long-shore currents. Many coastal regions began to see significant coastal degradation due to human development, the Detroit River losing as great as 97% of its coastal wetland habitats. Singapore, as well, documented the disappearance of the majority of its mangrove forests, coastal reefs, and mudflat regions between 1920 and 1990 due to shoreline development. Towards the end of the 20th century, coastal engineering practices underwent a gradual transition towards incorporating the natural environment into planning considerations. In stark contrast to hard engineering, employed with the sole purpose of improving navigation, industrial and commercial uses of the river, soft engineering takes a multi-faceted approach, developing shorelines for a multitude of benefits and incorporating consideration of fish and wildlife habitat. Tasked with the responsibility to construct and maintain United States Federally authorized coastal civil works projects, the U.S. Army Corps of Engineers plays a major part in the development of the principles of coastal engineering as practiced within the U.S. In part due to degradation of coastline across the United States, the Corps has since updated its coastal management practices with an increased emphasis on computer-based modeling, project upkeep, and environmental restoration. However, soft and hard engineering are not mutually exclusive; a blend of the two management practices can be used to design waterfronts, especially for high flow bodies of water. == Principles of Soft Shoreline Engineering == Imitate Nature - Imitating the characteristics of the natural environment is critical to the success of soft engineering efforts. Existing traits of a landscape provide telltale signs of the geomorphic forces at play. Trying to add vegetation to a barren area with high winds will not produce the intended results. Gentle Slopes - Gentle slopes are most commonly found in the natural environment and are the most stable under the forces of gravity. Gradually inclined slopes along banks and shorelines allow for the dissipation of wave energy over a greater distance, reducing the force of erosion. "Soft Armoring" - Soft armoring includes the use of materials such as live plants, shrubs, root wads, logs, vegetative mats, etc. These materials, which are alive, can adapt to changes in the environment and help maintain regular coastal processes by disrupting the natural shoreline in the least way possible. Soft armoring is also paramount to enhancing shoreline habitats and improving water quality. Material Variety - A variety of textures and vegetation enhances aesthetic, diversifies the natural landscape, and maximizes biodiversity. Native plants and endangered or threatened species should be used whenever possible. The use of locally abundant and easily accessible natural resources also cuts development costs significantly. == Techniques == === Planting === The most basic and fundamental form of soft shoreline engineering is adding native vegetation to degraded or damaged shoreline areas to bolster the structural integrity of the soil. The deep roots of the vegetation bind the soil together, strengthening the structural integrity of the soil and preventing it from cracking apart and crumbling into the body of water. An added layer of vegetation also protects embankments from corrosive forces such as rain and wind. === Rolled Erosion Control Products (RECP) === Rolled erosion control products are blankets or netting created with both natural and synthetic materials used to protect the surface of the ground from erosive forces and promote the growth of vegetation. RECPs are often used in locations highly susceptible to erosion, such as steep slopes, channels, and areas where natural vegetation is sparse. These products aid the growth of vegetation by protecting soil from raindrops, keeping seed in place, and maintaining moisture and temperature parameters consistent with plant growth. The typical composition of an RECP includes seed, fertilizer, degradable stakes, and a binding material. Although design varies by manufacturer, most RECPs are biodegradable or photodegradable and decompose after a given amount of time. === Coir Logs === Erosion control coir logs are natural fiber products designed to stabilize soil by supporting erosion prone areas such as river banks, slopes, hills, and streams. Coir is coconut fiber extracted from the outer husk of a coconut and used in products such as ropes, mats, and nets. Like RECPs, coir logs are natural and biodegradable, being composed primarily of densely packed coir fibers held together by a tubular coir twine netting. Coir fiber is strong and water resistant, making it a durable barrier against waves and river currents. Multiple sections of coir log can be joined together by twine to provide erosion control and prevention to vulnerable areas. Coir logs can also be vegetated and used to establish root systems of native plants along wetland edges. === Live Stakes and Fascines === Lives stakes and fascines are a specific tree or shrub species that thrive in moist soil conditions and can be strategically used to stabilize stream banks and shorelines. Live stakes are hardwood cuttings with the branches removed that, when planted in moist soil, will grow new plants from the stems of the cut branches. They can be used alone, implanted into 2-inch (5 cm) pilot holes in the soil, or used as a device to secure other bioengineering materials such as rolled erosion control products and coir logs. Fascines are similar live branches strapped together and laid horizontally across streambank contours to impede or prevent the flow of water and curb erosion. === Brush Mattress === Brush mattresses, also known as live brush mats or brush matting is a technique used to form immediate protective cover of a streambank. Brush mattresses are dense compilations of live stakes, fascines, and branch cuttings held down with additional stakes to protect the embankment. The brush mattress is intended to eventually take root and enhance the conditions for the colonization of native plants. Along with aiding in the restoration of riparian habitats, this product intercepts sediment flowing downstream and provides a number of benefits for fish and aquatic species by offering physical protection from predators, regulating the water temperature, and shading the stream. === Live Cribwalls === Live crib walls are structures that resemble that of a wooden log cabin built into a streambank and rilled with natural materials such as soil, dormant wood cuttings, and rock. The live crib wall is able to fortify stream banks with the combination of the sturdy log structure and the root mass that will sprout from the wood cuttings and take hold deep in the bank, armoring it from erosion. Although quite labor intensive, cribwalls can last for decades and provide excellent aquatic habitats under the surface of the body of water. Cribwalls have the ability to prevent the occurrence of a split channel in a stream but should not be used in streams with downcutting as the base of the structure will be compromised. === Encapsulated Soil Lifts === Encapsulated soil lifts are a technique that "encapsulates" soil in a biodegradable blanket and organized on a slope in such a way that creates the desired stream bank slope. The layers of soil, or lifts, are used to stabilize the banks of moderate to high level energy shorelines. Once constructed, the lifts are planted with the seeds of native flowers, shrubs and grasses. In addition to reducing dirt erosion in the body of water, soil lifts protect water quality and the encompassed riparian habitats. === Vegetated Riprap === Vegetated riprap is a soft shoreline engineering technique that is an alternative to conventional riprap for erosion protection. Conventional riprap is a form of rock armor, rubble, or concrete used to fortify shoreline structures against the forces of erosion. Vegetated riprap is a more economically efficient form of shoreline protection that enhances fish and wildlife habitat as well as softening the appearance and improving embankment aesthetic. Vegetated riprap incorporated native vegetation along with rocks to create live cuttings in the bank. This technique improves the natural habitat of aquatic species along with armoring the banks and redirecting water flows. === Geo Bags === Geo bags or erosion control bags/tubes act as sediment removing filters, protecting against shoreline erosion by trapping sludge and sand particles and preventing them from leaving the coastal area. The bags are designed to allow the natural flow of water to filter in and out without inhibition, limiting disruption to the coastline. These geo bags or tubes are designed to look natural in the coastal environment, as opposed to concrete alternatives, and are built to endure the outdoors. Geo bag material is typically composed of geotextile fabric and can be designed for different specifications. == Best Management Practices == In order to incorporate principles of soft engineering into practice, shorelines must be redeveloped to achieve multiple objectives. For example, soft shoreline engineering has the ability to decrease costs, stabilize banks, enhance aesthetic value, protect riparian habitats, expand public access, and support a diversity of wildlife. To achieve the goal of multiple objectives for waterfront development and design, a multi-disciplinary team must be formed to integrate environmental, social, and economic principles. The first step in implementing soft engineering is conducting a preliminary assessment of the site and determining whether soft engineering is applicable and practical. A typical assessment includes identifying the extent of the project area, evaluating existing uses, documenting amenities and characteristics such as habitats, species, public access, development, and considering impact of future desired use. If the team decides the site is fit to implement soft engineering, a complex process is designed in order to achieve the predetermined goals of the development and complete with objectives. Standards and targets must then be created to measure project development and progress. Interdisciplinary partnerships must be established at an early stage in the process to ensure the incorporation of environmental, social, and economic values, as well as target objectives implemented to measure progress. Priorities and alternative are established, with the team working together to decide on the best management practices to achieve maximum effectiveness. After best management practices have been determined and incorporated, project success is based upon the meeting of objectives and effective preservation and conservation efforts. == Case Studies == === Greater Detroit American Heritage River Initiative === In 1998, the President of the United States created the American Heritage River Initiative to restore and revitalize rivers and waterfronts through the use of newly introduced soft engineering techniques. A report by Schneider reported that 47.2% of the U.S. and Canadian Detroit River had been fortified with concrete or steel, in accordance with traditional hard engineering management practices. In 1999, a U.S. Canadian SSE conference developed the best management practices for SSE use, which was put into effect among the 38 SSE projects that took place in the Detroit River-western Lake Erie watershed. A grand total of $17.3 million was spent on these projects which aimed to improve riparian and aquatic habitat, restore natural shoreline, and treat stormwater. The study found that the economic benefits to ecological restoration are profound and provide compelling evidence for further investigation and investment into shoreline rehabilitation processes. Researchers also found that SSE not only improved the natural habitat, but from a social perspective, the efforts aided in reconnecting people to nature, fostering a sense of human attachment to the success and health of these waterfronts. === Mississippi === Beginning with British colonial establishment in 1819, Mississippi's coastline has undergone an extensive history of decline through alteration and land reclamation. Hilton and Manning found that from the period of 1922 to 1993, the area of mangroves, coral reefs, and intertidal mudflats decreased dramatically, the actual percentage of natural coastline dropping from 96 to 40%. In order to combat these deleterious anthropogenic effects, Mississippi's government came up with a Master Plan in 2008 which incorporated the modification of shorelines in accordance with the ecological principles of soft engineering. A study regarding the success of ecological engineering in Singapore found that the most effective way to introduce ecological principles into shoreline design and preservation is to implement a top down approach that coordinates and educates the multitude of agencies that are involved in coastal management. Mississippi's loss of natural coastline is just one example of the inevitable detriment of intensive human development and soft engineering techniques provide an effective way to balance shoreline conservation and restoration with the urban development that is sure to continue. == References == == See also == Hard engineering Ecological Engineering Erosion Control
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https://en.wikipedia.org/wiki/Soft_engineering
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Computer engineering (CE, CoE, or CpE) is a branch of engineering specialized in developing computer hardware and software. It integrates several fields of electrical engineering, electronics engineering and computer science. Computer engineering is referred to as electrical and computer engineering or computer science and engineering at some universities. Computer engineers require training in hardware-software integration, software design, and software engineering. It can encompass areas such as electromagnetism, artificial intelligence (AI), robotics, computer networks, computer architecture and operating systems. Computer engineers are involved in many hardware and software aspects of computing, from the design of individual microcontrollers, microprocessors, personal computers, and supercomputers, to circuit design. This field of engineering not only focuses on how computer systems themselves work, but also on how to integrate them into the larger picture. Robotics are one of the applications of computer engineering. Computer engineering usually deals with areas including writing software and firmware for embedded microcontrollers, designing VLSI chips, analog sensors, mixed signal circuit boards, Thermodynamics and Control systems. Computer engineers are also suited for robotics research, which relies heavily on using digital systems to control and monitor electrical systems like motors, communications, and sensors. In many institutions of higher learning, computer engineering students are allowed to choose areas of in-depth study in their junior and senior years because the full breadth of knowledge used in the design and application of computers is beyond the scope of an undergraduate degree. Other institutions may require engineering students to complete one or two years of general engineering before declaring computer engineering as their primary focus. == History == Computer engineering began in 1939 when John Vincent Atanasoff and Clifford Berry began developing the world's first electronic digital computer through physics, mathematics, and electrical engineering. John Vincent Atanasoff was once a physics and mathematics teacher for Iowa State University and Clifford Berry a former graduate under electrical engineering and physics. Together, they created the Atanasoff-Berry computer, also known as the ABC which took five years to complete. While the original ABC was dismantled and discarded in the 1940s, a tribute was made to the late inventors; a replica of the ABC was made in 1997, where it took a team of researchers and engineers four years and $350,000 to build. The modern personal computer emerged in the 1970s, after several breakthroughs in semiconductor technology. These include the first working transistor by William Shockley, John Bardeen and Walter Brattain at Bell Labs in 1947, in 1955, silicon dioxide surface passivation by Carl Frosch and Lincoln Derick, the first planar silicon dioxide transistors by Frosch and Derick in 1957, planar process by Jean Hoerni, the monolithic integrated circuit chip by Robert Noyce at Fairchild Semiconductor in 1959, the metal–oxide–semiconductor field-effect transistor (MOSFET, or MOS transistor) demonstrated by a team at Bell Labs in 1960 and the single-chip microprocessor (Intel 4004) by Federico Faggin, Marcian Hoff, Masatoshi Shima and Stanley Mazor at Intel in 1971. === History of computer engineering education === The first computer engineering degree program in the United States was established in 1971 at Case Western Reserve University in Cleveland, Ohio. As of 2015, there were 250 ABET-accredited computer engineering programs in the U.S. In Europe, accreditation of computer engineering schools is done by a variety of agencies as part of the EQANIE network. Due to increasing job requirements for engineers who can concurrently design hardware, software, firmware, and manage all forms of computer systems used in industry, some tertiary institutions around the world offer a bachelor's degree generally called computer engineering. Both computer engineering and electronic engineering programs include analog and digital circuit design in their curriculum. As with most engineering disciplines, having a sound knowledge of mathematics and science is necessary for computer engineers. == Education == Computer engineering is referred to as computer science and engineering at some universities. Most entry-level computer engineering jobs require at least a bachelor's degree in computer engineering, electrical engineering or computer science. Typically one must learn an array of mathematics such as calculus, linear algebra and differential equations, along with computer science. Degrees in electronic or electric engineering also suffice due to the similarity of the two fields. Because hardware engineers commonly work with computer software systems, a strong background in computer programming is necessary. According to BLS, "a computer engineering major is similar to electrical engineering but with some computer science courses added to the curriculum". Some large firms or specialized jobs require a master's degree. It is also important for computer engineers to keep up with rapid advances in technology. Therefore, many continue learning throughout their careers. This can be helpful, especially when it comes to learning new skills or improving existing ones. For example, as the relative cost of fixing a bug increases the further along it is in the software development cycle, there can be greater cost savings attributed to developing and testing for quality code as soon as possible in the process, particularly before release. === Professions === A person with a profession in computer engineering is called a computer engineer. == Applications and practice == There are two major focuses in computer engineering: hardware and software. === Computer hardware engineering === According to the United States BLS, job outlook employment for computer hardware engineers, the expected ten-year growth from 2019 to 2029 for computer hardware engineering was an estimated 2% and a total of 71,100 jobs. ("Slower than average" in their own words when compared to other occupations)". This is a decrease from the 2014 to 2024 BLS computer hardware engineering estimate of 3% and a total of 77,700 jobs; "and is down from 7% for the 2012 to 2022 BLS estimate and is further down from 9% in the BLS 2010 to 2020 estimate." Today, computer hardware is somewhat equal to electronic and computer engineering (ECE) and has been divided into many subcategories, the most significant being embedded system design. === Computer software engineering === According to the U.S. Bureau of Labor Statistics (BLS), "computer applications software engineers and computer systems software engineers are projected to be among the faster than average growing occupations" The expected ten-year growth as of 2014 for computer software engineering was an estimated seventeen percent and there was a total of 1,114,000 jobs that same year. This is down from the 2012 to 2022 BLS estimate of 22% for software developers. And, further down from the 30% 2010 to 2020 BLS estimate. In addition, growing concerns over cybersecurity add up to put computer software engineering high above the average rate of increase for all fields. However, some of the work will be outsourced in foreign countries. Due to this, job growth will not be as fast as during the last decade, as jobs that would have gone to computer software engineers in the United States would instead go to computer software engineers in countries such as India. In addition, the BLS job outlook for Computer Programmers, 2014–24 has an −8% (a decline, in their words), then a job outlook, 2019-29 of -9% (Decline), then a 10% decline for 2021-2031 and now an 11% decline for 2022-2032 for those who program computers (i.e. embedded systems) who are not computer application developers. Furthermore, women in software fields has been declining over the years even faster than other engineering fields. == Specialty areas == There are many specialty areas in the field of computer engineering. === Processor design === Processor design process involves choosing an instruction set and a certain execution paradigm (e.g. VLIW or RISC) and results in a microarchitecture, which might be described in e.g. VHDL or Verilog. CPU design is divided into design of the following components: datapaths (such as ALUs and pipelines), control unit: logic which controls the datapaths, memory components such as register files, caches, clock circuitry such as clock drivers, PLLs, clock distribution networks, pad transceiver circuitry, logic gate cell library which is used to implement the logic. === Coding, cryptography, and information protection === Computer engineers work in coding, applied cryptography, and information protection to develop new methods for protecting various information, such as digital images and music, fragmentation, copyright infringement and other forms of tampering by, for example, digital watermarking. === Communications and wireless networks === Those focusing on communications and wireless networks, work advancements in telecommunications systems and networks (especially wireless networks), modulation and error-control coding, and information theory. High-speed network design, interference suppression and modulation, design, and analysis of fault-tolerant system, and storage and transmission schemes are all a part of this specialty. === Compilers and operating systems === This specialty focuses on compilers and operating systems design and development. Engineers in this field develop new operating system architecture, program analysis techniques, and new techniques to assure quality. Examples of work in this field include post-link-time code transformation algorithm development and new operating system development. === Computational science and engineering === Computational science and engineering is a relatively new discipline. According to the Sloan Career Cornerstone Center, individuals working in this area, "computational methods are applied to formulate and solve complex mathematical problems in engineering and the physical and the social sciences. Examples include aircraft design, the plasma processing of nanometer features on semiconductor wafers, VLSI circuit design, radar detection systems, ion transport through biological channels, and much more". === Computer networks, mobile computing, and distributed systems === In this specialty, engineers build integrated environments for computing, communications, and information access. Examples include shared-channel wireless networks, adaptive resource management in various systems, and improving the quality of service in mobile and ATM environments. Some other examples include work on wireless network systems and fast Ethernet cluster wired systems. === Computer systems: architecture, parallel processing, and dependability === Engineers working in computer systems work on research projects that allow for reliable, secure, and high-performance computer systems. Projects such as designing processors for multithreading and parallel processing are included in this field. Other examples of work in this field include the development of new theories, algorithms, and other tools that add performance to computer systems. Computer architecture includes CPU design, cache hierarchy layout, memory organization, and load balancing. === Computer vision and robotics === In this specialty, computer engineers focus on developing visual sensing technology to sense an environment, representation of an environment, and manipulation of the environment. The gathered three-dimensional information is then implemented to perform a variety of tasks. These include improved human modeling, image communication, and human-computer interfaces, as well as devices such as special-purpose cameras with versatile vision sensors. === Embedded systems === Individuals working in this area design technology for enhancing the speed, reliability, and performance of systems. Embedded systems are found in many devices from a small FM radio to the space shuttle. According to the Sloan Cornerstone Career Center, ongoing developments in embedded systems include "automated vehicles and equipment to conduct search and rescue, automated transportation systems, and human-robot coordination to repair equipment in space." As of 2018, computer embedded systems specializations include system-on-chip design, the architecture of edge computing and the Internet of things. === Integrated circuits, VLSI design, testing and CAD === This specialty of computer engineering requires adequate knowledge of electronics and electrical systems. Engineers working in this area work on enhancing the speed, reliability, and energy efficiency of next-generation very-large-scale integrated (VLSI) circuits and microsystems. An example of this specialty is work done on reducing the power consumption of VLSI algorithms and architecture. === Signal, image and speech processing === Computer engineers in this area develop improvements in human–computer interaction, including speech recognition and synthesis, medical and scientific imaging, or communications systems. Other work in this area includes computer vision development such as recognition of human facial features. === Quantum computing === This area integrates the quantum behaviour of small particles such as superposition, interference and entanglement, with classical computers to solve complex problems and formulate algorithms much more efficiently. Individuals focus on fields like Quantum cryptography, physical simulations and quantum algorithms. == Benefits of Engineering in Society == An accessible avenue for obtaining information and opportunities in technology, especially for young students, is through digital platforms, enabling learning, exploration, and potential income generation at minimal cost and in regional languages, none of which would be possible without engineers. Computer engineering is important in the changes involved in industry 4.0, with engineers responsible for designing and optimizing the technology that surrounds our lives, from big data to AI. Their work not only facilitates global connections and knowledge access, but also plays a pivotal role in shaping our future, as technology continues to evolve rapidly, leading to a growing demand for skilled computer engineers. Engineering contributes to improving society by creating devices and structures impacting various aspects of our lives, from technology to infrastructure. Engineers also address challenges such as environmental protection and sustainable development, while developing medical treatments. As of 2016, the median annual wage across all BLS engineering categories was over $91,000. Some were much higher, with engineers working for petroleum companies at the top (over $128,000). Other top jobs include: Computer Hardware Engineer – $115,080, Aerospace Engineer – $109,650, Nuclear Engineer – $102,220. == See also == === Related fields === === Associations === IEEE Computer Society Association for Computing Machinery == Notes and references == === Notes === === References === == External links == Media related to Computer engineering at Wikimedia Commons
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https://en.wikipedia.org/wiki/Computer_engineering
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Tissue engineering is a biomedical engineering discipline that uses a combination of cells, engineering, materials methods, and suitable biochemical and physicochemical factors to restore, maintain, improve, or replace different types of biological tissues. Tissue engineering often involves the use of cells placed on tissue scaffolds in the formation of new viable tissue for a medical purpose, but is not limited to applications involving cells and tissue scaffolds. While it was once categorized as a sub-field of biomaterials, having grown in scope and importance, it can be considered as a field of its own. While most definitions of tissue engineering cover a broad range of applications, in practice, the term is closely associated with applications that repair or replace portions of or whole tissues (i.e. organs, bone, cartilage, blood vessels, bladder, skin, muscle etc.). Often, the tissues involved require certain mechanical and structural properties for proper functioning. The term has also been applied to efforts to perform specific biochemical functions using cells within an artificially-created support system (e.g. an artificial pancreas, or a bio artificial liver). The term regenerative medicine is often used synonymously with tissue engineering, although those involved in regenerative medicine place more emphasis on the use of stem cells or progenitor cells to produce tissues. == Overview == A commonly applied definition of tissue engineering, as stated by Langer and Vacanti, is "an interdisciplinary field that applies the principles of engineering and life sciences toward the development of biological substitutes that restore, maintain, or improve [Biological tissue] function or a whole organ". In addition, Langer and Vacanti also state that there are three main types of tissue engineering: cells, tissue-inducing substances, and a cells + matrix approach (often referred to as a scaffold). Tissue engineering has also been defined as "understanding the principles of tissue growth, and applying this to produce functional replacement tissue for clinical use". A further description goes on to say that an "underlying supposition of tissue engineering is that the employment of natural biology of the system will allow for greater success in developing therapeutic strategies aimed at the replacement, repair, maintenance, or enhancement of tissue function". Developments in the multidisciplinary field of tissue engineering have yielded a novel set of tissue replacement parts and implementation strategies. Scientific advances in biomaterials, stem cells, growth and differentiation factors, and biomimetic environments have created unique opportunities to fabricate or improve existing tissues in the laboratory from combinations of engineered extracellular matrices ("scaffolds"), cells, and biologically active molecules. Among the major challenges now facing tissue engineering is the need for more complex functionality, biomechanical stability, and vascularization in laboratory-grown tissues destined for transplantation. == Etymology == The historical origin of the term is unclear as the definition of the word has changed throughout the past few decades. The term first appeared in a 1984 publication that described the organization of an endothelium-like membrane on the surface of a long-implanted, synthetic ophthalmic prosthesis. The first modern use of the term as recognized today was in 1985 by the researcher, physiologist and bioengineer Yuan-Cheng Fung of the Engineering Research Center. He proposed the joining of the terms tissue (in reference to the fundamental relationship between cells and organs) and engineering (in reference to the field of modification of said tissues). The term was officially adopted in 1987. == History == === Ancient era (pre-17th century) === A rudimentary understanding of the inner workings of human tissues may date back further than most would expect. As early as the Neolithic period, sutures were being used to close wounds and aid in healing. Later on, societies such as ancient Egypt developed better materials for sewing up wounds such as linen sutures. Around 2500 BC in ancient India, skin grafts were developed by cutting skin from the buttock and suturing it to wound sites in the ear, nose, or lips. Ancient Egyptians often would graft skin from corpses onto living humans and even attempted to use honey as a type of antibiotic and grease as a protective barrier to prevent infection. In the 1st and 2nd centuries AD, Gallo-Romans developed wrought iron implants and dental implants could be found in ancient Mayans. === Enlightenment (17th century–19th century) === While these ancient societies had developed techniques that were way ahead of their time, they still lacked a mechanistic understanding of how the body was reacting to these procedures. This mechanistic approach came along in tandem with the development of the empirical method of science pioneered by René Descartes. Sir Isaac Newton began to describe the body as a "physiochemical machine" and postured that disease was a breakdown in the machine. In the 17th century, Robert Hooke discovered the cell and a letter from Benedict de Spinoza brought forward the idea of the homeostasis between the dynamic processes in the body. Hydra experiments performed by Abraham Trembley in the 18th century began to delve into the regenerative capabilities of cells. During the 19th century, a better understanding of how different metals reacted with the body led to the development of better sutures and a shift towards screw and plate implants in bone fixation. Further, it was first hypothesized in the mid-1800s that cell-environment interactions and cell proliferation were vital for tissue regeneration. === Modern era (20th and 21st centuries) === As time progresses and technology advances, there is a constant need for change in the approach researchers take in their studies. Tissue engineering has continued to evolve over centuries. In the beginning people used to look at and use samples directly from human or animal cadavers. Now, tissue engineers have the ability to remake many of the tissues in the body through the use of modern techniques such as microfabrication and three-dimensional bioprinting in conjunction with native tissue cells/stem cells. These advances have allowed researchers to generate new tissues in a much more efficient manner. For example, these techniques allow for more personalization which allow for better biocompatibility, decreased immune response, cellular integration, and longevity. There is no doubt that these techniques will continue to evolve, as we have continued to see microfabrication and bioprinting evolve over the past decade. In 1960, Wichterle and Lim were the first to publish experiments on hydrogels for biomedical applications by using them in contact lens construction. Work on the field developed slowly over the next two decades, but later found traction when hydrogels were repurposed for drug delivery. In 1984, Charles Hull developed bioprinting by converting a Hewlett-Packard inkjet printer into a device capable of depositing cells in 2-D. Three dimensional (3-D) printing is a type of additive manufacturing which has since found various applications in medical engineering, due to its high precision and efficiency. With biologist James Thompson's development of first human stem cell lines in 1998 followed by transplantation of first laboratory-grown internal organs in 1999 and creation of the first bioprinter in 2003 by the University of Missouri when they printed spheroids without the need of scaffolds, 3-D bioprinting became more conventionally used in medical field than ever before. So far, scientists have been able to print mini organoids and organs-on-chips that have rendered practical insights into the functions of a human body. Pharmaceutical companies are using these models to test drugs before moving on to animal studies. However, a fully functional and structurally similar organ has not been printed yet. A team at University of Utah has reportedly printed ears and successfully transplanted those onto children born with defects that left their ears partially developed. Today hydrogels are considered the preferred choice of bio-inks for 3-D bioprinting since they mimic cells' natural ECM while also containing strong mechanical properties capable of sustaining 3-D structures. Furthermore, hydrogels in conjunction with 3-D bioprinting allow researchers to produce different scaffolds which can be used to form new tissues or organs. 3-D printed tissues still face many challenges such as adding vasculature. Meanwhile, 3-D printing parts of tissues definitely will improve our understanding of the human body, thus accelerating both basic and clinical research. == Examples == As defined by Langer and Vacanti, examples of tissue engineering fall into one or more of three categories: "just cells," "cells and scaffold," or "tissue-inducing factors." In vitro meat: Edible artificial animal muscle tissue cultured in vitro. Bioartificial liver device, "Temporary Liver", Extracorporeal Liver Assist Device (ELAD): The human hepatocyte cell line (C3A line) in a hollow fiber bioreactor can mimic the hepatic function of the liver for acute instances of liver failure. A fully capable ELAD would temporarily function as an individual's liver, thus avoiding transplantation and allowing regeneration of their own liver. Artificial pancreas: Research involves using islet cells to regulate the body's blood sugar, particularly in cases of diabetes . Biochemical factors may be used to cause human pluripotent stem cells to differentiate (turn into) cells that function similarly to beta cells, which are in an islet cell in charge of producing insulin. Artificial bladders: Anthony Atala (Wake Forest University) has successfully implanted artificial bladders, constructed of cultured cells seeded onto a bladder-shaped scaffold, into seven out of approximately 20 human test subjects as part of a long-term experiment. Cartilage: lab-grown cartilage, cultured in vitro on a scaffold, was successfully used as an autologous transplant to repair patients' knees. Scaffold-free cartilage: Cartilage generated without the use of exogenous scaffold material. In this methodology, all material in the construct is cellular produced directly by the cells. Bioartificial heart: Doris Taylor's lab constructed a biocompatible rat heart by re-cellularising a de-cellularised rat heart. This scaffold and cells were placed in a bioreactor, where it matured to become a partially or fully transplantable organ. the work was called a "landmark". The lab first stripped the cells away from a rat heart (a process called "decellularization") and then injected rat stem cells into the decellularized rat heart. Tissue-engineered blood vessels: Blood vessels that have been grown in a lab and can be used to repair damaged blood vessels without eliciting an immune response. Tissue engineered blood vessels have been developed by many different approaches. They could be implanted as pre-seeded cellularized blood vessels, as acellular vascular grafts made with decellularized vessels or synthetic vascular grafts. Artificial skin constructed from human skin cells embedded in a hydrogel, such as in the case of bio-printed constructs for battlefield burn repairs. Artificial bone marrow: Bone marrow cultured in vitro to be transplanted serves as a "just cells" approach to tissue engineering. Tissue engineered bone: A structural matrix can be composed of metals such as titanium, polymers of varying degradation rates, or certain types of ceramics. Materials are often chosen to recruit osteoblasts to aid in reforming the bone and returning biological function. Various types of cells can be added directly into the matrix to expedite the process. Laboratory-grown penis: Decellularized scaffolds of rabbit penises were recellularised with smooth muscle and endothelial cells. The organ was then transplanted to live rabbits and functioned comparably to the native organ, suggesting potential as treatment for genital trauma. Oral mucosa tissue engineering uses a cells and scaffold approach to replicate the 3 dimensional structure and function of oral mucosa. == Cells as building blocks == Cells are one of the main components for the success of tissue engineering approaches. Tissue engineering uses cells as strategies for creation/replacement of new tissue. Examples include fibroblasts used for skin repair or renewal, chondrocytes used for cartilage repair (MACI–FDA approved product), and hepatocytes used in liver support systems Cells can be used alone or with support matrices for tissue engineering applications. An adequate environment for promoting cell growth, differentiation, and integration with the existing tissue is a critical factor for cell-based building blocks. Manipulation of any of these cell processes create alternative avenues for the development of new tissue (e.g., cell reprogramming - somatic cells, vascularization). === Isolation === Techniques for cell isolation depend on the cell source. Centrifugation and apheresis are techniques used for extracting cells from biofluids (e.g., blood). Whereas digestion processes, typically using enzymes to remove the extracellular matrix (ECM), are required prior to centrifugation or apheresis techniques to extract cells from tissues/organs. Trypsin and collagenase are the most common enzymes used for tissue digestion. While trypsin is temperature dependent, collagenase is less sensitive to changes in temperature. === Cell sources === Primary cells are those directly isolated from host tissue. These cells provide an ex-vivo model of cell behavior without any genetic, epigenetic, or developmental changes; making them a closer replication of in-vivo conditions than cells derived from other methods. This constraint however, can also make studying them difficult. These are mature cells, often terminally differentiated, meaning that for many cell types proliferation is difficult or impossible. Additionally, the microenvironments these cells exist in are highly specialized, often making replication of these conditions difficult. Secondary cells A portion of cells from a primary culture is moved to a new repository/vessel to continue being cultured. Medium from the primary culture is removed, the cells that are desired to be transferred are obtained, and then cultured in a new vessel with fresh growth medium. A secondary cell culture is useful in order to ensure that cells have both the room and nutrients that they require to grow. Secondary cultures are most notably used in any scenario in which a larger quantity of cells than can be found in the primary culture is desired. Secondary cells share the constraints of primary cells (see above) but have an added risk of contamination when transferring to a new vessel. === Genetic classifications of cells === Autologous: The donor and the recipient of the cells are the same individual. Cells are harvested, cultured or stored, and then reintroduced to the host. As a result of the host's own cells being reintroduced, an antigenic response is not elicited. The body's immune system recognizes these re-implanted cells as its own, and does not target them for attack. Autologous cell dependence on host cell health and donor site morbidity may be deterrents to their use. Adipose-derived and bone marrow-derived mesenchymal stem cells are commonly autologous in nature, and can be used in a myriad of ways, from helping repair skeletal tissue to replenishing beta cells in diabetic patients. Allogenic: Cells are obtained from the body of a donor of the same species as the recipient. While there are some ethical constraints to the use of human cells for in vitro studies (i.e. human brain tissue chimera development), the employment of dermal fibroblasts from human foreskin demonstrates an immunologically safe and thus a viable choice for allogenic tissue engineering of the skin. Xenogenic: These cells are derived isolated cells from alternate species from the recipient. A notable example of xenogeneic tissue utilization is cardiovascular implant construction via animal cells. Chimeric human-animal farming raises ethical concerns around the potential for improved consciousness from implanting human organs in animals. Syngeneic or isogenic: These cells describe those borne from identical genetic code. This imparts an immunologic benefit similar to autologous cell lines (see above). Autologous cells can be considered syngenic, but the classification also extends to non-autologously derived cells such as those from an identical twin, from genetically identical (cloned) research models, or induced stem cells (iSC) as related to the donor. === Stem cells === Stem cells are undifferentiated cells with the ability to divide in culture and give rise to different forms of specialized cells. Stem cells are divided into "adult" and "embryonic" stem cells according to their source. While there is still a large ethical debate related to the use of embryonic stem cells, it is thought that another alternative source – induced pluripotent stem cells – may be useful for the repair of diseased or damaged tissues, or may be used to grow new organs. Totipotent cells are stem cells which can divide into further stem cells or differentiate into any cell type in the body, including extra-embryonic tissue. Pluripotent cells are stem cells which can differentiate into any cell type in the body except extra-embryonic tissue. induced pluripotent stem cells (iPSCs) are subclass of pluripotent stem cells resembling embryonic stem cells (ESCs) that have been derived from adult differentiated cells. iPSCs are created by altering the expression of transcriptional factors in adult cells until they become like embryonic stem cells. Multipotent stem cells can be differentiated into any cell within the same class, such as blood or bone. A common example of multipotent cells is Mesenchymal stem cells (MSCs). == Scaffolds == Scaffolds are materials that have been engineered to cause desirable cellular interactions to contribute to the formation of new functional tissues for medical purposes. Cells are often 'seeded' into these structures capable of supporting three-dimensional tissue formation. Scaffolds mimic the extracellular matrix of the native tissue, recapitulating the in vivo milieu and allowing cells to influence their own microenvironments. They usually serve at least one of the following purposes: allowing cell attachment and migration, delivering and retaining cells and biochemical factors, enabling diffusion of vital cell nutrients and expressed products, and exerting certain mechanical and biological influences to modify the behaviour of the cell phase. In 2009, an interdisciplinary team led by the thoracic surgeon Thorsten Walles implanted the first bioartificial transplant that provides an innate vascular network for post-transplant graft supply successfully into a patient awaiting tracheal reconstruction. To achieve the goal of tissue reconstruction, scaffolds must meet some specific requirements. High porosity and adequate pore size are necessary to facilitate cell seeding and diffusion throughout the whole structure of both cells and nutrients. Biodegradability is often an essential factor since scaffolds should preferably be absorbed by the surrounding tissues without the necessity of surgical removal. The rate at which degradation occurs has to coincide as much as possible with the rate of tissue formation: this means that while cells are fabricating their own natural matrix structure around themselves, the scaffold is able to provide structural integrity within the body and eventually it will break down leaving the newly formed tissue which will take over the mechanical load. Injectability is also important for clinical uses. Recent research on organ printing is showing how crucial a good control of the 3D environment is to ensure reproducibility of experiments and offer better results. === Materials === Material selection is an essential aspect of producing a scaffold. The materials utilized can be natural or synthetic and can be biodegradable or non-biodegradable. Additionally, they must be biocompatible, meaning that they do not cause any adverse effects to cells. Silicone, for example, is a synthetic, non-biodegradable material commonly used as a drug delivery material, while gelatin is a biodegradable, natural material commonly used in cell-culture scaffolds The material needed for each application is different, and dependent on the desired mechanical properties of the material. Tissue engineering of long bone defects for example, will require a rigid scaffold with a compressive strength similar to that of cortical bone (100-150 MPa), which is much higher compared to a scaffold for skin regeneration. There are a few versatile synthetic materials used for many different scaffold applications. One of these commonly used materials is polylactic acid (PLA), a synthetic polymer. PLA – polylactic acid. This is a polyester which degrades within the human body to form lactic acid, a naturally occurring chemical which is easily removed from the body. Similar materials are polyglycolic acid (PGA) and polycaprolactone (PCL): their degradation mechanism is similar to that of PLA, but PCL degrades slower and PGA degrades faster. PLA is commonly combined with PGA to create poly-lactic-co-glycolic acid (PLGA). This is especially useful because the degradation of PLGA can be tailored by altering the weight percentages of PLA and PGA: More PLA – slower degradation, more PGA – faster degradation. This tunability, along with its biocompatibility, makes it an extremely useful material for scaffold creation. Scaffolds may also be constructed from natural materials: in particular different derivatives of the extracellular matrix have been studied to evaluate their ability to support cell growth. Protein based materials – such as collagen, or fibrin, and polysaccharidic materials- like chitosan or glycosaminoglycans (GAGs), have all proved suitable in terms of cell compatibility. Among GAGs, hyaluronic acid, possibly in combination with cross linking agents (e.g. glutaraldehyde, water-soluble carbodiimide, etc.), is one of the possible choices as scaffold material. Due to the covalent attachment of thiol groups to these polymers, they can crosslink via disulfide bond formation. The use of thiolated polymers (thiomers) as scaffold material for tissue engineering was initially introduced at the 4th Central European Symposium on Pharmaceutical Technology in Vienna 2001. As thiomers are biocompatible, exhibit cellular mimicking properties and efficiently support proliferation and differentiation of various cell types, they are extensively used as scaffolds for tissue engineering. Furthermore thiomers such as thiolated hyaluronic acid and thiolated chitosan were shown to exhibit wound healing properties and are subject of numerous clinical trials. Additionally, a fragment of an extracellular matrix protein, such as the RGD peptide, can be coupled to a non-bioactive material to promote cell attachment. Another form of scaffold is decellularized tissue. This is a process where chemicals are used to extracts cells from tissues, leaving just the extracellular matrix. This has the benefit of a fully formed matrix specific to the desired tissue type. However, the decellurised scaffold may present immune problems with future introduced cells. === Synthesis === A number of different methods have been described in the literature for preparing porous structures to be employed as tissue engineering scaffolds. Each of these techniques presents its own advantages, but none are free of drawbacks. ==== Nanofiber self-assembly ==== Molecular self-assembly is one of the few methods for creating biomaterials with properties similar in scale and chemistry to that of the natural in vivo extracellular matrix (ECM), a crucial step toward tissue engineering of complex tissues. Moreover, these hydrogel scaffolds have shown superiority in in vivo toxicology and biocompatibility compared to traditional macro-scaffolds and animal-derived materials. ==== Textile technologies ==== These techniques include all the approaches that have been successfully employed for the preparation of non-woven meshes of different polymers. In particular, non-woven polyglycolide structures have been tested for tissue engineering applications: such fibrous structures have been found useful to grow different types of cells. The principal drawbacks are related to the difficulties in obtaining high porosity and regular pore size. ==== Solvent casting and particulate leaching ==== Solvent casting and particulate leaching (SCPL) allows for the preparation of structures with regular porosity, but with limited thickness. First, the polymer is dissolved into a suitable organic solvent (e.g. polylactic acid could be dissolved into dichloromethane), then the solution is cast into a mold filled with porogen particles. Such porogen can be an inorganic salt like sodium chloride, crystals of saccharose, gelatin spheres or paraffin spheres. The size of the porogen particles will affect the size of the scaffold pores, while the polymer to porogen ratio is directly correlated to the amount of porosity of the final structure. After the polymer solution has been cast the solvent is allowed to fully evaporate, then the composite structure in the mold is immersed in a bath of a liquid suitable for dissolving the porogen: water in the case of sodium chloride, saccharose and gelatin or an aliphatic solvent like hexane for use with paraffin. Once the porogen has been fully dissolved, a porous structure is obtained. Other than the small thickness range that can be obtained, another drawback of SCPL lies in its use of organic solvents which must be fully removed to avoid any possible damage to the cells seeded on the scaffold. ==== Gas foaming ==== To overcome the need to use organic solvents and solid porogens, a technique using gas as a porogen has been developed. First, disc-shaped structures made of the desired polymer are prepared by means of compression molding using a heated mold. The discs are then placed in a chamber where they are exposed to high pressure CO2 for several days. The pressure inside the chamber is gradually restored to atmospheric levels. During this procedure the pores are formed by the carbon dioxide molecules that abandon the polymer, resulting in a sponge-like structure. The main problems resulting from such a technique are caused by the excessive heat used during compression molding (which prohibits the incorporation of any temperature labile material into the polymer matrix) and by the fact that the pores do not form an interconnected structure. ==== Emulsification freeze-drying ==== This technique does not require the use of a solid porogen like SCPL. First, a synthetic polymer is dissolved into a suitable solvent (e.g. polylactic acid in dichloromethane) then water is added to the polymeric solution and the two liquids are mixed in order to obtain an emulsion. Before the two phases can separate, the emulsion is cast into a mold and quickly frozen by means of immersion into liquid nitrogen. The frozen emulsion is subsequently freeze-dried to remove the dispersed water and the solvent, thus leaving a solidified, porous polymeric structure. While emulsification and freeze-drying allow for a faster preparation when compared to SCPL (since it does not require a time-consuming leaching step), it still requires the use of solvents. Moreover, pore size is relatively small and porosity is often irregular. Freeze-drying by itself is also a commonly employed technique for the fabrication of scaffolds. In particular, it is used to prepare collagen sponges: collagen is dissolved into acidic solutions of acetic acid or hydrochloric acid that are cast into a mold, frozen with liquid nitrogen and then lyophilized. ==== Thermally induced phase separation ==== Similar to the previous technique, the TIPS phase separation procedure requires the use of a solvent with a low melting point that is easy to sublime. For example, dioxane could be used to dissolve polylactic acid, then phase separation is induced through the addition of a small quantity of water: a polymer-rich and a polymer-poor phase are formed. Following cooling below the solvent melting point and some days of vacuum-drying to sublime the solvent, a porous scaffold is obtained. Liquid-liquid phase separation presents the same drawbacks of emulsification/freeze-drying. ==== Electrospinning ==== Electrospinning is a highly versatile technique that can be used to produce continuous fibers ranging in diameter from a few microns to a few nanometers. In a typical electrospinning set-up, the desired scaffold material is dissolved within a solvent and placed within a syringe. This solution is fed through a needle and a high voltage is applied to the tip and to a conductive collection surface. The buildup of electrostatic forces within the solution causes it to eject a thin fibrous stream towards the oppositely charged or grounded collection surface. During this process the solvent evaporates, leaving solid fibers leaving a highly porous network. This technique is highly tunable, with variation to solvent, voltage, working distance (distance from the needle to collection surface), flow rate of solution, solute concentration, and collection surface. This allows for precise control of fiber morphology. On a commercial level however, due to scalability reasons, there are 40 or sometimes 96 needles involved operating at once. The bottle-necks in such set-ups are: 1) Maintaining the aforementioned variables uniformly for all of the needles and 2) formation of "beads" in single fibers that we as engineers, want to be of a uniform diameter. By modifying variables such as the distance to collector, magnitude of applied voltage, or solution flow rate – researchers can dramatically change the overall scaffold architecture. Historically, research on electrospun fibrous scaffolds dates back to at least the late 1980s when Simon showed that electrospinning could be used to produce nano- and submicron-scale fibrous scaffolds from polymer solutions specifically intended for use as in vitro cell and tissue substrates. This early use of electrospun lattices for cell culture and tissue engineering showed that various cell types would adhere to and proliferate upon polycarbonate fibers. It was noted that as opposed to the flattened morphology typically seen in 2D culture, cells grown on the electrospun fibers exhibited a more rounded 3-dimensional morphology generally observed of tissues in vivo. ==== CAD/CAM technologies ==== Because most of the above techniques are limited when it comes to the control of porosity and pore size, computer assisted design and manufacturing techniques have been introduced to tissue engineering. First, a three-dimensional structure is designed using CAD software. The porosity can be tailored using algorithms within the software. The scaffold is then realized by using ink-jet printing of polymer powders or through Fused Deposition Modeling of a polymer melt. A 2011 study by El-Ayoubi et al. investigated "3D-plotting technique to produce (biocompatible and biodegradable) poly-L-Lactide macroporous scaffolds with two different pore sizes" via solid free-form fabrication (SSF) with computer-aided-design (CAD), to explore therapeutic articular cartilage replacement as an "alternative to conventional tissue repair". The study found the smaller the pore size paired with mechanical stress in a bioreactor (to induce in vivo-like conditions), the higher the cell viability in potential therapeutic functionality via decreasing recovery time and increasing transplant effectiveness. ==== Laser-assisted bioprinting ==== In a 2012 study, Koch et al. focused on whether Laser-assisted BioPrinting (LaBP) can be used to build multicellular 3D patterns in natural matrix, and whether the generated constructs are functioning and forming tissue. LaBP arranges small volumes of living cell suspensions in set high-resolution patterns. The investigation was successful, the researchers foresee that "generated tissue constructs might be used for in vivo testing by implanting them into animal models" (14). As of this study, only human skin tissue has been synthesized, though researchers project that "by integrating further cell types (e.g. melanocytes, Schwann cells, hair follicle cells) into the printed cell construct, the behavior of these cells in a 3D in vitro microenvironment similar to their natural one can be analyzed", which is useful for drug discovery and toxicology studies. ==== Self-assembled recombinant spider silk nanomembranes ==== Gustafsson et al. demonstrated free‐standing, bioactive membranes of cm-sized area, but only 250 nm thin, that were formed by self‐assembly of spider silk at the interface of an aqueous solution. The membranes uniquely combine nanoscale thickness, biodegradability, ultrahigh strain and strength, permeability to proteins and promote rapid cell adherence and proliferation. They demonstrated growing a coherent layer of keratinocytes. These spider silk nanomembranes have also been used to create a static in-vitro model of a blood vessel. ==== Tissue engineering in situ ==== In situ tissue regeneration is defined as the implantation of biomaterials (alone or in combination with cells and/or biomolecules) into the tissue defect, using the surrounding microenvironment of the organism as a natural bioreactor. This approach has found application in bone regeneration, allowing the formation of cell-seeded constructs directly in the operating room. == Assembly methods == A persistent problem within tissue engineering is mass transport limitations. Engineered tissues generally lack an initial blood supply, thus making it difficult for any implanted cells to obtain sufficient oxygen and nutrients to survive, or function properly. === Self-assembly === Self-assembly methods have been shown to be promising methods for tissue engineering. Self-assembly methods have the advantage of allowing tissues to develop their own extracellular matrix, resulting in tissue that better recapitulates biochemical and biomechanical properties of native tissue. Self-assembling engineered articular cartilage was introduced by Jerry Hu and Kyriacos A. Athanasiou in 2006 and applications of the process have resulted in engineered cartilage approaching the strength of native tissue. Self-assembly is a prime technology to get cells grown in a lab to assemble into three-dimensional shapes. To break down tissues into cells, researchers first have to dissolve the extracellular matrix that normally binds them together. Once cells are isolated, they must form the complex structures that make up our natural tissues. === Liquid-based template assembly === The air-liquid surface established by Faraday waves is explored as a template to assemble biological entities for bottom-up tissue engineering. This liquid-based template can be dynamically reconfigured in a few seconds, and the assembly on the template can be achieved in a scalable and parallel manner. Assembly of microscale hydrogels, cells, neuron-seeded micro-carrier beads, cell spheroids into various symmetrical and periodic structures was demonstrated with good cell viability. Formation of 3-D neural network was achieved after 14-day tissue culture. === Additive manufacturing === It might be possible to print organs, or possibly entire organisms using additive manufacturing techniques. A recent innovative method of construction uses an ink-jet mechanism to print precise layers of cells in a matrix of thermo-reversible gel. Endothelial cells, the cells that line blood vessels, have been printed in a set of stacked rings. When incubated, these fused into a tube. This technique has been referred to as "bioprinting" within the field as it involves the printing of biological components in a structure resembling the organ of focus. The field of three-dimensional and highly accurate models of biological systems is pioneered by multiple projects and technologies including a rapid method for creating tissues and even whole organs involve a 3-D printer that can bio-print the scaffolding and cells layer by layer into a working tissue sample or organ. The device is presented in a TED talk by Dr. Anthony Atala, M.D. the Director of the Wake Forest Institute for Regenerative Medicine, and the W.H. Boyce Professor and Chair of the Department of Urology at Wake Forest University, in which a kidney is printed on stage during the seminar and then presented to the crowd. It is anticipated that this technology will enable the production of livers in the future for transplantation and theoretically for toxicology and other biological studies as well. In 2015 Multi-Photon Processing (MPP) was employed for in vivo experiments by engineering artificial cartilage constructs. An ex vivo histological examination showed that certain pore geometry and the pre-growing of chondrocytes (Cho) prior to implantation significantly improves the performance of the created 3-D scaffolds. The achieved biocompatibility was comparable to the commercially available collagen membranes. The successful outcome of this study supports the idea that hexagonal-pore-shaped hybrid organic-inorganic micro-structured scaffolds in combination with Cho seeding may be successfully implemented for cartilage tissue engineering. Recently, tissue engineering has advanced with a focus on vascularization. Using Two-Photon Polymerization-based additive manufacturing, synthetic 3D microvessel networks are created from tubular hydrogel structures. These networks can perfuse tissues several cubic millimeters in size, enabling long-term viability and cell growth in vitro. This innovation marks a significant step forward in tissue engineering, facilitating the development of complex human tissue models. === Scaffolding === In 2013, using a 3-D scaffolding of Matrigel in various configurations, substantial pancreatic organoids was produced in vitro. Clusters of small numbers of cells proliferated into 40,000 cells within one week. The clusters transform into cells that make either digestive enzymes or hormones like insulin, self-organizing into branched pancreatic organoids that resemble the pancreas. The cells are sensitive to the environment, such as gel stiffness and contact with other cells. Individual cells do not thrive; a minimum of four proximate cells was required for subsequent organoid development. Modifications to the medium composition produced either hollow spheres mainly composed of pancreatic progenitors, or complex organoids that spontaneously undergo pancreatic morphogenesis and differentiation. Maintenance and expansion of pancreatic progenitors require active Notch and FGF signaling, recapitulating in vivo niche signaling interactions. The organoids were seen as potentially offering mini-organs for drug testing and for spare insulin-producing cells. Aside from Matrigel 3-D scaffolds, other collagen gel systems have been developed. Collagen/hyaluronic acid scaffolds have been used for modeling the mammary gland In Vitro while co-coculturing epithelial and adipocyte cells. The HyStem kit is another 3-D platform containing ECM components and hyaluronic acid that has been used for cancer research. Additionally, hydrogel constituents can be chemically modified to assist in crosslinking and enhance their mechanical properties. == Tissue culture == In many cases, creation of functional tissues and biological structures in vitro requires extensive culturing to promote survival, growth and inducement of functionality. In general, the basic requirements of cells must be maintained in culture, which include oxygen, pH, humidity, temperature, nutrients and osmotic pressure maintenance. Tissue engineered cultures also present additional problems in maintaining culture conditions. In standard cell culture, diffusion is often the sole means of nutrient and metabolite transport. However, as a culture becomes larger and more complex, such as the case with engineered organs and whole tissues, other mechanisms must be employed to maintain the culture, such as the creation of capillary networks within the tissue. Another issue with tissue culture is introducing the proper factors or stimuli required to induce functionality. In many cases, simple maintenance culture is not sufficient. Growth factors, hormones, specific metabolites or nutrients, chemical and physical stimuli are sometimes required. For example, certain cells respond to changes in oxygen tension as part of their normal development, such as chondrocytes, which must adapt to low oxygen conditions or hypoxia during skeletal development. Others, such as endothelial cells, respond to shear stress from fluid flow, which is encountered in blood vessels. Mechanical stimuli, such as pressure pulses seem to be beneficial to all kind of cardiovascular tissue such as heart valves, blood vessels or pericardium. === Bioreactors === In tissue engineering, a bioreactor is a device that attempts to simulate a physiological environment in order to promote cell or tissue growth in vitro. A physiological environment can consist of many different parameters such as temperature, pressure, oxygen or carbon dioxide concentration, or osmolality of fluid environment, and it can extend to all kinds of biological, chemical or mechanical stimuli. Therefore, there are systems that may include the application of forces such as electromagnetic forces, mechanical pressures, or fluid pressures to the tissue. These systems can be two- or three-dimensional setups. Bioreactors can be used in both academic and industry applications. General-use and application-specific bioreactors are also commercially available, which may provide static chemical stimulation or a combination of chemical and mechanical stimulation. Cell proliferation and differentiation are largely influenced by mechanical and biochemical cues in the surrounding extracellular matrix environment. Bioreactors are typically developed to replicate the specific physiological environment of the tissue being grown (e.g., flex and fluid shearing for heart tissue growth). This can allow specialized cell lines to thrive in cultures replicating their native environments, but it also makes bioreactors attractive tools for culturing stem cells. A successful stem-cell-based bioreactor is effective at expanding stem cells with uniform properties and/or promoting controlled, reproducible differentiation into selected mature cell types. There are a variety of bioreactors designed for 3D cell cultures. There are small plastic cylindrical chambers, as well as glass chambers, with regulated internal humidity and moisture specifically engineered for the purpose of growing cells in three dimensions. The bioreactor uses bioactive synthetic materials such as polyethylene terephthalate membranes to surround the spheroid cells in an environment that maintains high levels of nutrients. They are easy to open and close, so that cell spheroids can be removed for testing, yet the chamber is able to maintain 100% humidity throughout. This humidity is important to achieve maximum cell growth and function. The bioreactor chamber is part of a larger device that rotates to ensure equal cell growth in each direction across three dimensions. QuinXell Technologies now under Quintech Life Sciences from Singapore has developed a bioreactor known as the TisXell Biaxial Bioreactor which is specially designed for the purpose of tissue engineering. It is the first bioreactor in the world to have a spherical glass chamber with biaxial rotation; specifically to mimic the rotation of the fetus in the womb; which provides a conducive environment for the growth of tissues. Multiple forms of mechanical stimulation have also been combined into a single bioreactor. Using gene expression analysis, one academic study found that applying a combination of cyclic strain and ultrasound stimulation to pre-osteoblast cells in a bioreactor accelerated matrix maturation and differentiation. The technology of this combined stimulation bioreactor could be used to grow bone cells more quickly and effectively in future clinical stem cell therapies. MC2 Biotek has also developed a bioreactor known as ProtoTissue that uses gas exchange to maintain high oxygen levels within the cell chamber; improving upon previous bioreactors, since the higher oxygen levels help the cell grow and undergo normal cell respiration. Active areas of research on bioreactors includes increasing production scale and refining the physiological environment, both of which could improve the efficiency and efficacy of bioreactors in research or clinical use. Bioreactors are currently used to study, among other things, cell and tissue level therapies, cell and tissue response to specific physiological environment changes, and development of disease and injury. === Long fiber generation === In 2013, a group from the University of Tokyo developed cell laden fibers up to a meter in length and on the order of 100 μm in size. These fibers were created using a microfluidic device that forms a double coaxial laminar flow. Each 'layer' of the microfluidic device (cells seeded in ECM, a hydrogel sheath, and finally a calcium chloride solution). The seeded cells culture within the hydrogel sheath for several days, and then the sheath is removed with viable cell fibers. Various cell types were inserted into the ECM core, including myocytes, endothelial cells, nerve cell fibers, and epithelial cell fibers. This group then showed that these fibers can be woven together to fabricate tissues or organs in a mechanism similar to textile weaving. Fibrous morphologies are advantageous in that they provide an alternative to traditional scaffold design, and many organs (such as muscle) are composed of fibrous cells. === Bioartificial organs === An artificial organ is an engineered device that can be extra corporeal or implanted to support impaired or failing organ systems. Bioartificial organs are typically created with the intent to restore critical biological functions like in the replacement of diseased hearts and lungs, or provide drastic quality of life improvements like in the use of engineered skin on burn victims. While some examples of bioartificial organs are still in the research stage of development due to the limitations involved with creating functional organs, others are currently being used in clinical settings experimentally and commercially. ==== Lung ==== Extracorporeal membrane oxygenation (ECMO) machines, otherwise known as heart and lung machines, are an adaptation of cardiopulmonary bypass techniques that provide heart and lung support. It is used primarily to support the lungs for a prolonged but still temporary timeframe (1–30 days) and allow for recovery from reversible diseases. Robert Bartlett is known as the father of ECMO and performed the first treatment of a newborn using an ECMO machine in 1975. Skin Tissue-engineered skin is a type of bioartificial organ that is often used to treat burns, diabetic foot ulcers, or other large wounds that cannot heal well on their own. Artificial skin can be made from autografts, allografts, and xenografts. Autografted skin comes from a patient's own skin, which allows the dermis to have a faster healing rate, and the donor site can be re-harvested a few times. Allograft skin often comes from cadaver skin and is mostly used to treat burn victims. Lastly, xenografted skin comes from animals and provides a temporary healing structure for the skin. They assist in dermal regeneration, but cannot become part of the host skin. Tissue-engineered skin is now available in commercial products. Integra, originally used to only treat burns, consists of a collagen matrix and chondroitin sulfate that can be used as a skin replacement. The chondroitin sulfate functions as a component of proteoglycans, which helps to form the extracellular matrix. Integra can be repopulated and revascularized while maintaining its dermal collagen architecture, making it a bioartificial organ Dermagraft, another commercial-made tissue-engineered skin product, is made out of living fibroblasts. These fibroblasts proliferate and produce growth factors, collagen, and ECM proteins, that help build granulation tissue. ==== Heart ==== Since the number of patients awaiting a heart transplant is continuously increasing over time, and the number of patients on the waiting list surpasses the organ availability, artificial organs used as replacement therapy for terminal heart failure would help alleviate this difficulty. Artificial hearts are usually used to bridge the heart transplantation or can be applied as replacement therapy for terminal heart malfunction. The total artificial heart (TAH), first introduced by Dr. Vladimir P. Demikhov in 1937, emerged as an ideal alternative. Since then it has been developed and improved as a mechanical pump that provides long-term circulatory support and replaces diseased or damaged heart ventricles that cannot properly pump the blood, restoring thus the pulmonary and systemic flow. Some of the current TAHs include AbioCor, an FDA-approved device that comprises two artificial ventricles and their valves, and does not require subcutaneous connections, and is indicated for patients with biventricular heart failure. In 2010 SynCardia released the portable freedom driver that allows patients to have a portable device without being confined to the hospital. ==== Kidney ==== While kidney transplants are possible, renal failure is more often treated using an artificial kidney. The first artificial kidneys and the majority of those currently in use are extracorporeal, such as with hemodialysis, which filters blood directly, or peritoneal dialysis, which filters via a fluid in the abdomen. In order to contribute to the biological functions of a kidney such as producing metabolic factors or hormones, some artificial kidneys incorporate renal cells. There has been progress in the way of making these devices smaller and more transportable, or even implantable . One challenge still to be faced in these smaller devices is countering the limited volume and therefore limited filtering capabilities. Bioscaffolds have also been introduced to provide a framework upon which normal kidney tissue can be regenerated. These scaffolds encompass natural scaffolds (e.g., decellularized kidneys, collagen hydrogel, or silk fibroin), synthetic scaffolds (e.g., poly[lactic-co-glycolic acid] or other polymers), or a combination of two or more natural and synthetic scaffolds. These scaffolds can be implanted into the body either without cell treatment or after a period of stem cell seeding and incubation. In vitro and In vivo studies are being conducted to compare and optimize the type of scaffold and to assess whether cell seeding prior to implantation adds to the viability, regeneration and effective function of the kidneys. A recent systematic review and meta-analysis compared the results of published animal studies and identified that improved outcomes are reported with the use of hybrid (mixed) scaffolds and cell seeding; however, the meta-analysis of these results were not in agreement with the evaluation of descriptive results from the review. Therefore, further studies involving larger animals and novel scaffolds, and more transparent reproduction of previous studies are advisable. === Biomimetics === Biomimetics is a field that aims to produce materials and systems that replicate those present in nature. In the context of tissue engineering, this is a common approach used by engineers to create materials for these applications that are comparable to native tissues in terms of their structure, properties, and biocompatibility. Material properties are largely dependent on physical, structural, and chemical characteristics of that material. Subsequently, a biomimetic approach to system design will become significant in material integration, and a sufficient understanding of biological processes and interactions will be necessary. Replication of biological systems and processes may also be used in the synthesis of bio-inspired materials to achieve conditions that produce the desired biological material. Therefore, if a material is synthesized having the same characteristics of biological tissues both structurally and chemically, then ideally the synthesized material will have similar properties. This technique has an extensive history originating from the idea of using natural phenomenon as design inspiration for solutions to human problems. Many modern advancements in technology have been inspired by nature and natural systems, including aircraft, automobiles, architecture, and even industrial systems. Advancements in nanotechnology initiated the application of this technique to micro- and nano-scale problems, including tissue engineering. This technique has been used to develop synthetic bone tissues, vascular technologies, scaffolding materials and integration techniques, and functionalized nanoparticles. == Constructing neural networks in soft material == In 2018, scientists at Brandeis University reported their research on soft material embedded with chemical networks which can mimic the smooth and coordinated behavior of neural tissue. This research was funded by the U.S. Army Research Laboratory. The researchers presented an experimental system of neural networks, theoretically modeled as reaction-diffusion systems. Within the networks was an array of patterned reactors, each performing the Belousov-Zhabotinsky (BZ) reaction. These reactors could function on a nanoliter scale. The researchers state that the inspiration for their project was the movement of the blue ribbon eel. The eel's movements are controlled by electrical impulses determined by a class of neural networks called the central pattern generator. Central Pattern Generators function within the autonomic nervous system to control bodily functions such as respiration, movement, and peristalsis. Qualities of the reactor that were designed were the network topology, boundary conditions, initial conditions, reactor volume, coupling strength, and the synaptic polarity of the reactor (whether its behavior is inhibitory or excitatory). A BZ emulsion system with a solid elastomer polydimethylsiloxane (PDMS) was designed. Both light and bromine permeable PDMS have been reported as viable methods to create a pacemaker for neural networks. == Market == The history of the tissue engineering market can be divided into three major parts. The time before the crash of the biotech market in the early 2000s, the crash and the time afterward. === Beginning === Most early progress in tissue engineering research was done in the US. This is due to less strict regulations regarding stem cell research and more available funding than in other countries. This leads to the creation of academic startups many of them coming from Harvard or MIT. Examples are BioHybrid Technologies whose founder, Bill Chick, went to Harvard Medical School and focused on the creation of artificial pancreas. Another example would be Organogenesis Inc. whose founder went to MIT and worked on skin engineering products. Other companies with links to the MIT are TEI Biosciences, Therics and Guilford Pharmaceuticals. The renewed interest in biotechnologies in the 1980s leads to many private investors investing in these new technologies even though the business models of these early startups were often not very clear and did not present a path to long term profitability. Government sponsors were more restrained in their funding as tissue engineering was considered a high-risk investment. In the UK the market got off to a slower start even though the regulations on stem cell research were not strict as well. This is mainly due to more investors being less willing to invest in these new technologies which were considered to be high-risk investments. Another problem faced by British companies was getting the NHS to pay for their products. This especially because the NHS runs a cost-effectiveness analysis on all supported products. Novel technologies often do not do well in this respect. In Japan, the regulatory situation was quite different. First cell cultivation was only allowed in a hospital setting and second academic scientists employed by state-owned universities were not allowed outside employment until 1998. Moreover, the Japanese authorities took longer to approve new drugs and treatments than there US and European counterparts. For these reasons in the early days of the Japanese market, the focus was mainly on getting products that were already approved elsewhere in Japan and selling them. Contrary to the US market the early actors in Japan were mainly big firms or sub-companies of such big firms, such as J-TEC, Menicon and Terumo, and not small startups. After regulatory changes in 2014, which allowed cell cultivation outside of a hospital setting, the speed of research in Japan increased and Japanese companies also started to develop their own products. === Crash === Soon after the big boom, the first problems started to appear. There were problems getting products approved by the FDA and if they got approved there were often difficulties in getting insurance providers to pay for the products and getting it accepted by health care providers. For example, organogenesis ran into problems marketing its product and integrating its product in the health system. This partially due to the difficulties of handling living cells and the increased difficulties faced by physicians in using these products over conventional methods. Another example would be Advanced Tissue Sciences Dermagraft skin product which could not create a high enough demand without reimbursements from insurance providers. Reasons for this were $4000 price-tag and the circumstance that Additionally Advanced Tissue Sciences struggled to get their product known by physicians. The above examples demonstrate how companies struggled to make profit. This, in turn, lead investors to lose patience and stopping further funding. In consequence, several Tissue Engineering companies such as Organogenesis and Advanced Tissue Sciences filed for bankruptcy in the early 2000s. At this time, these were the only ones having commercial skin products on the market. === Reemergence === The technologies of the bankrupt or struggling companies were often bought by other companies which continued the development under more conservative business models. Examples of companies who sold their products after folding were Curis and Intercytex. Many of the companies abandoned their long-term goals of developing fully functional organs in favor of products and technologies that could turn a profit in the short run. Examples of these kinds of products are products in the cosmetic and testing industry. In other cases such as in the case of Advanced Tissue Sciences, the founders started new companies. In the 2010s the regulatory framework also started to facilitate faster time to market especially in the US as new centres and pathways were created by the FDA specifically aimed at products coming from living cells such as the Center for Biologics Evaluation and Research. The first tissue engineering products started to get commercially profitable in the 2010s. == Regulation == In Europe, regulation is currently split into three areas of regulation: medical devices, medicinal products, and biologics. Tissue engineering products are often of hybrid nature, as they are often composed of cells and a supporting structure. While some products can be approved as medicinal products, others need to gain approval as medical devices. Derksen explains in her thesis that tissue engineering researchers are sometimes confronted with regulation that does not fit the characteristics of tissue engineering. New regulatory regimes have been observed in Europe that tackle these issues. An explanation for the difficulties in finding regulatory consensus in this matter is given by a survey conducted in the UK. The authors attribute these problems to the close relatedness and overlap with other technologies such as xenotransplantation. It can therefore not be handled separately by regulatory bodies. Regulation is further complicated by the ethical controversies associated with this and related fields of research (e.g. stem cells controversy, ethics of organ transplantation). The same survey as mentioned above shows on the example of autologous cartilage transplantation that a specific technology can be regarded as 'pure' or 'polluted' by the same social actor. Two regulatory movements are most relevant to tissue engineering in the European Union. These are Directive 2004/23/EC on standards of quality and safety for the sourcing and processing of human tissues which was adopted by the European Parliament in 2004 and a proposed Human Tissue-Engineered Products regulation. The latter was developed under the auspices of the European Commission DG Enterprise and presented in Brussels in 2004. == See also == == Notes == == References == == External links == Cell-Based Bone Tissue Engineering Clinical Tissue Engineering Center State of Ohio Initiative for Tissue Engineering (National Center for Regenerative Medicine) Organ Printing Archived 28 August 2008 at the Wayback Machine Multi-site NSF-funded initiative LOEX Center Université Laval Initiative for Tissue Engineering
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https://en.wikipedia.org/wiki/Tissue_engineering
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Biochemical engineering, also known as bioprocess engineering, is a field of study with roots stemming from chemical engineering and biological engineering. It mainly deals with the design, construction, and advancement of unit processes that involve biological organisms (such as fermentation) or organic molecules (often enzymes) and has various applications in areas of interest such as biofuels, food, pharmaceuticals, biotechnology, and water treatment processes. The role of a biochemical engineer is to take findings developed by biologists and chemists in a laboratory and translate that to a large-scale manufacturing process. == History == For hundreds of years, humans have made use of the chemical reactions of biological organisms in order to create goods. In the mid-1800s, Louis Pasteur was one of the first people to look into the role of these organisms when he researched fermentation. His work also contributed to the use of pasteurization, which is still used to this day. By the early 1900s, the use of microorganisms had expanded, and was used to make industrial products. Up to this point, biochemical engineering hadn't developed as a field yet. It wasn't until 1928 when Alexander Fleming discovered penicillin that the field of biochemical engineering was established. After this discovery, samples were gathered from around the world in order to continue research into the characteristics of microbes from places such as soils, gardens, forests, rivers, and streams. Today, biochemical engineers can be found working in a variety of industries, from food to pharmaceuticals. This is due to the increasing need for efficiency and production which requires knowledge of how biological systems and chemical reactions interact with each other and how they can be used to meet these needs. == Applications == === Biotechnology === Biotechnology and biochemical engineering are closely related to each other as biochemical engineering can be considered a sub-branch of biotechnology. One of the primary focuses of biotechnology is in the medical field, where biochemical engineers work to design pharmaceuticals, artificial organs, biomedical devices, chemical sensors, and drug delivery systems. Biochemical engineers use their knowledge of chemical processes in biological systems in order to create tangible products that improve people's health. Specific areas of studies include metabolic, enzyme, and tissue engineering. The study of cell cultures is widely used in biochemical engineering and biotechnology due to its many applications in developing natural fuels, improving the efficiency in producing drugs and pharmaceutical processes, and also creating cures for disease. Other medical applications of biochemical engineering within biotechnology are genetics testing and pharmacogenomics. === Food Industry === Biochemical engineers primarily focus on designing systems that will improve the production, processing, packaging, storage, and distribution of food. Some commonly processed foods include wheat, fruits, and milk which undergo processes such as milling, dehydration, and pasteurization in order to become products that can be sold. There are three levels of food processing: primary, secondary, and tertiary. Primary food processing involves turning agricultural products into other products that can be turned into food, secondary food processing is the making of food from readily available ingredients, and tertiary food processing is commercial production of ready-to eat or heat-and-serve foods. Drying, pickling, salting, and fermenting foods were some of the oldest food processing techniques used to preserve food by preventing yeasts, molds, and bacteria to cause spoiling. Methods for preserving food have evolved to meet current standards of food safety but still use the same processes as the past. Biochemical engineers also work to improve the nutritional value of food products, such as in golden rice, which was developed to prevent vitamin A deficiency in certain areas where this was an issue. Efforts to advance preserving technologies can also ensure lasting retention of nutrients as foods are stored. Packaging plays a key role in preserving as well as ensuring the safety of the food by protecting the product from contamination, physical damage, and tampering. Packaging can also make it easier to transport and serve food. A common job for biochemical engineers working in the food industry is to design ways to perform all these processes on a large scale in order to meet the demands of the population. Responsibilities for this career path include designing and performing experiments, optimizing processes, consulting with groups to develop new technologies, and preparing project plans for equipment and facilities. === Pharmaceuticals === In the pharmaceutical industry, bioprocess engineering plays a crucial role in the large-scale production of biopharmaceuticals, such as monoclonal antibodies, vaccines, and therapeutic proteins. The development and optimization of bioreactors and fermentation systems are essential for the mass production of these products, ensuring consistent quality and high yields. For example, recombinant proteins like insulin and erythropoietin are produced through cell culture systems using genetically modified cells. The bioprocess engineer’s role is to optimize variables like temperature, pH, nutrient availability, and oxygen levels to maximize the efficiency of these systems. The growing field of gene therapy also relies on bioprocessing techniques to produce viral vectors, which are used to deliver therapeutic genes to patients. This involves scaling up processes from laboratory to industrial scale while maintaining safety and regulatory compliance. As the demand for biopharmaceutical products increases, advancements in bioprocess engineering continue to enable more sustainable and cost-effective manufacturing methods. == Education == Auburn University Biochemical engineering is not a major offered by many universities and is instead an area of interest under the chemical engineering. The following universities are known to offer degrees in biochemical engineering: Brown University – Providence, RI Christian Brothers University – Memphis, TN Colorado School of Mines – Golden, CO Rowan University – Glassboro, NJ University of Colorado Boulder – Boulder, CO University of Georgia – Athens, GA University of California, Davis – Davis, CA University College London – London, United Kingdom University of Southern California – Los Angeles, CA University of Western Ontario – Ontario, Canada Indian Institute of Technology (BHU) Varanasi – Varanasi, UP Indian Institute of Technology Delhi – Delhi Institute of Technology Tijuana – México University of Baghdad, College of Engineering, Al-Khwarizmi Biochemical Universidad Nacional de Río Negro - Río Negro, Argentina == See also == Biochemical engineering Biofuel from algae Biological hydrogen production (algae) Bioprocess Bioproducts engineering Bioproducts Bioreactor landfill Biosystems engineering Cell therapy Downstream (bioprocess) Electrochemical energy conversion Food engineering Industrial biotechnology Microbiology Moss bioreactor Photobioreactor Physical chemistry Unit operations Upstream (bioprocess) Use of biotechnology in pharmaceutical manufacturing == References == Shukla, A. A., Thömmes, J., & Hackl, M. (2012). Recent advances in downstream processing of therapeutic monoclonal antibodies. Biotechnology Advances, 30(3), 1548-1557. Walsh, G. (2018). Biopharmaceuticals: Biochemistry and Biotechnology (3rd ed.). Wiley.
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https://en.wikipedia.org/wiki/Biochemical_engineering
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Platform engineering is a software engineering discipline focused on the development of self-service toolchains, services, and processes to create an internal developer platform (IDP). The shared IDP can be utilized by software development teams, enabling them to innovate. Platform engineering uses components like configuration management, infrastructure orchestration, and role-based access control to improve reliability. The discipline is associated with DevOps and platform as a service practices. == Purpose & Impact == Platform engineering aims to improve software engineering productivity by creating streamlined toolchains that can be used by developers. It can be used for digital transformation, or to expand CI/CD setups. According to a panel of experts at PlatformCon 2024, it was stated that building an internal developer platform can improve more than just developer productivity. Platform engineering, which centralizes best practices and components for development teams, is gaining prominence as DevSecOps practices and frameworks become increasingly embedded across organizations. Platform engineering aims to normalize and standardize developer workflows by providing developers with optimized “golden paths” for most of their workloads and flexibility to define exceptions for the rest. Organizations can follow one of two paths when developing a new platform engineering initiative. One option is to build an authentication and visualization layer that sits across multiple point tools — but this does not solve the underlying problems of legacy technology stacks and tooling silos. Therefore, this would likely not be a long-term solution. Alternatively, the organization could implement an internal developer platform (IDP) that reduces the cognitive load on developers by bringing multiple technologies and tools into a single self-service experience. Platform engineering’s benefits include faster time to market, reduced security and compliance risk, and improved developer experience. Establishing a product-oriented culture and setting clear business goals are critical for success in platform engineering. Therefore it can be stated that platform engineering has increased importance wherever businesses strive to do more with less. == DevOps vs. SRE vs. Platform Engineering == DevOps serves as the overarching philosophy and set of guiding principles that advocate for collaboration between development and operations teams. It emphasizes automation, continuous integration, and continuous delivery to streamline software development and deployment. While DevOps provides the vision, SRE (Site Reliability Engineering) and Platform Engineering offer concrete methodologies and best practices to implement these principles in a structured manner. SRE is primarily concerned with ensuring system reliability, performance, and scalability by applying software engineering principles to IT operations. It focuses on monitoring, incident response, error budgets, and automation to minimize toil. In contrast, Platform Engineering is dedicated to building and maintaining internal developer platforms that abstract infrastructure complexities and enhance developer productivity by providing self-service tools, standardized workflows, and automated deployment pipelines. Platform Engineering treats internal developer platforms as a product, applying product management principles to ensure they meet the evolving needs of engineering teams. It focuses on creating and maintaining self-service platforms that provide standardized tools, automated workflows, and infrastructure abstraction. By adopting a platform-as-a-product mindset, platform engineering teams prioritize developer experience, scalability, security, and operational efficiency, ultimately accelerating software delivery across the organization. == Criticism of Platform Engineering == Despite its benefits, platform engineering faces several criticisms. One major concern is the complexity and overhead associated with building and maintaining such platforms. Additionally, creating a one-size-fits-all platform might not address the unique needs of all development teams, leading to inefficiencies and frustration. Siloed teams and a lack of focus on resolving operational issues can also hinder the effectiveness of the platforms created. == References ==
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https://en.wikipedia.org/wiki/Platform_engineering
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In engineering, a foundation is the element of a structure which connects it to the ground or more rarely, water (as with floating structures), transferring loads from the structure to the ground. Foundations are generally considered either shallow or deep. Foundation engineering is the application of soil mechanics and rock mechanics (geotechnical engineering) in the design of foundation elements of structures. == Purpose == Foundations provide the structure's stability from the ground: To distribute the weight of the structure over a large area in order to avoid overloading the underlying soil (possibly causing unequal settlement). To anchor the structure against natural forces including earthquakes, floods, droughts, frost heaves, tornadoes and wind. To provide a level surface for construction. To anchor the structure deeply into the ground, increasing its stability and preventing overloading. To prevent lateral movements of the supported structure (in some cases). == Requirements of a good foundation == The design and the construction of a well-performing foundation must possess some basic requirements: The design and the construction of the foundation is done such that it can sustain as well as transmit the dead and the imposed loads to the soil. This transfer has to be carried out without resulting in any form of settlement that can cause stability issues for the structure. Differential settlements can be avoided by having a rigid base for the foundation. These issues are more pronounced in areas where the superimposed loads are not uniform in nature. Based on the soil and area it is recommended to have a deeper foundation so that it can guard any form of damage or distress. These are mainly caused due to the problem of shrinkage and swelling because of temperature changes. The location of the foundation chosen must be an area that is not affected or influenced by future works or factors. == Historic types == === Earthfast or post in ground construction === Buildings and structures have a long history of being built with wood in contact with the ground. Post in ground construction may technically have no foundation. Timber pilings were used on soft or wet ground even below stone or masonry walls. In marine construction and bridge building a crisscross of timbers or steel beams in concrete is called grillage. === Padstones === Perhaps the simplest foundation is the padstone, a single stone which both spreads the weight on the ground and raises the timber off the ground. Staddle stones are a specific type of padstone. === Stone foundations === Dry stone and stones laid in mortar to build foundations are common in many parts of the world. Dry laid stone foundations may have been painted with mortar after construction. Sometimes the top, visible course of stone is hewn, quarried stones. Besides using mortar, stones can also be put in a gabion. One disadvantage is that if using regular steel rebars, the gabion would last much less long than when using mortar (due to rusting). Using weathering steel rebars could reduce this disadvantage somewhat. === Rubble-trench foundations === Rubble trench foundations are a shallow trench filled with rubble or stones. These foundations extend below the frost line and may have a drain pipe which helps groundwater drain away. They are suitable for soils with a capacity of more than 10 tonnes/m2 (2,000 pounds per square foot). == Gallery of shallow foundation types == == Modern types == === Shallow foundations === Often called footings, are usually embedded about a meter or so into soil. One common type is the spread footing which consists of strips or pads of concrete (or other materials) which extend below the frost line and transfer the weight from walls and columns to the soil or bedrock. Another common type of shallow foundation is the slab-on-grade foundation where the weight of the structure is transferred to the soil through a concrete slab placed at the surface. Slab-on-grade foundations can be reinforced mat slabs, which range from 25 cm to several meters thick, depending on the size of the building, or post-tensioned slabs, which are typically at least 20 cm for houses, and thicker for heavier structures. Another way to install ready-to-build foundations that is more environmentally friendly is to use screw piles. Screw pile installations have also extended to residential applications, with many homeowners choosing a screw pile foundation over other options. Some common applications for helical pile foundations include wooden decks, fences, garden houses, pergolas, and carports. === Deep foundations === Used to transfer the load of a structure down through the upper weak layer of topsoil to the stronger layer of subsoil below. There are different types of deep footings including impact driven piles, drilled shafts, caissons, screw piles, geo-piers and earth-stabilized columns. The naming conventions for different types of footings vary between different engineers. Historically, piles were wood, later steel, reinforced concrete, and pre-tensioned concrete. ==== Monopile foundation ==== A type of deep foundation which uses a single, generally large-diameter, structural element embedded into the earth to support all the loads (weight, wind, etc.) of a large above-surface structure. Many monopile foundations have been used in recent years for economically constructing fixed-bottom offshore wind farms in shallow-water subsea locations. For example, a single wind farm off the coast of England went online in 2008 with over 100 turbines, each mounted on a 4.74-meter-diameter monopile footing in ocean depths up to 16 meters of water. === Floating\barge === A floating foundation is one that sits on a body of water, rather than dry land. This type of foundation is used for some bridges and floating buildings. == Design == Foundations are designed to have an adequate load capacity depending on the type of subsoil/rock supporting the foundation by a geotechnical engineer, and the footing itself may be designed structurally by a structural engineer. The primary design concerns are settlement and bearing capacity. When considering settlement, total settlement and differential settlement is normally considered. Differential settlement is when one part of a foundation settles more than another part. This can cause problems to the structure which the foundation is supporting. Expansive clay soils can also cause problems. == See also == Underpinning Structural settlement Interference of the footings == References == == External links == Common examples of possible deformations of foundations arising from improper construction.
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https://en.wikipedia.org/wiki/Foundation_(engineering)
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Strain engineering refers to a general strategy employed in semiconductor manufacturing to enhance device performance. Performance benefits are achieved by modulating strain, as one example, in the transistor channel, which enhances electron mobility (or hole mobility) and thereby conductivity through the channel. Another example are semiconductor photocatalysts strain-engineered for more effective use of sunlight. == In CMOS manufacturing == The use of various strain engineering techniques has been reported by many prominent microprocessor manufacturers, including AMD, IBM, and Intel, primarily with regards to sub-130 nm technologies. One key consideration in using strain engineering in CMOS technologies is that PMOS and NMOS respond differently to different types of strain. Specifically, PMOS performance is best served by applying compressive strain to the channel, whereas NMOS receives benefit from tensile strain. Many approaches to strain engineering induce strain locally, allowing both n-channel and p-channel strain to be modulated independently. One prominent approach involves the use of a strain-inducing capping layer. CVD silicon nitride is a common choice for a strained capping layer, in that the magnitude and type of strain (e.g. tensile vs compressive) may be adjusted by modulating the deposition conditions, especially temperature. Standard lithography patterning techniques can be used to selectively deposit strain-inducing capping layers, to deposit a compressive film over only the PMOS, for example. Capping layers are key to the Dual Stress Liner (DSL) approach reported by IBM-AMD. In the DSL process, standard patterning and lithography techniques are used to selectively deposit a tensile silicon nitride film over the NMOS and a compressive silicon nitride film over the PMOS. A second prominent approach involves the use of a silicon-rich solid solution, especially silicon-germanium, to modulate channel strain. One manufacturing method involves epitaxial growth of silicon on top of a relaxed silicon-germanium underlayer. Tensile strain is induced in the silicon as the lattice of the silicon layer is stretched to mimic the larger lattice constant of the underlying silicon-germanium. Conversely, compressive strain could be induced by using a solid solution with a smaller lattice constant, such as silicon-carbon. See, e.g., U.S. Patent No. 7,023,018. Another closely related method involves replacing the source and drain region of a MOSFET with silicon-germanium. == In thin films == Strain can be induced in thin films with either epitaxial growth, or more recently, topological growth. Epitaxial strain in thin films generally arises due to lattice mismatch between the film and its substrate and triple junction restructuring at the surface triple junction, which arises either during film growth or due to thermal expansion mismatch. Tuning this epitaxial strain can be used to moderate the properties of thin films and induce phase transitions. The misfit parameter ( f {\displaystyle f} ) is given by the equation below: f = ( a s − a e ) / a e {\displaystyle f=(a_{s}-a_{e})/a_{e}} where a e {\displaystyle a_{e}} is the lattice parameter of the epitaxial film and a s {\displaystyle a_{s}} is the lattice parameter of the substrate. After some critical film thickness, it becomes energetically favorable to relieve some mismatch strain through the formation of misfit dislocations or microtwins. Misfit dislocations can be interpreted as a dangling bond at an interface between layers with different lattice constants. This critical thickness ( h c {\displaystyle h_{c}} ) was computed by Mathews and Blakeslee to be: h c = b ( 2 − ν c o s 2 α ) [ l n ( h c / b ) + 1 ] 8 π | f | ( 1 + ν ) c o s λ {\displaystyle h_{c}={\frac {b(2-\nu cos^{2}\alpha )[ln(h_{c}/b)+1]}{8\pi |f|(1+\nu )cos\lambda }}} where b {\displaystyle b} is the length of the Burgers vector, ν {\displaystyle \nu } is the Poisson ratio, α {\displaystyle \alpha } is the angle between the Burgers vector and misfit dislocation line, and λ {\displaystyle \lambda } is the angle between the Burgers vector and the vector normal to the dislocation's glide plane. The equilibrium in-plane strain for a thin film with a thickness ( h {\displaystyle h} ) that exceeds h c {\displaystyle h_{c}} is then given by the expression: ϵ | | = f | f | b ( 1 − ν c o s 2 ( α ) [ l n ( h / b ) + 1 ] 8 π | f | ( 1 + ν ) c o s λ {\displaystyle \epsilon _{||}={\frac {f}{|f|}}{\frac {b(1-\nu cos^{2}(\alpha )[ln(h/b)+1]}{8\pi |f|(1+\nu )cos\lambda }}} Strain relaxation at thin film interfaces via misfit dislocation nucleation and multiplication occurs in three stages which are distinguishable based on the relaxation rate. The first stage is dominated by glide of pre-existing dislocations and is characterized by a slow relaxation rate. The second stage has a faster relaxation rate, which depends on the mechanisms for dislocation nucleation in the material. Finally, the last stage represents a saturation in strain relaxation due to strain hardening. Strain engineering has been well-studied in complex oxide systems, in which epitaxial strain can strongly influence the coupling between the spin, charge, and orbital degrees of freedom, and thereby impact the electrical and magnetic properties. Epitaxial strain has been shown to induce metal-insulator transitions and shift the Curie temperature for the antiferromagnetic-to-ferromagnetic transition in La 1 − x Sr x MnO 3 {\displaystyle {\ce {La_{1-x}Sr_{x}MnO_{3}}}} . In alloy thin films, epitaxial strain has been observed to impact the spinodal instability, and therefore impact the driving force for phase separation. This is explained as a coupling between the imposed epitaxial strain and the system's composition-dependent elastic properties. Researchers more recently have achieved strain in thick oxide films larger than that achieved in epitaxial growth by incorporating nano-structured topologies (Guerra and Vezenov, 2002) and nanorods/nanopillars within an oxide film matrix. Following this work, researchers world-wide have created such self-organized, phase-separated, nanorod/nanopillar structures in numerous oxide films as reviewed here. In 2008, Thulin and Guerra published calculations of strain-modified anatase titania band structures, which included an indicated higher hole mobility with increasing strain. Additionally, in two dimensional materials such as WSe2 strain has been shown to induce conversion from an indirect semiconductor to a direct semiconductor allowing a hundred-fold increase in the light emission rate. == In III-N LEDs == Strain engineering plays a major role in III-N LEDs, one of the most ubiquitous and efficient LED varieties that has only gained popularity after the 2014 Nobel Prize in Physics. Most III-N LEDs utilize a combination of GaN and InGaN, the latter being used as the quantum well region. The composition of In within the InGaN layer can be tuned to change the color of the light emitted from these LEDs. However, the epilayers of the LED quantum well have inherently mismatched lattice constants, creating strain between the layers. Due to the quantum confined Stark effect (QCSE), the electron and hole wave functions are misaligned within the quantum well, resulting in a reduced overlap integral, decreased recombination probability, and increased carrier lifetime. As such, applying an external strain can negate the internal quantum well strain, reducing the carrier lifetime and making the LEDs a more attractive light source for communications and other applications requiring fast modulation speeds. With appropriate strain engineering, it is possible to grow III-N LEDs on Si substrates. This can be accomplished via strain relaxed templates, superlattices, and pseudo-substrates. Furthermore, electro-plated metal substrates have also shown promise in applying an external counterbalancing strain to increase the overall LED efficiency. === In DUV LEDs === In addition to traditional strain engineering that takes place with III-N LEDs, Deep Ultraviolet (DUV) LEDs, which use AlN, AlGaN, and GaN, undergo a polarity switch from TE to TM at a critical Al composition within the active region. The polarity switch arises from the negative value of AlN’s crystal field splitting, which results in its valence bands switching character at this critical Al composition. Studies have established a linear relationship between this critical composition within the active layer and the Al composition used in the substrate templating region, underscoring the importance of strain engineering in the character of light emitted from DUV LEDs. Furthermore, any existing lattice mismatch causes phase separation and surface roughness, in addition to creating dislocations and point defects. The former results in local current leakage while the latter enhances the nonradiative recombination process, both reducing the device's internal quantum efficiency (IQE). Active layer thickness can trigger the bending and annihilation of threading dislocations, surface roughening, phase separation, misfit dislocation formation, and point defects. All of these mechanisms compete across different thicknesses. By delaying strain accumulation to grow at a thicker epilayer before reaching the target relaxation degree, certain adverse effects can be reduced. == In nano-scale materials == Typically, the maximum elastic strain achievable in normal bulk materials ranges from 0.1% to 1%. This limits our ability to effectively modify material properties in a reversible and quantitative manner using strain. However, recent research on nanoscale materials has shown that the elastic strain range is much broader. Even the hardest material in nature, diamond, exhibits up to 9.0% uniform elastic strain at the nanoscale. Keeping in line with Moore's law, semiconductor devices are continuously shrinking in size to the nanoscale. With the concept of "smaller is stronger", elastic strain engineering can be fully exploited at the nanoscale. In nanoscale elastic strain engineering, the crystallographic direction plays a crucial role. Most materials are anisotropic, meaning their properties vary with direction. This is particularly true in elastic strain engineering, as applying strain in different crystallographic directions can have a significant impact on the material's properties. Taking diamond as an example, Density Functional Theory (DFT) simulations demonstrate distinct behaviors in the bandgap decreasing rates when strained along different directions. Straining along the <110> direction results in a higher bandgap decreasing rate, while straining along the <111> direction leads to a lower bandgap decreasing rate but a transition from an indirect to a direct bandgap. A similar indirect-direct bandgap transition can be observed in strained silicon. Theoretically, achieving this indirect-direct bandgap transition in silicon requires a strain of more than 14% uniaxial strain. == In 2D materials == In the case of elastic strain, when the limit is exceeded, plastic deformation occurs due to slip and dislocation movement in the microstructure of the material. Plastic deformation is not commonly utilized in strain engineering due to the difficulty in controlling its uniform outcome. Plastic deformation is more influenced by local distortion rather than the global stress field observed in elastic strain. However, 2D materials have a greater range of elastic strain compared to bulk materials because they lack typical plastic deformation mechanisms like slip and dislocation. Additionally, it is easier to apply strain along a specific crystallographic direction in 2D materials compared to bulk materials. Recent research has shown significant progress in strain engineering in 2D materials through techniques such as deforming the substrate, inducing material rippling, and creating lattice asymmetry. These methods of applying strain effectively enhance the electric, magnetic, thermal, and optical properties of the material. For example, in the reference provided, the optical gap of monolayer and bilayer MoS2 decreases at rates of approximately 45 and 120 meV/%, respectively, under 0-2.2% uniaxial strain. Additionally, the photoluminescence intensity of monolayer MoS2 decreases at 1% strain, indicating an indirect-to-direct bandgap transition. The reference also demonstrates that strain-engineered rippling in black phosphorus leads to bandgap variations between +10% and -30%. In the case of ReSe2, the literature shows the formation of local wrinkle structures when the substrate is relaxed after stretching. This folding process results in a redshift in the absorption spectrum peak, leading to increased light absorption and changes in magnetic properties and bandgap. The research team also conducted I-V curve tests on the stretched samples and found that a 30% stretching resulted in lower resistance compared to the unstretched samples. However, a 50% stretching showed the opposite effect, with higher resistance compared to the unstretched samples. This behavior can be attributed to the folding of ReSe2, with the folded regions being particularly weak. == See also == Strained silicon == References ==
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https://en.wikipedia.org/wiki/Strain_engineering
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Computer science and engineering (CSE) or computer science (CS) also integrated as electrical engineering and computer science (EECS) in some universities, is an academic subject comprising approaches of computer science and computer engineering. There is no clear division in computing between science and engineering, just like in the field of materials science and engineering. However, some classes are historically more related to computer science (e.g. data structures and algorithms), and other to computer engineering (e.g. computer architecture). CSE is also a term often used in Europe to translate the name of technical or engineering informatics academic programs. It is offered in both undergraduate as well postgraduate with specializations. == Academic courses == Academic programs vary between colleges, but typically include a combination of topics in computer science,computer engineering, and electrical engineering. Undergraduate courses usually include programming, algorithms and data structures, computer architecture, operating systems, computer networks, parallel computing, embedded systems, algorithms design, circuit analysis and electronics, digital logic and processor design, computer graphics, scientific computing, software engineering, database systems, digital signal processing, virtualization, computer simulations and games programming. CSE programs also include core subjects of theoretical computer science such as theory of computation, numerical methods, machine learning, programming theory and paradigms. Modern academic programs also cover emerging computing fields like image processing, data science, robotics, bio-inspired computing, computational biology, autonomic computing and artificial intelligence. Most CSE programs require introductory mathematical knowledge, hence the first year of study is dominated by mathematical courses, primarily discrete mathematics, mathematical analysis, linear algebra, probability, and statistics, as well as the introduction to physics and electrical and electronic engineering. Students usually also have the opportunity to choose one social science subject. == See also == Computer science Computer engineering Computer graphics (computer science) Bachelor of Technology == References ==
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https://en.wikipedia.org/wiki/Computer_science_and_engineering
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Geotechnical engineering, also known as geotechnics, is the branch of civil engineering concerned with the engineering behavior of earth materials. It uses the principles of soil mechanics and rock mechanics to solve its engineering problems. It also relies on knowledge of geology, hydrology, geophysics, and other related sciences. Geotechnical engineering has applications in military engineering, mining engineering, petroleum engineering, coastal engineering, and offshore construction. The fields of geotechnical engineering and engineering geology have overlapping knowledge areas. However, while geotechnical engineering is a specialty of civil engineering, engineering geology is a specialty of geology. == History == Humans have historically used soil as a material for flood control, irrigation purposes, burial sites, building foundations, and construction materials for buildings. Dykes, dams, and canals dating back to at least 2000 BCE—found in parts of ancient Egypt, ancient Mesopotamia, the Fertile Crescent, and the early settlements of Mohenjo Daro and Harappa in the Indus valley—provide evidence for early activities linked to irrigation and flood control. As cities expanded, structures were erected and supported by formalized foundations. The ancient Greeks notably constructed pad footings and strip-and-raft foundations. Until the 18th century, however, no theoretical basis for soil design had been developed, and the discipline was more of an art than a science, relying on experience. Several foundation-related engineering problems, such as the Leaning Tower of Pisa, prompted scientists to begin taking a more scientific-based approach to examining the subsurface. The earliest advances occurred in the development of earth pressure theories for the construction of retaining walls. Henri Gautier, a French royal engineer, recognized the "natural slope" of different soils in 1717, an idea later known as the soil's angle of repose. Around the same time, a rudimentary soil classification system was also developed based on a material's unit weight, which is no longer considered a good indication of soil type. The application of the principles of mechanics to soils was documented as early as 1773 when Charles Coulomb, a physicist and engineer, developed improved methods to determine the earth pressures against military ramparts. Coulomb observed that, at failure, a distinct slip plane would form behind a sliding retaining wall and suggested that the maximum shear stress on the slip plane, for design purposes, was the sum of the soil cohesion, c {\displaystyle c} , and friction σ {\displaystyle \sigma \,\!} tan ( ϕ ) {\displaystyle \tan(\phi \,\!)} , where σ {\displaystyle \sigma \,\!} is the normal stress on the slip plane and ϕ {\displaystyle \phi \,\!} is the friction angle of the soil. By combining Coulomb's theory with Christian Otto Mohr's 2D stress state, the theory became known as Mohr-Coulomb theory. Although it is now recognized that precise determination of cohesion is impossible because c {\displaystyle c} is not a fundamental soil property, the Mohr-Coulomb theory is still used in practice today. In the 19th century, Henry Darcy developed what is now known as Darcy's Law, describing the flow of fluids in a porous media. Joseph Boussinesq, a mathematician and physicist, developed theories of stress distribution in elastic solids that proved useful for estimating stresses at depth in the ground. William Rankine, an engineer and physicist, developed an alternative to Coulomb's earth pressure theory. Albert Atterberg developed the clay consistency indices that are still used today for soil classification. In 1885, Osborne Reynolds recognized that shearing causes volumetric dilation of dense materials and contraction of loose granular materials. Modern geotechnical engineering is said to have begun in 1925 with the publication of Erdbaumechanik by Karl von Terzaghi, a mechanical engineer and geologist. Considered by many to be the father of modern soil mechanics and geotechnical engineering, Terzaghi developed the principle of effective stress, and demonstrated that the shear strength of soil is controlled by effective stress. Terzaghi also developed the framework for theories of bearing capacity of foundations, and the theory for prediction of the rate of settlement of clay layers due to consolidation. Afterwards, Maurice Biot fully developed the three-dimensional soil consolidation theory, extending the one-dimensional model previously developed by Terzaghi to more general hypotheses and introducing the set of basic equations of Poroelasticity. In his 1948 book, Donald Taylor recognized that the interlocking and dilation of densely packed particles contributed to the peak strength of the soil. Roscoe, Schofield, and Wroth, with the publication of On the Yielding of Soils in 1958, established the interrelationships between the volume change behavior (dilation, contraction, and consolidation) and shearing behavior with the theory of plasticity using critical state soil mechanics. Critical state soil mechanics is the basis for many contemporary advanced constitutive models describing the behavior of soil. In 1960, Alec Skempton carried out an extensive review of the available formulations and experimental data in the literature about the effective stress validity in soil, concrete, and rock in order to reject some of these expressions, as well as clarify what expressions were appropriate according to several working hypotheses, such as stress-strain or strength behavior, saturated or non-saturated media, and rock, concrete or soil behavior. == Roles == === Geotechnical investigation === Geotechnical engineers investigate and determine the properties of subsurface conditions and materials. They also design corresponding earthworks and retaining structures, tunnels, and structure foundations, and may supervise and evaluate sites, which may further involve site monitoring as well as the risk assessment and mitigation of natural hazards. Geotechnical engineers and engineering geologists perform geotechnical investigations to obtain information on the physical properties of soil and rock underlying and adjacent to a site to design earthworks and foundations for proposed structures and for the repair of distress to earthworks and structures caused by subsurface conditions. Geotechnical investigations involve surface and subsurface exploration of a site, often including subsurface sampling and laboratory testing of retrieved soil samples. Sometimes, geophysical methods are also used to obtain data, which include measurement of seismic waves (pressure, shear, and Rayleigh waves), surface-wave methods and downhole methods, and electromagnetic surveys (magnetometer, resistivity, and ground-penetrating radar). Electrical tomography can be used to survey soil and rock properties and existing underground infrastructure in construction projects. Surface exploration can include on-foot surveys, geological mapping, geophysical methods, and photogrammetry. Geological mapping and interpretation of geomorphology are typically completed in consultation with a geologist or engineering geologist. Subsurface exploration usually involves in-situ testing (for example, the standard penetration test and cone penetration test). The digging of test pits and trenching (particularly for locating faults and slide planes) may also be used to learn about soil conditions at depth. Large-diameter borings are rarely used due to safety concerns and expense. Still, they are sometimes used to allow a geologist or engineer to be lowered into the borehole for direct visual and manual examination of the soil and rock stratigraphy. Various soil samplers exist to meet the needs of different engineering projects. The standard penetration test, which uses a thick-walled split spoon sampler, is the most common way to collect disturbed samples. Piston samplers, employing a thin-walled tube, are most commonly used to collect less disturbed samples. More advanced methods, such as the Sherbrooke block sampler, are superior but expensive. Coring frozen ground provides high-quality undisturbed samples from ground conditions, such as fill, sand, moraine, and rock fracture zones. Geotechnical centrifuge modeling is another method of testing physical-scale models of geotechnical problems. The use of a centrifuge enhances the similarity of the scale model tests involving soil because soil's strength and stiffness are susceptible to the confining pressure. The centrifugal acceleration allows a researcher to obtain large (prototype-scale) stresses in small physical models. === Foundation design === The foundation of a structure's infrastructure transmits loads from the structure to the earth. Geotechnical engineers design foundations based on the load characteristics of the structure and the properties of the soils and bedrock at the site. Generally, geotechnical engineers first estimate the magnitude and location of loads to be supported before developing an investigation plan to explore the subsurface and determine the necessary soil parameters through field and lab testing. Following this, they may begin the design of an engineering foundation. The primary considerations for a geotechnical engineer in foundation design are bearing capacity, settlement, and ground movement beneath the foundations. === Earthworks === Geotechnical engineers are also involved in the planning and execution of earthworks, which include ground improvement, slope stabilization, and slope stability analysis. ==== Ground improvement ==== Various geotechnical engineering methods can be used for ground improvement, including reinforcement geosynthetics such as geocells and geogrids, which disperse loads over a larger area, increasing the soil's load-bearing capacity. Through these methods, geotechnical engineers can reduce direct and long-term costs. ==== Slope stabilization ==== Geotechnical engineers can analyze and improve slope stability using engineering methods. Slope stability is determined by the balance of shear stress and shear strength. A previously stable slope may be initially affected by various factors, making it unstable. Nonetheless, geotechnical engineers can design and implement engineered slopes to increase stability. ===== Slope stability analysis ===== Stability analysis is needed to design engineered slopes and estimate the risk of slope failure in natural or designed slopes by determining the conditions under which the topmost mass of soil will slip relative to the base of soil and lead to slope failure. If the interface between the mass and the base of a slope has a complex geometry, slope stability analysis is difficult and numerical solution methods are required. Typically, the interface's exact geometry is unknown, and a simplified interface geometry is assumed. Finite slopes require three-dimensional models to be analyzed, so most slopes are analyzed assuming that they are infinitely wide and can be represented by two-dimensional models. == Sub-disciplines == === Geosynthetics === Geosynthetics are a type of plastic polymer products used in geotechnical engineering that improve engineering performance while reducing costs. This includes geotextiles, geogrids, geomembranes, geocells, and geocomposites. The synthetic nature of the products make them suitable for use in the ground where high levels of durability are required. Their main functions include drainage, filtration, reinforcement, separation, and containment. Geosynthetics are available in a wide range of forms and materials, each to suit a slightly different end-use, although they are frequently used together. Some reinforcement geosynthetics, such as geogrids and more recently, cellular confinement systems, have shown to improve bearing capacity, modulus factors and soil stiffness and strength. These products have a wide range of applications and are currently used in many civil and geotechnical engineering applications including roads, airfields, railroads, embankments, piled embankments, retaining structures, reservoirs, canals, dams, landfills, bank protection and coastal engineering. === Offshore === Offshore (or marine) geotechnical engineering is concerned with foundation design for human-made structures in the sea, away from the coastline (in opposition to onshore or nearshore engineering). Oil platforms, artificial islands and submarine pipelines are examples of such structures. There are a number of significant differences between onshore and offshore geotechnical engineering. Notably, site investigation and ground improvement on the seabed are more expensive; the offshore structures are exposed to a wider range of geohazards; and the environmental and financial consequences are higher in case of failure. Offshore structures are exposed to various environmental loads, notably wind, waves and currents. These phenomena may affect the integrity or the serviceability of the structure and its foundation during its operational lifespan and need to be taken into account in offshore design. In subsea geotechnical engineering, seabed materials are considered a two-phase material composed of rock or mineral particles and water. Structures may be fixed in place in the seabed—as is the case for piers, jetties and fixed-bottom wind turbines—or may comprise a floating structure that remains roughly fixed relative to its geotechnical anchor point. Undersea mooring of human-engineered floating structures include a large number of offshore oil and gas platforms and, since 2008, a few floating wind turbines. Two common types of engineered design for anchoring floating structures include tension-leg and catenary loose mooring systems. == Observational method == First proposed by Karl Terzaghi and later discussed in a paper by Ralph B. Peck, the observational method is a managed process of construction control, monitoring, and review, which enables modifications to be incorporated during and after construction. The method aims to achieve a greater overall economy without compromising safety by creating designs based on the most probable conditions rather than the most unfavorable. Using the observational method, gaps in available information are filled by measurements and investigation, which aid in assessing the behavior of the structure during construction, which in turn can be modified per the findings. The method was described by Peck as "learn-as-you-go". The observational method may be described as follows: General exploration sufficient to establish the rough nature, pattern, and properties of deposits. Assessment of the most probable conditions and the most unfavorable conceivable deviations. Creating the design based on a working hypothesis of behavior anticipated under the most probable conditions. Selection of quantities to be observed as construction proceeds and calculating their anticipated values based on the working hypothesis under the most unfavorable conditions. Selection, in advance, of a course of action or design modification for every foreseeable significant deviation of the observational findings from those predicted. Measurement of quantities and evaluation of actual conditions. Design modification per actual conditions The observational method is suitable for construction that has already begun when an unexpected development occurs or when a failure or accident looms or has already happened. It is unsuitable for projects whose design cannot be altered during construction. == See also == == Notes == == References == Bates and Jackson, 1980, Glossary of Geology: American Geological Institute. Krynine and Judd, 1957, Principles of Engineering Geology and Geotechnics: McGraw-Hill, New York. Pierfranco Ventura, Fondazioni, Modellazioni: Verifiche Statiche e Sismiche Strutture-Terreni, vol. I, Milano Hoepli, 2019, pp.770, ISBN 978-88203-8644-3 Pierfranco Ventura, Fondazioni, Applicazioni: Verifiche Statiche e Sismiche Strutture-Terreni, vol. II, , Milano, Hoepli, 2019, pp.749,ISBN 978-88-203-8645-0 https://www.hoeplieditore.it/hoepli-catalogo/articolo/fondazioni-modellazioni-pierfrancventura/9788820386443/1451 == External links == Worldwide Geotechnical Literature Database
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https://en.wikipedia.org/wiki/Geotechnical_engineering
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Reservoir engineering is a branch of petroleum engineering that applies scientific principles to the fluid flow through a porous medium during the development and production of oil and gas reservoirs so as to obtain a high economic recovery. The working tools of the reservoir engineer are subsurface geology, applied mathematics, and the basic laws of physics and chemistry governing the behavior of liquid and vapor phases of crude oil, natural gas, and water in reservoir rock. Of particular interest to reservoir engineers is generating accurate reserves estimates for use in financial reporting to the SEC and other regulatory bodies. Other job responsibilities include numerical reservoir modeling, production forecasting, well testing, well drilling and workover planning, economic modeling, and PVT analysis of reservoir fluids. Reservoir engineers also play a central role in field development planning, recommending appropriate and cost-effective reservoir depletion schemes such as waterflooding or gas injection to maximize hydrocarbon recovery. Due to legislative changes in many hydrocarbon-producing countries, they are also involved in the design and implementation of carbon sequestration projects in order to minimise the emission of greenhouse gases. == Types == Reservoir engineers often specialize in two areas: Surveillance engineering, i.e. monitoring of existing fields and optimization of production and injection rates. Surveillance engineers typically use analytical and empirical techniques to perform their work, including decline curve analysis, material balance modeling, and inflow/outflow analysis. Dynamic modeling, i.e. the conduct of reservoir simulation studies to determine optimal development plans for oil and gas reservoirs. Also, reservoir engineers perform and integrate well tests into their data for reservoirs in geothermal drilling. The dynamic model combines the static model, pressure- and saturation-dependent properties, well locations and geometries, as well as the facilities layout to calculate the pressure/saturation distribution into the reservoir, and the production profiles vs. time. == See also == Enhanced oil recovery Flow Zone Unit Fluid dynamics Gas/oil ratio Geothermal energy Petroleum Petroleum engineering Petroleum geology Reservoir simulation Reservoir modelling == Notes == == References == Craft, B.C. & Hawkins, M. Revised by Terry, R.E. 1990 "Applied Petroleum Reservoir Engineering" Second Edition (Prentice Hall). Dake, L.P., 1978, "Fundamentals of Reservoir Engineering" (Elsevier) Frick, Thomas C. 1962 "Petroleum Production Handbook, Vol II" (Society of Petroleum Engineers). Slider, H.C. 1976 "Practical Petroleum Reservoir Engineering Methods" (The Petroleum Publishing Company). Charles R. Smith, G. W. Tracy, R. Lance Farrar. 1999 "Applied Reservoir Engineering" (Oil & Gas Consultants International) == External links == Society of Petroleum Engineers Defining Reservoir Engineering Shaping the Way for a Better Future Energy Regulator Engineering
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https://en.wikipedia.org/wiki/Reservoir_engineering
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A Bachelor of Engineering (BE or BEng) or a Bachelor of Science in Engineering (BSc (Eng) or BSE) is an undergraduate academic degree awarded to a college graduate majoring in an engineering discipline at a higher education institution. In the United Kingdom, a Bachelor of Engineering degree program is accredited by one of the Engineering Council's professional engineering institutions as suitable for registration as an incorporated engineer or chartered engineer with further study to masters level. In Canada, a degree from a Canadian university can be accredited by the Canadian Engineering Accreditation Board (CEAB). Alternatively, it might be accredited directly by another professional engineering institution, such as the US-based Institute of Electrical and Electronics Engineers (IEEE). The Bachelor of Engineering contributes to the route to chartered engineer (UK), registered engineer or licensed professional engineer and has been approved by representatives of the profession. Similarly Bachelor of Engineering (BE) and Bachelor of Technology (B.Tech) in India is accredited by All India Council for Technical Education. Most universities in the United States and Europe award bachelor's degrees in engineering through various names. A less common and possibly the oldest variety of the degree in the English-speaking world is Baccalaureus in Arte Ingeniaria (B.A.I.), a Latin name meaning Bachelor in the Art of Engineering. Here Baccalaureus in Arte Ingeniaria implies excellence in carrying out the 'art' or 'function' of an engineer. Some South African universities refer to their engineering degrees as B.Ing. (Baccalaureus Ingenieurswese, in Afrikaans). == Engineering fields == A Bachelor of Engineering degree will usually be undertaken in one field of engineering, which is sometimes noted in the degree postnominals, as in B.E., B.AE. (Aero), or B.Eng (Elec). Common fields for the Bachelor of Engineering degree include the following fields: Aerospace Engineering Agricultural Engineering Architectural Engineering Automotive Engineering Biological Engineering — including Biochemical, Biomedical, Biosystems and Biomolecular Chemical Engineering — deals with the process of converting raw materials or chemicals into more useful or valuable forms Clean Technology — use energy, water and raw materials and other inputs more efficiently and productively. Create less waste or toxicity and deliver equal or superior performance. Computer Engineering Computer Science and Engineering Civil Engineering — a wide-ranging field, including building engineering, civil engineering, construction engineering, industrial, manufacturing, mechanical, materials and control engineering Electrical and Computer Engineering/Electronic Engineering — very diverse field, including Computer Engineering, Communication/Communication systems engineering, Information Technology, Electrical Engineering, Electronics Engineering, Microelectronic Engineering, Microelectronics, Nanotechnology, Mechatronics, Software Engineering, Systems, Wireless and Telecommunications, Photovoltaic and Power Engineering Control Engineering — a relatively new and more specialized subfield of Electrical Engineering that focuses on integrating Electrical Controls and their programming. Engineering Management — the application of engineering principles to the planning and operational management of industrial and manufacturing operations Environmental Engineering — includes fields such as Environmental, Geological, Geomatic, Mining, Marine and Ocean Engineering Fire Protection Engineering — the application of science and engineering principles to protect people and their environments from the destructive effects of fire and smoke. Geological Engineering — a hybrid discipline that comprises elements of civil engineering, mining engineering, petroleum engineering and earth sciences. Geomatics Engineering — acquisition, modeling analysis and management of spatial data. Focuses on satellite positioning, remote sensing, land surveying, wireless location and Geographic Information Systems (GIS). Geotechnical Engineering — a combination of civil and mining engineering and involves the analysis of earth materials. Information Engineering — same as Information Technology. Industrial Engineering — studies facilities planning, plant layout, work measurement, job design, methods engineering, human factors, manufacturing processes, operations management, statistical quality control, systems, psychology and basic operations management Instrumentation Engineering — a branch of engineering dealing with measurement Integrated Engineering — a multi-disciplinary, design-project-based engineering degree program. Leather Engineering — an applied chemistry type based on leather and its application. Manufacturing Engineering: Includes methods engineering, manufacturing process planning, tool design, metrology, Robotics, Computer integrated manufacturing, operations management and manufacturing management Materials Engineering — includes metallurgy, polymer and ceramic engineering Marine Engineering — includes the engineering of boats, ships, oil rigs and any other marine vessel or structure, as well as oceanographic engineering. Specifically, marine engineering is the discipline of applying engineering sciences, including mechanical engineering, electrical engineering, electronic engineering and computer science, to the development, design, operation and maintenance of watercraft propulsion and on-board systems and oceanographic technology. It includes but is not limited to power and propulsion plants, machinery, piping, automation and control systems for marine vehicles of any kind, such as surface ships and submarines. Mechanical Engineering — includes engineering of total systems where mechanical science principles apply to objects in motion including transportation, energy, buildings, aerospace and machine design. Explores the applications of the theoretical fields of Mechanics, kinematics, thermodynamics, materials science, structural analysis, manufacturing and electricity Mechatronics Engineering - includes a combination of mechanical engineering, electrical engineering, telecommunications engineering, control engineering and computer engineering Mining Engineering — deals with discovering, extracting, beneficiating, marketing and utilizing mineral deposits. Nuclear Engineering — customarily includes nuclear fission, nuclear fusion and related topics such as heat/thermodynamics transport, nuclear fuel or other related technology (e.g., radioactive waste disposal) and the problems of nuclear proliferation. May also include radiation protection, particle detectors and medical physics. Petroleum Engineering — a field of engineering concerned with the activities related to exploration and production of hydrocarbons from the Earth's subsurface. Plastics Engineering — A vast field which includes plastic processing, mold designing... Process Engineering — the understanding and application of the fundamental principles and laws of nature that allow humans to transform raw material and energy into products that are useful to society, at an industrial level. Production Engineering — a term used in the UK and Europe similar to Industrial Engineering in North America. It includes the engineering of machines, people, processes and management. Explores the applications of the theoretical field of Mechanics. Textile Engineering — based on the conversion of three types of fiber into yarn, then fabric, then textiles Robotics and Automation Engineering — relates all engineering fields for implementation in robotics and automation Structural Engineering — analyze, design, plan and research structural components, systems and loads, in order to achieve design goals including high-risk structures ensuring the safety and comfort of users or occupants in a wide range of specialties. Software Engineering — systematic application of scientific and technological knowledge, methods and experience to the design, implementation, testing and documentation of software Systems Engineering — focuses on the analysis, design, development and organization of complex systems == International variations == === Australia === In Australia, the Bachelor of Engineering (BE or BEng - depending on the institution) is a four-year undergraduate degree course and a professional qualification. The title of “engineer” is not protected in Australia, therefore anyone can claim to be an engineer and practice without the necessary competencies, understanding of standards or in compliance with a code of ethics. The industry has attempted to overcome the lack of title protection through chartership (CPEng), national registration (NER) and various state registration (RPEQ) programs which are usually obtained after a few years of professional practice. === Canada === In Canada, degrees awarded for undergraduate engineering studies include the Bachelor of Engineering (B.Eng. or B.E., depending on the institution); the Baccalauréat en génie (B.Ing., the French equivalent of a B.Eng.; sometimes referred to as a Baccalauréat en ingénierie); the Bachelor of Applied Science (B.A.Sc.); and the Bachelor of Science in Engineering (B.Sc.Eng.). The Canadian Engineering Accreditation Board (CEAB), a division of the Engineers Canada, sets out and maintains the standards of accreditation among Canadian undergraduate engineering programs. Graduates of those programs are deemed by the profession to have the required academic qualifications to be licensed as professional engineers in Canada. This practice is intended to maintain standards of education and allow mobility of engineers in different provinces of Canada. A CEAB-accredited degree is the minimum academic requirement for registration as a professional engineer anywhere in the country and the standard against which all other engineering academic qualifications are measured. Graduation from an accredited program, which normally involves four years of study, is a required first step to becoming a professional engineer. Regulation and accreditation are accomplished through a self-governing body (the name of which varies from province to province), which is given the power by statute to register and discipline engineers, as well as regulate the field of engineering in the individual provinces. Graduates of non-CEAB-accredited programs must demonstrate that their education is at least equivalent to that of a graduate of a CEAB-accredited program. === Nigeria === In Nigeria, the Bachelor of Engineering (B.Eng) is a five year undergraduate professional degree course. The title of "Engineer" or "Engr" is protected in Nigeria, making it impossible for any one to be addressed officially as one, if not a certified engineer. Certification comes with registration and accreditation by Council for the Regulation of Engineering in Nigeria (COREN). It is the regulatory body that governs the practice of engineering in Nigeria. The membership is required to practice engineering independently. It is a requirement for some engineering firms and is mandatory for government contracts. == See also == Bachelor's degree Bachelor of Technology Bachelor of Applied Technology Bachelor of Science Bachelor of Applied Science Bachelor of Science in Information Technology Engineer's degree Master's degree Master of Engineering Master of Science in Engineering Master of Science Master of Applied Science Master of Science in Information Technology Institute of Technology Vocational university Polytechnic (Greece) Polytechnic (Portugal) Polytechnic (United Kingdom) == References ==
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https://en.wikipedia.org/wiki/Bachelor_of_Engineering
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Biomedical engineering (BME) or medical engineering is the application of engineering principles and design concepts to medicine and biology for healthcare applications (e.g., diagnostic or therapeutic purposes). BME is also traditionally logical sciences to advance health care treatment, including diagnosis, monitoring, and therapy. Also included under the scope of a biomedical engineer is the management of current medical equipment in hospitals while adhering to relevant industry standards. This involves procurement, routine testing, preventive maintenance, and making equipment recommendations, a role also known as a Biomedical Equipment Technician (BMET) or as a clinical engineer. Biomedical engineering has recently emerged as its own field of study, as compared to many other engineering fields. Such an evolution is common as a new field transitions from being an interdisciplinary specialization among already-established fields to being considered a field in itself. Much of the work in biomedical engineering consists of research and development, spanning a broad array of subfields (see below). Prominent biomedical engineering applications include the development of biocompatible prostheses, various diagnostic and therapeutic medical devices ranging from clinical equipment to micro-implants, imaging technologies such as MRI and EKG/ECG, regenerative tissue growth, and the development of pharmaceutical drugs including biopharmaceuticals. == Subfields and related fields == === Bioinformatics === Bioinformatics is an interdisciplinary field that develops methods and software tools for understanding biological data. As an interdisciplinary field of science, bioinformatics combines computer science, statistics, mathematics, and engineering to analyze and interpret biological data. Bioinformatics is considered both an umbrella term for the body of biological studies that use computer programming as part of their methodology, as well as a reference to specific analysis "pipelines" that are repeatedly used, particularly in the field of genomics. Common uses of bioinformatics include the identification of candidate genes and nucleotides (SNPs). Often, such identification is made with the aim of better understanding the genetic basis of disease, unique adaptations, desirable properties (esp. in agricultural species), or differences between populations. In a less formal way, bioinformatics also tries to understand the organizational principles within nucleic acid and protein sequences. === Biomechanics === Biomechanics is the study of the structure and function of the mechanical aspects of biological systems, at any level from whole organisms to organs, cells and cell organelles, using the methods of mechanics. === Biomaterials === A biomaterial is any matter, surface, or construct that interacts with living systems. As a science, biomaterials is about fifty years old. The study of biomaterials is called biomaterials science or biomaterials engineering. It has experienced steady and strong growth over its history, with many companies investing large amounts of money into the development of new products. Biomaterials science encompasses elements of medicine, biology, chemistry, tissue engineering and materials science. === Biomedical optics === Biomedical optics combines the principles of physics, engineering, and biology to study the interaction of biological tissue and light, and how this can be exploited for sensing, imaging, and treatment. It has a wide range of applications, including optical imaging, microscopy, ophthalmoscopy, spectroscopy, and therapy. Examples of biomedical optics techniques and technologies include optical coherence tomography (OCT), fluorescence microscopy, confocal microscopy, and photodynamic therapy (PDT). OCT, for example, uses light to create high-resolution, three-dimensional images of internal structures, such as the retina in the eye or the coronary arteries in the heart. Fluorescence microscopy involves labeling specific molecules with fluorescent dyes and visualizing them using light, providing insights into biological processes and disease mechanisms. More recently, adaptive optics is helping imaging by correcting aberrations in biological tissue, enabling higher resolution imaging and improved accuracy in procedures such as laser surgery and retinal imaging. === Tissue engineering === Tissue engineering, like genetic engineering (see below), is a major segment of biotechnology – which overlaps significantly with BME. One of the goals of tissue engineering is to create artificial organs (via biological material) such as kidneys, livers, for patients that need organ transplants. Biomedical engineers are currently researching methods of creating such organs. Researchers have grown solid jawbones and tracheas from human stem cells towards this end. Several artificial urinary bladders have been grown in laboratories and transplanted successfully into human patients. Bioartificial organs, which use both synthetic and biological component, are also a focus area in research, such as with hepatic assist devices that use liver cells within an artificial bioreactor construct. == Genetic engineering == Genetic engineering, recombinant DNA technology, genetic modification/manipulation (GM) and gene splicing are terms that apply to the direct manipulation of an organism's genes. Unlike traditional breeding, an indirect method of genetic manipulation, genetic engineering utilizes modern tools such as molecular cloning and transformation to directly alter the structure and characteristics of target genes. Genetic engineering techniques have found success in numerous applications. Some examples include the improvement of crop technology (not a medical application, but see biological systems engineering), the manufacture of synthetic human insulin through the use of modified bacteria, the manufacture of erythropoietin in hamster ovary cells, and the production of new types of experimental mice such as the oncomouse (cancer mouse) for research. === Neural engineering === Neural engineering (also known as neuroengineering) is a discipline that uses engineering techniques to understand, repair, replace, or enhance neural systems. Neural engineers are uniquely qualified to solve design problems at the interface of living neural tissue and non-living constructs. Neural engineering can assist with numerous things, including the future development of prosthetics. For example, cognitive neural prosthetics (CNP) are being heavily researched and would allow for a chip implant to assist people who have prosthetics by providing signals to operate assistive devices. === Pharmaceutical engineering === Pharmaceutical engineering is an interdisciplinary science that includes drug engineering, novel drug delivery and targeting, pharmaceutical technology, unit operations of chemical engineering, and pharmaceutical analysis. It may be deemed as a part of pharmacy due to its focus on the use of technology on chemical agents in providing better medicinal treatment. == Hospital and medical devices == This is an extremely broad category—essentially covering all health care products that do not achieve their intended results through predominantly chemical (e.g., pharmaceuticals) or biological (e.g., vaccines) means, and do not involve metabolism. A medical device is intended for use in: the diagnosis of disease or other conditions in the cure, mitigation, treatment, or prevention of disease. Some examples include pacemakers, infusion pumps, the heart-lung machine, dialysis machines, artificial organs, implants, artificial limbs, corrective lenses, cochlear implants, ocular prosthetics, facial prosthetics, somato prosthetics, and dental implants. Stereolithography is a practical example of medical modeling being used to create physical objects. Beyond modeling organs and the human body, emerging engineering techniques are also currently used in the research and development of new devices for innovative therapies, treatments, patient monitoring, of complex diseases. Medical devices are regulated and classified (in the US) as follows (see also Regulation): Class I devices present minimal potential for harm to the user and are often simpler in design than Class II or Class III devices. Devices in this category include tongue depressors, bedpans, elastic bandages, examination gloves, and hand-held surgical instruments, and other similar types of common equipment. Class II devices are subject to special controls in addition to the general controls of Class I devices. Special controls may include special labeling requirements, mandatory performance standards, and postmarket surveillance. Devices in this class are typically non-invasive and include X-ray machines, PACS, powered wheelchairs, infusion pumps, and surgical drapes. Class III devices generally require premarket approval (PMA) or premarket notification (510k), a scientific review to ensure the device's safety and effectiveness, in addition to the general controls of Class I. Examples include replacement heart valves, hip and knee joint implants, silicone gel-filled breast implants, implanted cerebellar stimulators, implantable pacemaker pulse generators and endosseous (intra-bone) implants. === Medical imaging === Medical/biomedical imaging is a major segment of medical devices. This area deals with enabling clinicians to directly or indirectly "view" things not visible in plain sight (such as due to their size, and/or location). This can involve utilizing ultrasound, magnetism, UV, radiology, and other means. Alternatively, navigation-guided equipment utilizes electromagnetic tracking technology, such as catheter placement into the brain or feeding tube placement systems. For example, ENvizion Medical's ENvue, an electromagnetic navigation system for enteral feeding tube placement. The system uses an external field generator and several EM passive sensors enabling scaling of the display to the patient's body contour, and a real-time view of the feeding tube tip location and direction, which helps the medical staff ensure the correct placement in the GI tract. Imaging technologies are often essential to medical diagnosis, and are typically the most complex equipment found in a hospital including: fluoroscopy, magnetic resonance imaging (MRI), nuclear medicine, positron emission tomography (PET), PET-CT scans, projection radiography such as X-rays and CT scans, tomography, ultrasound, optical microscopy, and electron microscopy. === Medical implants === An implant is a kind of medical device made to replace and act as a missing biological structure (as compared with a transplant, which indicates transplanted biomedical tissue). The surface of implants that contact the body might be made of a biomedical material such as titanium, silicone or apatite depending on what is the most functional. In some cases, implants contain electronics, e.g. artificial pacemakers and cochlear implants. Some implants are bioactive, such as subcutaneous drug delivery devices in the form of implantable pills or drug-eluting stents. === Bionics === Artificial body part replacements are one of the many applications of bionics. Concerned with the intricate and thorough study of the properties and function of human body systems, bionics may be applied to solve some engineering problems. Careful study of the different functions and processes of the eyes, ears, and other organs paved the way for improved cameras, television, radio transmitters and receivers, and many other tools. === Biomedical sensors === In recent years biomedical sensors based in microwave technology have gained more attention. Different sensors can be manufactured for specific uses in both diagnosing and monitoring disease conditions, for example microwave sensors can be used as a complementary technique to X-ray to monitor lower extremity trauma. The sensor monitor the dielectric properties and can thus notice change in tissue (bone, muscle, fat etc.) under the skin so when measuring at different times during the healing process the response from the sensor will change as the trauma heals. == Clinical engineering == Clinical engineering is the branch of biomedical engineering dealing with the actual implementation of medical equipment and technologies in hospitals or other clinical settings. Major roles of clinical engineers include training and supervising biomedical equipment technicians (BMETs), selecting technological products/services and logistically managing their implementation, working with governmental regulators on inspections/audits, and serving as technological consultants for other hospital staff (e.g. physicians, administrators, I.T., etc.). Clinical engineers also advise and collaborate with medical device producers regarding prospective design improvements based on clinical experiences, as well as monitor the progression of the state of the art so as to redirect procurement patterns accordingly. Their inherent focus on practical implementation of technology has tended to keep them oriented more towards incremental-level redesigns and reconfigurations, as opposed to revolutionary research & development or ideas that would be many years from clinical adoption; however, there is a growing effort to expand this time-horizon over which clinical engineers can influence the trajectory of biomedical innovation. In their various roles, they form a "bridge" between the primary designers and the end-users, by combining the perspectives of being both close to the point-of-use, while also trained in product and process engineering. Clinical engineering departments will sometimes hire not just biomedical engineers, but also industrial/systems engineers to help address operations research/optimization, human factors, cost analysis, etc. Also, see safety engineering for a discussion of the procedures used to design safe systems. The clinical engineering department is constructed with a manager, supervisor, engineer, and technician. One engineer per eighty beds in the hospital is the ratio. Clinical engineers are also authorized to audit pharmaceutical and associated stores to monitor FDA recalls of invasive items. == Rehabilitation engineering == Rehabilitation engineering is the systematic application of engineering sciences to design, develop, adapt, test, evaluate, apply, and distribute technological solutions to problems confronted by individuals with disabilities. Functional areas addressed through rehabilitation engineering may include mobility, communications, hearing, vision, and cognition, and activities associated with employment, independent living, education, and integration into the community. While some rehabilitation engineers have master's degrees in rehabilitation engineering, usually a subspecialty of Biomedical engineering, most rehabilitation engineers have an undergraduate or graduate degrees in biomedical engineering, mechanical engineering, or electrical engineering. A Portuguese university provides an undergraduate degree and a master's degree in Rehabilitation Engineering and Accessibility. Qualification to become a Rehab' Engineer in the UK is possible via a University BSc Honours Degree course such as Health Design & Technology Institute, Coventry University. The rehabilitation process for people with disabilities often entails the design of assistive devices such as Walking aids intended to promote the inclusion of their users into the mainstream of society, commerce, and recreation. == Regulatory issues == Regulatory issues have been constantly increased in the last decades to respond to the many incidents caused by devices to patients. For example, from 2008 to 2011, in US, there were 119 FDA recalls of medical devices classified as class I. According to U.S. Food and Drug Administration (FDA), Class I recall is associated to "a situation in which there is a reasonable probability that the use of, or exposure to, a product will cause serious adverse health consequences or death" Regardless of the country-specific legislation, the main regulatory objectives coincide worldwide. For example, in the medical device regulations, a product must be 1), safe 2), effective and 3), applicable to all the manufactured devices. A product is safe if patients, users, and third parties do not run unacceptable risks of physical hazards, such as injury or death, in its intended use. Protective measures must be introduced on devices that are hazardous to reduce residual risks at an acceptable level if compared with the benefit derived from the use of it. A product is effective if it performs as specified by the manufacturer in the intended use. Proof of effectiveness is achieved through clinical evaluation, compliance to performance standards or demonstrations of substantial equivalence with an already marketed device. The previous features have to be ensured for all the manufactured items of the medical device. This requires that a quality system shall be in place for all the relevant entities and processes that may impact safety and effectiveness over the whole medical device lifecycle. The medical device engineering area is among the most heavily regulated fields of engineering, and practicing biomedical engineers must routinely consult and cooperate with regulatory law attorneys and other experts. The Food and Drug Administration (FDA) is the principal healthcare regulatory authority in the United States, having jurisdiction over medical devices, drugs, biologics, and combination products. The paramount objectives driving policy decisions by the FDA are safety and effectiveness of healthcare products that have to be assured through a quality system in place as specified under 21 CFR 829 regulation. In addition, because biomedical engineers often develop devices and technologies for "consumer" use, such as physical therapy devices (which are also "medical" devices), these may also be governed in some respects by the Consumer Product Safety Commission. The greatest hurdles tend to be 510K "clearance" (typically for Class 2 devices) or pre-market "approval" (typically for drugs and class 3 devices). In the European context, safety effectiveness and quality is ensured through the "Conformity Assessment" which is defined as "the method by which a manufacturer demonstrates that its device complies with the requirements of the European Medical Device Directive". The directive specifies different procedures according to the class of the device ranging from the simple Declaration of Conformity (Annex VII) for Class I devices to EC verification (Annex IV), Production quality assurance (Annex V), Product quality assurance (Annex VI) and Full quality assurance (Annex II). The Medical Device Directive specifies detailed procedures for Certification. In general terms, these procedures include tests and verifications that are to be contained in specific deliveries such as the risk management file, the technical file, and the quality system deliveries. The risk management file is the first deliverable that conditions the following design and manufacturing steps. The risk management stage shall drive the product so that product risks are reduced at an acceptable level with respect to the benefits expected for the patients for the use of the device. The technical file contains all the documentation data and records supporting medical device certification. FDA technical file has similar content although organized in a different structure. The Quality System deliverables usually include procedures that ensure quality throughout all product life cycles. The same standard (ISO EN 13485) is usually applied for quality management systems in the US and worldwide. In the European Union, there are certifying entities named "Notified Bodies", accredited by the European Member States. The Notified Bodies must ensure the effectiveness of the certification process for all medical devices apart from the class I devices where a declaration of conformity produced by the manufacturer is sufficient for marketing. Once a product has passed all the steps required by the Medical Device Directive, the device is entitled to bear a CE marking, indicating that the device is believed to be safe and effective when used as intended, and, therefore, it can be marketed within the European Union area. The different regulatory arrangements sometimes result in particular technologies being developed first for either the U.S. or in Europe depending on the more favorable form of regulation. While nations often strive for substantive harmony to facilitate cross-national distribution, philosophical differences about the optimal extent of regulation can be a hindrance; more restrictive regulations seem appealing on an intuitive level, but critics decry the tradeoff cost in terms of slowing access to life-saving developments. === RoHS II === Directive 2011/65/EU, better known as RoHS 2 is a recast of legislation originally introduced in 2002. The original EU legislation "Restrictions of Certain Hazardous Substances in Electrical and Electronics Devices" (RoHS Directive 2002/95/EC) was replaced and superseded by 2011/65/EU published in July 2011 and commonly known as RoHS 2. RoHS seeks to limit the dangerous substances in circulation in electronics products, in particular toxins and heavy metals, which are subsequently released into the environment when such devices are recycled. The scope of RoHS 2 is widened to include products previously excluded, such as medical devices and industrial equipment. In addition, manufacturers are now obliged to provide conformity risk assessments and test reports – or explain why they are lacking. For the first time, not only manufacturers but also importers and distributors share a responsibility to ensure Electrical and Electronic Equipment within the scope of RoHS complies with the hazardous substances limits and have a CE mark on their products. === IEC 60601 === The new International Standard IEC 60601 for home healthcare electro-medical devices defining the requirements for devices used in the home healthcare environment. IEC 60601-1-11 (2010) must now be incorporated into the design and verification of a wide range of home use and point of care medical devices along with other applicable standards in the IEC 60601 3rd edition series. The mandatory date for implementation of the EN European version of the standard is June 1, 2013. The US FDA requires the use of the standard on June 30, 2013, while Health Canada recently extended the required date from June 2012 to April 2013. The North American agencies will only require these standards for new device submissions, while the EU will take the more severe approach of requiring all applicable devices being placed on the market to consider the home healthcare standard. === AS/NZS 3551:2012 === AS/ANS 3551:2012 is the Australian and New Zealand standards for the management of medical devices. The standard specifies the procedures required to maintain a wide range of medical assets in a clinical setting (e.g. Hospital). The standards are based on the IEC 606101 standards. The standard covers a wide range of medical equipment management elements including, procurement, acceptance testing, maintenance (electrical safety and preventive maintenance testing) and decommissioning. == Training and certification == === Education === Biomedical engineers require considerable knowledge of both engineering and biology, and typically have a Bachelor's (B.Sc., B.S., B.Eng. or B.S.E.) or Master's (M.S., M.Sc., M.S.E., or M.Eng.) or a doctoral (Ph.D., or MD-PhD) degree in BME (Biomedical Engineering) or another branch of engineering with considerable potential for BME overlap. As interest in BME increases, many engineering colleges now have a Biomedical Engineering Department or Program, with offerings ranging from the undergraduate (B.Sc., B.S., B.Eng. or B.S.E.) to doctoral levels. Biomedical engineering has only recently been emerging as its own discipline rather than a cross-disciplinary hybrid specialization of other disciplines; and BME programs at all levels are becoming more widespread, including the Bachelor of Science in Biomedical Engineering which includes enough biological science content that many students use it as a "pre-med" major in preparation for medical school. The number of biomedical engineers is expected to rise as both a cause and effect of improvements in medical technology. In the U.S., an increasing number of undergraduate programs are also becoming recognized by ABET as accredited bioengineering/biomedical engineering programs. As of 2023, 155 programs are currently accredited by ABET. In Canada and Australia, accredited graduate programs in biomedical engineering are common. For example, McMaster University offers an M.A.Sc, an MD/PhD, and a PhD in Biomedical engineering. The first Canadian undergraduate BME program was offered at University of Guelph as a four-year B.Eng. program. The Polytechnique in Montreal is also offering a bachelors's degree in biomedical engineering as is Flinders University. As with many degrees, the reputation and ranking of a program may factor into the desirability of a degree holder for either employment or graduate admission. The reputation of many undergraduate degrees is also linked to the institution's graduate or research programs, which have some tangible factors for rating, such as research funding and volume, publications and citations. With BME specifically, the ranking of a university's hospital and medical school can also be a significant factor in the perceived prestige of its BME department/program. Graduate education is a particularly important aspect in BME. While many engineering fields (such as mechanical or electrical engineering) do not need graduate-level training to obtain an entry-level job in their field, the majority of BME positions do prefer or even require them. Since most BME-related professions involve scientific research, such as in pharmaceutical and medical device development, graduate education is almost a requirement (as undergraduate degrees typically do not involve sufficient research training and experience). This can be either a Masters or Doctoral level degree; while in certain specialties a Ph.D. is notably more common than in others, it is hardly ever the majority (except in academia). In fact, the perceived need for some kind of graduate credential is so strong that some undergraduate BME programs will actively discourage students from majoring in BME without an expressed intention to also obtain a master's degree or apply to medical school afterwards. Graduate programs in BME, like in other scientific fields, are highly varied, and particular programs may emphasize certain aspects within the field. They may also feature extensive collaborative efforts with programs in other fields (such as the university's Medical School or other engineering divisions), owing again to the interdisciplinary nature of BME. M.S. and Ph.D. programs will typically require applicants to have an undergraduate degree in BME, or another engineering discipline (plus certain life science coursework), or life science (plus certain engineering coursework). Education in BME also varies greatly around the world. By virtue of its extensive biotechnology sector, its numerous major universities, and relatively few internal barriers, the U.S. has progressed a great deal in its development of BME education and training opportunities. Europe, which also has a large biotechnology sector and an impressive education system, has encountered trouble in creating uniform standards as the European community attempts to supplant some of the national jurisdictional barriers that still exist. Recently, initiatives such as BIOMEDEA have sprung up to develop BME-related education and professional standards. Other countries, such as Australia, are recognizing and moving to correct deficiencies in their BME education. Also, as high technology endeavors are usually marks of developed nations, some areas of the world are prone to slower development in education, including in BME. === Licensure/certification === As with other learned professions, each state has certain (fairly similar) requirements for becoming licensed as a registered Professional Engineer (PE), but, in US, in industry such a license is not required to be an employee as an engineer in the majority of situations (due to an exception known as the industrial exemption, which effectively applies to the vast majority of American engineers). The US model has generally been only to require the practicing engineers offering engineering services that impact the public welfare, safety, safeguarding of life, health, or property to be licensed, while engineers working in private industry without a direct offering of engineering services to the public or other businesses, education, and government need not be licensed. This is notably not the case in many other countries, where a license is as legally necessary to practice engineering as it is for law or medicine. Biomedical engineering is regulated in some countries, such as Australia, but registration is typically only recommended and not required. In the UK, mechanical engineers working in the areas of Medical Engineering, Bioengineering or Biomedical engineering can gain Chartered Engineer status through the Institution of Mechanical Engineers. The Institution also runs the Engineering in Medicine and Health Division. The Institute of Physics and Engineering in Medicine (IPEM) has a panel for the accreditation of MSc courses in Biomedical Engineering and Chartered Engineering status can also be sought through IPEM. The Fundamentals of Engineering exam – the first (and more general) of two licensure examinations for most U.S. jurisdictions—does now cover biology (although technically not BME). For the second exam, called the Principles and Practices, Part 2, or the Professional Engineering exam, candidates may select a particular engineering discipline's content to be tested on; there is currently not an option for BME with this, meaning that any biomedical engineers seeking a license must prepare to take this examination in another category (which does not affect the actual license, since most jurisdictions do not recognize discipline specialties anyway). However, the Biomedical Engineering Society (BMES) is, as of 2009, exploring the possibility of seeking to implement a BME-specific version of this exam to facilitate biomedical engineers pursuing licensure. Beyond governmental registration, certain private-sector professional/industrial organizations also offer certifications with varying degrees of prominence. One such example is the Certified Clinical Engineer (CCE) certification for Clinical engineers. == Career prospects == In 2012 there were about 19,400 biomedical engineers employed in the US, and the field was predicted to grow by 5% (faster than average) from 2012 to 2022. Biomedical engineering has the highest percentage of female engineers compared to other common engineering professions. Now as of 2023, there are 19,700 jobs for this degree, the average pay for a person in this field is around $100,730.00 and making around $48.43 an hour. There is also expected to be a 7% increase in jobs from here 2023 to 2033 (even faster than the last average). == Notable figures == Julia Tutelman Apter (deceased) – One of the first specialists in neurophysiological research and a founding member of the Biomedical Engineering Society Earl Bakken (deceased) – Invented the first transistorised pacemaker, co-founder of Medtronic. Forrest Bird (deceased) – aviator and pioneer in the invention of mechanical ventilators Y.C. Fung (deceased) – professor emeritus at the University of California, San Diego, considered by many to be the founder of modern biomechanics Leslie Geddes (deceased) – professor emeritus at Purdue University, electrical engineer, inventor, and educator of over 2000 biomedical engineers, received a National Medal of Technology in 2006 from President George Bush for his more than 50 years of contributions that have spawned innovations ranging from burn treatments to miniature defibrillators, ligament repair to tiny blood pressure monitors for premature infants, as well as a new method for performing cardiopulmonary resuscitation (CPR). Willem Johan Kolff (deceased) – pioneer of hemodialysis as well as in the field of artificial organs Robert Langer – Institute Professor at MIT, runs the largest BME laboratory in the world, pioneer in drug delivery and tissue engineering John Macleod (deceased) – one of the co-discoverers of insulin at Case Western Reserve University. Alfred E. Mann – Physicist, entrepreneur and philanthropist. A pioneer in the field of Biomedical Engineering. J. Thomas Mortimer – Emeritus professor of biomedical engineering at Case Western Reserve University. Pioneer in Functional Electrical Stimulation (FES) Robert M. Nerem – professor emeritus at Georgia Institute of Technology. Pioneer in regenerative tissue, biomechanics, and author of over 300 published works. His works have been cited more than 20,000 times cumulatively. P. Hunter Peckham – Donnell Professor of Biomedical Engineering and Orthopaedics at Case Western Reserve University. Pioneer in Functional Electrical Stimulation (FES) Nicholas A. Peppas – Chaired Professor in Engineering, University of Texas at Austin, pioneer in drug delivery, biomaterials, hydrogels and nanobiotechnology. Robert Plonsey – professor emeritus at Duke University, pioneer of electrophysiology Otto Schmitt (deceased) – biophysicist with significant contributions to BME, working with biomimetics Ascher Shapiro (deceased) – Institute Professor at MIT, contributed to the development of the BME field, medical devices (e.g. intra-aortic balloons) Gordana Vunjak-Novakovic – University Professor at Columbia University, pioneer in tissue engineering and bioreactor design John G. Webster – professor emeritus at the University of Wisconsin–Madison, a pioneer in the field of instrumentation amplifiers for the recording of electrophysiological signals Fred Weibell, coauthor of Biomedical Instrumentation and Measurements U.A. Whitaker (deceased) – provider of the Whitaker Foundation, which supported research and education in BME by providing over $700 million to various universities, helping to create 30 BME programs and helping finance the construction of 13 buildings == See also == Biomedicine – Branch of medical science that applies biological and physiological principles to clinical practice Cardiophysics – interdisciplinary science that stands at the junction of cardiology and medical physicsPages displaying wikidata descriptions as a fallback Computational anatomy – Interdisciplinary field of biology Medical physics – Application of physics in medicine or healthcare Physiome – Wholistic physiological dynamics of an organism Biomedical Engineering and Instrumentation Program (BEIP) == References == 45. ^Bureau of Labor Statistics, U.S. Department of Labor, Occupational Outlook Handbook, "Bioengineers and Biomedical Engineers", retrieved October 27, 2024. == Further reading == Bronzino, Joseph D. (April 2006). The Biomedical Engineering Handbook (Third ed.). [CRC Press]. ISBN 978-0-8493-2124-5. Archived from the original on 2015-02-24. Retrieved 2009-06-22. Villafane, Carlos (June 2009). Biomed: From the Student's Perspective (First ed.). [Techniciansfriend.com]. ISBN 978-1-61539-663-4. == External links == Media related to Biomedical engineering at Wikimedia Commons
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Engineering management is the application of engineering methods, tools, and techniques to business management systems. Engineering management is a career that brings together the technological problem-solving ability of engineering and the organizational, administrative, legal and planning abilities of management in order to oversee the operational performance of complex engineering-driven enterprises. Universities offering bachelor degrees in engineering management typically have programs covering courses such as engineering management, project management, operations management, logistics, supply chain management, programming concepts, programming applications, operations research, engineering law, value engineering, quality control, quality assurance, six sigma, safety engineering, systems engineering, engineering leadership, accounting, applied engineering design, business statistics and calculus. A Master of Engineering Management (MEM) and Master of Business Engineering (MBE) are sometimes compared to a Master of Business Administration (MBA) for professionals seeking a graduate degree as a qualifying credential for a career in engineering management. == History == Stevens Institute of Technology is believed to have the oldest engineering management department, established as the School of Business Engineering in 1908. This was later called the Bachelor of Engineering in Engineering Management (BEEM) program and moved into the School of Systems and Enterprises. Syracuse University established the first graduate engineering management degree in the United States, which was first offered in 1957. In 1967 the first university department explicitly titled "Engineering Management" was founded at the Missouri University of Science and Technology (Missouri S&T, formerly the University of Missouri-Rolla, formerly Missouri School of Mines). Inside the United States, other notable engineering management programs includes: In 1959, Western Michigan University began offering the predecessor to the modern engineering management bachelor's degree (titled "Industrial Supervision") and in 1977, Western Michigan University started its MS degree in Manufacturing Administration, later renamed as Engineering Management. In 1998, University of Wisconsin–Madison established the predecessor to their online graduate engineering management degree (titled "Master of Engineering in Professional Practice"). Michigan Technological University began an Engineering Management program in the School of Business & Economics in the Fall of 2012. Outside the United States, engineering management includes: In Germany the first department concentrating on Engineering Management was established 1927 at the Technische Hochschule in Charlottenburg (now Technische Universität Berlin). In Turkey the Istanbul Technical University has a Management Engineering Department established in 1982, offering a number of graduate and undergraduate programs in Management Engineering (in English). In UK the University of Warwick has a specialised department WMG (previously known as Warwick Manufacturing Group) established in 1980, which offers a graduate programme in MSc Engineering Business Management. In Canada, Memorial University of Newfoundland has started a complete master's degree Program in Engineering Management. In Denmark, the Technical University of Denmark offers a MSc program in Engineering Management (in English). In Pakistan, University of Engineering and Technology, Taxila, University of Engineering and Technology, Lahore and National University of Science and Technology (NUST) offer admission both at Master and Doctorate level in Engineering Management while Capital University of Science & Technology (CUST), NED University of Engineering & Technology, Karachi and Ghulam Ishaq Khan Institute of Engineering Sciences and Technology have been running a Master of Engineering/MS in Engineering Management program. A variant of this program is within Quality Management. COMSATS (CIIT) offers a MSc Project Management program to Local and Overseas Pakistanis as an on-campus/off-campus student. In Italy, the first Engineering Management program was established in 1972 at the University of Calabria by Beniamino Andreatta. Politecnico di Milano offers degrees in Management Engineering., among many other public or private (and publicly-accredited) universities belonging to the same post-secondary academic degrees' classification. In Morocco, École Nationale Supérieure des Mines de Rabat offers an Engineering Management degree (three years of study full time with a selective admission for Associate or bachelor degree holders). The degree offered is referred to locally as Diplôme d'Ingénieur and is equivalent to Master level degree. In Russia, since 2014 the Faculty of Engineering Management of The Russian Presidential Academy of National Economy and Public Administration (RANEPA) offers bachelor's and master's degrees in Engineering Management. In France, the EPF will offer, from January 2018, a 2-year Engineering & Management major in English for the 4th and 5th years of its 5-year Engineering master's degree. The final two years are open to students who have completed an undergraduate engineering degree elsewhere. == Areas of practice == Engineering management is a broad field and can cover a wide range of technical and managerial topics. An important resource is the Engineering Management Body of Knowledge (EMBoK). The topics below are representative of typical topics in the field. === Leadership and organization management === Leadership and organization management are concerned with the skills involving positive direction of technical organizations and motivation of employees. Often a manager must shape engineering policy within an organization. === Operations, operations research, and supply chain === Operations management is concerned with designing and controlling the process of production and redesigning business operations in the production of goods or services. Operations research deals with quantitative models of complex operations and uses these models to support decision-making in any sector of industry or public services. Supply chain management is the process of planning, implementing and managing the flow of goods, services and related information from the point of origin to the point of consumption. === Engineering law === Engineering law and the related statutes are critical to management practice and engineering. Engineering legislation makes engineering a controlled activity and an engineering manager must know which statutes apply to their practice. Codes of ethics can be enshrined in law. Professional misconduct and negligence are defined in law. An engineering manager must be licensed as an engineer and may have engineers, technicians and natural scientists reporting to her or him. Understanding how licensed engineers supervise non-licensed technicians and natural scientists is critical to safe practice. An engineering manager must always use engineering legislation to push back against schedule pressure or budget pressure to ensure public safety. === Management of technology === Introducing and utilizing new technology is a major route to cost reduction and quality improvement in production engineering. The management of technology (MOT) theme builds on the foundation of management topics in accounting, finance, economics, organizational behavior and organizational design. Courses in this theme deal with operational and organizational issues related to managing innovation and technological change. === New product development and product engineering === New product development (NPD) is the complete process of bringing a new product to market. Product engineering refers to the process of designing and developing a device, assembly, or system such that it be produced as an item for sale through some production manufacturing process. Product engineering usually entails activity dealing with issues of cost, producibility, quality, performance, reliability, serviceability, intended lifespan and user features. Project management techniques are used to manage the design and development progress using the phase-gate model in the product development process. Design for manufacturability (also sometimes known as design for manufacturing or DFM) is the general engineering art of designing products in such a way that they are easy to manufacture. === Systems engineering === Systems engineering is an interdisciplinary field of engineering and engineering management that focuses on how to design and manage complex systems over their life cycles. === Industrial engineering === Industrial engineering is a branch of engineering which deals with the optimization of complex processes, systems or organizations. Industrial engineers work to eliminate waste of time, money, materials, man-hours, machine time, energy and other resources that do not generate value. === Management science === Management science uses various scientific research-based principles, strategies, and analytical methods including mathematical modeling, statistics and numerical algorithms to improve an organization's ability to enact rational and meaningful management decisions by arriving at optimal or near optimal solutions to complex decision problems. === Engineering design management === Engineering design management represents the adaptation and application of customary management practices, with the intention of achieving a productive engineering design process. Engineering design management is primarily applied in the context of engineering design teams, whereby the activities, outputs and influences of design teams are planned, guided, monitored and controlled. === Human factors safety culture === Critical to management success in engineering is the study of human factors and safety culture involved with highly complex tasks within organizations large and small. In complex engineering systems, human factors safety culture can be critical in preventing catastrophe and minimizing the realized hazard rate. Critical areas of safety culture are minimizing blame avoidance, minimizing power distance, an appropriate ambiguity tolerance and minimizing a culture of concealment. Increasing organizational empathy and an ability to clearly report problems up the chain of management is important to the success of any engineering program. Managing an engineering firm is in opposition to the management of a law firm. Law firms keep secrets while engineering firms succeed when information is deiminated clearly and quickly. Engineering managers must push against a culture of concealment which may be promoted by the law department. Managers in an engineering firm must be ready to push back against schedule and budget constraints from the executive suite. Engineering managers must use engineering law to push back against the executive suite to ensure public safety. The executive suite in an engineering organization can become consumed with financial data imperiling public safety. == Education == Engineering management programs typically include instruction in accounting, economics, finance, project management, systems engineering, industrial engineering, mathematical modeling and optimization, management information systems, quality control and six sigma, operations management, operations research, human resources management, industrial psychology, safety and health. There are many options for entering into engineering management, albeit that the foundation requirement is an engineering license. === Undergraduate degrees === Although most engineering management programs are geared toward graduate studies, there are a number of institutions that teach EM at the undergraduate level. Over twenty undergraduate engineering management related programs are accredited by ABET including: West Point (United States Military Academy), Western Michigan University (ABET-accredited by ETAC of ABET), Stevens Institute of Technology, Clarkson University, Gonzaga University, Virginia Tech, Arizona State University, and the Missouri University of Science and Technology. Graduates of these programs regularly command nearly $65,000 their first year out of school. Outside the US, Istanbul Technical University Management Engineering Department offers an undergraduate degree in Management Engineering, attracting top students. The University of Waterloo offers a 4-year undergraduate degree (five years including co-op education) in the field of Management Engineering. This is the first program of its kind in Canada. In Peru, Universidad del Pacífico offers a five-year undergraduate degree in this field, the first program in this country. In Germany, ESB Business School offers a 4-year undergraduate program which consists of five semesters at ESB Business School, two mandatory internships, one is mandatory to be in another country than Germany, and also one mandatory semester abroad. In the annual applied university ranking of the magazine Wirtschaftswoche, the Engineering Management course of ESB Business School is ranked on place five of all applied universities in Germany. The magazine surveyed more than 500 recruiters in the German industry from which university they are most likely to recruit students and which universities satisfy their needs regarding experience in working with projects, multilingual education, and ability to communicate most. === Graduate degrees === Many universities offer Master of Engineering Management degrees. Northwestern University offers the Master of Engineering Management (MEM) program since 1976. The program is administered out of the Department of Industrial Engineering and Management Sciences. Students take courses across different schools of the university such as McCormick school of Engineering, Kellogg School of Management, Farley Center for Entrepreneurship and Innovation, Segal Design Institute. Graduates students are admitted based on eligibility criteria that includes minimum work experience of 3 years. Missouri S&T is credited with awarding the first Ph.D. in Engineering Management in 1984. The National Institute of Industrial Engineering based in Mumbai has been awarding degrees in the field of Post Graduate Diploma in Industrial Engineering since 1973 and the Fellowship (Doctoral) degrees have been awarded since 2008. Western Michigan University began offering the MS in Manufacturing Administration degree in 1977 and later renamed the degree as Master of Science in Engineering Management. WMU's MSEM alumni work in the automotive, medical, manufacturing, and service sectors, often in roles of project manager, engineering manager, and senior leadership in engineering and technical organizations. Cornell University started one of the first Engineering Management Masters programs in 1988 with the launch of their Master of Engineering (M.Eng.) in Engineering Management. The program allows students access to courses and programs in the College of Engineering, Johnson School of Management, and across Cornell University more broadly. Massachusetts Institute of Technology offers a Master in System Design and Management, which is a member of the Consortium of Engineering Management. Lamar University offers a Master of Engineering Management degree with flexible content to adjust to diverse engineering fields, with core content that includes operations management, accounting, and decision sciences. Netaji Subhas Institute of Technology (NSIT) New Delhi also provides M.tech degree in Engineering management. Admission to this program happens through GATE (Graduate Aptitude Test in Engineering) examination. Students in the University of Kansas' Engineering Management Program are practicing professionals employed by over 100 businesses, manufacturing, government or consulting firms. There are over 200 actively enrolled students in the program and approximately 500 alumni. Istanbul Technical University Management Engineering Department offers a graduate degree, and a Ph.D. in Management Engineering. == Management engineering consulting == Large and small engineering driven firms often require the expertise of external management consultants that specialize in companies where engineering practice and product development are key drivers of value. Most engineering management consultants will have as a minimum a professional engineering qualification. But usually they will also have graduate degrees in engineering and or business or a management consulting designation. It involves providing management consulting service that is specific to professional engineering practice or to the engineering industry sector. Engineering management consultancies, are typically boutique firms and have a more specialized focus than the traditional mainstream consulting firms, A T Kearney, Boston Consulting Group, KPMG, PWC, and McKinsey. Applied science and engineering practice requires a combination of "management art", science, and engineering practice. There are many professional service companies delivering services in a consultancy type relationship to the engineering industry, including law, accounting, human resources, marketing, politics, economics, finance, public affairs, and communication. Commonly, engineering management consultants are used when firms require a combination of special technical knowledge, and management know how, to enhance knowledge or transform organizational performance and also keep any intellectual property developed confidential. Engineering management consulting is concerned with the development, improvement, implementation and evaluation of integrated systems of organizations, people, money, knowledge, information, equipment, energy, materials and/or processes. Management Engineering Consultants strive to improve upon existing organizations, processes, products or systems. Engineering management consulting draws upon the principles and methods of engineering analysis and synthesis, as well as the mathematical, physical and social sciences together with the principles and methods of engineering design to specify, predict, and evaluate the results to be obtained from such systems or processes. Engineering management consulting can focus on the social impact of the product, process or system that is being analyzed. There is also an overlap between engineering management consulting and management science in services that require the adoption of more analytical approaches to problem solving. Examples of where engineering management consulting might be used include developing and leading a company wide business transformation initiative, or designing and implementing a new product development process, designing and implementing a manufacturing engineering process, including an automated assembly workstation. Management engineers may specialize in the acquisition and implementation of computer aided design (CAD), computer-aided manufacturing (CAM) and computer-aided engineering (CAE) applications. Services may include strategizing for various operational logistics, new product introductions, or consulting as an efficiency expert. It may include using management science techniques to develop a new financial algorithm or loan system for a bank, streamlining operation and emergency room location or usage in a hospital, planning complex distribution schemes for materials or products (referred to as supply chain management), and shortening lines (or queues) at a bank, hospital, or a theme park. Management engineering consultants typically use computer simulation (especially discrete event simulation), along with extensive mathematical tools and modeling and computational methods for system analysis, evaluation, and optimization. == Professional organizations == There are a number of societies and organizations dedicated to the field of engineering management. One of the largest societies is a division of IEEE, the Engineering Management Society, which regularly publishes a trade magazine. Another prominent professional organization in the field is the American Society for Engineering Management (ASEM), which was founded in 1979 by a group of 20 engineering managers from industry. ASEM currently certifies engineering managers (two levels) via the Certified Associate in Engineering Management (CAEM) or Certified Professional in Engineering Management (CPEM) certification exam. The Master of Engineering Management Programs Consortium is a consortium of nine universities intended to raise the value and visibility of the MEM degree. Also, engineering management graduate programs have the possibility of being accredited by ABET, ATMAE, or ASEM. In Canada, the Canadian Society for Engineering Management (CSEM) is a constituent society of the Engineering Institute of Canada (EIC), Canada's oldest learned engineering society. == See also == Business engineering Business manager Construction management Engineering information management Engineering law Enterprise engineering Industrial engineering List of engineering topics List of management topics Remote laboratory Systems engineering Associations American Society for Engineering Management (ASEM) INFORMS == References == == Further reading == Eric T-S. Pan|Pan, Eric T-S. Perpetual Business Machines: Principles of Success for Technical Professionals ISBN 0-9754480-0-5 == External links == American Society for Engineering Management (ASEM) Engineering Management Review - A Publication of the IEEE IEEE Transactions on Engineering Management Journal EngineeringDone All about Engineering ASEM International Annual Conference (IAC) Canadian Society for Engineering Management, CSEM Associations Society of engineering and management systems Institute of Industrial and Systems Engineers
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Clinical engineering is a specialty within biomedical engineering responsible for using medical technology to optimize healthcare delivery. Clinical engineers train and supervise biomedical equipment technicians (BMETs), working with governmental regulators on hospital inspections and audits, and serve as technological consultants for other hospital staff (i.e., Physicians, Administrators, IT). Clinical engineers also assist manufacturers in improving the design of medical equipment and maintain state-of-the-art hospital supply chains. With training in both product design and point-of-use experience, clinical engineers bridge the gap between product developers and end-users. The focus on practical implementations tends to keep clinical engineers oriented towards incremental redesigns, as opposed to revolutionary or cutting-edge ideas far-off of implementation for clinical use. However, there is an effort to expand this time horizon, over which clinical engineers can influence the trajectory of biomedical innovation. Clinical engineering departments at large hospitals will sometimes hire not only biomedical engineers, but also industrial and systems engineers to address topics such as operations research, human factors, cost analysis, and safety. == History == The term clinical engineering was first used in a 1969 paper by Landoll and Caceres. Caceres, a cardiologist, is generally credited with coining the term. The broader field of biomedical engineering also has a relatively recent history, with the first inter-society engineering meeting focused on engineering in medicine probably held in 1948. However, the general notion of applying engineering to medicine can be traced back to centuries. For example, Stephen Hales' work in the early 18th century, which led to the invention of the ventilator and the discovery of blood pressure, involved applying engineering techniques to medicine. In the early 1970s, clinical engineering was thought to require many new professionals. Estimates of the time for the US ranged as high as 5,000 to 8,000 clinical engineers, or 1 per 250 hospital beds. === Credentialization === The International Certification Commission for Clinical Engineers (ICC) was formed under the sponsorship of the Association for the Advancement of Medical Instrumentation (AAMI) in the early 1970s to provide a formal certification process for clinical engineers. A similar certification program was formed by academic institutions offering graduate degrees in clinical engineering as the American Board of Clinical Engineering (ABCE). In 1979, the ABCE dissolved, and those certified under its program were accepted into the ICC certification program. By 1985, only 350 clinical engineers had become certified. After a 1998 survey demonstrating no viable market for its certification program, the AAMI ceased accepting new applicants in July 1999. The new, current clinical engineering certification (CCE) started in 2002 under the sponsorship of the American College of Clinical Engineering (ACCE) and is administered by the ACCE Healthcare Technology Foundation. In 2004, the first year the certification process was underway, 112 individuals were granted certification based upon their previous ICC certification, and three individuals were awarded the new certification. By the time of the 2006-2007 AHTF Annual Report (c. June 30, 2007), 147 individuals had become HTF certified clinical engineers. == Definition and terminology == A clinical engineer was defined by the ACCE in 1991 as "a professional who supports and advances patient care by applying engineering and managerial skills to healthcare technology." Clinical engineering is also recognized by the Biomedical Engineering Society, the major professional organization for biomedical engineering, as being a branch within the field of biomedical engineering. There are at least two issues with the ACCE definition that often cause confusion. First, it is unclear how "clinical engineer" is a subset of "biomedical engineer". The terms are often used interchangeably: some hospitals refer to their relevant departments as "Clinical Engineering" departments, while others call them "Biomedical Engineering" departments. The technicians are almost universally referred to as "biomedical equipment technicians," regardless of the department they work under. However, the term biomedical engineer is generally thought to be more all-encompassing, as it includes engineers who design medical devices for manufacturers, or in academia. In contrast, clinical engineers generally work in hospitals solving problems close to where the equipment is actually used. Clinical engineers in some countries, such as India, are trained to innovate and find technological solutions for clinical needs. The other issue, not evident from the ACCE definition, is the appropriate educational background for a clinical engineer. Generally, certification programs expect applicants to hold an accredited bachelor's degree in engineering (or at least engineering technology). === Potential new name === In 2011, AAMI arranged a meeting to discuss a new name for clinical engineering. After careful debate, the vast majority decided on "Healthcare Technology Management". Due to confusion about the dividing line between clinical engineers (engineers) and BMETs (technicians), the word engineering was deemed limiting from the administrator's perspective and unworkable from the educator's perspective. An ABET-accredited college could not name an associate degree program "engineering". Also, the adjective, clinical, limited the scope of the field to hospitals. It remains unresolved how widely accepted this change will be, how this will affect the Clinical Engineering Certification or the formal recognition of clinical engineering as a subset of biomedical engineering. For regulatory and licensure reasons, true engineering specialties must be defined in a way that distinguishes them from the technicians they work alongside. == Certification == Certification in clinical engineering is governed by the Board of Examiners for Clinical Engineering Certification. To be eligible, a candidate must hold appropriate credentials (such as an accredited engineering or engineering-technology degree), have specific and relevant experience, and pass an examination. The certification process involves a three-hour written examination of up to 150 multiple-choice questions and a separate oral exam. Weight is given to applicants who are already licensed and registered Professional Engineers, which has extensive requirements itself. In Canada, the term 'engineer' is protected by law. As a result, a candidate must be registered as a Professional Engineer (P.Eng.) before they can become a Certified Clinical Engineer. == In the UK == Clinical engineers in the UK typically work within the NHS. Clinical engineering is a modality of the clinical scientist profession, registered by the HCPC. The responsibilities of clinical engineers are varied and often include providing specialist clinical services, inventing and developing medical devices, and medical device management. The roles typically involve both patient contact and academic research. Clinical engineering units within an NHS organization are often part of a larger medical physics department. Clinical engineers are supported and represented by the Institute of Physics and Engineering in Medicine, within which the clinical engineering special interest group oversees the engineering activities. The three primary aims of Clinical Engineering with the NHS are: To ensure medical equipment in the clinical environment is available and appropriate to the needs of the clinical service. To ensure medical equipment functions effectively and safely. To ensure medical equipment and its management represents value for patient benefit. === Registration === Clinical engineers are registered with the HCPC, or the RCT (Register of Clinical Technologist). Assessments prior to registration are provided by the National School of Healthcare Science, the Association of Clinical Scientists or the AHCS. There are two HCPC programs for becoming a clinical scientist. The first is a Certificate of Attainment, awarded for completing the NHS Scientist Training Programme (STP). The second is the Certificate of Equivalence, awarded on successful demonstration of equivalence to the STP. This route is normally chosen by individuals that have significant scientific experience prior to seeking registration. Both are provided by the AHCS. === Electronics and Biomedical Engineering === EBME technicians and engineers in the UK work in the NHS and private sector. They are part of the Clinical Engineering familiar in the UK. Their role is to manage and maintain medical equipment assets in NHS and private healthcare organizations. They are professionally registered with the Engineering Council as Chartered Engineers, Incorporated Engineers, or engineering technicians. The EBME community share their knowledge on the EBME Forums. There is also an annual 2-day National Exhibition and Conference, wherein engineers meet to learn about the latest medical products and to attend the 500-seat conference where academic and business leaders share their expertise. The conference was founded in 2009 as a way of improving healthcare through sharing knowledge from experienced professionals involved in medical equipment management. == In India == Healthcare has increasingly become technology-driven and requires trained manpower to keep pace with the growing demand for professionals in the field. An M-Tech Clinical Engineering course was initiated by Indian Institute of Technology Madras, Sree Chitra Thirunal Institute of Medical Sciences and Technology, Trivandrum and Christian Medical College, Vellore, to address the country's need for human resource development. This was aimed at indigenous biomedical device development as well as technology management in order to contribute to the overall development of healthcare delivery in the country. During the course, students of engineering are given an insight into biology, medicine, relevant electronic background, clinical practices, device development, and even management aspects. Students are paired with clinical doctors from CMC and SCTIMST to get hands-on experience during internships. An important aspect of this training is simultaneous, long-term, and detailed exposure to the clinical environment as well as to medical device development activity. This will help students understand how to recognize unmet clinical needs and contribute to the creation of future medical devices. Engineers will be trained to handle and oversee the safe and effective use of technology in healthcare delivery sites as part of the program. The minimum qualification for joining this course is a bachelor's degree in any discipline of engineering, technology, or architecture, and a valid GATE score with an interview process in that field. == See also == Biomedical engineering == References == == Further reading == Villafane, Carlos, CBET. (June 2009). Biomed: From the Student's Perspective, First Edition. [Techniciansfriend.com]. ISBN 978-1-61539-663-4.{{cite book}}: CS1 maint: multiple names: authors list (link) Medical engineering stories in the news School of Engineering and Materials Science, Queen Mary University of London == External links == EBME website EBME website for Medical, Biomedical, and Clinical engineering professionals.
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In geotechnical engineering, a caisson (; borrowed from French caisson 'box', from Italian cassone 'large box', an augmentative of cassa) is a watertight retaining structure. It is used, for example, to work on the foundations of a bridge pier, for the construction of a concrete dam, or for the repair of ships. Caissons are constructed in such a way that the water can be pumped out, keeping the work environment dry. When piers are being built using an open caisson, and it is not practical to reach suitable soil, friction pilings may be driven to form a suitable sub-foundation. These piles are connected by a foundation pad upon which the column pier is erected. Caisson engineering has been used since at least the 19th century, with three prominent examples being the Royal Albert Bridge (completed in 1859), the Eads Bridge (completed in 1874), and the Brooklyn Bridge (completed in 1883). == Types == To install a caisson in place, it is brought down through soft mud until a suitable foundation material is encountered. While bedrock is preferred, a stable, hard mud is sometimes used when bedrock is too deep. The four main types of caisson are box caisson, open caisson, pneumatic caisson and monolithic caisson. === Box === A box caisson is a prefabricated box (with sides and a bottom); where required it is set down on a prepared base. Once in place, it is filled with ballast to become part of the works, such as the foundation for a bridge pier. Hollow concrete structures are generally less dense than water so a box caisson must be secured to prevent it from moving offsite until it can be filled with ballast. Sometimes elaborate anchoring systems may be required, such as in tidal zones. Adjustable anchoring systems combined with a GPS survey enable engineers to position a box caisson with pinpoint accuracy. === Open === An open caisson is similar to a box caisson, except that it does not have a bottom face. It is suitable for use in soft clays (e.g. in some river-beds), but not for where there may be large obstructions in the ground. An open caisson that is used in soft grounds or high water tables, where open trench excavations are impractical, can also be used to install deep manholes, pump stations and reception/launch pits for microtunnelling, pipe jacking and other operations. A caisson is sunk by self-weight, concrete or water ballast placed on top, or by hydraulic jacks. The leading edge (or cutting shoe) of the caisson is sloped out at a sharp angle to aid sinking in a vertical manner; it is usually made of steel. The shoe is generally wider than the caisson to reduce friction, and the leading edge may be supplied with pressurised bentonite slurry, which swells in water, stabilizing settlement by filling depressions and voids. An open caisson may fill with water during sinking. The material is excavated by clamshell excavator bucket on crane. The formation level subsoil may still not be suitable for excavation or bearing capacity. The water in the caisson (due to a high water table) balances the upthrust forces of the soft soils underneath. If dewatered, the base may "pipe" or "boil", causing the caisson to sink. To combat this problem, piles may be driven from the surface to act as: Load-bearing walls, in that they transmit loads to deeper soils. Anchors, in that they resist flotation because of the friction at the interface between their surfaces and the surrounding earth into which they have been driven. H-beam sections (typical column sections, due to resistance to bending in all axis) may be driven at angles "raked" to rock or other firmer soils; the H-beams are left extended above the base. A reinforced concrete plug may be placed under the water, a process known as tremie concrete placement. When the caisson is dewatered, this plug acts as a pile cap, resisting the upward forces of the subsoil. === Monolithic === A monolithic caisson (or simply a monolith) is larger than the other types of caisson, but similar to open caissons. Such caissons are often found in quay walls, where resistance to impact from ships is required. === Pneumatic === Shallow caissons may be open to the air, whereas pneumatic caissons (sometimes called pressurized caissons), which penetrate soft mud, are bottomless boxes sealed at the top and filled with compressed air to keep water and mud out at depth. An airlock allows access to the chamber. Workers, called sandhogs in American English, move mud and rock debris (called muck) from the edge of the workspace to a water-filled pit, connected by a tube (called the muck tube) to the surface. A crane at the surface removes the soil with a clamshell bucket. The water pressure in the tube balances the air pressure, with excess air escaping up the muck tube. The pressurized air flow must be constant to ensure regular air changes for the workers and prevent excessive inflow of mud or water at the base of the caisson. When the caisson hits bedrock, the sandhogs exit through the airlock and fill the box with concrete, forming a solid foundation pier. A pneumatic (compressed-air) caisson has the advantage of providing dry working conditions, which is better for placing concrete. It is also well suited for foundations for which other methods might cause settlement of adjacent structures. Construction workers who leave the pressurized environment of the caisson must decompress at a rate that allows symptom-free release of inert gases dissolved in the body tissues if they are to avoid decompression sickness, a condition first identified in caisson workers, and originally named "caisson disease" in recognition of the occupational hazard. Construction of the Brooklyn Bridge, which was built with the help of pressurised caissons, resulted in numerous workers being either killed or permanently injured by caisson disease during its construction. Barotrauma of the ears, sinus cavities and lungs and dysbaric osteonecrosis are other risks. == Other uses == Caissons have also been used in the installation of hydraulic elevators where a single-stage ram is installed below the ground level. Caissons, codenamed Phoenix, were an integral part of the Mulberry harbours used during the World War II Allied invasion of Normandy. == Other meanings == Boat lift caissons: The word caisson is also used as a synonym for the moving trough part of caisson locks, canal lifts and inclines in which boats and ships rest while being lifted from one canal elevation to another; the water is retained on the inside of the caisson, or excluded from the caisson, according to the respective operating principle. Structural caissons: Caisson is also sometimes used as a colloquial term for a reinforced concrete structure formed by pouring into a hollow cylindrical form, typically by placing a caisson form below grade in an open excavation and pouring once backfill is complete, or by drilling at grade, although this can be problematic with deep caissons, as unsupported excavations can collapse before the caisson form can be inserted. In this manner, the earth placed around the empty caisson form provides stability and strength, allowing concrete to be poured with fewer complications and with less risk of a form blowout. While, technically, only the form itself is actually a caisson, it is not uncommon for any below-grade cast concrete pillar to be referred to as, simply, a caisson. Ventilation filtration systems: The word caisson is also used as a name for an airtight housing for ventilation filters in facilities that handle hazardous materials. The housing usually has an upstream compartment for a pre-filter element and a downstream compartment for a high-efficiency filter element. It may have multiple sets of compartments. The housing has gasketed access doors to allow for the change out of the filter elements. The housing is usually equipped with connection points used to test the efficiency of the filters and monitor changes in the differential pressure across the filter media. == See also == Suction caisson – Open bottomed tube anchor embedded and released by pressure differential Air lock diving-bell plant – Underwater work support barge used at Gibraltar, a mobile barge-mounted engineering caisson used in the Port of Gibraltar Cofferdam – Barrier allowing liquid to be pumped out of an enclosed area, a temporary water-excluding structure built in place, sometimes surrounding a working area as does an open caisson. Offshore geotechnical engineering – Sub-field of engineering concerned with human-made structures in the sea, for information on geotechnical considerations. == Patents == U.S. patent 123,002 – Improvement in construction of sub-aqueous foundations == References == == External links == Works related to Caisson at Wikisource
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Prompt engineering is the process of structuring or crafting an instruction in order to produce the best possible output from a generative artificial intelligence (AI) model. A prompt is natural language text describing the task that an AI should perform. A prompt for a text-to-text language model can be a query, a command, or a longer statement including context, instructions, and conversation history. Prompt engineering may involve phrasing a query, specifying a style, choice of words and grammar, providing relevant context, or describing a character for the AI to mimic. When communicating with a text-to-image or a text-to-audio model, a typical prompt is a description of a desired output such as "a high-quality photo of an astronaut riding a horse" or "Lo-fi slow BPM electro chill with organic samples". Prompting a text-to-image model may involve adding, removing, or emphasizing words to achieve a desired subject, style, layout, lighting, and aesthetic. == History == In 2018, researchers first proposed that all previously separate tasks in natural language processing (NLP) could be cast as a question-answering problem over a context. In addition, they trained a first single, joint, multi-task model that would answer any task-related question like "What is the sentiment" or "Translate this sentence to German" or "Who is the president?" The AI boom saw an increase in the amount of "prompting technique" to get the model to output the desired outcome and avoid nonsensical output, a process characterized by trial-and-error. After the release of ChatGPT in 2022, prompt engineering was soon seen as an important business skill, albeit one with an uncertain economic future. A repository for prompts reported that over 2,000 public prompts for around 170 datasets were available in February 2022. In 2022, the chain-of-thought prompting technique was proposed by Google researchers. In 2023, several text-to-text and text-to-image prompt databases were made publicly available. The Personalized Image-Prompt (PIP) dataset, a generated image-text dataset that has been categorized by 3,115 users, has also been made available publicly in 2024. == Text-to-text == Multiple distinct prompt engineering techniques have been published. === Chain-of-thought === According to Google Research, chain-of-thought (CoT) prompting is a technique that allows large language models (LLMs) to solve a problem as a series of intermediate steps before giving a final answer. In 2022, Google Brain reported that chain-of-thought prompting improves reasoning ability by inducing the model to answer a multi-step problem with steps of reasoning that mimic a train of thought. Chain-of-thought techniques were developed to help LLMs handle multi-step reasoning tasks, such as arithmetic or commonsense reasoning questions. For example, given the question, "Q: The cafeteria had 23 apples. If they used 20 to make lunch and bought 6 more, how many apples do they have?", Google claims that a CoT prompt might induce the LLM to answer "A: The cafeteria had 23 apples originally. They used 20 to make lunch. So they had 23 - 20 = 3. They bought 6 more apples, so they have 3 + 6 = 9. The answer is 9." When applied to PaLM, a 540 billion parameter language model, according to Google, CoT prompting significantly aided the model, allowing it to perform comparably with task-specific fine-tuned models on several tasks, achieving state-of-the-art results at the time on the GSM8K mathematical reasoning benchmark. It is possible to fine-tune models on CoT reasoning datasets to enhance this capability further and stimulate better interpretability. An example of a CoT prompting: Q: {question} A: Let's think step by step. As originally proposed by Google, each CoT prompt included a few Q&A examples. This made it a few-shot prompting technique. However, according to researchers at Google and the University of Tokyo, simply appending the words "Let's think step-by-step", has also proven effective, which makes CoT a zero-shot prompting technique. OpenAI claims that this prompt allows for better scaling as a user no longer needs to formulate many specific CoT Q&A examples. === In-context learning === In-context learning, refers to a model's ability to temporarily learn from prompts. For example, a prompt may include a few examples for a model to learn from, such as asking the model to complete "maison → house, chat → cat, chien →" (the expected response being dog), an approach called few-shot learning. In-context learning is an emergent ability of large language models. It is an emergent property of model scale, meaning that breaks in downstream scaling laws occur, leading to its efficacy increasing at a different rate in larger models than in smaller models. Unlike training and fine-tuning, which produce lasting changes, in-context learning is temporary. Training models to perform in-context learning can be viewed as a form of meta-learning, or "learning to learn". === Self-consistency decoding === Self-consistency decoding performs several chain-of-thought rollouts, then selects the most commonly reached conclusion out of all the rollouts. === Tree-of-thought === Tree-of-thought prompting generalizes chain-of-thought by generating multiple lines of reasoning in parallel, with the ability to backtrack or explore other paths. It can use tree search algorithms like breadth-first, depth-first, or beam. === Prompting to estimate model sensitivity === Research consistently demonstrates that LLMs are highly sensitive to subtle variations in prompt formatting, structure, and linguistic properties. Some studies have shown up to 76 accuracy points across formatting changes in few-shot settings. Linguistic features significantly influence prompt effectiveness—such as morphology, syntax, and lexico-semantic changes—which meaningfully enhance task performance across a variety of tasks. Clausal syntax, for example, improves consistency and reduces uncertainty in knowledge retrieval. This sensitivity persists even with larger model sizes, additional few-shot examples, or instruction tuning. To address sensitivity of models and make them more robust, several methods have been proposed. FormatSpread facilitates systematic analysis by evaluating a range of plausible prompt formats, offering a more comprehensive performance interval. Similarly, PromptEval estimates performance distributions across diverse prompts, enabling robust metrics such as performance quantiles and accurate evaluations under constrained budgets. === Automatic prompt generation === ==== Retrieval-augmented generation ==== Retrieval-augmented generation (RAG) is a technique that enables generative artificial intelligence (Gen AI) models to retrieve and incorporate new information. It modifies interactions with a large language model (LLM) so that the model responds to user queries with reference to a specified set of documents, using this information to supplement information from its pre-existing training data. This allows LLMs to use domain-specific and/or updated information. RAG improves large language models (LLMs) by incorporating information retrieval before generating responses. Unlike traditional LLMs that rely on static training data, RAG pulls relevant text from databases, uploaded documents, or web sources. According to Ars Technica, "RAG is a way of improving LLM performance, in essence by blending the LLM process with a web search or other document look-up process to help LLMs stick to the facts." This method helps reduce AI hallucinations, which have led to real-world issues like chatbots inventing policies or lawyers citing nonexistent legal cases. By dynamically retrieving information, RAG enables AI to provide more accurate responses without frequent retraining. ==== Graph retrieval-augmented generation ==== GraphRAG (coined by Microsoft Research) is a technique that extends RAG with the use of a knowledge graph (usually, LLM-generated) to allow the model to connect disparate pieces of information, synthesize insights, and holistically understand summarized semantic concepts over large data collections. It was shown to be effective on datasets like the Violent Incident Information from News Articles (VIINA). Earlier work showed the effectiveness of using a knowledge graph for question answering using text-to-query generation. These techniques can be combined to search across both unstructured and structured data, providing expanded context, and improved ranking. ==== Using language models to generate prompts ==== Large language models (LLM) themselves can be used to compose prompts for large language models. The automatic prompt engineer algorithm uses one LLM to beam search over prompts for another LLM: There are two LLMs. One is the target LLM, and another is the prompting LLM. Prompting LLM is presented with example input-output pairs, and asked to generate instructions that could have caused a model following the instructions to generate the outputs, given the inputs. Each of the generated instructions is used to prompt the target LLM, followed by each of the inputs. The log-probabilities of the outputs are computed and added. This is the score of the instruction. The highest-scored instructions are given to the prompting LLM for further variations. Repeat until some stopping criteria is reached, then output the highest-scored instructions. CoT examples can be generated by LLM themselves. In "auto-CoT", a library of questions are converted to vectors by a model such as BERT. The question vectors are clustered. Questions close to the centroid of each cluster are selected, in order to have a subset of diverse questions. An LLM does zero-shot CoT on each selected question. The question and the corresponding CoT answer are added to a dataset of demonstrations. These diverse demonstrations can then added to prompts for few-shot learning. == Text-to-image == In 2022, text-to-image models like DALL-E 2, Stable Diffusion, and Midjourney were released to the public. These models take text prompts as input and use them to generate images. === Prompt formats === Early text-to-image models typically don't understand negation, grammar and sentence structure in the same way as large language models, and may thus require a different set of prompting techniques. The prompt "a party with no cake" may produce an image including a cake. As an alternative, negative prompts allow a user to indicate, in a separate prompt, which terms should not appear in the resulting image. Techniques such as framing the normal prompt into a sequence-to-sequence language modeling problem can be used to automatically generate an output for the negative prompt. A text-to-image prompt commonly includes a description of the subject of the art, the desired medium (such as digital painting or photography), style (such as hyperrealistic or pop-art), lighting (such as rim lighting or crepuscular rays), color, and texture. Word order also affects the output of a text-to-image prompt. Words closer to the start of a prompt may be emphasized more heavily. The Midjourney documentation encourages short, descriptive prompts: instead of "Show me a picture of lots of blooming California poppies, make them bright, vibrant orange, and draw them in an illustrated style with colored pencils", an effective prompt might be "Bright orange California poppies drawn with colored pencils". === Artist styles === Some text-to-image models are capable of imitating the style of particular artists by name. For example, the phrase in the style of Greg Rutkowski has been used in Stable Diffusion and Midjourney prompts to generate images in the distinctive style of Polish digital artist Greg Rutkowski. Famous artists such as Vincent van Gogh and Salvador Dalí have also been used for styling and testing. == Non-text prompts == Some approaches augment or replace natural language text prompts with non-text input. === Textual inversion and embeddings === For text-to-image models, textual inversion performs an optimization process to create a new word embedding based on a set of example images. This embedding vector acts as a "pseudo-word" which can be included in a prompt to express the content or style of the examples. === Image prompting === In 2023, Meta's AI research released Segment Anything, a computer vision model that can perform image segmentation by prompting. As an alternative to text prompts, Segment Anything can accept bounding boxes, segmentation masks, and foreground/background points. === Using gradient descent to search for prompts === In "prefix-tuning", "prompt tuning", or "soft prompting", floating-point-valued vectors are searched directly by gradient descent to maximize the log-likelihood on outputs. Formally, let E = { e 1 , … , e k } {\displaystyle \mathbf {E} =\{\mathbf {e_{1}} ,\dots ,\mathbf {e_{k}} \}} be a set of soft prompt tokens (tunable embeddings), while X = { x 1 , … , x m } {\displaystyle \mathbf {X} =\{\mathbf {x_{1}} ,\dots ,\mathbf {x_{m}} \}} and Y = { y 1 , … , y n } {\displaystyle \mathbf {Y} =\{\mathbf {y_{1}} ,\dots ,\mathbf {y_{n}} \}} be the token embeddings of the input and output respectively. During training, the tunable embeddings, input, and output tokens are concatenated into a single sequence concat ( E ; X ; Y ) {\displaystyle {\text{concat}}(\mathbf {E} ;\mathbf {X} ;\mathbf {Y} )} , and fed to the LLMs. The losses are computed over the Y {\displaystyle \mathbf {Y} } tokens; the gradients are backpropagated to prompt-specific parameters: in prefix-tuning, they are parameters associated with the prompt tokens at each layer; in prompt tuning, they are merely the soft tokens added to the vocabulary. More formally, this is prompt tuning. Let an LLM be written as L L M ( X ) = F ( E ( X ) ) {\displaystyle LLM(X)=F(E(X))} , where X {\displaystyle X} is a sequence of linguistic tokens, E {\displaystyle E} is the token-to-vector function, and F {\displaystyle F} is the rest of the model. In prefix-tuning, one provides a set of input-output pairs { ( X i , Y i ) } i {\displaystyle \{(X^{i},Y^{i})\}_{i}} , and then use gradient descent to search for arg max Z ~ ∑ i log P r [ Y i | Z ~ ∗ E ( X i ) ] {\displaystyle \arg \max _{\tilde {Z}}\sum _{i}\log Pr[Y^{i}|{\tilde {Z}}\ast E(X^{i})]} . In words, log P r [ Y i | Z ~ ∗ E ( X i ) ] {\displaystyle \log Pr[Y^{i}|{\tilde {Z}}\ast E(X^{i})]} is the log-likelihood of outputting Y i {\displaystyle Y^{i}} , if the model first encodes the input X i {\displaystyle X^{i}} into the vector E ( X i ) {\displaystyle E(X^{i})} , then prepend the vector with the "prefix vector" Z ~ {\displaystyle {\tilde {Z}}} , then apply F {\displaystyle F} . For prefix tuning, it is similar, but the "prefix vector" Z ~ {\displaystyle {\tilde {Z}}} is pre-appended to the hidden states in every layer of the model. An earlier result uses the same idea of gradient descent search, but is designed for masked language models like BERT, and searches only over token sequences, rather than numerical vectors. Formally, it searches for arg max X ~ ∑ i log P r [ Y i | X ~ ∗ X i ] {\displaystyle \arg \max _{\tilde {X}}\sum _{i}\log Pr[Y^{i}|{\tilde {X}}\ast X^{i}]} where X ~ {\displaystyle {\tilde {X}}} is ranges over token sequences of a specified length. == Limitations == While the process of writing and refining a prompt for an LLM or generative AI shares some parallels with an iterative engineering design process, such as through discovering 'best principles' to reuse and discovery through reproducible experimentation, the actual learned principles and skills depend heavily on the specific model being learned rather than being generalizable across the entire field of prompt-based generative models. Such patterns are also volatile and exhibit significantly different results from seemingly insignificant prompt changes. According to The Wall Street Journal in 2025, the job of prompt engineer was one of the hottest in 2023, but has become obsolete due to models that better intuit user intent and to company trainings. == Prompt injection == Prompt injection is a cybersecurity exploit in which adversaries craft inputs that appear legitimate but are designed to cause unintended behavior in machine learning models, particularly large language models (LLMs). This attack takes advantage of the model's inability to distinguish between developer-defined prompts and user inputs, allowing adversaries to bypass safeguards and influence model behaviour. While LLMs are designed to follow trusted instructions, they can be manipulated into carrying out unintended responses through carefully crafted inputs. == References ==
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https://en.wikipedia.org/wiki/Prompt_engineering
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Railway engineering is a multi-faceted engineering discipline dealing with the design, construction and operation of all types of rail transport systems. It encompasses a wide range of engineering disciplines, including civil engineering, computer engineering, electrical engineering, mechanical engineering, industrial engineering and production engineering. A great many other engineering sub-disciplines are also called upon. == History == With the advent of the railways in the early nineteenth century, a need arose for a specialized group of engineers capable of dealing with the unique problems associated with railway engineering. As the railways expanded and became a major economic force, a great many engineers became involved in the field, probably the most notable in Britain being Richard Trevithick, George Stephenson and Isambard Kingdom Brunel. Today, railway systems engineering continues to be a vibrant field of engineering. == Subfields == Mechanical engineering Command, control & railway signalling Office systems design Data center design SCADA Network design Electrical engineering Energy electrification Third rail Fourth rail Overhead contact system Civil engineering Permanent way engineering Light rail systems On-track plant Rail systems integration Train control systems Cab signalling Railway vehicle engineering Rolling resistance Curve resistance Wheel–rail interface Hunting oscillation Railway systems engineering Railway signalling Fare collection CCTV Public address Intrusion detection Access control Systems integration == Professional organisations == In the UK: The Railway Division of the Institution of Mechanical Engineers (IMechE). In the US: The American Railway Engineering and Maintenance-of-Way Association (AREMA) In the Philippines: Philippine Railway Engineers' Association, (PREA) Inc. Worldwide: The Institute of Railway Signal Engineers (IRSE) == See also == == External links == Institution of Mechanical Engineers - Railway Division AAR == References ==
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https://en.wikipedia.org/wiki/Railway_engineering
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Algorithm engineering focuses on the design, analysis, implementation, optimization, profiling and experimental evaluation of computer algorithms, bridging the gap between algorithmics theory and practical applications of algorithms in software engineering. It is a general methodology for algorithmic research. == Origins == In 1995, a report from an NSF-sponsored workshop "with the purpose of assessing the current goals and directions of the Theory of Computing (TOC) community" identified the slow speed of adoption of theoretical insights by practitioners as an important issue and suggested measures to reduce the uncertainty by practitioners whether a certain theoretical breakthrough will translate into practical gains in their field of work, and tackle the lack of ready-to-use algorithm libraries, which provide stable, bug-free and well-tested implementations for algorithmic problems and expose an easy-to-use interface for library consumers. But also, promising algorithmic approaches have been neglected due to difficulties in mathematical analysis. The term "algorithm engineering" was first used with specificity in 1997, with the first Workshop on Algorithm Engineering (WAE97), organized by Giuseppe F. Italiano. == Difference from algorithm theory == Algorithm engineering does not intend to replace or compete with algorithm theory, but tries to enrich, refine and reinforce its formal approaches with experimental algorithmics (also called empirical algorithmics). This way it can provide new insights into the efficiency and performance of algorithms in cases where the algorithm at hand is less amenable to algorithm theoretic analysis, formal analysis pessimistically suggests bounds which are unlikely to appear on inputs of practical interest, the algorithm relies on the intricacies of modern hardware architectures like data locality, branch prediction, instruction stalls, instruction latencies which the machine model used in Algorithm Theory is unable to capture in the required detail, the crossover between competing algorithms with different constant costs and asymptotic behaviors needs to be determined. == Methodology == Some researchers describe algorithm engineering's methodology as a cycle consisting of algorithm design, analysis, implementation and experimental evaluation, joined by further aspects like machine models or realistic inputs. They argue that equating algorithm engineering with experimental algorithmics is too limited, because viewing design and analysis, implementation and experimentation as separate activities ignores the crucial feedback loop between those elements of algorithm engineering. === Realistic models and real inputs === While specific applications are outside the methodology of algorithm engineering, they play an important role in shaping realistic models of the problem and the underlying machine, and supply real inputs and other design parameters for experiments. === Design === Compared to algorithm theory, which usually focuses on the asymptotic behavior of algorithms, algorithm engineers need to keep further requirements in mind: Simplicity of the algorithm, implementability in programming languages on real hardware, and allowing code reuse. Additionally, constant factors of algorithms have such a considerable impact on real-world inputs that sometimes an algorithm with worse asymptotic behavior performs better in practice due to lower constant factors. === Analysis === Some problems can be solved with heuristics and randomized algorithms in a simpler and more efficient fashion than with deterministic algorithms. Unfortunately, this makes even simple randomized algorithms difficult to analyze because there are subtle dependencies to be taken into account. === Implementation === Huge semantic gaps between theoretical insights, formulated algorithms, programming languages and hardware pose a challenge to efficient implementations of even simple algorithms, because small implementation details can have rippling effects on execution behavior. The only reliable way to compare several implementations of an algorithm is to spend an considerable amount of time on tuning and profiling, running those algorithms on multiple architectures, and looking at the generated machine code. === Experiments === See: Experimental algorithmics === Application engineering === Implementations of algorithms used for experiments differ in significant ways from code usable in applications. While the former prioritizes fast prototyping, performance and instrumentation for measurements during experiments, the latter requires thorough testing, maintainability, simplicity, and tuning for particular classes of inputs. === Algorithm libraries === Stable, well-tested algorithm libraries like LEDA play an important role in technology transfer by speeding up the adoption of new algorithms in applications. Such libraries reduce the required investment and risk for practitioners, because it removes the burden of understanding and implementing the results of academic research. == Conferences == Two main conferences on Algorithm Engineering are organized annually, namely: Symposium on Experimental Algorithms (SEA), established in 1997 (formerly known as WEA). SIAM Meeting on Algorithm Engineering and Experiments (ALENEX), established in 1999. The 1997 Workshop on Algorithm Engineering (WAE'97) was held in Venice (Italy) on September 11–13, 1997. The Third International Workshop on Algorithm Engineering (WAE'99) was held in London, UK in July 1999. The first Workshop on Algorithm Engineering and Experimentation (ALENEX99) was held in Baltimore, Maryland on January 15–16, 1999. It was sponsored by DIMACS, the Center for Discrete Mathematics and Theoretical Computer Science (at Rutgers University), with additional support from SIGACT, the ACM Special Interest Group on Algorithms and Computation Theory, and SIAM, the Society for Industrial and Applied Mathematics. == References ==
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https://en.wikipedia.org/wiki/Algorithm_engineering
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Porsche Engineering (Porsche Engineering Group GmbH) was established in 2001 as a wholly owned subsidiary of Porsche AG, with headquarters in Weissach, and traces its history back to 1931 when Porsche created its first engineering office subsidiary. Porsche Engineering Group has been re-organized into Porsche Consulting (subsidiary of Porsche AG) and Porsche Engineering (subsidiary of Porsche SE). Porsche Engineering has offered consultancy services to various other car manufacturers for many years including Audi, Mercedes-Benz, Opel, Studebaker, Lada, SEAT, and Zastava Automobiles. Since 2012 the company has managed the former FIAT owned Nardò Ring in Italy. == Notable non-Porsche products == Torsion bar suspension developed by Porsche, was patented in 1931 Lada Niva (VAZ-2121) engineered with help of Porsche (circa 1975) Lada Samara was partly developed by Porsche in 1984 SEAT Ibiza engine in 1984 Harley-Davidson Revolution 60-degree v-twin water-cooled engine and gearbox that is used in their V-Rod motorcycle Audi RS2 1993 C88 a prototype family car designed in 1994 by Porsche for the Chinese government Opel Zafira complete vehicle development resulting in the Zafira A launched in 1998 Second-gen Scania PRT - PE designed for Scania a completely new cab for its PRT, along with other parts. Kortezh engine Note: Mercedes-Benz OM602 engine was designed by Ferdinand Piëch after he left Porsche. == References == == External links == Official website
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https://en.wikipedia.org/wiki/Porsche_Engineering
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In engineering and systems theory, redundancy is the intentional duplication of critical components or functions of a system with the goal of increasing reliability of the system, usually in the form of a backup or fail-safe, or to improve actual system performance, such as in the case of GNSS receivers, or multi-threaded computer processing. In many safety-critical systems, such as fly-by-wire and hydraulic systems in aircraft, some parts of the control system may be triplicated, which is formally termed triple modular redundancy (TMR). An error in one component may then be out-voted by the other two. In a triply redundant system, the system has three sub components, all three of which must fail before the system fails. Since each one rarely fails, and the sub components are designed to preclude common failure modes (which can then be modelled as independent failure), the probability of all three failing is calculated to be extraordinarily small; it is often outweighed by other risk factors, such as human error. Electrical surges arising from lightning strikes are an example of a failure mode which is difficult to fully isolate, unless the components are powered from independent power busses and have no direct electrical pathway in their interconnect (communication by some means is required for voting). Redundancy may also be known by the terms "majority voting systems" or "voting logic". Redundancy sometimes produces less, instead of greater reliability – it creates a more complex system which is prone to various issues, it may lead to human neglect of duty, and may lead to higher production demands which by overstressing the system may make it less safe. Redundancy is one form of robustness as practiced in computer science. Geographic redundancy has become important in the data center industry, to safeguard data against natural disasters and political instability (see below). == Forms of redundancy == In computer science, there are four major forms of redundancy: Hardware redundancy, such as dual modular redundancy and triple modular redundancy Information redundancy, such as error detection and correction methods Time redundancy, performing the same operation multiple times such as multiple executions of a program or multiple copies of data transmitted Software redundancy such as N-version programming A modified form of software redundancy, applied to hardware may be: Distinct functional redundancy, such as both mechanical and hydraulic braking in a car. Applied in the case of software, code written independently and distinctly different but producing the same results for the same inputs. Structures are usually designed with redundant parts as well, ensuring that if one part fails, the entire structure will not collapse. A structure without redundancy is called fracture-critical, meaning that a single broken component can cause the collapse of the entire structure. Bridges that failed due to lack of redundancy include the Silver Bridge and the Interstate 5 bridge over the Skagit River. Parallel and combined systems demonstrate different level of redundancy. The models are subject of studies in reliability and safety engineering. === Dissimilar redundancy === Unlike traditional redundancy, which uses more than one of the same thing, dissimilar redundancy uses different things. The idea is that the different things are unlikely to contain identical flaws. The voting method may involve additional complexity if the two things take different amounts of time. Dissimilar redundancy is often used with software, because identical software contains identical flaws. The chance of failure is reduced by using at least two different types of each of the following processors, operating systems, software, sensors, types of actuators (electric, hydraulic, pneumatic, manual mechanical, etc.) communications protocols, communications hardware, communications networks, communications paths === Geographic redundancy === Geographic redundancy corrects the vulnerabilities of redundant devices deployed by geographically separating backup devices. Geographic redundancy reduces the likelihood of events such as power outages, floods, HVAC failures, lightning strikes, tornadoes, building fires, wildfires, and mass shootings disabling most of the system if not the entirety of it. Geographic redundancy locations can be more than 621 miles (999 km) continental, more than 62 miles apart and less than 93 miles (150 km) apart, less than 62 miles apart, but not on the same campus, or different buildings that are more than 300 feet (91 m) apart on the same campus. The following methods can reduce the risks of damage by a fire conflagration: large buildings at least 80 feet (24 m) to 110 feet (34 m) apart, but sometimes a minimum of 210 feet (64 m) apart.: 9 high-rise buildings at least 82 feet (25 m) apart: 12 open spaces clear of flammable vegetation within 200 feet (61 m) on each side of objects different wings on the same building, in rooms that are separated by more than 300 feet (91 m) different floors on the same wing of a building in rooms that are horizontally offset by a minimum of 70 feet (21 m) with fire walls between the rooms that are on different floors two rooms separated by another room, leaving at least a 70-foot gap between the two rooms there should be a minimum of two separated fire walls and on opposite sides of a corridor Geographic redundancy is used by Amazon Web Services (AWS), Google Cloud Platform (GCP), Microsoft Azure, Netflix, Dropbox, Salesforce, LinkedIn, PayPal, Twitter, Facebook, Apple iCloud, Cisco Meraki, and many others to provide geographic redundancy, high availability, fault tolerance and to ensure availability and reliability for their cloud services. As another example, to minimize risk of damage from severe windstorms or water damage, buildings can be located at least 2 miles (3.2 km) away from the shore, with an elevation of at least 5 feet (1.5 m) above sea level. For additional protection, they can be located at least 100 feet (30 m) away from flood plain areas. == Functions of redundancy == The two functions of redundancy are passive redundancy and active redundancy. Both functions prevent performance decline from exceeding specification limits without human intervention using extra capacity. Passive redundancy uses excess capacity to reduce the impact of component failures. One common form of passive redundancy is the extra strength of cabling and struts used in bridges. This extra strength allows some structural components to fail without bridge collapse. The extra strength used in the design is called the margin of safety. Eyes and ears provide working examples of passive redundancy. Vision loss in one eye does not cause blindness but depth perception is impaired. Hearing loss in one ear does not cause deafness but directionality is lost. Performance decline is commonly associated with passive redundancy when a limited number of failures occur. Active redundancy eliminates performance declines by monitoring the performance of individual devices, and this monitoring is used in voting logic. The voting logic is linked to switching that automatically reconfigures the components. Error detection and correction and the Global Positioning System (GPS) are two examples of active redundancy. Electrical power distribution provides an example of active redundancy. Several power lines connect each generation facility with customers. Each power line includes monitors that detect overload. Each power line also includes circuit breakers. The combination of power lines provides excess capacity. Circuit breakers disconnect a power line when monitors detect an overload. Power is redistributed across the remaining lines. At the Toronto Airport, there are 4 redundant electrical lines. Each of the 4 lines supply enough power for the entire airport. A spot network substation uses reverse current relays to open breakers to lines that fail, but lets power continue to flow the airport. Electrical power systems use power scheduling to reconfigure active redundancy. Computing systems adjust the production output of each generating facility when other generating facilities are suddenly lost. This prevents blackout conditions during major events such as an earthquake. == Disadvantages == Charles Perrow, author of Normal Accidents, has said that sometimes redundancies backfire and produce less, not more reliability. This may happen in three ways: First, redundant safety devices result in a more complex system, more prone to errors and accidents. Second, redundancy may lead to shirking of responsibility among workers. Third, redundancy may lead to increased production pressures, resulting in a system that operates at higher speeds, but less safely. == Voting logic == Voting logic uses performance monitoring to determine how to reconfigure individual components so that operation continues without violating specification limitations of the overall system. Voting logic often involves computers, but systems composed of items other than computers may be reconfigured using voting logic. Circuit breakers are an example of a form of non-computer voting logic. The simplest voting logic in computing systems involves two components: primary and alternate. They both run similar software, but the output from the alternate remains inactive during normal operation. The primary monitors itself and periodically sends an activity message to the alternate as long as everything is OK. All outputs from the primary stop, including the activity message, when the primary detects a fault. The alternate activates its output and takes over from the primary after a brief delay when the activity message ceases. Errors in voting logic can cause both outputs to be active or inactive at the same time, or cause outputs to flutter on and off. A more reliable form of voting logic involves an odd number of three devices or more. All perform identical functions and the outputs are compared by the voting logic. The voting logic establishes a majority when there is a disagreement, and the majority will act to deactivate the output from other device(s) that disagree. A single fault will not interrupt normal operation. This technique is used with avionics systems, such as those responsible for operation of the Space Shuttle. == Calculating the probability of system failure == Each duplicate component added to the system decreases the probability of system failure according to the formula:- p = ∏ i = 1 n p i {\displaystyle {p}=\prod _{i=1}^{n}p_{i}} where: n {\displaystyle n} – number of components p i {\displaystyle p_{i}} – probability of component i failing p {\displaystyle p} – the probability of all components failing (system failure) This formula assumes independence of failure events. That means that the probability of a component B failing given that a component A has already failed is the same as that of B failing when A has not failed. There are situations where this is unreasonable, such as using two power supplies connected to the same socket in such a way that if one power supply failed, the other would too. It also assumes that only one component is needed to keep the system running. == Redundancy and high availability == You can achieve higher availability through redundancy. Let's say you have three redundant components: A, B and C. You can use following formula to calculate availability of the overall system: Availability of redundant components = 1 - (1 - availability of component A) X (1 - availability of component B) X (1 - availability of component C) In corollary, if you have N parallel components each having X availability, then: Availability of parallel components = 1 - (1 - X)^ N Using redundant components can exponentially increase the availability of overall system. For example if each of your hosts has only 50% availability, by using 10 of hosts in parallel, you can achieve 99.9023% availability. Note that redundancy doesn't always lead to higher availability. In fact, redundancy increases complexity which in turn reduces availability. According to Marc Brooker, to take advantage of redundancy, ensure that: You achieve a net-positive improvement in the overall availability of your system Your redundant components fail independently Your system can reliably detect healthy redundant components Your system can reliably scale out and scale-in redundant components. == See also == == References == == External links == Secure Propulsion using Advanced Redundant Control Using powerline as a redundant communication channel Flammini, Francesco; Marrone, Stefano; Mazzocca, Nicola; Vittorini, Valeria (2009). "A new modeling approach to the safety evaluation of N-modular redundant computer systems in presence of imperfect maintenance". Reliability Engineering & System Safety. 94 (9): 1422–1432. arXiv:1304.6656. doi:10.1016/j.ress.2009.02.014. S2CID 6932645.
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https://en.wikipedia.org/wiki/Redundancy_(engineering)
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Elecon Engineering Company Limited is an Indian multinational company headquartered in Anand, Gujarat. The company specializes in the manufacturing of industrial gear and material handling equipment. Elecon is one of the largest Asian manufacturers of industrial gears and material handling equipment for core major sector like power, steel, cement, sugar, paper, mining, rubber and many more. Elecon group has subsidiaries such as Eimco Elecon Ltd, Elecon Hydraulics, Elecon Information Technology Ltd (EITL) and Tech Elecon Pvt. Ltd. (TEPL). == History == Elecon Engineering was established in 1951 in Goregaon, Mumbai by Ishwarbhai B. Patel. The company's early focus was on engineering, procurement and construction projects in India and initially manufactured custom manufacturing conveyor systems. The company was then registered as a Private Limited company on 11 January 1960. In May 1960, the company moved to its current location in Vallabh Vidyanagar, Gujarat (now part of Anand). Later, the company was listed on the Bombay Stock Exchange and the National Stock Exchange. In 1976, the company established its Gear Division, specialising in power transmission equipment and industrial gears. It designs and manufactures Bucket-wheel excavator, worm drives, helical gears, planetary gears, couplings, Custom built gearboxes, loose gears and spiral bevel gears up to 1000 mm diameter. Its products target industries such as rubber, sugar, plastic, power, marine and mining industries etc. In 2012, Elecon Engineering secured two prestigious orders from the NTPC and Tecpro Systems. == Divisions == Power Transmission, Elecon's Power Transmission product range includes Helical Gears, Worm Gears, Fluid, Geared & Flexible Couplings, Planetary Gearbox, Special Gears including Gear drive for seven roll stands in Tube Mill plant, Sheet metal un-coiler gearbox, Gear drive for piercing milling seamless tube plant, Assel mill gearbox in seamless tube plant, Drive for briquetting mill in continuous steel plant for hot strip mill, 330KW wind mill gear drive unit, Drive for sponge iron kiln, Marine gearbox for advanced offshore patrol vessel propulsion, among others. Materials Handling Equipment, Elecon's Materials Handling division manufactures Belt Conveyors, Idlers and Pulleys , Elevators and Chain Conveyors, Stackers, Reclaimers, Stacker-cum-Reclaimers, Barrel type Blender Reclaimers, Bridge type Bucket Wheel Reclaimer, Wagon Tipplers and Beetle Marshalling Equipment, Side Arm Chargers & Pusher Car, Ship loader and Unloaders, Crawler and Rail mounted Trippers, Wagon Loaders, Crawler mounted Bucket Wheel Excavator, Spreader, Mobile, Transfer Conveyors and other surface Mining Equipment, Specialized shiftable conveyors for open cast mines, Drive heads and long-distance conveyors, Salt Scraper and Scraper Reclaimer, Cable Reeling Drum, Apron Feeders, Paddle Feeders, Vibrating Feeders and Reciprocating Feeders, Roller Screen, Grizzly Feeders, Bin Vibrators, Impactors, Ring Granulators, Double/Single Roll Crushers, Hammer Mill Crushers, Rotary Breakers, Transfer Cars, Wind Turbine Generators. Foundry Division, Elecon's Foundry Division (EFD) provides casting and machining services to several other companies other than Elecon group. == Acquisitions and subsidiaries == === Acquisitions === In October 2010, Elecon acquired the Benzlers-Radicon Group, the power transmission division of UK-based David Brown Ltd. === Subsidiaries === Source: Radicon Transmission UK Limited Elecon Singapore pte.Limited Elecon Middle East FZE Benzler System AB -Sweden AB Banzlers -Sweden Radicon Drive System Inc. - US Banzlers Transmission A.S. - Denmark Benzlers Antriebstechnik G.m.b.h. Banzlers TBA B.V. -Netherlands OY banzlers AB-Finland The Group of Companies Emtici Engineering Power Build Private Limited Vijay M. Mistry Construction Pvt. Ltd Modsonic Instruments Mfg. Co. (P) Ltd. Elecon Hydraulics Associates Eimco Elecon (India) Ltd. == References ==
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https://en.wikipedia.org/wiki/Elecon_Engineering
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Acoustical engineering (also known as acoustic engineering) is the branch of engineering dealing with sound and vibration. It includes the application of acoustics, the science of sound and vibration, in technology. Acoustical engineers are typically concerned with the design, analysis and control of sound. One goal of acoustical engineering can be the reduction of unwanted noise, which is referred to as noise control. Unwanted noise can have significant impacts on animal and human health and well-being, reduce attainment by students in schools, and cause hearing loss. Noise control principles are implemented into technology and design in a variety of ways, including control by redesigning sound sources, the design of noise barriers, sound absorbers, suppressors, and buffer zones, and the use of hearing protection (earmuffs or earplugs). Besides noise control, acoustical engineering also covers positive uses of sound, such as the use of ultrasound in medicine, programming digital synthesizers, designing concert halls to enhance the sound of orchestras and specifying railway station sound systems so that announcements are intelligible. == Acoustic engineer (professional) == Acoustic engineers usually possess a bachelor's degree or higher qualification in acoustics, physics or another engineering discipline. Practicing as an acoustic engineer usually requires a bachelor's degree with significant scientific and mathematical content. Acoustic engineers might work in acoustic consultancy, specializing in particular fields, such as architectural acoustics, environmental noise or vibration control. In other industries, acoustic engineers might: design automobile sound systems; investigate human response to sounds, such as urban soundscapes and domestic appliances; develop audio signal processing software for mixing desks, and design loudspeakers and microphones for mobile phones. Acousticians are also involved in researching and understanding sound scientifically. Some positions, such as faculty require a Doctor of Philosophy. In most countries, a degree in acoustics can represent the first step towards professional certification and the degree program may be certified by a professional body. After completing a certified degree program the engineer must satisfy a range of requirements before being certified. Once certified, the engineer is designated the title of Chartered Engineer (in most Commonwealth countries). == Subdisciplines == The listed subdisciplines are loosely based on the PACS (Physics and Astronomy Classification Scheme) coding used by the Acoustical Society of America. === Aeroacoustics === Aeroacoustics is concerned with how noise is generated by the movement of air, for instance via turbulence, and how sound propagates through the fluid air. Aeroacoustics plays an important role in understanding how noise is generated by aircraft and wind turbines, as well as exploring how wind instruments work. === Audio signal processing === Audio signal processing is the electronic manipulation of audio signals using analog and digital signal processing. It is done for a variety of reasons, including: to enhance a sound, e.g. by applying an audio effect such as reverberation; to remove unwanted noises from a signal, e.g. echo cancellation in internet voice calls; to compress an audio signal to allow efficient transmission, e.g. perceptual coding in MP3 and Opus to understand the content of the signal, e.g. identification of music tracks via music information retrieval. Audio engineers develop and use audio signal processing algorithms. === Architectural acoustics === Architectural acoustics (also known as building acoustics) is the science and engineering of achieving a good sound within a building. Architectural acoustics can be about achieving good speech intelligibility in a theatre, restaurant or railway station, enhancing the quality of music in a concert hall or recording studio, or suppressing noise to make offices and homes more productive and pleasant places to work and live. Architectural acoustic design is usually done by acoustic consultants. === Bioacoustics === Bioacoustics concerns the scientific study of sound production and hearing in animals. It can include: acoustic communication and associated animal behavior and evolution of species; how sound is produced by animals; the auditory mechanisms and neurophysiology of animals; the use of sound to monitor animal populations, and the effect of man-made noise on animals. === Electroacoustics === This branch of acoustic engineering deals with the design of headphones, microphones, loudspeakers, sound systems, sound reproduction, and recording. There has been a rapid increase in the use of portable electronic devices which can reproduce sound and rely on electroacoustic engineering, e.g. mobile phones, portable media players, and tablet computers. The term "electroacoustics" is also used to describe a set of electrokinetic effects that occur in heterogeneous liquids under influence of ultrasound. === Environmental noise === Environmental acoustics is concerned with the control of noise and vibrations caused by traffic, aircraft, industrial equipment, recreational activities and anything else that might be considered a nuisance. Acoustical engineers concerned with environmental acoustics face the challenge of measuring or predicting likely noise levels, determining an acceptable level for that noise, and determining how the noise can be controlled. Environmental acoustics work is usually done by acoustic consultants or those working in environmental health. Recent research work has put a strong emphasis on soundscapes, the positive use of sound (e.g. fountains, bird song), and the preservation of tranquility. === Musical acoustics === Musical acoustics is concerned with researching and describing the physics of music and its perception – how sounds employed as music work. This includes: the function and design of musical instruments including electronic synthesizers; the human voice (the physics and neurophysiology of singing); computer analysis of music and composition; the clinical use of music in music therapy, and the perception and cognition of music. === Noise control === Noise control is a set of strategies to reduce noise pollution by reducing noise at its source, by inhibiting sound propagation using noise barriers or similar, or by the use of ear protection (earmuffs or earplugs). Control at the source is the most cost-effective way of providing noise control. Noise control engineering applied to cars and trucks is known as noise, vibration, and harshness (NVH). Other techniques to reduce product noise include vibration isolation, application of acoustic absorbent and acoustic enclosures. Acoustical engineering can go beyond noise control to look at what is the best sound for a product, for instance, manipulating the sound of door closures on automobiles. === Psychoacoustics === Psychoacoustics tries to explain how humans respond to what they hear, whether that is an annoying noise or beautiful music. In many branches of acoustic engineering, a human listener is a final arbitrator as to whether a design is successful, for instance, whether sound localisation works in a surround sound system. "Psychoacoustics seeks to reconcile acoustical stimuli and all the scientific, objective, and physical properties that surround them, with the physiological and psychological responses evoked by them." === Speech === Speech is a major area of study for acoustical engineering, including the production, processing and perception of speech. This can include physics, physiology, psychology, audio signal processing and linguistics. Speech recognition and speech synthesis are two important aspects of the machine processing of speech. Ensuring speech is transmitted intelligibly, efficiently and with high quality; in rooms, through public address systems and through telephone systems are other important areas of study. === Ultrasonics === Ultrasonics deals with sound waves in solids, liquids and gases at frequencies too high to be heard by the average person. Specialist areas include medical ultrasonics (including medical ultrasonography), sonochemistry, nondestructive testing, material characterisation and underwater acoustics (sonar). === Underwater acoustics === Underwater acoustics is the scientific study of sound in water. It is concerned with both natural and man-made sound and its generation underwater; how it propagates, and the perception of the sound by animals. Applications include sonar to locate submerged objects such as submarines, underwater communication by animals, observation of sea temperatures for climate change monitoring, and marine biology. === Vibration and dynamics === Acoustic engineers working on vibration study the motions and interactions of mechanical systems with their environments, including measurement, analysis and control. This might include: ground vibrations from railways and construction; vibration isolation to reduce noise getting into recording studios; studying the effects of vibration on humans (vibration white finger); vibration control to protect a bridge from earthquakes, or modelling the propagation of structure-borne sound through buildings. == Fundamental science == Although the way in which sound interacts with its surroundings is often extremely complex, there are a few ideal sound wave behaviours that are fundamental to understanding acoustical design. Complex sound wave behaviors include absorption, reverberation, diffraction, and refraction. Absorption is the loss of energy that occurs when a sound wave reflects off of a surface, and refers to both the sound energy transmitted through and dissipated by the surface material. Reverberation is the persistence of sound caused by repeated boundary reflections after the source of the sound stops. This principle is particularly important in enclosed spaces. Diffraction is the bending of sound waves around surfaces in the path of the wave. Refraction is the bending of sound waves caused by changes in the medium through which the wave is passing. For example, temperature gradients can cause sound wave refraction. Acoustical engineers apply these fundamental concepts, along with mathematical analysis, to control sound for a variety of applications. == Associations == Acoustical Society of America Technical Committee on Engineering Acoustics Audio Engineering Society Australian Acoustical Society Canadian Acoustical Association Institute of Acoustics, Chinese Academy of Sciences Institute of Acoustics (United Kingdom) Danish Sound Cluster (Denmark) == See also == Audio Engineering Category:Acoustical engineers Category:Audio engineers == References == Barron, R. (2003). Industrial noise control and acoustics. New York: Marcel Dekker Inc. Retrieved from CRCnetBase Hemond, C. (1983). In Ingerman S. ( Ed.), Engineering acoustics and noise control. New Jersey: Prentice-Hall. Highway traffic noise barriers at a glance. Retrieved February 1, 2010, from http://www.fhwa.dot.gov/environment/keepdown.htm Archived 2011-06-15 at the Wayback Machine Kinsler, L., Frey, A., Coppens, A., & Sanders, J. (Eds.). (2000). Fundamentals of acoustics (4th ed.). New York: John Wiley and Sons. Kleppe, J. (1989). Engineering applications of acoustics. Sparks, Nevada: Artech House. Moser, M. (2009). Engineering acoustics (S. Zimmerman, R. Ellis Trans.). (2nd ed.). Berlin: Springer-Verlag.
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https://en.wikipedia.org/wiki/Acoustical_engineering
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Software engineering is a branch of both computer science and engineering focused on designing, developing, testing, and maintaining software applications. It involves applying engineering principles and computer programming expertise to develop software systems that meet user needs. The terms programmer and coder overlap software engineer, but they imply only the construction aspect of a typical software engineer workload. A software engineer applies a software development process, which involves defining, implementing, testing, managing, and maintaining software systems, as well as developing the software development process itself. == History == Beginning in the 1960s, software engineering was recognized as a separate field of engineering. The development of software engineering was seen as a struggle. Problems included software that was over budget, exceeded deadlines, required extensive debugging and maintenance, and unsuccessfully met the needs of consumers or was never even completed. In 1968, NATO held the first software engineering conference, where issues related to software were addressed. Guidelines and best practices for the development of software were established. The origins of the term software engineering have been attributed to various sources. The term appeared in a list of services offered by companies in the June 1965 issue of "Computers and Automation" and was used more formally in the August 1966 issue of Communications of the ACM (Volume 9, number 8) in "President's Letter to the ACM Membership" by Anthony A. Oettinger. It is also associated with the title of a NATO conference in 1968 by Professor Friedrich L. Bauer. Margaret Hamilton described the discipline of "software engineering" during the Apollo missions to give what they were doing legitimacy. At the time, there was perceived to be a "software crisis". The 40th International Conference on Software Engineering (ICSE 2018) celebrates 50 years of "Software Engineering" with the Plenary Sessions' keynotes of Frederick Brooks and Margaret Hamilton. In 1984, the Software Engineering Institute (SEI) was established as a federally funded research and development center headquartered on the campus of Carnegie Mellon University in Pittsburgh, Pennsylvania, United States. Watts Humphrey founded the SEI Software Process Program, aimed at understanding and managing the software engineering process. The Process Maturity Levels introduced became the Capability Maturity Model Integration for Development (CMMI-DEV), which defined how the US Government evaluates the abilities of a software development team. Modern, generally accepted best practices for software engineering have been collected by the ISO/IEC JTC 1/SC 7 subcommittee and published as the Software Engineering Body of Knowledge (SWEBOK). Software engineering is considered one of the major computing disciplines. == Terminology == === Definition === Notable definitions of software engineering include: "The systematic application of scientific and technological knowledge, methods, and experience to the design, implementation, testing, and documentation of software."—The Bureau of Labor Statistics—IEEE Systems and software engineering – Vocabulary "The application of a systematic, disciplined, quantifiable approach to the development, operation, and maintenance of software."—IEEE Standard Glossary of Software Engineering Terminology "An engineering discipline that is concerned with all aspects of software production."—Ian Sommerville "The establishment and use of sound engineering principles in order to economically obtain software that is reliable and works efficiently on real machines."—Fritz Bauer "A branch of computer science that deals with the design, implementation, and maintenance of complex computer programs."—Merriam-Webster "'Software engineering' encompasses not just the act of writing code, but all of the tools and processes an organization uses to build and maintain that code over time. [...] Software engineering can be thought of as 'programming integrated over time.'"—Software Engineering at Google The term has also been used less formally: as the informal contemporary term for the broad range of activities that were formerly called computer programming and systems analysis as the broad term for all aspects of the practice of computer programming, as opposed to the theory of computer programming, which is formally studied as a sub-discipline of computer science as the term embodying the advocacy of a specific approach to computer programming, one that urges that it be treated as an engineering discipline rather than an art or a craft, and advocates the codification of recommended practices === Suitability === Individual commentators have disagreed sharply on how to define software engineering or its legitimacy as an engineering discipline. David Parnas has said that software engineering is, in fact, a form of engineering. Steve McConnell has said that it is not, but that it should be. Donald Knuth has said that programming is an art and a science. Edsger W. Dijkstra claimed that the terms software engineering and software engineer have been misused in the United States. == Workload == === Requirements analysis === Requirements engineering is about elicitation, analysis, specification, and validation of requirements for software. Software requirements can be functional, non-functional or domain. Functional requirements describe expected behaviors (i.e. outputs). Non-functional requirements specify issues like portability, security, maintainability, reliability, scalability, performance, reusability, and flexibility. They are classified into the following types: interface constraints, performance constraints (such as response time, security, storage space, etc.), operating constraints, life cycle constraints (maintainability, portability, etc.), and economic constraints. Knowledge of how the system or software works is needed when it comes to specifying non-functional requirements. Domain requirements have to do with the characteristic of a certain category or domain of projects. === Design === Software design is the process of making high-level plans for the software. Design is sometimes divided into levels: Interface design plans the interaction between a system and its environment as well as the inner workings of the system. Architectural design plans the major components of a system, including their responsibilities, properties, and interfaces between them. Detailed design plans internal elements, including their properties, relationships, algorithms and data structures. === Construction === Software construction typically involves programming (a.k.a. coding), unit testing, integration testing, and debugging so as to implement the design."Software testing is related to, but different from, ... debugging". Testing during this phase is generally performed by the programmer and with the purpose to verify that the code behaves as designed and to know when the code is ready for the next level of testing. === Testing === Software testing is an empirical, technical investigation conducted to provide stakeholders with information about the quality of the software under test. When described separately from construction, testing typically is performed by test engineers or quality assurance instead of the programmers who wrote it. It is performed at the system level and is considered an aspect of software quality. === Program analysis === Program analysis is the process of analyzing computer programs with respect to an aspect such as performance, robustness, and security. === Maintenance === Software maintenance refers to supporting the software after release. It may include but is not limited to: error correction, optimization, deletion of unused and discarded features, and enhancement of existing features. Usually, maintenance takes up 40% to 80% of project cost. == Education == Knowledge of computer programming is a prerequisite for becoming a software engineer. In 2004, the IEEE Computer Society produced the SWEBOK, which has been published as ISO/IEC Technical Report 1979:2005, describing the body of knowledge that they recommend to be mastered by a graduate software engineer with four years of experience. Many software engineers enter the profession by obtaining a university degree or training at a vocational school. One standard international curriculum for undergraduate software engineering degrees was defined by the Joint Task Force on Computing Curricula of the IEEE Computer Society and the Association for Computing Machinery, and updated in 2014. A number of universities have Software Engineering degree programs; as of 2010, there were 244 Campus Bachelor of Software Engineering programs, 70 Online programs, 230 Masters-level programs, 41 Doctorate-level programs, and 69 Certificate-level programs in the United States. In addition to university education, many companies sponsor internships for students wishing to pursue careers in information technology. These internships can introduce the student to real-world tasks that typical software engineers encounter every day. Similar experience can be gained through military service in software engineering. === Software engineering degree programs === Half of all practitioners today have degrees in computer science, information systems, or information technology. A small but growing number of practitioners have software engineering degrees. In 1987, the Department of Computing at Imperial College London introduced the first three-year software engineering bachelor's degree in the world; in the following year, the University of Sheffield established a similar program. In 1996, the Rochester Institute of Technology established the first software engineering bachelor's degree program in the United States; however, it did not obtain ABET accreditation until 2003, the same year as Rice University, Clarkson University, Milwaukee School of Engineering, and Mississippi State University. In 1997, PSG College of Technology in Coimbatore, India was the first to start a five-year integrated Master of Science degree in Software Engineering. Since then, software engineering undergraduate degrees have been established at many universities. A standard international curriculum for undergraduate software engineering degrees, SE2004, was defined by a steering committee between 2001 and 2004 with funding from the Association for Computing Machinery and the IEEE Computer Society. As of 2004, about 50 universities in the U.S. offer software engineering degrees, which teach both computer science and engineering principles and practices. The first software engineering master's degree was established at Seattle University in 1979. Since then, graduate software engineering degrees have been made available from many more universities. Likewise in Canada, the Canadian Engineering Accreditation Board (CEAB) of the Canadian Council of Professional Engineers has recognized several software engineering programs. In 1998, the US Naval Postgraduate School (NPS) established the first doctorate program in Software Engineering in the world. Additionally, many online advanced degrees in Software Engineering have appeared such as the Master of Science in Software Engineering (MSE) degree offered through the Computer Science and Engineering Department at California State University, Fullerton. Steve McConnell opines that because most universities teach computer science rather than software engineering, there is a shortage of true software engineers. ETS (École de technologie supérieure) University and UQAM (Université du Québec à Montréal) were mandated by IEEE to develop the Software Engineering Body of Knowledge (SWEBOK), which has become an ISO standard describing the body of knowledge covered by a software engineer. == Profession == Legal requirements for the licensing or certification of professional software engineers vary around the world. In the UK, there is no licensing or legal requirement to assume or use the job title Software Engineer. In some areas of Canada, such as Alberta, British Columbia, Ontario, and Quebec, software engineers can hold the Professional Engineer (P.Eng) designation and/or the Information Systems Professional (I.S.P.) designation. In Europe, Software Engineers can obtain the European Engineer (EUR ING) professional title. Software Engineers can also become professionally qualified as a Chartered Engineer through the British Computer Society. In the United States, the NCEES began offering a Professional Engineer exam for Software Engineering in 2013, thereby allowing Software Engineers to be licensed and recognized. NCEES ended the exam after April 2019 due to lack of participation. Mandatory licensing is currently still largely debated, and perceived as controversial. The IEEE Computer Society and the ACM, the two main US-based professional organizations of software engineering, publish guides to the profession of software engineering. The IEEE's Guide to the Software Engineering Body of Knowledge – 2004 Version, or SWEBOK, defines the field and describes the knowledge the IEEE expects a practicing software engineer to have. The most current version is SWEBOK v4. The IEEE also promulgates a "Software Engineering Code of Ethics". === Employment === There are an estimated 26.9 million professional software engineers in the world as of 2022, up from 21 million in 2016. Many software engineers work as employees or contractors. Software engineers work with businesses, government agencies (civilian or military), and non-profit organizations. Some software engineers work for themselves as freelancers. Some organizations have specialists to perform each of the tasks in the software development process. Other organizations require software engineers to do many or all of them. In large projects, people may specialize in only one role. In small projects, people may fill several or all roles at the same time. Many companies hire interns, often university or college students during a summer break, or externships. Specializations include analysts, architects, developers, testers, technical support, middleware analysts, project managers, software product managers, educators, and researchers. Most software engineers and programmers work 40 hours a week, but about 15 percent of software engineers and 11 percent of programmers worked more than 50 hours a week in 2008. Potential injuries in these occupations are possible because like other workers who spend long periods sitting in front of a computer terminal typing at a keyboard, engineers and programmers are susceptible to eyestrain, back discomfort, Thrombosis, Obesity, and hand and wrist problems such as carpal tunnel syndrome. ==== United States ==== The U. S. Bureau of Labor Statistics (BLS) counted 1,365,500 software developers holding jobs in the U.S. in 2018. Due to its relative newness as a field of study, formal education in software engineering is often taught as part of a computer science curriculum, and many software engineers hold computer science degrees. The BLS estimates from 2023 to 2033 that computer software engineering would increase by 17%. This is down from the 2022 to 2032 BLS estimate of 25% for software engineering. And, is further down from their 30% 2010 to 2020 BLS estimate. Due to this trend, job growth may not be as fast as during the last decade, as jobs that would have gone to computer software engineers in the United States would instead be outsourced to computer software engineers in countries such as India and other foreign countries. In addition, the BLS Job Outlook for Computer Programmers, the U.S. Bureau of Labor Statistics (BLS) Occupational Outlook predicts a decline of -7 percent from 2016 to 2026, a further decline of -9 percent from 2019 to 2029, a decline of -10 percent from 2021 to 2031. and then a decline of -11 percent from 2022 to 2032. Since computer programming can be done from anywhere in the world, companies sometimes hire programmers in countries where wages are lower. Furthermore, the ratio of women in many software fields has also been declining over the years as compared to other engineering fields. Then there is the additional concern that recent advances in Artificial Intelligence might impact the demand for future generations of Software Engineers. However, this trend may change or slow in the future as many current software engineers in the U.S. market flee the profession or age out of the market in the next few decades. === Certification === The Software Engineering Institute offers certifications on specific topics like security, process improvement and software architecture. IBM, Microsoft and other companies also sponsor their own certification examinations. Many IT certification programs are oriented toward specific technologies, and managed by the vendors of these technologies. These certification programs are tailored to the institutions that would employ people who use these technologies. Broader certification of general software engineering skills is available through various professional societies. As of 2006, the IEEE had certified over 575 software professionals as a Certified Software Development Professional (CSDP). In 2008 they added an entry-level certification known as the Certified Software Development Associate (CSDA). The ACM had a professional certification program in the early 1980s, which was discontinued due to lack of interest. The ACM and the IEEE Computer Society together examined the possibility of licensing of software engineers as Professional Engineers in the 1990s, but eventually decided that such licensing was inappropriate for the professional industrial practice of software engineering. John C. Knight and Nancy G. Leveson presented a more balanced analysis of the licensing issue in 2002. In the U.K. the British Computer Society has developed a legally recognized professional certification called Chartered IT Professional (CITP), available to fully qualified members (MBCS). Software engineers may be eligible for membership of the British Computer Society or Institution of Engineering and Technology and so qualify to be considered for Chartered Engineer status through either of those institutions. In Canada the Canadian Information Processing Society has developed a legally recognized professional certification called Information Systems Professional (ISP). In Ontario, Canada, Software Engineers who graduate from a Canadian Engineering Accreditation Board (CEAB) accredited program, successfully complete PEO's (Professional Engineers Ontario) Professional Practice Examination (PPE) and have at least 48 months of acceptable engineering experience are eligible to be licensed through the Professional Engineers Ontario and can become Professional Engineers P.Eng. The PEO does not recognize any online or distance education however; and does not consider Computer Science programs to be equivalent to software engineering programs despite the tremendous overlap between the two. This has sparked controversy and a certification war. It has also held the number of P.Eng holders for the profession exceptionally low. The vast majority of working professionals in the field hold a degree in CS, not SE. Given the difficult certification path for holders of non-SE degrees, most never bother to pursue the license. === Impact of globalization === The initial impact of outsourcing, and the relatively lower cost of international human resources in developing third world countries led to a massive migration of software development activities from corporations in North America and Europe to India and later: China, Russia, and other developing countries. This approach had some flaws, mainly the distance / time zone difference that prevented human interaction between clients and developers and the massive job transfer. This had a negative impact on many aspects of the software engineering profession. For example, some students in the developed world avoid education related to software engineering because of the fear of offshore outsourcing (importing software products or services from other countries) and of being displaced by foreign visa workers. Although statistics do not currently show a threat to software engineering itself; a related career, computer programming does appear to have been affected. Nevertheless, the ability to smartly leverage offshore and near-shore resources via the follow-the-sun workflow has improved the overall operational capability of many organizations. When North Americans leave work, Asians are just arriving to work. When Asians are leaving work, Europeans arrive to work. This provides a continuous ability to have human oversight on business-critical processes 24 hours per day, without paying overtime compensation or disrupting a key human resource, sleep patterns. While global outsourcing has several advantages, global – and generally distributed – development can run into serious difficulties resulting from the distance between developers. This is due to the key elements of this type of distance that have been identified as geographical, temporal, cultural and communication (that includes the use of different languages and dialects of English in different locations). Research has been carried out in the area of global software development over the last 15 years and an extensive body of relevant work published that highlights the benefits and problems associated with the complex activity. As with other aspects of software engineering research is ongoing in this and related areas. === Prizes === There are various prizes in the field of software engineering: ACM-AAAI Allen Newell Award- USA. Awarded to career contributions that have breadth within computer science, or that bridge computer science and other disciplines. BCS Lovelace Medal. Awarded to individuals who have made outstanding contributions to the understanding or advancement of computing. ACM SIGSOFT Outstanding Research Award, selected for individual(s) who have made "significant and lasting research contributions to the theory or practice of software engineering." More ACM SIGSOFT Awards. The Codie award, a yearly award issued by the Software and Information Industry Association for excellence in software development within the software industry. Harlan Mills Award for "contributions to the theory and practice of the information sciences, focused on software engineering". ICSE Most Influential Paper Award. Jolt Award, also for the software industry. Stevens Award given in memory of Wayne Stevens. == Criticism == Some call for licensing, certification and codified bodies of knowledge as mechanisms for spreading the engineering knowledge and maturing the field. Some claim that the concept of software engineering is so new that it is rarely understood, and it is widely misinterpreted, including in software engineering textbooks, papers, and among the communities of programmers and crafters. Some claim that a core issue with software engineering is that its approaches are not empirical enough because a real-world validation of approaches is usually absent, or very limited and hence software engineering is often misinterpreted as feasible only in a "theoretical environment." Edsger Dijkstra, a founder of many of the concepts in software development today, rejected the idea of "software engineering" up until his death in 2002, arguing that those terms were poor analogies for what he called the "radical novelty" of computer science: A number of these phenomena have been bundled under the name "Software Engineering". As economics is known as "The Miserable Science", software engineering should be known as "The Doomed Discipline", doomed because it cannot even approach its goal since its goal is self-contradictory. Software engineering, of course, presents itself as another worthy cause, but that is eyewash: if you carefully read its literature and analyse what its devotees actually do, you will discover that software engineering has accepted as its charter "How to program if you cannot." == See also == === Study and practice === Computer science Data engineering Software craftsmanship Software development Release engineering === Roles === Programmer Systems analyst Systems architect === Professional aspects === Bachelor of Science in Information Technology Bachelor of Software Engineering List of software engineering conferences List of computer science journals (including software engineering journals) Software Engineering Institute == References == === Citations === === Sources === == Further reading == Pierre Bourque; Richard E. (Dick) Fairley, eds. (2014). Guide to the Software Engineering Body of Knowledge Version 3.0 (SWEBOK). IEEE Computer Society. Roger S. Pressman; Bruce Maxim (January 23, 2014). Software Engineering: A Practitioner's Approach (8th ed.). McGraw-Hill. ISBN 978-0-07-802212-8. Ian Sommerville (March 24, 2015). Software Engineering (10th ed.). Pearson Education Limited. ISBN 978-0-13-394303-0. Jalote, Pankaj (2005) [1991]. An Integrated Approach to Software Engineering (3rd ed.). Springer. ISBN 978-0-387-20881-7. Bruegge, Bernd; Dutoit, Allen (2009). Object-oriented software engineering : using UML, patterns, and Java (3rd ed.). Prentice Hall. ISBN 978-0-13-606125-0. Oshana, Robert (2019-06-21). Software engineering for embedded systems : methods, practical techniques, and applications (Second ed.). Kidlington, Oxford, United Kingdom. ISBN 978-0-12-809433-4. == External links == Pierre Bourque; Richard E. Fairley, eds. (2004). Guide to the Software Engineering Body of Knowledge Version 3.0 (SWEBOK), https://www.computer.org/web/swebok/v3. IEEE Computer Society. The Open Systems Engineering and Software Development Life Cycle Framework Archived 2010-07-18 at the Wayback Machine OpenSDLC.org the integrated Creative Commons SDLC Software Engineering Institute Carnegie Mellon
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https://en.wikipedia.org/wiki/Software_engineering
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Engineering is the practice of using natural science, mathematics, and the engineering design process to solve problems within technology, increase efficiency and productivity, and improve systems. Modern engineering comprises many subfields which include designing and improving infrastructure, machinery, vehicles, electronics, materials, and energy systems. The discipline of engineering encompasses a broad range of more specialized fields of engineering, each with a more specific emphasis for applications of mathematics and science. See glossary of engineering. The word engineering is derived from the Latin ingenium. == Definition == The American Engineers' Council for Professional Development (the predecessor of the Accreditation Board for Engineering and Technology aka ABET) has defined "engineering" as: The creative application of scientific principles to design or develop structures, machines, apparatus, or manufacturing processes, or works utilizing them singly or in combination; or to construct or operate the same with full cognizance of their design; or to forecast their behavior under specific operating conditions; all as respects an intended function, economics of operation and safety to life and property. == History == Engineering has existed since ancient times, when humans devised inventions such as the wedge, lever, wheel and pulley, etc. The term engineering is derived from the word engineer, which itself dates back to the 14th century when an engine'er (literally, one who builds or operates a siege engine) referred to "a constructor of military engines". In this context, now obsolete, an "engine" referred to a military machine, i.e., a mechanical contraption used in war (for example, a catapult). Notable examples of the obsolete usage which have survived to the present day are military engineering corps, e.g., the U.S. Army Corps of Engineers. The word "engine" itself is of even older origin, ultimately deriving from the Latin ingenium (c. 1250), meaning "innate quality, especially mental power, hence a clever invention." Later, as the design of civilian structures, such as bridges and buildings, matured as a technical discipline, the term civil engineering entered the lexicon as a way to distinguish between those specializing in the construction of such non-military projects and those involved in the discipline of military engineering. === Ancient era === The pyramids in ancient Egypt, ziggurats of Mesopotamia, the Acropolis and Parthenon in Greece, the Roman aqueducts, Via Appia and Colosseum, Teotihuacán, and the Brihadeeswarar Temple of Thanjavur, among many others, stand as a testament to the ingenuity and skill of ancient civil and military engineers. Other monuments, no longer standing, such as the Hanging Gardens of Babylon and the Pharos of Alexandria, were important engineering achievements of their time and were considered among the Seven Wonders of the Ancient World. The six classic simple machines were known in the ancient Near East. The wedge and the inclined plane (ramp) were known since prehistoric times. The wheel, along with the wheel and axle mechanism, was invented in Mesopotamia (modern Iraq) during the 5th millennium BC. The lever mechanism first appeared around 5,000 years ago in the Near East, where it was used in a simple balance scale, and to move large objects in ancient Egyptian technology. The lever was also used in the shadoof water-lifting device, the first crane machine, which appeared in Mesopotamia c. 3000 BC, and then in ancient Egyptian technology c. 2000 BC. The earliest evidence of pulleys date back to Mesopotamia in the early 2nd millennium BC, and ancient Egypt during the Twelfth Dynasty (1991–1802 BC). The screw, the last of the simple machines to be invented, first appeared in Mesopotamia during the Neo-Assyrian period (911–609) BC. The Egyptian pyramids were built using three of the six simple machines, the inclined plane, the wedge, and the lever, to create structures like the Great Pyramid of Giza. The earliest civil engineer known by name is Imhotep. As one of the officials of the Pharaoh, Djosèr, he probably designed and supervised the construction of the Pyramid of Djoser (the Step Pyramid) at Saqqara in Egypt around 2630–2611 BC. The earliest practical water-powered machines, the water wheel and watermill, first appeared in the Persian Empire, in what are now Iraq and Iran, by the early 4th century BC. Kush developed the Sakia during the 4th century BC, which relied on animal power instead of human energy. Hafirs were developed as a type of reservoir in Kush to store and contain water as well as boost irrigation. Sappers were employed to build causeways during military campaigns. Kushite ancestors built speos during the Bronze Age between 3700 and 3250 BC. Bloomeries and blast furnaces were also created during the 7th centuries BC in Kush. Ancient Greece developed machines in both civilian and military domains. The Antikythera mechanism, an early known mechanical analog computer, and the mechanical inventions of Archimedes, are examples of Greek mechanical engineering. Some of Archimedes' inventions, as well as the Antikythera mechanism, required sophisticated knowledge of differential gearing or epicyclic gearing, two key principles in machine theory that helped design the gear trains of the Industrial Revolution, and are widely used in fields such as robotics and automotive engineering. Ancient Chinese, Greek, Roman and Hunnic armies employed military machines and inventions such as artillery which was developed by the Greeks around the 4th century BC, the trireme, the ballista and the catapult, the trebuchet by Chinese circa 6th-5th century BCE. === Middle Ages === The earliest practical wind-powered machines, the windmill and wind pump, first appeared in the Muslim world during the Islamic Golden Age, in what are now Iran, Afghanistan, and Pakistan, by the 9th century AD. The earliest practical steam-powered machine was a steam jack driven by a steam turbine, described in 1551 by Taqi al-Din Muhammad ibn Ma'ruf in Ottoman Egypt. The cotton gin was invented in India by the 6th century AD, and the spinning wheel was invented in the Islamic world by the early 11th century, both of which were fundamental to the growth of the cotton industry. The spinning wheel was also a precursor to the spinning jenny, which was a key development during the early Industrial Revolution in the 18th century. The earliest programmable machines were developed in the Muslim world. A music sequencer, a programmable musical instrument, was the earliest type of programmable machine. The first music sequencer was an automated flute player invented by the Banu Musa brothers, described in their Book of Ingenious Devices, in the 9th century. In 1206, Al-Jazari invented programmable automata/robots. He described four automaton musicians, including drummers operated by a programmable drum machine, where they could be made to play different rhythms and different drum patterns. Before the development of modern engineering, mathematics was used by artisans and craftsmen, such as millwrights, clockmakers, instrument makers and surveyors. Aside from these professions, universities were not believed to have had much practical significance to technology.: 32 A standard reference for the state of mechanical arts during the Renaissance is given in the mining engineering treatise De re metallica (1556), which also contains sections on geology, mining, and chemistry. De re metallica was the standard chemistry reference for the next 180 years. === Modern era === The science of classical mechanics, sometimes called Newtonian mechanics, formed the scientific basis of much of modern engineering. With the rise of engineering as a profession in the 18th century, the term became more narrowly applied to fields in which mathematics and science were applied to these ends. Similarly, in addition to military and civil engineering, the fields then known as the mechanic arts became incorporated into engineering. Canal building was an important engineering work during the early phases of the Industrial Revolution. John Smeaton was the first self-proclaimed civil engineer and is often regarded as the "father" of civil engineering. He was an English civil engineer responsible for the design of bridges, canals, harbors, and lighthouses. He was also a capable mechanical engineer and an eminent physicist. Using a model water wheel, Smeaton conducted experiments for seven years, determining ways to increase efficiency.: 127 Smeaton introduced iron axles and gears to water wheels.: 69 Smeaton also made mechanical improvements to the Newcomen steam engine. Smeaton designed the third Eddystone Lighthouse (1755–59) where he pioneered the use of 'hydraulic lime' (a form of mortar which will set under water) and developed a technique involving dovetailed blocks of granite in the building of the lighthouse. He is important in the history, rediscovery of, and development of modern cement, because he identified the compositional requirements needed to obtain "hydraulicity" in lime; work which led ultimately to the invention of Portland cement. Applied science led to the development of the steam engine. The sequence of events began with the invention of the barometer and the measurement of atmospheric pressure by Evangelista Torricelli in 1643, demonstration of the force of atmospheric pressure by Otto von Guericke using the Magdeburg hemispheres in 1656, laboratory experiments by Denis Papin, who built experimental model steam engines and demonstrated the use of a piston, which he published in 1707. Edward Somerset, 2nd Marquess of Worcester published a book of 100 inventions containing a method for raising waters similar to a coffee percolator. Samuel Morland, a mathematician and inventor who worked on pumps, left notes at the Vauxhall Ordinance Office on a steam pump design that Thomas Savery read. In 1698 Savery built a steam pump called "The Miner's Friend". It employed both vacuum and pressure. Iron merchant Thomas Newcomen, who built the first commercial piston steam engine in 1712, was not known to have any scientific training.: 32 The application of steam-powered cast iron blowing cylinders for providing pressurized air for blast furnaces lead to a large increase in iron production in the late 18th century. The higher furnace temperatures made possible with steam-powered blast allowed for the use of more lime in blast furnaces, which enabled the transition from charcoal to coke. These innovations lowered the cost of iron, making horse railways and iron bridges practical. The puddling process, patented by Henry Cort in 1784 produced large scale quantities of wrought iron. Hot blast, patented by James Beaumont Neilson in 1828, greatly lowered the amount of fuel needed to smelt iron. With the development of the high pressure steam engine, the power to weight ratio of steam engines made practical steamboats and locomotives possible. New steel making processes, such as the Bessemer process and the open hearth furnace, ushered in an area of heavy engineering in the late 19th century. One of the most famous engineers of the mid-19th century was Isambard Kingdom Brunel, who built railroads, dockyards and steamships. The Industrial Revolution created a demand for machinery with metal parts, which led to the development of several machine tools. Boring cast iron cylinders with precision was not possible until John Wilkinson invented his boring machine, which is considered the first machine tool. Other machine tools included the screw cutting lathe, milling machine, turret lathe and the metal planer. Precision machining techniques were developed in the first half of the 19th century. These included the use of gigs to guide the machining tool over the work and fixtures to hold the work in the proper position. Machine tools and machining techniques capable of producing interchangeable parts lead to large scale factory production by the late 19th century. The United States Census of 1850 listed the occupation of "engineer" for the first time with a count of 2,000. There were fewer than 50 engineering graduates in the U.S. before 1865. The first PhD in engineering (technically, applied science and engineering) awarded in the United States went to Josiah Willard Gibbs at Yale University in 1863; it was also the second PhD awarded in science in the U.S. In 1870 there were a dozen U.S. mechanical engineering graduates, with that number increasing to 43 per year in 1875. In 1890, there were 6,000 engineers in civil, mining, mechanical and electrical. There was no chair of applied mechanism and applied mechanics at Cambridge until 1875, and no chair of engineering at Oxford until 1907. Germany established technical universities earlier. The foundations of electrical engineering in the 1800s included the experiments of Alessandro Volta, Michael Faraday, Georg Ohm and others and the invention of the electric telegraph in 1816 and the electric motor in 1872. The theoretical work of James Maxwell (see: Maxwell's equations) and Heinrich Hertz in the late 19th century gave rise to the field of electronics. The later inventions of the vacuum tube and the transistor further accelerated the development of electronics to such an extent that electrical and electronics engineers currently outnumber their colleagues of any other engineering specialty. Chemical engineering developed in the late nineteenth century. Industrial scale manufacturing demanded new materials and new processes and by 1880 the need for large scale production of chemicals was such that a new industry was created, dedicated to the development and large scale manufacturing of chemicals in new industrial plants. The role of the chemical engineer was the design of these chemical plants and processes. Originally deriving from the manufacture of ceramics and its putative derivative metallurgy, materials science is one of the oldest forms of engineering. Modern materials science evolved directly from metallurgy, which itself evolved from the use of fire. Important elements of modern materials science were products of the Space Race; the understanding and engineering of the metallic alloys, and silica and carbon materials, used in building space vehicles enabling the exploration of space. Materials science has driven, and been driven by, the development of revolutionary technologies such as rubbers, plastics, semiconductors, and biomaterials. Aeronautical engineering deals with aircraft design process design while aerospace engineering is a more modern term that expands the reach of the discipline by including spacecraft design. Its origins can be traced back to the aviation pioneers around the start of the 20th century although the work of Sir George Cayley has recently been dated as being from the last decade of the 18th century. Early knowledge of aeronautical engineering was largely empirical with some concepts and skills imported from other branches of engineering. Only a decade after the successful flights by the Wright brothers, there was extensive development of aeronautical engineering through development of military aircraft that were used in World War I. Meanwhile, research to provide fundamental background science continued by combining theoretical physics with experiments. == Branches of engineering == Engineering is a broad discipline that is often broken down into several sub-disciplines. Although most engineers will usually be trained in a specific discipline, some engineers become multi-disciplined through experience. Engineering is often characterized as having five main branches: chemical engineering, civil engineering, electrical engineering, materials science and engineering, and mechanical engineering. Below is a list of recognized branches of engineering. There are additional sub-disciplines as well. == Interdisciplinary engineering == Interdisciplinary engineering draws from more than one of the principle branches of the practice. Historically, naval engineering and mining engineering were major branches. Other engineering fields are manufacturing engineering, acoustical engineering, corrosion engineering, instrumentation and control, automotive, information engineering, petroleum, systems, audio, software, architectural, biosystems, and textile engineering. These and other branches of engineering are represented in the 36 licensed member institutions of the UK Engineering Council. New specialties sometimes combine with the traditional fields and form new branches – for example, Earth systems engineering and management involves a wide range of subject areas including engineering studies, environmental science, engineering ethics and philosophy of engineering. == Practice == One who practices engineering is called an engineer, and those licensed to do so may have more formal designations such as Professional Engineer, Chartered Engineer, Incorporated Engineer, Ingenieur, European Engineer, or Designated Engineering Representative. == Methodology == In the engineering design process, engineers apply mathematics and sciences such as physics to find novel solutions to problems or to improve existing solutions. Engineers need proficient knowledge of relevant sciences for their design projects. As a result, many engineers continue to learn new material throughout their careers. If multiple solutions exist, engineers weigh each design choice based on their merit and choose the solution that best matches the requirements. The task of the engineer is to identify, understand, and interpret the constraints on a design in order to yield a successful result. It is generally insufficient to build a technically successful product, rather, it must also meet further requirements. Constraints may include available resources, physical, imaginative or technical limitations, flexibility for future modifications and additions, and other factors, such as requirements for cost, safety, marketability, productivity, and serviceability. By understanding the constraints, engineers derive specifications for the limits within which a viable object or system may be produced and operated. === Problem solving === Engineers use their knowledge of science, mathematics, logic, economics, and appropriate experience or tacit knowledge to find suitable solutions to a particular problem. Creating an appropriate mathematical model of a problem often allows them to analyze it (sometimes definitively), and to test potential solutions. More than one solution to a design problem usually exists so the different design choices have to be evaluated on their merits before the one judged most suitable is chosen. Genrich Altshuller, after gathering statistics on a large number of patents, suggested that compromises are at the heart of "low-level" engineering designs, while at a higher level the best design is one which eliminates the core contradiction causing the problem. Engineers typically attempt to predict how well their designs will perform to their specifications prior to full-scale production. They use, among other things: prototypes, scale models, simulations, destructive tests, nondestructive tests, and stress tests. Testing ensures that products will perform as expected but only in so far as the testing has been representative of use in service. For products, such as aircraft, that are used differently by different users failures and unexpected shortcomings (and necessary design changes) can be expected throughout the operational life of the product. Engineers take on the responsibility of producing designs that will perform as well as expected and, except those employed in specific areas of the arms industry, will not harm people. Engineers typically include a factor of safety in their designs to reduce the risk of unexpected failure. The study of failed products is known as forensic engineering. It attempts to identify the cause of failure to allow a redesign of the product and so prevent a re-occurrence. Careful analysis is needed to establish the cause of failure of a product. The consequences of a failure may vary in severity from the minor cost of a machine breakdown to large loss of life in the case of accidents involving aircraft and large stationary structures like buildings and dams. === Computer use === As with all modern scientific and technological endeavors, computers and software play an increasingly important role. As well as the typical business application software there are a number of computer aided applications (computer-aided technologies) specifically for engineering. Computers can be used to generate models of fundamental physical processes, which can be solved using numerical methods. One of the most widely used design tools in the profession is computer-aided design (CAD) software. It enables engineers to create 3D models, 2D drawings, and schematics of their designs. CAD together with digital mockup (DMU) and CAE software such as finite element method analysis or analytic element method allows engineers to create models of designs that can be analyzed without having to make expensive and time-consuming physical prototypes. These allow products and components to be checked for flaws; assess fit and assembly; study ergonomics; and to analyze static and dynamic characteristics of systems such as stresses, temperatures, electromagnetic emissions, electrical currents and voltages, digital logic levels, fluid flows, and kinematics. Access and distribution of all this information is generally organized with the use of product data management software. There are also many tools to support specific engineering tasks such as computer-aided manufacturing (CAM) software to generate CNC machining instructions; manufacturing process management software for production engineering; EDA for printed circuit board (PCB) and circuit schematics for electronic engineers; MRO applications for maintenance management; and Architecture, engineering and construction (AEC) software for civil engineering. In recent years the use of computer software to aid the development of goods has collectively come to be known as product lifecycle management (PLM). == Social context == The engineering profession engages in a range of activities, from collaboration at the societal level, and smaller individual projects. Almost all engineering projects are obligated to a funding source: a company, a set of investors, or a government. The types of engineering that are less constrained by such a funding source, are pro bono, and open-design engineering. Engineering has interconnections with society, culture and human behavior. Most products and constructions used by modern society, are influenced by engineering. Engineering activities have an impact on the environment, society, economies, and public safety. Engineering projects can be controversial. Examples from different engineering disciplines include: the development of nuclear weapons, the Three Gorges Dam, the design and use of sport utility vehicles and the extraction of oil. In response, some engineering companies have enacted serious corporate and social responsibility policies. The attainment of many of the Millennium Development Goals requires the achievement of sufficient engineering capacity to develop infrastructure and sustainable technological development. Overseas development and relief NGOs make considerable use of engineers, to apply solutions in disaster and development scenarios. Some charitable organizations use engineering directly for development: Engineers Without Borders Engineers Against Poverty Registered Engineers for Disaster Relief Engineers for a Sustainable World Engineering for Change Engineering Ministries International Engineering companies in more developed economies face challenges with regard to the number of engineers being trained, compared with those retiring. This problem is prominent in the UK where engineering has a poor image and low status. There are negative economic and political issues that this can cause, as well as ethical issues. It is agreed the engineering profession faces an "image crisis". The UK holds the most engineering companies compared to other European countries, together with the United States. === Code of ethics === Many engineering societies have established codes of practice and codes of ethics to guide members and inform the public at large. The National Society of Professional Engineers code of ethics states: Engineering is an important and learned profession. As members of this profession, engineers are expected to exhibit the highest standards of honesty and integrity. Engineering has a direct and vital impact on the quality of life for all people. Accordingly, the services provided by engineers require honesty, impartiality, fairness, and equity, and must be dedicated to the protection of the public health, safety, and welfare. Engineers must perform under a standard of professional behavior that requires adherence to the highest principles of ethical conduct. In Canada, engineers wear the Iron Ring as a symbol and reminder of the obligations and ethics associated with their profession. == Relationships with other disciplines == === Science === Scientists study the world as it is; engineers create the world that has never been. There exists an overlap between the sciences and engineering practice; in engineering, one applies science. Both areas of endeavor rely on accurate observation of materials and phenomena. Both use mathematics and classification criteria to analyze and communicate observations. Scientists may also have to complete engineering tasks, such as designing experimental apparatus or building prototypes. Conversely, in the process of developing technology, engineers sometimes find themselves exploring new phenomena, thus becoming, for the moment, scientists or more precisely "engineering scientists". In the book What Engineers Know and How They Know It, Walter Vincenti asserts that engineering research has a character different from that of scientific research. First, it often deals with areas in which the basic physics or chemistry are well understood, but the problems themselves are too complex to solve in an exact manner. There is a "real and important" difference between engineering and physics as similar to any science field has to do with technology. Physics is an exploratory science that seeks knowledge of principles while engineering uses knowledge for practical applications of principles. The former equates an understanding into a mathematical principle while the latter measures variables involved and creates technology. For technology, physics is an auxiliary and in a way technology is considered as applied physics. Though physics and engineering are interrelated, it does not mean that a physicist is trained to do an engineer's job. A physicist would typically require additional and relevant training. Physicists and engineers engage in different lines of work. But PhD physicists who specialize in sectors of engineering physics and applied physics are titled as Technology officer, R&D Engineers and System Engineers. An example of this is the use of numerical approximations to the Navier–Stokes equations to describe aerodynamic flow over an aircraft, or the use of the finite element method to calculate the stresses in complex components. Second, engineering research employs many semi-empirical methods that are foreign to pure scientific research, one example being the method of parameter variation. As stated by Fung et al. in the revision to the classic engineering text Foundations of Solid Mechanics: Engineering is quite different from science. Scientists try to understand nature. Engineers try to make things that do not exist in nature. Engineers stress innovation and invention. To embody an invention the engineer must put his idea in concrete terms, and design something that people can use. That something can be a complex system, device, a gadget, a material, a method, a computing program, an innovative experiment, a new solution to a problem, or an improvement on what already exists. Since a design has to be realistic and functional, it must have its geometry, dimensions, and characteristics data defined. In the past engineers working on new designs found that they did not have all the required information to make design decisions. Most often, they were limited by insufficient scientific knowledge. Thus they studied mathematics, physics, chemistry, biology and mechanics. Often they had to add to the sciences relevant to their profession. Thus engineering sciences were born. Although engineering solutions make use of scientific principles, engineers must also take into account safety, efficiency, economy, reliability, and constructability or ease of fabrication as well as the environment, ethical and legal considerations such as patent infringement or liability in the case of failure of the solution. === Medicine and biology === The study of the human body, albeit from different directions and for different purposes, is an important common link between medicine and some engineering disciplines. Medicine aims to sustain, repair, enhance and even replace functions of the human body, if necessary, through the use of technology. Modern medicine can replace several of the body's functions through the use of artificial organs and can significantly alter the function of the human body through artificial devices such as, for example, brain implants and pacemakers. The fields of bionics and medical bionics are dedicated to the study of synthetic implants pertaining to natural systems. Conversely, some engineering disciplines view the human body as a biological machine worth studying and are dedicated to emulating many of its functions by replacing biology with technology. This has led to fields such as artificial intelligence, neural networks, fuzzy logic, and robotics. There are also substantial interdisciplinary interactions between engineering and medicine. Both fields provide solutions to real world problems. This often requires moving forward before phenomena are completely understood in a more rigorous scientific sense and therefore experimentation and empirical knowledge is an integral part of both. Medicine, in part, studies the function of the human body. The human body, as a biological machine, has many functions that can be modeled using engineering methods. The heart for example functions much like a pump, the skeleton is like a linked structure with levers, the brain produces electrical signals etc. These similarities as well as the increasing importance and application of engineering principles in medicine, led to the development of the field of biomedical engineering that uses concepts developed in both disciplines. Newly emerging branches of science, such as systems biology, are adapting analytical tools traditionally used for engineering, such as systems modeling and computational analysis, to the description of biological systems. === Art === There are connections between engineering and art, for example, architecture, landscape architecture and industrial design (even to the extent that these disciplines may sometimes be included in a university's Faculty of Engineering). The Art Institute of Chicago, for instance, held an exhibition about the art of NASA's aerospace design. Robert Maillart's bridge design is perceived by some to have been deliberately artistic. At the University of South Florida, an engineering professor, through a grant with the National Science Foundation, has developed a course that connects art and engineering. Among famous historical figures, Leonardo da Vinci is a well-known Renaissance artist and engineer, and a prime example of the nexus between art and engineering. === Business === Business engineering deals with the relationship between professional engineering, IT systems, business administration and change management. Engineering management or "Management engineering" is a specialized field of management concerned with engineering practice or the engineering industry sector. The demand for management-focused engineers (or from the opposite perspective, managers with an understanding of engineering), has resulted in the development of specialized engineering management degrees that develop the knowledge and skills needed for these roles. During an engineering management course, students will develop industrial engineering skills, knowledge, and expertise, alongside knowledge of business administration, management techniques, and strategic thinking. Engineers specializing in change management must have in-depth knowledge of the application of industrial and organizational psychology principles and methods. Professional engineers often train as certified management consultants in the very specialized field of management consulting applied to engineering practice or the engineering sector. This work often deals with large scale complex business transformation or business process management initiatives in aerospace and defence, automotive, oil and gas, machinery, pharmaceutical, food and beverage, electrical and electronics, power distribution and generation, utilities and transportation systems. This combination of technical engineering practice, management consulting practice, industry sector knowledge, and change management expertise enables professional engineers who are also qualified as management consultants to lead major business transformation initiatives. These initiatives are typically sponsored by C-level executives. === Other fields === In political science, the term engineering has been borrowed for the study of the subjects of social engineering and political engineering, which deal with forming political and social structures using engineering methodology coupled with political science principles. Marketing engineering and financial engineering have similarly borrowed the term. == See also == Lists Glossaries Related subjects == References == == Further reading == == External links == The dictionary definition of engineering at Wiktionary Learning materials related to Engineering at Wikiversity Quotations related to Engineering at Wikiquote Works related to Engineering at Wikisource
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https://en.wikipedia.org/wiki/Engineering
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Engineering education is the activity of teaching knowledge and principles to the professional practice of engineering. It includes an initial education (Dip.Engg.)and (B.Engg.) or (M.Engg.), and any advanced education and specializations that follow. Engineering education is typically accompanied by additional postgraduate examinations and supervised training as the requirements for a professional engineering license. The length of education, and training to qualify as a basic professional engineer, is typically five years, with 15–20 years for an engineer who takes responsibility for major projects. Science, technology, engineering, and mathematics (STEM) education in primary and secondary schools often serves as the foundation for engineering education at the university level. In the United States, engineering education is a part of the STEM initiative in public schools. Service-learning in engineering education is gaining popularity within the variety of disciplinary focuses within engineering education including chemical engineering, civil engineering, mechanical engineering, industrial engineering, computer engineering, electrical engineering, architectural engineering, and other engineering education. The field of academic inquiry regarding the education of engineers is called engineering education research. == Africa == === Ghana === Ghana's engineering training landscape bridges the gap between theory and practice, equipping students with the technical knowledge and hands-on skills valued by the engineering industry. Students interested in engineering can enter the field at different levels. Traditional Secondary Technical Schools: These schools offer programs leading to the West African Senior Secondary School Certificate (WASSCE), which prepares students for university-level engineering programs. STEM Secondary Schools: Specialized senior high schools providing specialized training in Robotics, Aerospace Engineering, Biomedical and Agricultural Science Technical and Vocational Education and Training (TVET) Schools: These schools provide vocational training, awarding the National Vocational Training Institute (NVTI) certificate. This prepares students for immediate entry into specific technical trades. Polytechnics and Technical Universities: Offer Higher National Diplomas (HNDs) in engineering disciplines, typically lasting three years. These programs have a strong emphasis on practical skills and application, preparing graduates for immediate employment. Some polytechnics have also transitioned to offering four-year Bachelor of Technology (BTech) degrees. Universities: Offer four-year Bachelor of Science (BSc) degrees in various engineering fields like civil, mechanical, electrical, or computer engineering. Ghana's engineering profession is regulated by the Ghana Institution of Engineers (GhIE), an autonomous body established in 1968. Its authority stems from the Engineering Council Act 2011 (Act 819) and the Professional Bodies Registration Decree NRCD143 of 1973. === Kenya === Engineering training in Kenya is typically provided by the universities. Registration of engineers is governed by the Engineers Registration Act. A candidate stands to qualify as a registered engineer, R.Eng., if they are a holder of a minimum of four years of post-secondary Engineering Education and a minimum of three years of postgraduate work experience. All registrations are undertaken by the Engineers Registration Board which is a statutory body established through an Act of the Kenyan Parliament in 1969. A minor revision was done in 1992 to accommodate Technician Engineer grade. The board has been given the responsibility of regulating the activities and conduct of Practicing Engineers in the Republic of Kenya in accordance with the functions and powers conferred upon it by the Act. Under CAP 530 of the Laws of Kenya, it is illegal for an engineer to practice or call themself an engineer if not registered with the board. Registration with the board is thus a license to practice engineering in Kenya. === Nigeria === Engineering training is provided by universities subject to accreditation by the National Universities Commission (NUC) and the Council for Regulation of Engineering in Nigeria (COREN). A candidate can be registered as an engineer after completion of a five-year Bachelor's degree (or equivalent) and four years of post-graduate work experience. Previously, postgraduate education in engineering could be counted towards work experience. A candidate trained through a polytechnic may also be certified as a registered engineer on completion of a two-year Ordinary National Diploma (OND), a two-year Higher National Diploma (HND) and a post-graduate diploma (PGD) all in the same engineering discipline with two years of work experience after the PGD. Registration allows use of the protected title, registered Engineer (Engr). An alternative version, Registered Engineer (R. Eng) is also used although it is not formally recognized by COREN. Any person not registered as an engineer may not use any title that implies that they are registered Engineers. It is illegal to carry out engineering practice without a COREN registration. All unregistered engineers must work under supervision of an Engr. COREN also recognizes other cadres of engineering work- technologists, technicians and craftsmen. Technologists and technicians are trained by polytechnics while craftsmen are trained by technical colleges. Technologists can become registered Engineering Technologists (Eng Tech) on completion of a two-year Ordinary National Diploma (OND), a two-year Higher National Diploma (HND) and three years of post-graduate work experience. A technician can be certified as a registered Engineering Technician (Tech) after completion of a two-year OND and two-years of post-graduate work experience. A craftsman can become a registered Engineering Craftsman after passing the technical exam of the West African Examinations Council or National Business and Technical Examinations Board or a Trade Test Grade 1 from the Federal Ministry of Labour. In addition, two years of work experience are required. === South Africa === Engineering training in South Africa is typically provided by the universities, universities of technology and colleges for Technical and Vocational Education and Training (previously Further Education and Training). The qualifications provided by these institutions must have an Engineering Council of South Africa (ECSA) accreditation for the qualification for graduates and diplomats of these institutions to be registered as Candidate Certificated Engineers, Candidate Engineers, Candidate Engineering Technologists and Candidate Engineering Technicians. There are many benefits to these attributes. The academic training performed by the universities is typically in the form of a four-year BSc(Eng), BIng or BEng degree. For the degree to be accredited, the course material must conform to the ECSA Graduate Attributes (GA). Professional Engineers (Pr Eng) are persons that are accredited by ECSA as engineering professionals. Legally, a Professional Engineer's sign off is required for any major project to be implemented, in order to ensure the safety and standards of the project. Professional Engineering Technologists (Pr Tech Eng) and Professional Engineering Technicians (Pr Techni Eng) are other members of the engineering team. Professional Certificated Engineers (Pr Cert Eng) are people who hold one of seven Government Certificates of Competency and who have been registered by ECSA as engineering professionals. The categories of professionals are differentiated by the degree of complexity of work carried out, where Professional Engineers are expected to solve complex engineering problems, Professional Engineering Technologists and Professional Certificated Engineers, broadly defined engineering problems and Professional Engineering Technicians, well-defined engineering problems. === Tanzania === Engineering training in Tanzania is typically provided by various universities and technical institutions in the country. Graduate engineers are registered by the Engineers Registration Board (ERB) after undergoing three years of practical training. A candidate stands to qualify as a professional engineer, P.Eng., if they are a holder of a minimum four years post-secondary Engineering Education and a minimum of three years of postgraduate work experience. Engineers Registration Board is a statutory body established through an Act of the Tanzanian Parliament in 1968. Minor revision was done in 1997 to address the issue of engineering professional excellence in the country. The board has been given the responsibility of regulating the activities and conduct of Practicing Engineers in the United Republic of Tanzania in accordance with the functions and powers conferred upon it by the Act. According to Tanzania Laws, it is illegal for an engineer to practice or call themself an engineer if not registered with the board. Registration with the board is thus a license to practice engineering in United Republic of Tanzania. == Asia == === Bangladesh === To be educated in engineering education in Bangladesh, one has to study for a long time. This length of time is required because a fashion engineer in Bangladesh has to acquire technical education from an early age. Technical School & College Engineer means skilled in technical education. And to be proficient in technical education, you have to be educated in technical education from childhood. So you have to pass (2 years) Secondary and (2 years) Higher Secondary from Technical School & College under Bangladesh Technical Education Board. Polytechnic/University Polytechnics and universities mainly offer engineering degrees. After secondary and higher secondary, one can get admission in polytechnic & University. Polytechnic & university institutes offer 4-year (Dip.Engg.)and BSc.Engg degrees. Different types of engineering degrees in Diploma are Electrical Engineering, Civil Engineering, Computer Engineering, Electronic Engineering, Marine Engineering, Mechanical Engineering, etc. === Hong Kong === In Hong Kong, engineering degree programmes (4-year bachelor's degree) are offered by public universities funded by the University Grant Committee (UGC). There are 94 UGC-funded programmes in engineering and technology offered by City University of Hong Kong, the Chinese University of Hong Kong, the Hong Kong Polytechnic University, the Hong Kong University of Science and Technology, and the University of Hong Kong. For example, the Faculty of Engineering of the University of Hong Kong (HKU) has five departments providing undergraduate, postgraduate and research degrees in civil engineering, Computer Science, Electrical and Electronic Engineering, Industrial and Manufacturing Systems Engineering, as well as Mechanical Engineering. All programmes of Bachelor of Engineering under the Joint University Programmes Admissions System (JUPAS) code 6963 being offered are accredited by the Hong Kong Institution of Engineers (HKIE). With that standing, the professional qualification of HKU engineering graduates is mutually recognized by most countries, such as the United States, Australia, Canada, Japan, Korea, New Zealand, Singapore and South Africa. Applicants with other local / international /national qualifications such as GCE A-level, International Baccalaureate (IB) or SAT can apply through the Non-JUPAS Route. The Hong Kong Institution of Engineers (the HKIE) accredits individual engineering degree programmes. The process of professional accreditation also considers the appropriate Faculty in terms of its overall philosophy, objectives and resources. The professional accreditation of engineering degree programmes in the universities is normally initiated by a university issuing an invitation to the HKIE's Accreditation Board to carry out appropriate accreditation exercises. To become a professional engineer, senior secondary (Form 4 to Form 6) school students start by choosing science and technology related subjects, while at least passing English and Mathematics in the Hong Kong Diploma of Secondary Education examinations. Secondary school graduates have to enroll in an HKIE accredited engineering programme, join the universities' engineering students society and join the HKIE as a student member. After completing a bachelor's degree in engineering, graduates undergo two to three years of engineering graduate training and gaining another two to three years relevant working experience. Upon passing the Professional Assessment, the candidate will be conferred member by the HKIE, finally becoming a Professional Engineer. The engineering profession in Hong Kong has 21 engineering disciplines, namely Aircraft, Biomedical, Building, Building Services, Chemical, Civil Control, Automation & Instrumentation, Electrical, Electronics, Energy, Environmental, Fire, Gas, Geotechnical, Information, Logistics & Transportation, Manufacturing & Industrial, Marine & Naval Architecture, Materials, Mechanical, as well as Structural engineering. In 2019, the Asian Society of Engineering Education (AsiaSEE) is founded in Hong Kong by Dr. Cecilia K.Y. Chan and over twenty founding members around Asia. AsiaSEE is the first Asian regional network of higher educational institutions leaders with commitment to improve engineering education. The vision of AsiaSEE is to be the trusted body in Asia to facilitate communications and cooperation in engineering education between members, institutions, industries, stakeholders and like-minded societies in the world. The mission of AsiaSEE is to contribute to the advancement and enhancement in engineering education via research and practice for the future generation.} === Uzbekistan === Turin Polytechnic University in Tashkent Tashkent State Technical University Tashkent Institute of Irrigation and Melioration Tashkent Automobile and Road Construction Institut === India === More than 5,000 universities and colleges offer engineering courses in India. === Indonesia === Sepuluh Nopember Institute of Technology Bandung Institute of Technology Faculty of Engineering of Sebelas Maret University Faculty of Engineering of Andalas University Faculty of Engineering of Sultan Ageng Tirtayasa University Faculty of Engineering of University of Indonesia Faculty of Engineering of Gadjah Mada University Faculty of Engineering of Diponegoro University Faculty of Engineering of Universitas Negeri Padang Faculty of Engineering of Universitas Negeri Malang Faculty of Engineering of Hasanuddin University Faculty of Engineering of University of Surabaya === Malaysia === Activities on engineering education in Malaysia are spearheaded by the Society of Engineering Education Malaysia (SEEM). SEEM was established in 2008 and launched on 23 February 2009. The idea of establishing the Society of Engineering Education was initiated in April 2005 with the creating of a Pro-team Committee for SEEM. The objectives of this society are to contribute to the development of education in the fields of engineering education and science and technology, including teaching and learning, counseling, research, service and public relations. Universiti Teknologi Malaysia Centre For Engineering Education, CEE Universiti Tunku Abdul Rahman Tunku Abdul Rahman University College Southern University College Universiti Malaysia Pahang === Pakistan === In Pakistan, engineering education is accredited by the Pakistan Engineering Council, a statutory body, constituted under the PEC Act No. V of 1976 of the constitution of Pakistan and amended vide Ordinance No.XXIII of 2006, to regulate the engineering profession in the country. It aims to achieve rapid and sustainable growth in all national, economic and social fields. The council is responsible for maintaining realistic and internationally relevant standards of professional competence and ethics for engineers in the country. PEC interacts with the Government, both at the Federal and Provincial level by participating in Commissions, Committees and Advisory Bodies. PEC is a fully representative body of the engineering community in the country. PEC has a full signatory status with Washington Accord. === Philippines === The Professional Regulation Commission is the regulating body for engineers in the Philippines. In the Philippines the Center for Innovation in Engineering Education (CIEE) at Batangas State University - The National Engineering University operates with a visionary goals to elevate the standard of engineering education in the country and to cultivate individuals equipped to lead in the dynamic global knowledge economy. With a strategic focus on fostering academic and industry leaders, CIEE acts as a nucleus, fostering collaborations among interdisciplinary experts. This collective synergy promotes a seamless exchange of knowledge and resources, bridging the gap between academia and industry. CIEE's multifaceted support spans from steering engineering curriculum development to achieving targeted advancements in research, teaching methodologies, and assessment pedagogies. Notably, the Center spearheads professional training initiatives, empowering capacity building not only within our institution but across Higher Education Institutions (HEIs). Integral to its mission, CIEE diligently cultivates and manages crucial industry partnerships, facilitating ongoing advancements in engineering education. Furthermore, the Center's commitment extends globally, evidenced by its orchestration of international conferences in engineering education and overseeing the publication of scholarly works, fostering widespread dissemination of pioneering ideas and research. === Sri Lanka === === Taiwan === Engineering is one of the most popular majors among universities in Taiwan. The engineering degrees are over a quarter of the bachelor's degrees in Taiwan. Campuses include the National Taiwan University of Science and Technology. == Europe == === Austria === In Austria, similar to Germany, an engineering degree can be obtained from either universities or Fachhochschulen (universities of applied sciences). As in most of Europe, the education usually consists of a 3-year bachelor's degree and a 2-year master's degree. A lower engineering degree is offered by Höheren Technische Lehranstalten, (HTL, Higher Technical Institute), a form of secondary college which reaches from grade 9 to 13. There are disciplines like civil engineering, electronics, information technology, etc. In the 5th year of HTL, as in other secondary schools in Austria, there is a final exam, called Matura. Graduates obtain an Ingenieur engineering degree after three years of work in the studied field. === Bulgaria === The beginning of higher engineering education in Bulgaria is established by the Law for Establishing a Higher Technical School in Sofia in 1941. Only two years later however because of the bombs flying over Sofia, the school was evacuated in Lovech, and the regular classes were discontinued. The learning process started again in 1945 when the university became a State Polytechnic. In Bulgaria, engineers are trained in the three basic degrees – bachelor, master and doctor. Since the Bologna declaration, students receive a bachelor's degree (4 years of studies), optionally followed by a master's degree (1 years of studies). The science and engineering courses include lecture and laboratory education. The main subjects to be studied are mathematics, physics, chemistry, electrical engineering, etc. The degree received after completing with a state exam or defense of a thesis. Absolvents are awarded with the Ing. title always put in front of one's name. Some of engineering specialties are completely traditional, such as machine building, computer and software engineering, automation, electrical engineering, electronics. Newer specialties are engineering design, mechatronics, aviation engineering, industrial engineering. The following technical universities prepare mainly engineers in Bulgaria: Technical University Sofia Technical University Varna Technical University Gabrovo University of Forestry University of Architecture, Civil Engineering and Geodesy University of Chemical Technology and Metallurgy Sofia Agricultural University Plovdiv University of Mining and Geology "St. Ivan Rilski" The Bulgarian engineers are united in the Federation of Scientific and Technical Unions, established in 1949. It comprises 33 territorial and 19 national unions. === Denmark === In Denmark, the engineering degree is delivered by either universities or engineering colleges (e.g. Engineering College of Aarhus). Students receive first a baccalaureate degree (3 years of studies) followed by a master's degree (1–2 years of studies) according to the principles of the Bologna declaration. The engineering doctorate degree is the PhD (additional 3 years of studies). === Finland === Finland's system is derived from Germany's system. Two kinds of universities are recognized, the universities and the universities of applied sciences. Universities award typically 'Bachelor of Science in Technology' and 'Master of Science in Technology' degrees. Bachelor's degree is a three-year degree as master's degree is equivalent for two-year full-time studies. In Finnish the master's degree is called diplomi-insinööri, similarly as in Germany (Diplom-Ingenieur). The degrees are awarded by engineering schools or faculties in universities (in Aalto University, Oulu, Turku, Vaasa and Åbo Akademi University) or by separate universities of technology (Tampere UT and Lappeenranta UT). The degree is a scientific, theoretical taught master's degree. Master's thesis is important part of master's degree studies. Master's degree qualifies for further study into Licentiate or doctorate. Because of the Bologna process, the degree tekniikan kandidaatti ("Bachelor of Technology"), corresponding to three years of study into the master's degree, has been introduced. The universities of applied sciences are regional universities that award 3.5-, to 4-year engineer degrees insinööri (amk). An engineer's degree is normally 240 ECTS. There are 20 universities of applied sciences in Finland with a vide range of disciplines. The aim of the degree is professional competency with an emphasis on practical problem solving in engineering. Normally the teaching language is Finnish but there are also universities with Swedish as language of instruction, and most universities of applied sciences offer some degrees in English, too. These universities also award a Master of Engineering degree, designed for engineers already involved in the working life with at least two years of professional experience. === France === In France, the engineering degree is mainly delivered by "Grandes Écoles d'Ingénieurs" (graduate schools of engineering) upon completion of 3 years of Master's studies. Many Écoles recruit undergraduate students from CPGE (two- or three-year high level program after the Baccalauréat), even though some of them include an integrated undergraduate cycle. Other students accessing these Grandes Ecoles may come from other horizons, such as DUT or BTS (technical two-year university degrees) or standard two-year university degrees. In all cases, recruitment is highly selective. Hence graduate engineers in France have studied a minimum of five years after the baccalaureate. Since 2013, the French engineering degree is recognized by the AACRAO as a Master of Science in engineering. To be able to deliver the engineering degree, an École Master 's curriculum has to be validated by the Commission des titres d'ingénieur (Commission of the Engineering Title). It is important for the external observer to note that the system in France is extremely demanding in its entrance requirements (numerus clausus, using student rank in exams as the only criterion), despite being almost free of tuition fees, and much stricter in regards to the academic level of applying students than many other systems. The system focuses solely on selecting students by their engineering fundamental disciplines (mathematics, physics) abilities rather than their financial ability to finance large tuition fees, thus enabling a wider population access to higher education. In fact, being a graduate engineer in France is considered as being near/at the top of the social/professional ladder. The engineering profession grew from the military and the nobility in the 18th century. Before the French Revolution, engineers were trained in schools for technical officers, like "École d'Arts et Métiers" (Arts et Métiers ParisTech) established in 1780. Then, other schools were created, for instance the École polytechnique and the Conservatoire national des arts et métiers which was established in 1794. Polytechnique is one of the grandes écoles that have traditionally prepared technocrats to lead French government and industry, and has been one of the most privileged routes into the elite divisions of the civil service known as the "grands corps de l'État". Inside a French company the title of Ingénieur refers to a rank in qualification and is not restricted. Therefore, there are sometimes Ingénieurs des Ventes (Sales Engineers), Ingénieur Marketing, Ingénieur Bancaire (Banking Engineer), Ingénieur Recherche & Développement (R&D Engineer), etc. === Germany === In Germany, the term Ingenieur (engineer) is legally protected and may only be used by graduates of a university degree program in engineering. Such degrees are offered by universities (Universitäten), including Technische Universitäten (universities of technology) and Technische Hochschulen, or Fachhochschulen (universities of applied sciences). Since the Bologna reforms, students receive a bachelor's degree (3–4 years of studies), optionally followed by a master's degree (1–2 years of studies). Prior to the country adopting the Bologna system, the first and only pre-doctorate degree received after completing engineering education at university was the German Diplomingenieur (Dipl.-Ing.). The engineering doctorate is the Doktoringenieur (Dr.-Ing.). === Italy === In Italy, the engineering degree and "engineer" title is delivered by polytechnic universities upon completion of 3 years of studies (laurea). Additional master's degree (2 years) and doctorate programs (3 years) provide the title of "dottore di ricerca in ingegneria". Students that started studies in polytechnic universities before 2005 (when Italy adopted the Bologna declaration) need to complete a 5-year program to get the engineer title. In this case the master's degree is obtained after 1 year of studies. Only people with an engineer title can be employed as "engineers". Still, some with competence and experience in an engineering field that do not have such a title, can still be employed to perform engineering tasks as "specialist", "assistant", "technologist" or "technician". But, only engineers can take legal responsibility and provide guarantee upon the work done by a team in their area of expertise. Sometimes a company working in this area, which temporarily does not have any employees with an engineer title must pay for an external service of an engineering audit to provide legal guarantee for their products or services. === The Netherlands === In the Netherlands there are two ways to study engineering, i.e. at the Dutch 'technical hogeschool', which is a professional school (equivalent to a university of applied sciences internationally) and awards a practically orientated degree with the pre-nominal ing. after four years study. Or at the university, which offers a more academically oriented degree with the pre-nominal ir. after five years study. Both are abbreviations of the title Ingenieur. In 2002 when the Netherlands switched to the Bachelor-Master system. This is a consequence of the Bologna process. In this accord 29 European countries agreed to harmonize their higher education system and create a European higher education area. In this system the professional schools award bachelor's degrees like BEng or BASc after four years study. And the universities with engineering programs award the bachelor's degree BSc after the third year. A university bachelor is usually continuing his education for one or two more years to earn his master's degree MSc. Adjacent to these degrees, the old titles of the pre-populated system are still in use. A vocational bachelor may be admitted to a university master's degree program although often they are required to take additional courses. === Poland === In Poland after 3,5–4 years of technical studies, one gets inżynier degree (inż.), which corresponds to BSc or BEng After that, one can continue studies, and after 2 years of post-graduate programme (supplementary studies) can obtain additional MSc (or MEng) degree, called magister, mgr, and that time one has two degrees: magister inżynier, mgr inż. (literally: master engineer). The mgr degree formerly (until full adaptation of Bologna process by university) could be obtained in integrated 5 years BSc-MSc programme studies. Graduates having magister inżynier degree, can start 4 years doctorate studies (PhD), which require opening of doctoral proceedings (przewód doktorski), carrying out own research, passing some exams (e.g. foreign language, philosophy, economy, leading subjects), writing and defense of doctoral thesis. Some PhD students have also classes with undergraduate students (BSc, MSc). Graduate of doctorate studies of technical university holds scientific degree of doktor nauk technicznych, dr inż., (literally: "doctor of technical sciences") or other e.g. Doktor Nauk Chemicznych (lit. "doctor of chemical sciences"). === Portugal === In Portugal, there are two paths to study engineering: the polytechnic and the university paths. In theory, but many times not so much in practice, the polytechnic path is more practical oriented, the university path being more research oriented. In this system, the polytechnic institutes award a licenciatura (bachelor) in engineering degree after three years of study, that can be complemented by a mestrado (master) in engineering after two plus years of study. Regarding the universities, they offer both engineering programs similar to those of the polytechnics (three years licenciatura plus two years mestrado) as mestrado integrados (integrated master's) in engineering programs. The mestrado integrado programs take five years of study to complete, awarding a licenciatura degree in engineering sciences after the first three years and a mestrado degree in engineering after the whole five years. Further, the universities also offer doutoramento (PhD) programs in engineering. Being an holder of an academic degree in engineering is not enough to practice the profession of engineer and to have the legal right of the use of the title engenheiro (engineer) in Portugal. For that, it is necessary to be admitted and be a member of the Ordem dos Engenheiros (Portuguese institution of engineers). At the Ordem dos Engenheiros, an engineer is classified as an E1, E2 or E3 grade engineer, accordingly with the higher engineer degree he or she holds. Holders of the ancient pre-Bologna declaration five years licenciatura degrees in engineering are classified as E2 engineers. === Romania === In Romania, the engineering degree and "engineer" title is delivered by technology and polytechnics universities upon completion of 4 years of studies. Additional master's degree (2 years) and doctorate programs (4–5 years) provide the title of "doctor inginer". Students that started studies in polytechnic universities before 2005 (when Romania adopted the Bologna declaration) needed to complete a 5-year program to get the engineer title. In this case the master's degree is obtained after 1 year of studies. Only people with an engineer title can be employed as engineers. Still, some with competence and experience in an engineering field that do not have such a title, can still be employed to perform engineering tasks as "specialist", "assistant", "technologist" or "technician". But, only engineers can take legal responsibility and provide guarantee upon the work done by a team in their area of expertise. Sometimes a company working in this area, which temporarily does not have any employees with an engineer title must pay for an external service of an engineering audit to provide legal guarantee for their products or services. === Russia === Moscow School of Mathematics and Navigation was a first Russian educational institution founded by Peter the Great in 1701. It provided Russians with technical education for the first time and much of its curriculum was devoted to producing sailors, engineers, cartographers and bombardiers to support Russian expanding navy and army. Then in 1810, the Saint Petersburg Military engineering-technical university becomes the first engineering higher learning institution in the Russian Empire, after addition of officers classes and application of five-year term of teaching. So initially more rigorisms of standards and teaching terms became the traditional historical feature of the Russian engineering education in the 19th century. === Slovakia === In Slovakia, an engineer (inžinier) is considered to be a person holding master's degree in technical sciences or economics. Several technical and economic universities offer 4-5-year master study in the fields of chemistry, agriculture, material technology, computer science, electrical and mechanical engineering, nuclear physics and technology or economics. A bachelor's degree in similar field is prerequisite. Absolvents are awarded with the Ing. title always put in front of one's name; eventual follow-up doctoral study is offered both by universities and some institutes of the Slovak Academy of Sciences. === Spain === In Spain, the engineering degree is delivered by universities in Engineering Schools, called "Escuelas de Ingeniería". Like with any other degree in Spain, students need to pass a series of examinations based on Bachillerato's subjects (Selectividad), select their bachelor's degree, and their marks determine whether they are access the degree they want or not. Students receive first a grado degree (4 years of studies) followed by a master's degree (1–2 years of studies) according to the principles of the Bologna declaration, though traditionally, the degree received after completing an engineering education is the Spanish title of "Ingeniero". Using the title "Ingeniero" is legally regulated and limited to the according academic graduates. === Sweden === An institution offering engineering education is called "teknisk högskola" (institute of technology). These schools primarily offers five-year programmes resulting in the civilingenjör degree (not to be confused with the narrower English term "civil engineer"), internationally corresponding to a Master of Science in Engineering degree. These programmes typically offers a strong backing in the natural sciences, and the degree also opens up for doctoral (PHD) studies towards the degree "teknologie doktor". Civilingenjör programmes are offered in a broad range of fields: Engineering physics, Chemistry, Civil engineering, surveying, Industrial engineering and management, etc. There also are shorter three-year programmes called högskoleingenjör (Bachelor of Science in Engineering) that are typically more applied. === Turkey === In Turkey, engineering degrees range from a bachelor's degree in engineering (for a four-year period), to a master's degree (adding two years), and to a doctoral degree (usually four to five years). The title is limited by law to people with an engineering degree, and the use of the title by others (even persons with much more work experience) is illegal. The Union of Chambers of Turkish Engineers and Architects (UCTEA) was established in 1954 and separates engineers and architects to professional branches, with the condition of being within the framework of laws and regulations and in accordance with the present conditions, requirements and possibilities and to also establishes new Chambers for the group of engineers and architects, whose professional or working areas are similar or the same. UCTEA is maintaining its activities with its 23 Chambers, 194 branches of its Chambers and 39 Provincial Coordination Councils. Approximately, graduates of 70 related academic disciplines in engineering, architecture and city planning are members of the Chambers of UCTEA. === United Kingdom === In the UK, like in the United States and Canada, most professional engineers are trained in universities, but some can start in a technical apprenticeship and either enroll in a university engineering degree later, or enroll in one of the Engineering Council UK programmes (level 6 – bachelor's and 7 – master's) administered by the City and Guilds of London Institute. A recent trend has seen the rise of both bachelor's and master's degree higher engineering apprenticeships. All accredited engineering courses and apprenticeships are assessed and approved by the various professional engineering institutions reflecting the subject by engineering discipline covered; IMechE, IET, BCS, ICE, IStructE etc. Many of these institutions date back to the 19th century, and have previously administered their own engineering examination programmes. They have become globally renowned as premier learned societies. The degree then counts in part to qualifying as a Chartered Engineer after a period (usually 4–8 years beyond the first degree) of structured professional practice, professional practice peer review and, if required, further exams to then become a corporate member of the relevant professional body. The term 'Chartered Engineer' is regulated by Royal Assent and its use is restricted only to those registered; the awarding of this status is devolved to the professional institutions by the Engineering Council. In the UK (except Scotland), most engineering courses take three years for an undergraduate bachelors (BEng) and four years for an undergraduate master's. Students who read a four-year engineering course are awarded a Masters of Engineering (as opposed to Masters of Science in Engineering) Some universities allow a student to opt out after one year before completion of the programme and receive a Higher National Diploma if a student has successfully completed the second year, or a Higher National Certificate if only successfully completed year one. Many courses also include an option of a year in industry, which is usually a year before completion. Students who opt for this are awarded a 'sandwich degree'. BEng graduates may be registered as an "Incorporated Engineer" by the Engineering Council after a period of structured professional practice, professional practice peer review and, if required, further exams to then become a member of the relevant professional body. Again, the term 'Incorporated Engineer' is regulated by Royal Assent and its use is restricted only to those registered; the awarding of this status is devolved to the professional institutions by the Engineering Council. Unlike the US and Canada, engineers do not require a licence to practice the profession in the UK. In the UK, the term "engineer" can be applied to non-degree vocations such as technologists, technicians, draftsmen, machinists, mechanics, plumbers, electricians, repair people, semi-skilled and even unskilled occupations. In recent developments by government and industry, to address the growing skills deficit in many fields of UK engineering, there has been a strong emphasis placed on dealing with engineering in school and providing students with positive role models from a young age. == Middle East == === Israel === In Israel, several universities and colleges provide engineering degrees. These universities include the Technion Institute of Technology, Tel Aviv University, Bar Ilan University, Ben Gurion University, the Hebrew University of Jerusalem and more. == North America == === Canada === Engineering degree education in Canada is highly regulated by the Canadian Council of Professional Engineers (Engineers Canada) and its Canadian Engineering Accreditation Board (CEAB). In Canada, there are 43 institutions offering 278 engineering accredited programs delivering a bachelor's degree after a term of 4 years. Many schools also offer graduate level degrees in the applied sciences. Accreditation means that students who successfully complete the accredited program will have received sufficient engineering knowledge in order to meet the knowledge requirements of licensure as a Professional Engineer. Alternately, Canadian graduates of unaccredited 3-year diploma, BSc, BTech, or BEng programs can qualify for professional license by association examinations. Some of the schools include: Concordia University, École de technologie supérieure, École Polytechnique de Montréal, University of Toronto, University of Manitoba, University of Saskatchewan, University of Victoria, University of Calgary, University of Alberta, University of British Columbia, McGill University, Dalhousie University, Toronto Metropolitan University, York University, University of Regina, Carleton University, McMaster University, University of Ottawa, Queen's University, University of New Brunswick, UOIT, University of Waterloo, University of Guelph, University of Windsor, Memorial University of Newfoundland, and Royal Military College of Canada. Every university offering engineering degrees in Canada needs to be accredited by the CEAB (Canadian Engineering Accreditation Board), thus ensuring high standards are enforced at all universities. Engineering degrees in Canada are distinct from degrees in engineering technology which are more applied degrees or diplomas. An engineering education in Canada can culminate by qualifying as a professional engineer (P.Eng.) licensee. === Mexico === In the case of Mexico, education in the engineering field could be taken from public and private universities. Both types of colleges and universities can confer degrees of BEng, BSc, MEng, MSc and PhD through the presentation and dissertation of a thesis or other kind of requirements such as technical reports and knowledge exams among others. The first University in Mexico to offers degrees in some engineering fields was the Royal and Pontifical University of Mexico, established under the Spanish rule; the degrees offered included Mines Engineering and Physical Mathematical state-of-the-art knowledge from Europe. Then came the 19th century and lack of political stability. The universities founded under Spanish rule were closed and reopened and the Engineering teaching tradition was lost; the University of Mexico, University of Guadalajara and University of Mérida suffered this. Then the liberal rule created the Arts and Handcraft schools were opened without the same success as the universities. In the 20th century and with the success of the Mexican Revolution some of the old colleges were reopened and the old Arts and Handcraft schools were joined to the new universities. In 1936 the National Polytechnic Institute of Mexico was created as an educational alternative for workers' sons and their families. A short time later the Regional Institutes of Technology were founded as a branch of the Polytechnic Institute in a few states of the republic, though most of them do not have any university in their own territory. Right now the Regional Institutes of Technology have been merged into one single entity labeled as Mexican National Technological Institute. The National Polytechnic Institute is the ensign university of the Mexican federal government on engineering education. === United States === The first professional degree in engineering is a bachelor's degree with few exceptions. Interest in engineering has grown since 1999; the number of bachelor's degrees issued has increased by 20%. Most bachelor's degree engineering programs are four years long and require about two years of core courses followed by two years of specialized discipline specific courses. This is where a typical engineering student would learn mathematics (single- and multi-variable calculus and elementary differential equations), general chemistry, English composition, general and modern physics, computer science (typically programming), and introductory engineering in several areas that are required for a satisfactory engineering background and to be successful in their program of choice. Several courses in social sciences or humanities are often also required, but are commonly elective courses from a broad choice. Required common engineering courses typically include engineering drawing/computer-aided-design, materials engineering, statics and dynamics, strength of materials, basic circuits, thermodynamics, fluid mechanics, and perhaps some systems or industrial engineering. The science and engineering courses include lecture and laboratory education, either in the same course(s) or in separate courses. However, some professors and educators believe that engineering programs should change to focus more on professional engineering practice, and engineering courses should be taught more by professional engineering practitioners and not by engineering researchers. Many engineering degree programs admit students directly to a specialization as a first-year, but those which don't often require students to decide on a specialization by the end of the first or second year of study. Specializations often include architectural engineering, civil engineering (including structural engineering), mechanical engineering, electrical engineering (often including computer engineering), chemical engineering, nuclear engineering, biological engineering, industrial engineering, aerospace engineering, materials engineering (including metallurgical engineering), agricultural engineering, and many other specializations. After choosing a specialization, an engineering student will begin to take classes that will build on the fundamentals and gain their specialized knowledge and skills. Toward the end of their undergraduate education, engineering students often undertake an open-ended design or other special project specific to their field. It is common for University students who are studying engineering to partake in different forms of career development during their undergraduate studies. These often take the form of paid internships, cooperative education programs (also referred to as "co-ops"), research experiences, or service learning. These types of experiences may be facilitated by the students' universities, or sought out by the students independently. ==== Internships ==== Engineering internships are typically pursued by undergraduate students during the summer recess between the Spring and Fall semesters of the standard semester-based academic cycle (although some US universities abide by a 'quarter' or 'trimester' cycle). These internships usually have a duration of 8–12 weeks and may be part-time or full-time as well as paid or unpaid depending on the company; sometimes, students receive academic credit as an alternative or in addition to a wage. Shorter duration full-time internships over winter and other breaks are often available too, especially for those who have completed summer internships with the same firm. Internships are offered as temporary positions by engineering companies, and are often competitive in certain fields. They provide a way for companies to recruit and get familiar with individual students as potential full-time employment after graduation. Engineering internships also have numerous benefits for participating students. They provide hands-on learning outside of the classroom as well as an opportunity for the student to discover if their current choice of engineering discipline is appropriate based on their level of enjoyment of their internship role. Additionally, research and internship experiences have been shown to have a positive effect on engineering task self-efficacy (ETSE), a measure of a students' perception of their ability to perform engineering functions and related tasks. It is also considered advantageous to have internship or co-op experience before completion of undergraduate studies, as students who have practical engineering experience are considered to be more attractive to engineering employers. ==== Cooperative Education Programs ==== Cooperative Education Programs (often referred to as 'co-ops') are similar to internships insofar as they are employment opportunities offered to undergraduate students by engineering employers; however, they are intended to take place concurrently with the students' academic studies. Co-ops are sometimes part-time roles that are ongoing throughout the academic semester, with the student expected to invest between 10 and 30 hours a week depending on the severity of their course load. Some American universities, such as Northeastern University and Drexel University, incorporate co-ops into their students' plan of study in the form of alternating semesters of full-time work and full-time classes; these programs typically take an additional year to complete compared to most 4-year undergraduate engineering programs in the US, even though Northeastern currently has a 4-year undergraduate program that integrates full-time co-ops with full-time studies. Co-ops are considered to be a valuable form of professional development, and may be undertaken by students who are looking to bolster their resumes with hopes of securing better salary offers when looking to secure their first job. ==== Licensing ==== After formal education, the engineer will often enter an internship or engineer in training status for approximately four years. To achieve Engineering Intern (E.I.) or Engineer-in-Training (EIT) status, an individual must be the recipient of an engineering degree from an institution accredited by the Engineering Accreditation Commission (EAC) of the ABET, formerly the Accreditation Board for Engineering and Technology, Inc., as well as pass the Fundamentals of Engineering Exam (often abbreviated to the 'FE Exam'). The FE Exam is offered by the National Council for Examiners for Engineering and Surveying (NCEES) for the following disciplines: Mechanical Engineering, Civil Engineering, Industrial & Systems Engineering, Chemical Engineering, Electrical & Computer Engineering, Environmental Engineering, or Other Disciplines (also referred to as "General Engineering"). The FE Exam is held at remote testing locations four times throughout the year and can be taken by college graduates as well as current college students. After successfully passing the Fundamentals of Engineering Exam and receiving an ABET-accredited engineering degree, an aspiring engineer may apply for engineer-in-training status with their state's licensing board. If granted, they may use the suffix E.I.T. to denote their status as an engineer-in-training. After that time, the engineer in training can decide whether or not to take a state licensing test to make them a Professional Engineer. The licensing process varies state-by-state, but generally they require the engineer-in-training to possess four years of verifiable work experience in their engineering field, as well as successfully pass the NCEES Principles and Practice of Engineering (PE) Exam for their engineering discipline. After successful completion of that test, the Professional engineer can place the suffix P.E. after their name signifying that they are now a Professional Engineer and they can affix their P.E. seal to drawings and reports, for example. They can also serve as expert witnesses in their areas of expertise. Achieving the status of ' Professional Engineer is one of the highest levels of achievement one can attain in the engineering industry. Engineers with this status are generally highly sought-after by employers, especially in the field of Civil Engineering. There are also graduate degree options for an engineer. Many engineers decide to complete a master's degree in some field of engineering or business administration or get education in law, medicine, or other field. Two types of doctorate are available also, the traditional PhD or the Doctor of Engineering. The PhD focuses on research and academic excellence, whereas the doctor of engineering focuses on practical engineering. The education requirements are the same for both degrees; however, the dissertation required is different. The PhD also requires the standard research problem, where the doctor of engineering focuses on a practical dissertation. In present undergraduate engineering education, the emphasis on linear systems develops a way of thinking that dismisses nonlinear dynamics as spurious oscillations. The linear systems approach oversimplifies the dynamics of nonlinear systems. Hence, the undergraduate students and teachers should recognize the educational value of chaotic dynamics. Practicing engineers will also have more insight of nonlinear circuits and systems by having an exposure to chaotic phenomena. After graduation, continuing education courses may be needed to keep a government-issued professional engineer (PE) license valid, to keep skills fresh, to expand skills, or to keep up with new technology. == Caribbean == === Trinidad and Tobago === Engineering degree education in Trinidad and Tobago is not regulated by the Board of Professional Engineers of Trinidad and Tobago (BOETT) or the location Engineering Association (APETT). Professional Engineers registed with BOETT are given the credentials "R.Eng.". == South America == === Argentina === Engineering education programs at universities in Argentina span a variety of disciplines and typically require five–six years of studies to complete. Most degree programs begin with foundational courses in mathematics, statistics, and the physical sciences during the first and second years, then move on to courses specific to the students' plan of study. After receiving a degree, an engineering student will go on to complete an external evaluation in order to become accredited as an engineer. There are many universities and technical schools across Argentina that offer degree programs in engineering education. The National Technological University (Universidad Tecnológica Nacional, UTN) is recognized as one of the best engineering institutions in the country, with degrees in the following disciplines offered across its 33 campuses: Aeronautical Engineering Civil Engineering Electrical Engineering Electronics Engineering Electro-mechanical Engineering Automotive Engineering Information Systems Engineering Railway Engineering Mechanical Engineering Metallurgical Engineering Naval Engineering Fisheries Engineering Chemical Engineering Textile Engineering Outlined in the Argentinian Law 'Ley de Educacion Superior No. 24521' is the requirement for all universities to include a compulsory external evaluation for accreditation of certain professions, such as Law, Medicine, and Engineering, which are also strictly governed by other laws. Accreditation of engineers in Argentina is under the authority of the CONEAU (Comision Nacional de Evaluación y Acreditación Universitaria 1997), which performs the functions of coordinating and executing external evaluations and accrediting graduate and post-graduate university studies in the field of engineering. === Brazil === In Brazil, education in engineering is offered by both public and private institutions. A degree in engineering requires five to six years of studies, comprising the core courses, specific subjects, an internship and a Course Completion Paper. Due to the nature of college admissions in Brazil, most students have to declare their major before entering college. This said, the first two years of a degree in engineering consist mostly of the core courses (calculus, physics, programming, etc.) along with a few specific subjects as well as some courses in humanities. After this period, some institutions offer specializations within the different fields of engineering (i.e. a student majoring in electrical engineering can choose to specialize in electronics or telecommunications) although most institutions balance their workload in order to give the students a consistent knowledge of every specialization. Towards the end of their undergraduate education, students are required to develop the Course Completion Paper under the guidance of an adviser to be presented to and graded by a number of professors. In some institutions, students are also required to pursue an internship (the amount of time depends on the institution). In order to pursue a career in engineering, graduates must first register with and abide by the rules of the Regional Counsel of Engineering and Agronomy of their state, a regional representative of the Federal Counsel of Engineering and Agronomy, a certification board for engineers, agronomists, geologists and other professionals of the applied sciences. == See also == List of engineering schools Education and training of electrical and electronics engineers Education for Chemical Engineers Engineering education research Engineer's degree Global Engineering Education Institute of technology Problem-based learning Project-based learning == Notes == == References == Douglas, Josh; Iversen, Eric; Kalyandurg, Chitra (November 2004), Engineering in the K-12 classroom: An analysis of current practices & guidelines for the future (PDF), Washington, D.C.: American Society for Engineering Education, pp. 1–23, archived from the original (PDF) on 2 April 2012, retrieved 18 September 2011 Dym, C.L.; Agogino, A.M; Eris, O.; Frey, D.D.; Leifer, L.J. (2005), "Engineering Design Thinking, Teaching, and Learning" (PDF), Journal of Engineering Education, 94 (1): 103–120, doi:10.1002/j.2168-9830.2005.tb00832.x, S2CID 1002433, archived from the original (PDF) on 30 March 2012 Wankat, Phillip C.; Oreovicz, Frank S. (1993), Teaching Engineering, New York: McGraw-Hill, ISBN 978-0-07-068154-5
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https://en.wikipedia.org/wiki/Engineering_education
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Quantum engineering is the development of technology that capitalizes on the laws of quantum mechanics. This type of engineering uses quantum mechanics to develop technologies such as quantum sensors and quantum computers. Devices that rely on quantum mechanical effects such as lasers, MRI imagers and transistors have revolutionized many areas of technology. New technologies are being developed that rely on phenomena such as quantum coherence and on progress achieved in the last century in understanding and controlling atomic-scale systems. Quantum mechanical effects are used as a resource in novel technologies with far-reaching applications, including quantum sensors and novel imaging techniques, secure communication (quantum internet) and quantum computing. == History == The field of quantum technology was explored in a 1997 book by Gerard J. Milburn. It was then followed by a 2003 article by Milburn and Jonathan P. Dowling, and a separate publication by David Deutsch on the same year. The application of quantum mechanics was evident in several technologies. These include laser systems, transistors and semiconductor devices, as well as other devices such as MRI imagers. The UK Defence Science and Technology Laboratory (DSTL) grouped these devices as 'quantum 1.0' to differentiate them from what it dubbed as 'quantum 2.0'. This is a definition of the class of devices that actively create, manipulate, and read out quantum states of matter using the effects of superposition and entanglement. From 2010 onwards, multiple governments have established programmes to explore quantum technologies, such as the UK National Quantum Technologies Programme, which created four quantum 'hubs'. These hubs are found at the Centre for Quantum Technologies in Singapore, and QuTech, a Dutch center to develop a topological quantum computer. In 2016, the European Union introduced the Quantum Technology Flagship, a €1 Billion, 10-year-long megaproject, similar in size to earlier European Future and Emerging Technologies Flagship projects. In December 2018, the United States passed the National Quantum Initiative Act, which provides a US$1 billion annual budget for quantum research. China is building the world's largest quantum research facility with a planned investment of 76 billion Yuan (approx. €10 Billion). Indian government has also invested 8000 crore Rupees (approx. US$1.02 Billion) over 5-years to boost quantum technologies under its National Quantum Mission. In the private sector, large companies have made multiple investments in quantum technologies. Organizations such as Google, D-wave systems, and University of California Santa Barbara have formed partnerships and investments to develop quantum technology. == Applications == === Secure communications === Quantum secure communication is a method that is expected to be 'quantum safe' in the advent of quantum computing systems that could break current cryptography systems using methods such as Shor's algorithm. These methods include quantum key distribution (QKD), a method of transmitting information using entangled light in a way that makes any interception of the transmission obvious to the user. Another method is the quantum random number generator, which is capable of producing truly random numbers unlike non-quantum algorithms that merely imitate randomness. === Computing === Quantum computers are expected to have a number of important uses in computing fields such as optimization and machine learning. They are perhaps best known for their expected ability to carry out Shor's algorithm, which can be used to factorize large numbers and is an important process in the securing of data transmissions. Quantum simulators are types of quantum computers intended to simulate a real world system, such as a chemical compound. Quantum simulators are simpler to build as opposed to general purpose quantum computers because complete control over every component is not necessary. Current quantum simulators under development include ultracold atoms in optical lattices, trapped ions, arrays of superconducting qubits, and others. === Sensors === Quantum sensors are expected to have a number of applications in a wide variety of fields including positioning systems, communication technology, electric and magnetic field sensors, gravimetry as well as geophysical areas of research such as civil engineering and seismology. == Education programs == Quantum engineering is evolving into its own engineering discipline. The quantum industry requires a quantum-literate workforce, a missing resource at the moment. Currently, scientists in the field of quantum technology have mostly either a physics or engineering background and have acquired their ”quantum engineering skills” by experience. A survey of more than twenty companies aimed to understand the scientific, technical, and “soft” skills required of new hires into the quantum industry. Results show that companies often look for people that are familiar with quantum technologies and simultaneously possess excellent hands-on lab skills. Several technical universities have launched education programs in this domain. For example, ETH Zurich has initiated a Master of Science in Quantum Engineering, a joint venture between the electrical engineering department (D-ITET) and the physics department (D-PHYS), EPFL offers a dedicated Master's program in Quantum Science and Engineering, combining coursework in quantum physics and engineering with research opportunities, and the University of Waterloo has launched integrated postgraduate engineering programs within the Institute for Quantum Computing. Similar programs are being pursued at Delft University, Technical University of Munich, MIT, CentraleSupélec and other technical universities. In the realm of undergraduate studies, opportunities for specialization are sparse. Nevertheless, some institutions have begun to offer programs. The Université de Sherbrooke offers a Bachelor of Science in quantum information, University of Waterloo offers a quantum specialization in its electrical engineering program, and the University of New South Wales offers a bachelor of quantum engineering. A report on the development of this bachelor degree has been published in IEEE Transactions on Quantum Engineering. Students are trained in signal and information processing, optoelectronics and photonics, integrated circuits (bipolar, CMOS) and electronic hardware architectures (VLSI, FPGA, ASIC). In addition, they are exposed to emerging applications such as quantum sensing, quantum communication and cryptography and quantum information processing. They learn the principles of quantum simulation and quantum computing, and become familiar with different quantum processing platforms, such as trapped ions, and superconducting circuits. Hands-on laboratory projects help students to develop the technical skills needed for the practical realization of quantum devices, consolidating their education in quantum science and technologies. == See also == Quantum supremacy Noisy intermediate-scale quantum era Timeline of quantum computing and communication == References ==
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https://en.wikipedia.org/wiki/Quantum_engineering
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Integrated Engineering is a degree program (and similar concept programs such as Interdisciplinary and Multidisciplinary Engineering) combining aspects from traditional engineering studies and liberal arts, meant to prepare graduates for multi-disciplinary and project-based workplaces. Integrated engineers acquire background in core disciplines such as: materials, solid mechanics, fluid mechanics, and systems involving chemical, electro-mechanical, biological and environmental components. In the United States ,an alliance of Integrated - type programs has been formed called the Alliance for Integrated Engineering (A4IE). == Academia and Accreditation == === Institutions === Currently, the following academic institutions are known to offer Integrated Engineering programs: Canada University of British Columbia University of Western Ontario UK The New Model Institute for Technology and Engineering (NMITE) University of Bath University of Cardiff University of Liverpool University of Nottingham Anglia Ruskin University University Centre Peterborough United States Arizona State University Florida International University Lafayette College Lehigh University Southern Utah University Minnesota State University, Mankato (Iron Range Engineering) Texas A&M University University of Alabama at Birmingham University of Texas at El Paso (E-Lead Program) University of San Diego Wake Forest University Washington and Lee University Germany Baden-Wuerttemberg Cooperative State University (DHBW) South Westphalia University of Applied Sciences Estonia Tallinn University of Technology Korea Chung-Ang University Trinidad and Tobago University of Trinidad and Tobago Thailand Chiang Mai University === Canada === Integrated Engineering originated at the University of Western Ontario in Ontario, Canada and in 2000 the Applied Science Faculty of the University of British Columbia also began a degree program for Integrated Engineering. In Canada, the program has been fully accredited by the Canadian Engineering Accreditation Board and engineers are able to obtain a Professional Engineer (P.Eng) Certificate. === United Kingdom === In 1988, the Engineering Council UK, identified the need for routes to qualification for Chartered (Professional) Engineers that: meet the identified needs of industry, increase access to engineering education by more students, provide a balanced curriculum combining the subjects that engineers use most often and directed towards the needs of the majority of engineers. This is the fundamental definition for Integrated Engineering. The qualities looked for by industry when recruiting graduates were identified as: flexibility and broad education, ability to understand non engineering functions, ability to solve problems, knowledge of the principles of engineering and ability to apply them in practical situations, information skills, experience of project work, especially cross linked projects, ability to work as a member of a team, presentation and communication skills. Engineering Council UK, 1988, An Integrated Engineering Degree Programme. Engineering Council UK, 1988, Admissions to Universities - Action to increase the supply of engineers. Following open competition for additional funding provided by the UK Department for Technology and Industry, and industrial supporters including British Petroleum, six universities were selected from thirty three applicants. Four "Pilot Programmes" were launched at Cardiff University, Nottingham Trent University, Portsmouth University and Sheffield Hallam University. In 1989, The Nottingham Trent University (UK) admitted students to first of the Engineering Council's new Integrated Engineering Degree Programme courses. The course was accredited, at the CEng and European Engineer level, by the Institutions of Mechanical Engineers, Electrical Engineers and Manufacturing Engineers. Generic engineering programmes are common. Integrated Engineering is distinct through emphasizing the development of personal competencies, especially the ability of students to work within groups. It is design led, and integration of all the subjects of study is a defining characteristic, achieved partly through the medium of project based learning. Following the successful experience at The Nottingham Trent University, Integrated Engineering programmes were established in 1993, at selected universities in Bulgaria and Hungary, with the aid of European Union funding granted under the Tempus Programme. In University of Liverpool, the Integrated Engineering Program is accredited by the Institution of Mechanical Engineers and the Institution of Electrical Engineers, and can lead to Chartered Engineer status. In Anglia Ruskin University, the Integrated Engineering Program is accredited by the Institution of Engineering and Technology, and can lead to Incorporated Engineer status. === United States === In the U.S. there are several Integrated engineering education programs. Southern Utah University requires its students to pass the Fundamentals of Engineering exam (FE) before they graduate; and received ABET accreditation in 2004 that extended retroactively through October 2003. The graduates are also able to obtain a Professional Engineer (P.E.) license. Minnesota State University, Mankato has developed a collaborative Integrated engineering program to provide engineering education at MNSCU Community Colleges in the Northern Higher Education District in former Iron Range communities. This partnership allows students to stay near home, while earning a bachelor of science in integrated engineering while focusing on local engineering needs of manufacturers and businesses. As part of the program students are also required to sit for the FE examination prior to graduation and are eligible to sit for the P.E. exam license as the program is also ABET accredited. === Germany === In Germany the [(Baden-Wuerttemberg Cooperative State University (DHBW))] introduced a flexible M.Eng. program in 2015, to fit to the industrial demand for generally educated engineers for Integrated Industry, known as Industry 4.0 in Germany. The graduated school program "Integrated Engineering" is administered at the Center for Advances Studies in Heilbronn and requires at least two years professional experience as an engineer for admission. === Korea === In Korea the Department of Integrative Engineering at Chung-Ang University aims to develop human resources that will contribute to building a knowledge infrastructure by effectively responding to rapid educational and social changes. The department will focus on developing fundamental and application technologies by realizing future-oriented converging technologies and, through a global network, on strengthening convergence-related competitiveness at the university and national level. To accomplish the goals, based on imaginative education using an innovative system, the department will develop “integrative engineering” people who are equipped with initiative research abilities. === Trinidad and Tobago === The Bachelor of Applied Science (B.A.S.c) and Master of Engineering (M.Eng) programs in Utilities Engineering was validated in December 2008 at the University of Trinidad and Tobago. These programs are geared towards the Electrical and Mechanical engineering disciplines that exist within the broad area of Integrated Engineering. Prior to the introduction of the programs most of the engineers in the utilities sector were specialized in one branch of engineering mainly Electrical or Mechanical. The sector required an engineer who was multi-skilled and versed in both disciplines. The Utilities Engineer therefore performs a wide range of maintenance and operational duties in the following industries: Process Industry, Electric Utilities (generation, distribution and efficient utilization), Transportation Industry, Processing and Manufacturing Industry, Water and sanitation industry, Mining and Smelting Industry, Renewable and Green Energy Industry. == See also == University of Western Ontario University of British Columbia Engineering Undergraduate Society of the University of British Columbia Southern Utah University Chung-Ang University == References == == External links == Southern Utah University: Integrated Engineering and Pre-Engineering University of British Columbia: Integrated Engineering University of Western Ontario: Integrated Engineering University of Liverpool: Integrated Engineering University of Windsor: Integrated Engineering University of Nottingham: Integrated Engineering Anglia Ruskin University University Centre Peterborough Chung-Ang University, Seoul, Korea: Integrative Engineering University of Trinidad and Tobago: Utilities Engineering University of San Diego: Integrated Engineering
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Geological engineering is a discipline of engineering concerned with the application of geological science and engineering principles to fields, such as civil engineering, mining, environmental engineering, and forestry, among others. The work of geological engineers often directs or supports the work of other engineering disciplines such as assessing the suitability of locations for civil engineering, environmental engineering, mining operations, and oil and gas projects by conducting geological, geoenvironmental, geophysical, and geotechnical studies. They are involved with impact studies for facilities and operations that affect surface and subsurface environments. The engineering design input and other recommendations made by geological engineers on these projects will often have a large impact on construction and operations. Geological engineers plan, design, and implement geotechnical, geological, geophysical, hydrogeological, and environmental data acquisition. This ranges from manual ground-based methods to deep drilling, to geochemical sampling, to advanced geophysical techniques and satellite surveying. Geological engineers are also concerned with the analysis of past and future ground behaviour, mapping at all scales, and ground characterization programs for specific engineering requirements. These analyses lead geological engineers to make recommendations and prepare reports which could have major effects on the foundations of construction, mining, and civil engineering projects. Some examples of projects include rock excavation, building foundation consolidation, pressure grouting, hydraulic channel erosion control, slope and fill stabilization, landslide risk assessment, groundwater monitoring, and assessment and remediation of contamination. In addition, geological engineers are included on design teams that develop solutions to surface hazards, groundwater remediation, underground and surface excavation projects, and resource management. Like mining engineers, geological engineers also conduct resource exploration campaigns, mine evaluation and feasibility assessments, and contribute to the ongoing efficiency, sustainability, and safety of active mining projects == History == While the term geological engineering was not coined until the 19th century, principles of geological engineering are demonstrated through millennia of human history. === Ancient engineering === One of the oldest examples of geological engineering principles is the Euphrates tunnel, which was constructed around 2180 B.C. – 2160 B.C... This, and other tunnels and qanats from around the same time were used by ancient civilizations such as Babylon and Persia for the purposes of irrigation. Another famous example where geological engineering principles were used in an ancient engineering project was the construction of the Eupalinos aqueduct tunnel in Ancient Greece. This was the first tunnel to be constructed inward from both ends using principles of geometry and trigonometry, marking a significant milestone for both civil engineering and geological engineering === Geological engineering as a discipline === Although projects that applied geological engineering principles in their design and construction have been around for thousands of years, these were included within the civil engineering discipline for most of this time. Courses in geological engineering have been offered since the early 1900s; however, these remained specialized offerings until a large increase in demand arose in the mid-20th century. This demand was created by issues encountered from development of increasingly large and ambitious structures, human-generated waste, scarcity of mineral and energy resources, and anthropogenic climate change – all of which created the need for a more specialized field of engineering with professional engineers who were also experts in geological or Earth sciences. Notable disasters that are attributed to the formal creation of the geological engineering discipline include dam failures in the United States and western Europe in the 1950s and 1960s. These most famously include the St Francis dam failure (1928), Malpasset dam failure (1959), and the Vajont dam failure (1963), where a lack of knowledge of geology resulted in almost 3,000 deaths between the latter two alone. The Malpasset dam failure is regarded as the largest civil engineering disaster of the 20th century in France and Vajont dam failure is still the deadliest landslide in European history. == Education == Post-secondary degrees in geological engineering are offered at various universities around the world but are concentrated primarily in North America. Geological engineers often obtain degrees that include courses in both geological or Earth sciences and engineering. To practice as a professional geological engineer, a bachelor's degree in a related discipline from an accredited institution is required. For certain positions, a Master’s or Doctorate degree in a related engineering discipline may be required. After obtaining these degrees, an individual who wishes to practice as a professional geological engineer must go through the process of becoming licensed by a professional association or regulatory body in their jurisdiction. === Canadian institutions === In Canada, 8 universities are accredited by Engineers Canada to offer undergraduate degrees in geological engineering. Many of these universities also offer graduate degree programs in geological engineering. These include: Queen’s University (Department of Geological Sciences and Geological Engineering) (1975 – present), École Polytechnique (1965 – present), Université Laval (1965 – present), Université du Québec à Chicoutimi (1983 – present), University of British Columbia (1965 – present), University of New Brunswick (jointly administered by Department of Earth Sciences and Department of Civil Engineering) (1984 – present), University of Saskatchewan (1965 – present), and University of Waterloo (1986 – present). === American institutions === In the United States there are 13 geological engineering programs recognized by the Engineering Accreditation Commission (EAC) of the Accreditation Board for Engineering and Technology (ABET). These include: Colorado School of Mines (1936 – present), Michigan Technological University (1951 – present), Missouri University of Science and Technology (1973 – present), Montana Technological University (1972–present), South Dakota School of Mines and Technology (1950 – present), The University of Utah (1952 – present), University of Alaska-Fairbanks (1941 – present), University of Minnesota Twin Cities (1950 – present), University of Mississippi (1987 – present), University of Nevada, Reno (1958 – present), University of North Dakota (1984 – present), University of Texas at Austin (1998 – present), and University of Wisconsin – Madison (1993 – present). === Other institutions === Universities in other countries that hold accreditation to offer degree programs in geological engineering from the EAC by the ABET include: Escuela Superior Politécnica Del Litoral, Guayaquil, Ecuador (2018 – present), Istanbul Technical University, Istanbul, Turkey (2009 – present), Universidad Nacional de Ingeniería, Rímac, Peru (2017 – present), and Universidad Politécnica de Madrid, Madrid, Spain (2014 – present). == Specializations == In geological engineering there are multiple subdisciplines which analyze different aspects of Earth sciences and apply them to a variety of engineering projects. The subdisciplines listed below are commonly taught at the undergraduate level, and each has overlap with disciplines external to geological engineering. However, a geological engineer who specializes in one of these subdisciplines throughout their education may still be licensed to work in any of the other subdisciplines. === Geoenvironmental and hydrogeological engineering === Geoenvironmental engineering is the subdiscipline of geological engineering that focuses on preventing or mitigating the environmental effects of anthropogenic contaminants within soil and water. It solves these issues via the development of processes and infrastructure for the supply of clean water, waste disposal, and control of pollution of all kinds. The work of geoenvironmental engineers largely deals with investigating the migration, interaction, and result of contaminants; remediating contaminated sites; and protecting uncontaminated sites. Typical work of a geoenvironmental engineer includes: The preparation, review, and update of environmental investigation reports, The design of projects such as water reclamation facilities or groundwater monitoring wells which lead to the protection of the environment, Conducting feasibility studies and economic analyses of environmental projects, Obtaining and revising permits, plans, and standard procedures, Providing technical expertise for environmental remediation projects which require legal actions, The analysis of groundwater data for the purpose of quality-control checks, The site investigation and monitoring of environmental remediation and sustainability projects to ensure compliance with environmental regulations, and Advising corporations and government agencies regarding procedures for cleaning up contaminated sites. === Mineral and energy resource exploration engineering === Mineral and energy resource exploration (commonly known as MinEx for short) is the subdiscipline of geological engineering that applies modern tools and concepts to the discovery and sustainable extraction of natural mineral and energy resources. A geological engineer who specializes in this field may work on several stages of mineral exploration and mining projects, including exploration and orebody delineation, mine production operations, mineral processing, and environmental impact and risk assessment programs for mine tailings and other mine waste. Like a mining engineer, mineral and energy resource exploration engineers may also be responsible for the design, finance, and management of mine sites. === Geophysical engineering (applied geophysics) === Geophysical engineering is the subdiscipline of geological engineering that applies geophysics principles to the design of engineering projects such as tunnels, dams, and mines or for the detection of subsurface geohazards, groundwater, and pollution. Geophysical investigations are undertaken from ground surface, in boreholes, or from space to analyze ground conditions, composition, and structure at all scales. Geophysical techniques apply a variety of physics principles such as seismicity, magnetism, gravity, and resistivity. This subdiscipline was created in the early 1990s as a result of an increased demand in more accurate subsurface information created by a rapidly increasing global population. Geophysical engineering and applied geophysics differ from traditional geophysics primarily by their need for marginal returns and optimized designs and practices as opposed to satisfying regulatory requirements at a minimum cost == Job responsibilities == Geological engineers are responsible for the planning, development, and coordination of site investigation and data acquisition programs for geological, geotechnical, geophysical, geoenvironmental, and hydrogeological studies. These studies are traditionally conducted for civil engineering, mining, petroleum, waste management, and regional development projects but are becoming increasingly focused on environmental and coastal engineering projects and on more specialized projects for long-term underground nuclear waste storage. Geological engineers are also responsible for analyzing and preparing recommendations and reports to improve construction of foundations for civil engineering projects such as rock and soil excavation, pressure grouting, and hydraulic channel erosion control. In addition, geological engineers analyze and prepare recommendations and reports on the settlement of buildings, stability of slopes and fills, and probable effects of landslides and earthquakes to support construction and civil engineering projects. They must design means to safely excavate and stabilize the surrounding rock or soil in underground excavations and surface construction, in addition to managing water flow from, and within these excavations. Geological engineers also perform a primary role in all forms of underground infrastructure including tunnelling, mining, hydropower projects, shafts, deep repositories and caverns for power, storage, industrial activities, and recreation. Moreover, geological engineers design monitoring systems, analyze natural and induced ground response, and prepare recommendations and reports on the settlement of buildings, stability of slopes and fills, and the probable effects of natural disasters to support construction and civil engineering projects. In some jobs, geological engineers conduct theoretical and applied studies of groundwater flow and contamination to develop site specific solutions which treat the contaminants and allow for safe construction. Additionally, they design means to manage and protect surface and groundwater resources and remediation solutions in the event of contamination. If working on a mine site, geological engineers may be tasked with planning, development, coordination, and conducting theoretical and experimental studies in mining exploration, mine evaluation and feasibility studies relative to the mining industry. They conduct surveys and studies of ore deposits, ore reserve calculations, and contribute mineral resource expertise, geotechnical and geomechanical design and monitoring expertise and environmental management to a developing or ongoing mining operation. In a variety of projects, they may be expected to design and perform geophysical investigations from surface using boreholes or from space to analyze ground conditions, composition, and structure at all scales == Professional associations and licensing == Professional Engineering Licenses may be issued through a municipal, provincial/state, or federal/national government organization, depending on the jurisdiction. The purpose of this licensing process is to ensure professional engineers possess the necessary technical knowledge, real-world experience, and basic understanding of the local legal system to practice engineering at a professional level. In Canada, the United States, Japan, South Korea, Bangladesh, and South Africa, the title of Professional Engineer is granted through licensure. In the United Kingdom, Ireland, India, and Zimbabwe the granted title is Chartered Engineer . In Australia, the granted title is Chartered Professional Engineer. Lastly, in the European Union, the granted title is European Engineer. All these titles have similar requirements for accreditation, including a recognized post-secondary degree and relevant work experience. === Canada === In Canada, Professional Engineer (P.Eng.) and Professional Geoscientist (P.Geo.) licenses are regulated by provincial professional bodies which have the groundwork for their legislation laid out by Engineers Canada and Geoscientists Canada. The provincial organizations are listed in the table below. === United States === In the United States, all individuals seeking to become a Professional Engineer (P.E.) must attain their license through the Engineering Accreditation Commission (EAC) of the Accreditation Board for Engineering and Technology (ABET). Licenses to be a Certified Professional Geologist in the United States are issued and regulated by the American Institute of Professional Geologists (AIPG) == Professional Societies == Professional societies in geological engineering are not-for-profit organizations that seek to advance and promote the represented profession(s) and connect professionals using networking, regular conferences, meetings, and other events, as well as provide platforms to publish technical literature through forms of conference proceedings, books, technical standards, and suggested methods, and provide opportunities for professional development such as short courses, workshops, and technical tours. Some regional, national, and international professional societies relevant to geological engineers are listed here: American Geophysical Union (AGU) American Geosciences Institute (AGI) American Rock Mechanics Association (ARMA) Association of Environmental and Engineering Geologists (AEG) Association for Mineral Exploration (AME) Atlantic Geoscience Society (AGS) Canadian Dam Association (CDA) Canadian Federation of Earth Sciences (CFES) Canadian Geophysical Union (CGU) Canadian Geotechnical Society (CGS) Canadian Institute of Mining, Metallurgy and Petroleum (CIM) Canadian Society of Petroleum Geologists (CSPG) Canadian Rock Mechanics Association (CARMA) European Association of Geoscientists & Engineers (EAGE) European Geosciences Union (EGU) European Federation of Geologists (EFG) Geological Association of Canada (GAC) Geological Society of America (GSA) Geoscience Information Society (GSIS) Institute of Materials, Minerals and Mining (IOM3) International Association for Engineering Geology and the Environment (IAEG) International Association of Hydrogeologists (IAH) International Council on Mining and Metals (ICMM) International Society for Rock Mechanics and Rock Engineering (ISRM) International Society for Soil Mechanics and Geotechnical Engineering (ISSMGE) International Tunnelling Association (ITA) International Union of Geological Sciences (IUGS) Mineralogical Association of Canada (MAC) Mining Association of Canada (MAC) Prospectors and Developers Association of Canada (PDAC) Society for Mining, Metallurgy & Exploration (SME) Society of Exploration Geophysicists (SEG) Tunnelling Association of Canada (TAC) U.S. Geological Survey (USGS) U.S. National Mining Association (NMA) == Distinction from engineering geology == Engineering geologists and geological engineers are both interested in the study of the Earth, its shifting movement, and alterations, and the interactions of human society and infrastructure with, on, and in Earth materials. Both disciplines require licenses from professional bodies in most jurisdictions to conduct related work. The primary difference between geological engineers and engineering geologists is that geological engineers are licensed professional engineers (and sometimes also professional geoscientists/geologists) with a combined understanding of Earth sciences and engineering principles, while engineering geologists are geological scientists whose work focusses on applications to engineering projects, and they may be licensed professional geoscientists/geologists, but not professional engineers. The following subsections provide more details on the differing responsibilities between engineering geologists and geological engineers. === Engineering geology === Engineering geologists are applied geological scientists who assess problems that might arise before, during, and after an engineering project. They are trained to be aware of potential problems like: landslides, faults, unstable ground, groundwater challenges, and floodplains. They use a variety of field and laboratory testing techniques to characterize ground materials that might affect the construction, the long-term safety, or environmental footprint of a project. Job responsibilities of an engineering geologist include: collecting samples and surveys, conducting lab tests on samples, assessing in situ soil or rock conditions at many scales, preparing reports based on testing and on-site observations for clients, and creating geological models, maps, and sections. === Geological engineering === Geological engineers are engineers with extensive knowledge of geological or Earth sciences as well as engineering geology, engineering principles, and engineering design practices. These professionals are qualified to perform the role of or interact with engineering geologists. Their primary focus, however, is the use of engineering geology data, as well as engineering skills to: Design advanced exploration programs, environmental management or remediation projects including: Groundwater extraction and sustainability, Natural hazard mitigation systems, Energy resource exploration and extraction, Mineral resource exploration and extraction, and Environmental remediation. Design Infrastructure, including: Surface works, Foundations, Tunnels, Dams, Caverns, and Other construction that interfaces with the ground. Oversee components of mining including: Advanced resource assessment and economics, Mineral processing, Mine planning, and Geomechanical and geotechnical stability. In all these activities, the geological model, geological history, and environment, as well as measured engineering properties of relevant Earth materials are critical to engineering design and decision making. == References == == See also == Civil engineering Engineering geology Geology Environmental engineering Mining engineering Petroleum engineering
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Metallurgy is a domain of materials science and engineering that studies the physical and chemical behavior of metallic elements, their inter-metallic compounds, and their mixtures, which are known as alloys. Metallurgy encompasses both the science and the technology of metals, including the production of metals and the engineering of metal components used in products for both consumers and manufacturers. Metallurgy is distinct from the craft of metalworking. Metalworking relies on metallurgy in a similar manner to how medicine relies on medical science for technical advancement. A specialist practitioner of metallurgy is known as a metallurgist. The science of metallurgy is further subdivided into two broad categories: chemical metallurgy and physical metallurgy. Chemical metallurgy is chiefly concerned with the reduction and oxidation of metals, and the chemical performance of metals. Subjects of study in chemical metallurgy include mineral processing, the extraction of metals, thermodynamics, electrochemistry, and chemical degradation (corrosion). In contrast, physical metallurgy focuses on the mechanical properties of metals, the physical properties of metals, and the physical performance of metals. Topics studied in physical metallurgy include crystallography, material characterization, mechanical metallurgy, phase transformations, and failure mechanisms. Historically, metallurgy has predominately focused on the production of metals. Metal production begins with the processing of ores to extract the metal, and includes the mixture of metals to make alloys. Metal alloys are often a blend of at least two different metallic elements. However, non-metallic elements are often added to alloys in order to achieve properties suitable for an application. The study of metal production is subdivided into ferrous metallurgy (also known as black metallurgy) and non-ferrous metallurgy, also known as colored metallurgy. Ferrous metallurgy involves processes and alloys based on iron, while non-ferrous metallurgy involves processes and alloys based on other metals. The production of ferrous metals accounts for 95% of world metal production. Modern metallurgists work in both emerging and traditional areas as part of an interdisciplinary team alongside material scientists and other engineers. Some traditional areas include mineral processing, metal production, heat treatment, failure analysis, and the joining of metals (including welding, brazing, and soldering). Emerging areas for metallurgists include nanotechnology, superconductors, composites, biomedical materials, electronic materials (semiconductors) and surface engineering. == Etymology and pronunciation == Metallurgy derives from the Ancient Greek μεταλλουργός, metallourgós, "worker in metal", from μέταλλον, métallon, "mine, metal" + ἔργον, érgon, "work" The word was originally an alchemist's term for the extraction of metals from minerals, the ending -urgy signifying a process, especially manufacturing: it was discussed in this sense in the 1797 Encyclopædia Britannica. In the late 19th century, metallurgy's definition was extended to the more general scientific study of metals, alloys, and related processes. In English, the pronunciation is the more common one in the United Kingdom. The pronunciation is the more common one in the US and is the first-listed variant in various American dictionaries, including Merriam-Webster Collegiate and American Heritage. == History == The earliest metal employed by humans appears to be gold, which can be found "native". Small amounts of natural gold, dating to the late Paleolithic period, 40,000 BC, have been found in Spanish caves. Silver, copper, tin and meteoric iron can also be found in native form, allowing a limited amount of metalworking in early cultures. Early cold metallurgy, using native copper not melted from mineral has been documented at sites in Anatolia and at the site of Tell Maghzaliyah in Iraq, dating from the 7th/6th millennia BC. The earliest archaeological support of smelting (hot metallurgy) in Eurasia is found in the Balkans and Carpathian Mountains, as evidenced by findings of objects made by metal casting and smelting dated to around 6200–5000 BC, with the invention of copper metallurgy. Certain metals, such as tin, lead, and copper can be recovered from their ores by simply heating the rocks in a fire or blast furnace in a process known as smelting. The first evidence of copper smelting, dating from the 6th millennium BC, has been found at archaeological sites in Majdanpek, Jarmovac and Pločnik, in present-day Serbia. The site of Pločnik has produced a smelted copper axe dating from 5,500 BC, belonging to the Vinča culture. The Balkans and adjacent Carpathian region were the location of major Chalcolithic cultures including Vinča, Varna, Karanovo, Gumelnița and Hamangia, which are often grouped together under the name of 'Old Europe'. With the Carpatho-Balkan region described as the 'earliest metallurgical province in Eurasia', its scale and technical quality of metal production in the 6th–5th millennia BC totally overshadowed that of any other contemporary production centre. The earliest documented use of lead (possibly native or smelted) in the Near East dates from the 6th millennium BC, is from the late Neolithic settlements of Yarim Tepe and Arpachiyah in Iraq. The artifacts suggest that lead smelting may have predated copper smelting. Metallurgy of lead has also been found in the Balkans during the same period. Copper smelting is documented at sites in Anatolia and at the site of Tal-i Iblis in southeastern Iran from c. 5000 BC. Copper smelting is first documented in the Delta region of northern Egypt in c. 4000 BC, associated with the Maadi culture. This represents the earliest evidence for smelting in Africa. The Varna Necropolis, Bulgaria, is a burial site located in the western industrial zone of Varna, approximately 4 km from the city centre, internationally considered one of the key archaeological sites in world prehistory. The oldest gold treasure in the world, dating from 4,600 BC to 4,200 BC, was discovered at the site. The gold piece dating from 4,500 BC, found in 2019 in Durankulak, near Varna is another important example. Other signs of early metals are found from the third millennium BC in Palmela, Portugal, Los Millares, Spain, and Stonehenge, United Kingdom. The precise beginnings, however, have not be clearly ascertained and new discoveries are both continuous and ongoing. In approximately 1900 BC, ancient iron smelting sites existed in Tamil Nadu. In the Near East, about 3,500 BC, it was discovered that by combining copper and tin, a superior metal could be made, an alloy called bronze. This represented a major technological shift known as the Bronze Age. The extraction of iron from its ore into a workable metal is much more difficult than for copper or tin. The process appears to have been invented by the Hittites in about 1200 BC, beginning the Iron Age. The secret of extracting and working iron was a key factor in the success of the Philistines. Historical developments in ferrous metallurgy can be found in a wide variety of past cultures and civilizations. This includes the ancient and medieval kingdoms and empires of the Middle East and Near East, ancient Iran, ancient Egypt, ancient Nubia, and Anatolia in present-day Turkey, Ancient Nok, Carthage, the Celts, Greeks and Romans of ancient Europe, medieval Europe, ancient and medieval China, ancient and medieval India, ancient and medieval Japan, amongst others. A 16th century book by Georg Agricola, De re metallica, describes the highly developed and complex processes of mining metal ores, metal extraction, and metallurgy of the time. Agricola has been described as the "father of metallurgy". == Extraction == Extractive metallurgy is the practice of removing valuable metals from an ore and refining the extracted raw metals into a purer form. In order to convert a metal oxide or sulphide to a purer metal, the ore must be reduced physically, chemically, or electrolytically. Extractive metallurgists are interested in three primary streams: feed, concentrate (metal oxide/sulphide) and tailings (waste). After mining, large pieces of the ore feed are broken through crushing or grinding in order to obtain particles small enough, where each particle is either mostly valuable or mostly waste. Concentrating the particles of value in a form supporting separation enables the desired metal to be removed from waste products. Mining may not be necessary, if the ore body and physical environment are conducive to leaching. Leaching dissolves minerals in an ore body and results in an enriched solution. The solution is collected and processed to extract valuable metals. Ore bodies often contain more than one valuable metal. Tailings of a previous process may be used as a feed in another process to extract a secondary product from the original ore. Additionally, a concentrate may contain more than one valuable metal. That concentrate would then be processed to separate the valuable metals into individual constituents. == Metal and its alloys == Much effort has been placed on understanding iron–carbon alloy system, which includes steels and cast irons. Plain carbon steels (those that contain essentially only carbon as an alloying element) are used in low-cost, high-strength applications, where neither weight nor corrosion are a major concern. Cast irons, including ductile iron, are also part of the iron-carbon system. Iron-Manganese-Chromium alloys (Hadfield-type steels) are also used in non-magnetic applications such as directional drilling. Other engineering metals include aluminium, chromium, copper, magnesium, nickel, titanium, zinc, and silicon. These metals are most often used as alloys with the noted exception of silicon, which is not a metal. Other forms include: Stainless steel, particularly Austenitic stainless steels, galvanized steel, nickel alloys, titanium alloys, or occasionally copper alloys are used, where resistance to corrosion is important. Aluminium alloys and magnesium alloys are commonly used, when a lightweight strong part is required such as in automotive and aerospace applications. Copper-nickel alloys (such as Monel) are used in highly corrosive environments and for non-magnetic applications. Nickel-based superalloys like Inconel are used in high-temperature applications such as gas turbines, turbochargers, pressure vessels, and heat exchangers. For extremely high temperatures, single crystal alloys are used to minimize creep. In modern electronics, high purity single crystal silicon is essential for metal-oxide-silicon transistors (MOS) and integrated circuits. == Production == In production engineering, metallurgy is concerned with the production of metallic components for use in consumer or engineering products. This involves production of alloys, shaping, heat treatment and surface treatment of product. The task of the metallurgist is to achieve balance between material properties, such as cost, weight, strength, toughness, hardness, corrosion, fatigue resistance and performance in temperature extremes. To achieve this goal, the operating environment must be carefully considered. Determining the hardness of the metal using the Rockwell, Vickers, and Brinell hardness scales is a commonly used practice that helps better understand the metal's elasticity and plasticity for different applications and production processes. In a saltwater environment, most ferrous metals and some non-ferrous alloys corrode quickly. Metals exposed to cold or cryogenic conditions may undergo a ductile to brittle transition and lose their toughness, becoming more brittle and prone to cracking. Metals under continual cyclic loading can suffer from metal fatigue. Metals under constant stress at elevated temperatures can creep. === Metalworking processes === Casting – molten metal is poured into a shaped mold. Variants of casting include sand casting, investment casting, also called the lost wax process, die casting, centrifugal casting, both vertical and horizontal, and continuous castings. Each of these forms has advantages for certain metals and applications considering factors like magnetism and corrosion. Forging – a red-hot billet is hammered into shape. Rolling – a billet is passed through successively narrower rollers to create a sheet. Extrusion – a hot and malleable metal is forced under pressure through a die, which shapes it before it cools. Machining – lathes, milling machines and drills cut the cold metal to shape. Sintering – a powdered metal is heated in a non-oxidizing environment after being compressed into a die. Fabrication – sheets of metal are cut with guillotines or gas cutters and bent and welded into structural shape. Laser cladding – metallic powder is blown through a movable laser beam (e.g. mounted on a NC 5-axis machine). The resulting melted metal reaches a substrate to form a melt pool. By moving the laser head, it is possible to stack the tracks and build up a three-dimensional piece. 3D printing – Sintering or melting amorphous powder metal in a 3D space to make any object to shape. Cold-working processes, in which the product's shape is altered by rolling, fabrication or other processes, while the product is cold, can increase the strength of the product by a process called work hardening. Work hardening creates microscopic defects in the metal, which resist further changes of shape. === Heat treatment === Metals can be heat-treated to alter the properties of strength, ductility, toughness, hardness and resistance to corrosion. Common heat treatment processes include annealing, precipitation strengthening, quenching, and tempering: Annealing process softens the metal by heating it and then allowing it to cool very slowly, which gets rid of stresses in the metal and makes the grain structure large and soft-edged so that, when the metal is hit or stressed it dents or perhaps bends, rather than breaking; it is also easier to sand, grind, or cut annealed metal. Quenching is the process of cooling metal very quickly after heating, thus "freezing" the metal's molecules in the very hard martensite form, which makes the metal harder. Tempering relieves stresses in the metal that were caused by the hardening process; tempering makes the metal less hard while making it better able to sustain impacts without breaking. Often, mechanical and thermal treatments are combined in what are known as thermo-mechanical treatments for better properties and more efficient processing of materials. These processes are common to high-alloy special steels, superalloys and titanium alloys. === Plating === Electroplating is a chemical surface-treatment technique. It involves bonding a thin layer of another metal such as gold, silver, chromium or zinc to the surface of the product. This is done by selecting the coating material electrolyte solution, which is the material that is going to coat the workpiece (gold, silver, zinc). There needs to be two electrodes of different materials: one the same material as the coating material and one that is receiving the coating material. Two electrodes are electrically charged and the coating material is stuck to the work piece. It is used to reduce corrosion as well as to improve the product's aesthetic appearance. It is also used to make inexpensive metals look like the more expensive ones (gold, silver). === Shot peening === Shot peening is a cold working process used to finish metal parts. In the process of shot peening, small round shot is blasted against the surface of the part to be finished. This process is used to prolong the product life of the part, prevent stress corrosion failures, and also prevent fatigue. The shot leaves small dimples on the surface like a peen hammer does, which cause compression stress under the dimple. As the shot media strikes the material over and over, it forms many overlapping dimples throughout the piece being treated. The compression stress in the surface of the material strengthens the part and makes it more resistant to fatigue failure, stress failures, corrosion failure, and cracking. === Thermal spraying === Thermal spraying techniques are another popular finishing option, and often have better high temperature properties than electroplated coatings. Thermal spraying, also known as a spray welding process, is an industrial coating process that consists of a heat source (flame or other) and a coating material that can be in a powder or wire form, which is melted then sprayed on the surface of the material being treated at a high velocity. The spray treating process is known by many different names such as HVOF (High Velocity Oxygen Fuel), plasma spray, flame spray, arc spray and metalizing. === Electroless deposition === Electroless deposition (ED) or electroless plating is defined as the autocatalytic process through which metals and metal alloys are deposited onto nonconductive surfaces. These nonconductive surfaces include plastics, ceramics, and glass etc., which can then become decorative, anti-corrosive, and conductive depending on their final functions. Electroless deposition is a chemical processes that create metal coatings on various materials by autocatalytic chemical reduction of metal cations in a liquid bath. == Characterization == Metallurgists study the microscopic and macroscopic structure of metals using metallography, a technique invented by Henry Clifton Sorby. In metallography, an alloy of interest is ground flat and polished to a mirror finish. The sample can then be etched to reveal the microstructure and macrostructure of the metal. The sample is then examined in an optical or electron microscope, and the image contrast provides details on the composition, mechanical properties, and processing history. Crystallography, often using diffraction of x-rays or electrons, is another valuable tool available to the modern metallurgist. Crystallography allows identification of unknown materials and reveals the crystal structure of the sample. Quantitative crystallography can be used to calculate the amount of phases present as well as the degree of strain to which a sample has been subjected. Current advanced characterization techniques, which are used frequently in this field are: Scanning Electron Microscopy (SEM), Transmission Electron Microscopy (TEM), Electron Backscattered Diffraction (EBSD) and Atom-Probe Tomography (APT). == See also == == References ==
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In engineering, macro-engineering (alternatively known as mega engineering) is the implementation of large-scale design projects. It can be seen as a branch of civil engineering or structural engineering applied on a large landmass. In particular, macro-engineering is the process of marshaling and managing of resources and technology on a large scale to carry out complex tasks that last over a long period. In contrast to conventional engineering projects, macro-engineering projects (called macro-projects or mega-projects) are multidisciplinary, involving collaboration from all fields of study. Because of the size of macro-projects they are usually international. Macro-engineering is an evolving field that has only recently started to receive attention. Because we routinely deal with challenges that are multinational in scope, such as global warming and pollution, macro-engineering is emerging as a transcendent solution to worldwide problems. Macro-engineering is distinct from Megascale engineering due to the scales where they are applied. Where macro-engineering is currently practical, mega-scale engineering is still within the domain of speculative fiction because it deals with projects on a planetary or stellar scale. == Projects == Macro engineering examples include the construction of the Panama Canal and the Suez Canal. == Planned projects == Examples of projects include the Channel Tunnel and the planned Gibraltar Tunnel. Two intellectual centers focused on macro-engineering theory and practice are the Candida Oancea Institute in Bucharest, and The Center for Macro Projects and Diplomacy at Roger Williams University in Bristol, Rhode Island. == See also == == References == Frank P. Davidson and Kathleen Lusk Brooke, BUILDING THE WORLD: AN ENCYCLOPEDIA OF THE GREAT ENGINEERING PROJECTS IN HISTORY, two volumes (Greenwood Publishing Group, Oxford UK, 2006) V. Badescu, R.B. Cathcart and R.D. Schuiling, MACRO-ENGINEERING: A CHALLENGE FOR THE FUTURE (Springer, The Netherlands, 2006) R.B. Cathcart, V. Badescu with Ramesh Radhakrishnan, (2006): Macro-Engineers' Dreams Archived 2013-10-24 at the Wayback Machine PDF, 175pp. Accessed 24 May 2013 Alexander Bolonkin and Richard B. Cathcart, Macro-Projects (NOVA Publishing, 2009) Viorel Badescu and R.B. Cathcart, Macro-engineering Seawater (Springer, 2010), 880 pages. R.B. Cathcart, MACRO-IMAGINEERING OUR DOSMOZOICUM. (Lambert Academic Publishing, 2018) 154 pages. == External links == Engineering and the Future of Technology Megaengineering at Popular Mechanics
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https://en.wikipedia.org/wiki/Macro-engineering
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Mechanical engineering is the study of physical machines and mechanisms that may involve force and movement. It is an engineering branch that combines engineering physics and mathematics principles with materials science, to design, analyze, manufacture, and maintain mechanical systems. It is one of the oldest and broadest of the engineering branches. Mechanical engineering requires an understanding of core areas including mechanics, dynamics, thermodynamics, materials science, design, structural analysis, and electricity. In addition to these core principles, mechanical engineers use tools such as computer-aided design (CAD), computer-aided manufacturing (CAM), computer-aided engineering (CAE), and product lifecycle management to design and analyze manufacturing plants, industrial equipment and machinery, heating and cooling systems, transport systems, motor vehicles, aircraft, watercraft, robotics, medical devices, weapons, and others. Mechanical engineering emerged as a field during the Industrial Revolution in Europe in the 18th century; however, its development can be traced back several thousand years around the world. In the 19th century, developments in physics led to the development of mechanical engineering science. The field has continually evolved to incorporate advancements; today mechanical engineers are pursuing developments in such areas as composites, mechatronics, and nanotechnology. It also overlaps with aerospace engineering, metallurgical engineering, civil engineering, structural engineering, electrical engineering, manufacturing engineering, chemical engineering, industrial engineering, and other engineering disciplines to varying amounts. Mechanical engineers may also work in the field of biomedical engineering, specifically with biomechanics, transport phenomena, biomechatronics, bionanotechnology, and modelling of biological systems. == History == The application of mechanical engineering can be seen in the archives of various ancient and medieval societies. The six classic simple machines were known in the ancient Near East. The wedge and the inclined plane (ramp) were known since prehistoric times. Mesopotamian civilization is credited with the invention of the wheel by several, mainly old sources. However, some recent sources either suggest that it was invented independently in both Mesopotamia and Eastern Europe or credit prehistoric Eastern Europeans with the invention of the wheel The lever mechanism first appeared around 5,000 years ago in the Near East, where it was used in a simple balance scale, and to move large objects in ancient Egyptian technology. The lever was also used in the shadoof water-lifting device, the first crane machine, which appeared in Mesopotamia circa 3000 BC. The earliest evidence of pulleys date back to Mesopotamia in the early 2nd millennium BC. The Saqiyah was developed in the Kingdom of Kush during the 4th century BC. It relied on animal power reducing the tow on the requirement of human energy. Reservoirs in the form of Hafirs were developed in Kush to store water and boost irrigation. Bloomeries and blast furnaces were developed during the seventh century BC in Meroe. Kushite sundials applied mathematics in the form of advanced trigonometry. The earliest practical water-powered machines, the water wheel and watermill, first appeared in the Persian Empire, in what are now Iraq and Iran, by the early 4th century BC. In ancient Greece, the works of Archimedes (287–212 BC) influenced mechanics in the Western tradition. The geared Antikythera mechanisms was an Analog computer invented around the 2nd century BC. In Roman Egypt, Heron of Alexandria (c. 10–70 AD) created the first steam-powered device (Aeolipile). In China, Zhang Heng (78–139 AD) improved a water clock and invented a seismometer, and Ma Jun (200–265 AD) invented a chariot with differential gears. The medieval Chinese horologist and engineer Su Song (1020–1101 AD) incorporated an escapement mechanism into his astronomical clock tower two centuries before escapement devices were found in medieval European clocks. He also invented the world's first known endless power-transmitting chain drive. The cotton gin was invented in India by the 6th century AD, and the spinning wheel was invented in the Islamic world by the early 11th century, Dual-roller gins appeared in India and China between the 12th and 14th centuries. The worm gear roller gin appeared in the Indian subcontinent during the early Delhi Sultanate era of the 13th to 14th centuries. During the Islamic Golden Age (7th to 15th century), Muslim inventors made remarkable contributions in the field of mechanical technology. Al-Jazari, who was one of them, wrote his famous Book of Knowledge of Ingenious Mechanical Devices in 1206 and presented many mechanical designs. In the 17th century, important breakthroughs in the foundations of mechanical engineering occurred in England and the Continent. The Dutch mathematician and physicist Christiaan Huygens invented the pendulum clock in 1657, which was the first reliable timekeeper for almost 300 years, and published a work dedicated to clock designs and the theory behind them. In England, Isaac Newton formulated his laws of motion and developed calculus, which would become the mathematical basis of physics. Newton was reluctant to publish his works for years, but he was finally persuaded to do so by his colleagues, such as Edmond Halley. Gottfried Wilhelm Leibniz, who earlier designed a mechanical calculator, is also credited with developing the calculus during the same time period. During the early 19th century Industrial Revolution, machine tools were developed in England, Germany, and Scotland. This allowed mechanical engineering to develop as a separate field within engineering. They brought with them manufacturing machines and the engines to power them. The first British professional society of mechanical engineers was formed in 1847 Institution of Mechanical Engineers, thirty years after the civil engineers formed the first such professional society Institution of Civil Engineers. On the European continent, Johann von Zimmermann (1820–1901) founded the first factory for grinding machines in Chemnitz, Germany in 1848. In the United States, the American Society of Mechanical Engineers (ASME) was formed in 1880, becoming the third such professional engineering society, after the American Society of Civil Engineers (1852) and the American Institute of Mining Engineers (1871). The first schools in the United States to offer an engineering education were the United States Military Academy in 1817, an institution now known as Norwich University in 1819, and Rensselaer Polytechnic Institute in 1825. Education in mechanical engineering has historically been based on a strong foundation in mathematics and science. == Education == Degrees in mechanical engineering are offered at various universities worldwide. Mechanical engineering programs typically take four to five years of study depending on the place and university and result in a Bachelor of Engineering (B.Eng. or B.E.), Bachelor of Science (B.Sc. or B.S.), Bachelor of Science Engineering (B.Sc.Eng.), Bachelor of Technology (B.Tech.), Bachelor of Mechanical Engineering (B.M.E.), or Bachelor of Applied Science (B.A.Sc.) degree, in or with emphasis in mechanical engineering. In Spain, Portugal and most of South America, where neither B.S. nor B.Tech. programs have been adopted, the formal name for the degree is "Mechanical Engineer", and the course work is based on five or six years of training. In Italy the course work is based on five years of education, and training, but in order to qualify as an Engineer one has to pass a state exam at the end of the course. In Greece, the coursework is based on a five-year curriculum. In the United States, most undergraduate mechanical engineering programs are accredited by the Accreditation Board for Engineering and Technology (ABET) to ensure similar course requirements and standards among universities. The ABET web site lists 302 accredited mechanical engineering programs as of 11 March 2014. Mechanical engineering programs in Canada are accredited by the Canadian Engineering Accreditation Board (CEAB), and most other countries offering engineering degrees have similar accreditation societies. In Australia, mechanical engineering degrees are awarded as Bachelor of Engineering (Mechanical) or similar nomenclature, although there are an increasing number of specialisations. The degree takes four years of full-time study to achieve. To ensure quality in engineering degrees, Engineers Australia accredits engineering degrees awarded by Australian universities in accordance with the global Washington Accord. Before the degree can be awarded, the student must complete at least 3 months of on the job work experience in an engineering firm. Similar systems are also present in South Africa and are overseen by the Engineering Council of South Africa (ECSA). In India, to become an engineer, one needs to have an engineering degree like a B.Tech. or B.E., have a diploma in engineering, or by completing a course in an engineering trade like fitter from the Industrial Training Institute (ITIs) to receive a "ITI Trade Certificate" and also pass the All India Trade Test (AITT) with an engineering trade conducted by the National Council of Vocational Training (NCVT) by which one is awarded a "National Trade Certificate". A similar system is used in Nepal. Some mechanical engineers go on to pursue a postgraduate degree such as a Master of Engineering, Master of Technology, Master of Science, Master of Engineering Management (M.Eng.Mgt. or M.E.M.), a Doctor of Philosophy in engineering (Eng.D. or Ph.D.) or an engineer's degree. The master's and engineer's degrees may or may not include research. The Doctor of Philosophy includes a significant research component and is often viewed as the entry point to academia. The Engineer's degree exists at a few institutions at an intermediate level between the master's degree and the doctorate. === Coursework === Standards set by each country's accreditation society are intended to provide uniformity in fundamental subject material, promote competence among graduating engineers, and to maintain confidence in the engineering profession as a whole. Engineering programs in the U.S., for example, are required by ABET to show that their students can "work professionally in both thermal and mechanical systems areas." The specific courses required to graduate, however, may differ from program to program. Universities and institutes of technology will often combine multiple subjects into a single class or split a subject into multiple classes, depending on the faculty available and the university's major area(s) of research. The fundamental subjects required for mechanical engineering usually include: Mathematics (in particular, calculus, differential equations, and linear algebra) Basic physical sciences (including physics and chemistry) Statics and dynamics Strength of materials and solid mechanics Materials engineering, composites Thermodynamics, heat transfer, energy conversion, and HVAC Fuels, combustion, internal combustion engine Fluid mechanics (including fluid statics and fluid dynamics) Mechanism and Machine design (including kinematics and dynamics) Instrumentation and measurement Manufacturing engineering, technology, or processes Vibration, control theory and control engineering Hydraulics and Pneumatics Mechatronics and robotics Engineering design and product design Drafting, computer-aided design (CAD) and computer-aided manufacturing (CAM) Mechanical engineers are also expected to understand and be able to apply basic concepts from chemistry, physics, tribology, chemical engineering, civil engineering, and electrical engineering. All mechanical engineering programs include multiple semesters of mathematical classes including calculus, and advanced mathematical concepts including differential equations, partial differential equations, linear algebra, differential geometry, and statistics, among others. In addition to the core mechanical engineering curriculum, many mechanical engineering programs offer more specialized programs and classes, such as control systems, robotics, transport and logistics, cryogenics, fuel technology, automotive engineering, biomechanics, vibration, optics and others, if a separate department does not exist for these subjects. Most mechanical engineering programs also require varying amounts of research or community projects to gain practical problem-solving experience. In the United States it is common for mechanical engineering students to complete one or more internships while studying, though this is not typically mandated by the university. Cooperative education is another option. Future work skills research puts demand on study components that feed student's creativity and innovation. == Job duties == Mechanical engineers research, design, develop, build, and test mechanical and thermal devices, including tools, engines, and machines. Mechanical engineers typically do the following: Analyze problems to see how mechanical and thermal devices might help solve the problem. Design or redesign mechanical and thermal devices using analysis and computer-aided design. Develop and test prototypes of devices they design. Analyze the test results and change the design as needed. Oversee the manufacturing process for the device. Manage a team of professionals in specialized fields like mechanical drafting and designing, prototyping, 3D printing or/and CNC Machines specialists. Mechanical engineers design and oversee the manufacturing of many products ranging from medical devices to new batteries. They also design power-producing machines such as electric generators, internal combustion engines, and steam and gas turbines as well as power-using machines, such as refrigeration and air-conditioning systems. Like other engineers, mechanical engineers use computers to help create and analyze designs, run simulations and test how a machine is likely to work. === License and regulation === Engineers may seek license by a state, provincial, or national government. The purpose of this process is to ensure that engineers possess the necessary technical knowledge, real-world experience, and knowledge of the local legal system to practice engineering at a professional level. Once certified, the engineer is given the title of Professional Engineer United States, Canada, Japan, South Korea, Bangladesh and South Africa), Chartered Engineer (in the United Kingdom, Ireland, India and Zimbabwe), Chartered Professional Engineer (in Australia and New Zealand) or European Engineer (much of the European Union). In the U.S., to become a licensed Professional Engineer (PE), an engineer must pass the comprehensive FE (Fundamentals of Engineering) exam, work a minimum of 4 years as an Engineering Intern (EI) or Engineer-in-Training (EIT), and pass the "Principles and Practice" or PE (Practicing Engineer or Professional Engineer) exams. The requirements and steps of this process are set forth by the National Council of Examiners for Engineering and Surveying (NCEES), composed of engineering and land surveying licensing boards representing all U.S. states and territories. In Australia (Queensland and Victoria) an engineer must be registered as a Professional Engineer within the State in which they practice, for example Registered Professional Engineer of Queensland or Victoria, RPEQ or RPEV. respectively. In the UK, current graduates require a BEng plus an appropriate master's degree or an integrated MEng degree, a minimum of 4 years post graduate on the job competency development and a peer-reviewed project report to become a Chartered Mechanical Engineer (CEng, MIMechE) through the Institution of Mechanical Engineers. CEng MIMechE can also be obtained via an examination route administered by the City and Guilds of London Institute. In most developed countries, certain engineering tasks, such as the design of bridges, electric power plants, and chemical plants, must be approved by a professional engineer or a chartered engineer. "Only a licensed engineer, for instance, may prepare, sign, seal and submit engineering plans and drawings to a public authority for approval, or to seal engineering work for public and private clients." This requirement can be written into state and provincial legislation, such as in the Canadian provinces, for example the Ontario or Quebec's Engineer Act. In other countries, such as the UK, no such legislation exists; however, practically all certifying bodies maintain a code of ethics independent of legislation, that they expect all members to abide by or risk expulsion. === Salaries and workforce statistics === The total number of engineers employed in the U.S. in 2015 was roughly 1.6 million. Of these, 278,340 were mechanical engineers (17.28%), the largest discipline by size. In 2012, the median annual income of mechanical engineers in the U.S. workforce was $80,580. The median income was highest when working for the government ($92,030), and lowest in education ($57,090). In 2014, the total number of mechanical engineering jobs was projected to grow 5% over the next decade. As of 2009, the average starting salary was $58,800 with a bachelor's degree. == Subdisciplines == The field of mechanical engineering can be thought of as a collection of many mechanical engineering science disciplines. Several of these subdisciplines which are typically taught at the undergraduate level are listed below, with a brief explanation and the most common application of each. Some of these subdisciplines are unique to mechanical engineering, while others are a combination of mechanical engineering and one or more other disciplines. Most work that a mechanical engineer does uses skills and techniques from several of these subdisciplines, as well as specialized subdisciplines. Specialized subdisciplines, as used in this article, are more likely to be the subject of graduate studies or on-the-job training than undergraduate research. Several specialized subdisciplines are discussed in this section. === Mechanics === Mechanics is, in the most general sense, the study of forces and their effect upon matter. Typically, engineering mechanics is used to analyze and predict the acceleration and deformation (both elastic and plastic) of objects under known forces (also called loads) or stresses. Subdisciplines of mechanics include Statics, the study of non-moving bodies under known loads, how forces affect static bodies Dynamics, the study of how forces affect moving bodies. Dynamics includes kinematics (about movement, velocity, and acceleration) and kinetics (about forces and resulting accelerations). Mechanics of materials, the study of how different materials deform under various types of stress Fluid mechanics, the study of how fluids react to forces Kinematics, the study of the motion of bodies (objects) and systems (groups of objects), while ignoring the forces that cause the motion. Kinematics is often used in the design and analysis of mechanisms. Continuum mechanics, a method of applying mechanics that assumes that objects are continuous (rather than discrete) Mechanical engineers typically use mechanics in the design or analysis phases of engineering. If the engineering project were the design of a vehicle, statics might be employed to design the frame of the vehicle, in order to evaluate where the stresses will be most intense. Dynamics might be used when designing the car's engine, to evaluate the forces in the pistons and cams as the engine cycles. Mechanics of materials might be used to choose appropriate materials for the frame and engine. Fluid mechanics might be used to design a ventilation system for the vehicle (see HVAC), or to design the intake system for the engine. === Mechatronics and robotics === Mechatronics is a combination of mechanics and electronics. It is an interdisciplinary branch of mechanical engineering, electrical engineering and software engineering that is concerned with integrating electrical and mechanical engineering to create hybrid automation systems. In this way, machines can be automated through the use of electric motors, servo-mechanisms, and other electrical systems in conjunction with special software. A common example of a mechatronics system is a CD-ROM drive. Mechanical systems open and close the drive, spin the CD and move the laser, while an optical system reads the data on the CD and converts it to bits. Integrated software controls the process and communicates the contents of the CD to the computer. Robotics is the application of mechatronics to create robots, which are often used in industry to perform tasks that are dangerous, unpleasant, or repetitive. These robots may be of any shape and size, but all are preprogrammed and interact physically with the world. To create a robot, an engineer typically employs kinematics (to determine the robot's range of motion) and mechanics (to determine the stresses within the robot). Robots are used extensively in industrial automation engineering. They allow businesses to save money on labor, perform tasks that are either too dangerous or too precise for humans to perform them economically, and to ensure better quality. Many companies employ assembly lines of robots, especially in Automotive Industries and some factories are so robotized that they can run by themselves. Outside the factory, robots have been employed in bomb disposal, space exploration, and many other fields. Robots are also sold for various residential applications, from recreation to domestic applications. === Structural analysis === Structural analysis is the branch of mechanical engineering (and also civil engineering) devoted to examining why and how objects fail and to fix the objects and their performance. Structural failures occur in two general modes: static failure, and fatigue failure. Static structural failure occurs when, upon being loaded (having a force applied) the object being analyzed either breaks or is deformed plastically, depending on the criterion for failure. Fatigue failure occurs when an object fails after a number of repeated loading and unloading cycles. Fatigue failure occurs because of imperfections in the object: a microscopic crack on the surface of the object, for instance, will grow slightly with each cycle (propagation) until the crack is large enough to cause ultimate failure. Failure is not simply defined as when a part breaks, however; it is defined as when a part does not operate as intended. Some systems, such as the perforated top sections of some plastic bags, are designed to break. If these systems do not break, failure analysis might be employed to determine the cause. Structural analysis is often used by mechanical engineers after a failure has occurred, or when designing to prevent failure. Engineers often use online documents and books such as those published by ASM to aid them in determining the type of failure and possible causes. Once theory is applied to a mechanical design, physical testing is often performed to verify calculated results. Structural analysis may be used in an office when designing parts, in the field to analyze failed parts, or in laboratories where parts might undergo controlled failure tests. === Thermodynamics and thermo-science === Thermodynamics is an applied science used in several branches of engineering, including mechanical and chemical engineering. At its simplest, thermodynamics is the study of energy, its use and transformation through a system. Typically, engineering thermodynamics is concerned with changing energy from one form to another. As an example, automotive engines convert chemical energy (enthalpy) from the fuel into heat, and then into mechanical work that eventually turns the wheels. Thermodynamics principles are used by mechanical engineers in the fields of heat transfer, thermofluids, and energy conversion. Mechanical engineers use thermo-science to design engines and power plants, heating, ventilation, and air-conditioning (HVAC) systems, heat exchangers, heat sinks, radiators, refrigeration, insulation, and others. === Design and drafting === Drafting or technical drawing is the means by which mechanical engineers design products and create instructions for manufacturing parts. A technical drawing can be a computer model or hand-drawn schematic showing all the dimensions necessary to manufacture a part, as well as assembly notes, a list of required materials, and other pertinent information. A U.S. mechanical engineer or skilled worker who creates technical drawings may be referred to as a drafter or draftsman. Drafting has historically been a two-dimensional process, but computer-aided design (CAD) programs now allow the designer to create in three dimensions. Instructions for manufacturing a part must be fed to the necessary machinery, either manually, through programmed instructions, or through the use of a computer-aided manufacturing (CAM) or combined CAD/CAM program. Optionally, an engineer may also manually manufacture a part using the technical drawings. However, with the advent of computer numerically controlled (CNC) manufacturing, parts can now be fabricated without the need for constant technician input. Manually manufactured parts generally consist of spray coatings, surface finishes, and other processes that cannot economically or practically be done by a machine. Drafting is used in nearly every subdiscipline of mechanical engineering, and by many other branches of engineering and architecture. Three-dimensional models created using CAD software are also commonly used in finite element analysis (FEA) and computational fluid dynamics (CFD). == Modern tools == Many mechanical engineering companies, especially those in industrialized nations, have incorporated computer-aided engineering (CAE) programs into their existing design and analysis processes, including 2D and 3D solid modeling computer-aided design (CAD). This method has many benefits, including easier and more exhaustive visualization of products, the ability to create virtual assemblies of parts, and the ease of use in designing mating interfaces and tolerances. Other CAE programs commonly used by mechanical engineers include product lifecycle management (PLM) tools and analysis tools used to perform complex simulations. Analysis tools may be used to predict product response to expected loads, including fatigue life and manufacturability. These tools include finite element analysis (FEA), computational fluid dynamics (CFD), and computer-aided manufacturing (CAM). Using CAE programs, a mechanical design team can quickly and cheaply iterate the design process to develop a product that better meets cost, performance, and other constraints. No physical prototype need be created until the design nears completion, allowing hundreds or thousands of designs to be evaluated, instead of a relative few. In addition, CAE analysis programs can model complicated physical phenomena which cannot be solved by hand, such as viscoelasticity, complex contact between mating parts, or non-Newtonian flows. As mechanical engineering begins to merge with other disciplines, as seen in mechatronics, multidisciplinary design optimization (MDO) is being used with other CAE programs to automate and improve the iterative design process. MDO tools wrap around existing CAE processes, allowing product evaluation to continue even after the analyst goes home for the day. They also use sophisticated optimization algorithms to more intelligently explore possible designs, often finding better, innovative solutions to difficult multidisciplinary design problems. == Areas of research == Mechanical engineers are constantly pushing the boundaries of what is physically possible in order to produce safer, cheaper, and more efficient machines and mechanical systems. Some technologies at the cutting edge of mechanical engineering are listed below (see also exploratory engineering). === Micro electro-mechanical systems (MEMS) === Micron-scale mechanical components such as springs, gears, fluidic and heat transfer devices are fabricated from a variety of substrate materials such as silicon, glass and polymers like SU8. Examples of MEMS components are the accelerometers that are used as car airbag sensors, modern cell phones, gyroscopes for precise positioning and microfluidic devices used in biomedical applications. === Friction stir welding (FSW) === Friction stir welding, a new type of welding, was discovered in 1991 by The Welding Institute (TWI). The innovative steady state (non-fusion) welding technique joins materials previously un-weldable, including several aluminum alloys. It plays an important role in the future construction of airplanes, potentially replacing rivets. Current uses of this technology to date include welding the seams of the aluminum main Space Shuttle external tank, Orion Crew Vehicle, Boeing Delta II and Delta IV Expendable Launch Vehicles and the SpaceX Falcon 1 rocket, armor plating for amphibious assault ships, and welding the wings and fuselage panels of the new Eclipse 500 aircraft from Eclipse Aviation among an increasingly growing pool of uses. === Composites === Composites or composite materials are a combination of materials which provide different physical characteristics than either material separately. Composite material research within mechanical engineering typically focuses on designing (and, subsequently, finding applications for) stronger or more rigid materials while attempting to reduce weight, susceptibility to corrosion, and other undesirable factors. Carbon fiber reinforced composites, for instance, have been used in such diverse applications as spacecraft and fishing rods. === Mechatronics === Mechatronics is the synergistic combination of mechanical engineering, electronic engineering, and software engineering. The discipline of mechatronics began as a way to combine mechanical principles with electrical engineering. Mechatronic concepts are used in the majority of electro-mechanical systems. Typical electro-mechanical sensors used in mechatronics are strain gauges, thermocouples, and pressure transducers. === Nanotechnology === At the smallest scales, mechanical engineering becomes nanotechnology—one speculative goal of which is to create a molecular assembler to build molecules and materials via mechanosynthesis. For now that goal remains within exploratory engineering. Areas of current mechanical engineering research in nanotechnology include nanofilters, nanofilms, and nanostructures, among others. === Finite element analysis === Finite Element Analysis is a computational tool used to estimate stress, strain, and deflection of solid bodies. It uses a mesh setup with user-defined sizes to measure physical quantities at a node. The more nodes there are, the higher the precision. This field is not new, as the basis of Finite Element Analysis (FEA) or Finite Element Method (FEM) dates back to 1941. But the evolution of computers has made FEA/FEM a viable option for analysis of structural problems. Many commercial software applications such as NASTRAN, ANSYS, and ABAQUS are widely used in industry for research and the design of components. Some 3D modeling and CAD software packages have added FEA modules. In the recent times, cloud simulation platforms like SimScale are becoming more common. Other techniques such as finite difference method (FDM) and finite-volume method (FVM) are employed to solve problems relating heat and mass transfer, fluid flows, fluid surface interaction, etc. === Biomechanics === Biomechanics is the application of mechanical principles to biological systems, such as humans, animals, plants, organs, and cells. Biomechanics also aids in creating prosthetic limbs and artificial organs for humans. Biomechanics is closely related to engineering, because it often uses traditional engineering sciences to analyze biological systems. Some simple applications of Newtonian mechanics and/or materials sciences can supply correct approximations to the mechanics of many biological systems. In the past decade, reverse engineering of materials found in nature such as bone matter has gained funding in academia. The structure of bone matter is optimized for its purpose of bearing a large amount of compressive stress per unit weight. The goal is to replace crude steel with bio-material for structural design. Over the past decade the Finite element method (FEM) has also entered the Biomedical sector highlighting further engineering aspects of Biomechanics. FEM has since then established itself as an alternative to in vivo surgical assessment and gained the wide acceptance of academia. The main advantage of Computational Biomechanics lies in its ability to determine the endo-anatomical response of an anatomy, without being subject to ethical restrictions. This has led FE modelling to the point of becoming ubiquitous in several fields of Biomechanics while several projects have even adopted an open source philosophy (e.g. BioSpine). === Computational fluid dynamics === Computational fluid dynamics, usually abbreviated as CFD, is a branch of fluid mechanics that uses numerical methods and algorithms to solve and analyze problems that involve fluid flows. Computers are used to perform the calculations required to simulate the interaction of liquids and gases with surfaces defined by boundary conditions. With high-speed supercomputers, better solutions can be achieved. Ongoing research yields software that improves the accuracy and speed of complex simulation scenarios such as turbulent flows. Initial validation of such software is performed using a wind tunnel with the final validation coming in full-scale testing, e.g. flight tests. === Acoustical engineering === Acoustical engineering is one of many other sub-disciplines of mechanical engineering and is the application of acoustics. Acoustical engineering is the study of Sound and Vibration. These engineers work effectively to reduce noise pollution in mechanical devices and in buildings by soundproofing or removing sources of unwanted noise. The study of acoustics can range from designing a more efficient hearing aid, microphone, headphone, or recording studio to enhancing the sound quality of an orchestra hall. Acoustical engineering also deals with the vibration of different mechanical systems. == Related fields == Manufacturing engineering, aerospace engineering, automotive engineering and marine engineering are grouped with mechanical engineering at times. A bachelor's degree in these areas will typically have a difference of a few specialized classes. == See also == Automobile engineering Index of mechanical engineering articles Lists Associations Wikibooks == References == == Further reading == Burstall, Aubrey F. (1965). A History of Mechanical Engineering. The MIT Press. ISBN 978-0-262-52001-0. Marks' Standard Handbook for Mechanical Engineers (11 ed.). McGraw-Hill. 2007. ISBN 978-0-07-142867-5. Oberg, Erik; Franklin D. Jones; Holbrook L. Horton; Henry H. Ryffel; Christopher McCauley (2016). Machinery's Handbook (30th ed.). New York: Industrial Press Inc. ISBN 978-0-8311-3091-6. == External links == Mechanical engineering at MTU.edu
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River engineering is a discipline of civil engineering which studies human intervention in the course, characteristics, or flow of a river with the intention of producing some defined benefit. People have intervened in the natural course and behaviour of rivers since before recorded history—to manage the water resources, to protect against flooding, or to make passage along or across rivers easier. Since the Yuan Dynasty and Ancient Roman times, rivers have been used as a source of hydropower. From the late 20th century onward, the practice of river engineering has responded to environmental concerns broader than immediate human benefit. Some river engineering projects have focused exclusively on the restoration or protection of natural characteristics and habitats. == Hydromodification == Hydromodification encompasses the systematic response to alterations to riverine and non-riverine water bodies such as coastal waters (estuaries and bays) and lakes. The U.S. Environmental Protection Agency (EPA) has defined hydromodification as the "alteration of the hydrologic characteristics of coastal and non-coastal waters, which in turn could cause degradation of water resources." River engineering has often resulted in unintended systematic responses, such as reduced habitat for fish and wildlife, and alterations of water temperature and sediment transport patterns. Beginning in the late 20th century, the river engineering discipline has been more focused on repairing hydromodified degradations and accounting for potential systematic response to planned alterations by considering fluvial geomorphology. Fluvial geomorphology is the study of how rivers change their form over time. Fluvial geomorphology is the cumulation of a number of sciences including open channel hydraulics, sediment transport, hydrology, physical geology, and riparian ecology. River engineering practitioners attempt to understand fluvial geomorphology, implement a physical alteration, and maintain public safety.: 3–13ff == Characteristics of rivers == The size of rivers above any tidal limit and their average freshwater discharge are proportionate to the extent of their basins and the amount of rain which, after falling over these basins, reaches the river channels in the bottom of the valleys, by which it is conveyed to the sea. The drainage basin of a river is the expanse of country bounded by a watershed (called a "divide" in North America) over which rainfall flows down towards the river traversing the lowest part of the valley, whereas the rain falling on the far slope of the watershed flows away to another river draining an adjacent basin. River basins vary in extent according to the configuration of the country, ranging from the insignificant drainage areas of streams rising on high ground near the coast and flowing straight down into the sea, up to immense tracts of continents, where rivers rising on the slopes of mountain ranges far inland have to traverse vast stretches of valleys and plains before reaching the ocean. The size of the largest river basin of any country depends on the extent of the continent in which it is situated, its position in relation to the hilly regions in which rivers generally arise and the sea into which they flow, and the distance between the source and the outlet into the sea of the river draining it. The rate of flow of rivers depends mainly upon their fall, also known as the gradient or slope. When two rivers of different sizes have the same fall, the larger river has the quicker flow, as its retardation by friction against its bed and banks is less in proportion to its volume than is the case with the smaller river. The fall available in a section of a river approximately corresponds to the slope of the country it traverses; as rivers rise close to the highest part of their basins, generally in hilly regions, their fall is rapid near their source and gradually diminishes, with occasional irregularities, until, in traversing plains along the latter part of their course, their fall usually becomes quite gentle. Accordingly, in large basins, rivers in most cases begin as torrents with a variable flow, and end as gently flowing rivers with a comparatively regular discharge. The irregular flow of rivers throughout their course forms one of the main difficulties in devising works for mitigating inundations or for increasing the navigable capabilities of rivers. In tropical countries subject to periodical rains, the rivers are in flood during the rainy season and have hardly any flow during the rest of the year, while in temperate regions, where the rainfall is more evenly distributed throughout the year, evaporation causes the available rainfall to be much less in hot summer weather than in the winter months, so that the rivers fall to their low stage in the summer and are liable to be in flood in the winter. In fact, with a temperate climate, the year may be divided into a warm and a cold season, extending from May to October and from November to April in the Northern hemisphere respectively; the rivers are low and moderate floods are of rare occurrence during the warm period, and the rivers are high and subject to occasional heavy floods after a considerable rainfall during the cold period in most years. The only exceptions are rivers which have their sources amongst mountains clad with perpetual snow and are fed by glaciers; their floods occur in the summer from the melting of snow and ice, as exemplified by the Rhône above the Lake of Geneva, and the Arve which joins it below. But even these rivers are liable to have their flow modified by the influx of tributaries subject to different conditions, so that the Rhone below Lyon has a more uniform discharge than most rivers, as the summer floods of the Arve are counteracted to a great extent by the low stage of the Saône flowing into the Rhone at Lyon, which has its floods in the winter when the Arve, on the contrary, is low. Another serious obstacle encountered in river engineering consists in the large quantity of detritus they bring down in flood-time, derived mainly from the disintegration of the surface layers of the hills and slopes in the upper parts of the valleys by glaciers, frost and rain. The power of a current to transport materials varies with its velocity, so that torrents with a rapid fall near the sources of rivers can carry down rocks, boulders and large stones, which are by degrees ground by attrition in their onward course into slate, gravel, sand and silt, simultaneously with the gradual reduction in fall, and, consequently, in the transporting force of the current. Accordingly, under ordinary conditions, most of the materials brought down from the high lands by torrential water courses are carried forward by the main river to the sea, or partially strewn over flat alluvial plains during floods; the size of the materials forming the bed of the river or borne along by the stream is gradually reduced on proceeding seawards, so that in the Po River in Italy, for instance, pebbles and gravel are found for about 140 miles below Turin, sand along the next 100 miles, and silt and mud in the last 110 miles (176 km). == Channelization == The removal of obstructions, natural or artificial (e.g., trunks of trees, boulders and accumulations of gravel) from a river bed furnishes a simple and efficient means of increasing the discharging capacity of its channel. Such removals will consequently lower the height of floods upstream. Every impediment to the flow, in proportion to its extent, raises the level of the river above it so as to produce the additional artificial fall necessary to convey the flow through the restricted channel, thereby reducing the total available fall. Reducing the length of the channel by substituting straight cuts for a winding course is the only way in which the effective fall can be increased. This involves some loss of capacity in the channel as a whole, and in the case of a large river with a considerable flow it is difficult to maintain a straight cut owing to the tendency of the current to erode the banks and form again a sinuous channel. Even if the cut is preserved by protecting the banks, it is liable to produce changes shoals and raise the flood-level in the channel just below its termination. Nevertheless, where the available fall is exceptionally small, as in land originally reclaimed from the sea, such as the English Fenlands, and where, in consequence, the drainage is in a great measure artificial, straight channels have been formed for the rivers. Because of the perceived value in protecting these fertile, low-lying lands from inundation, additional straight channels have also been provided for the discharge of rainfall, known as drains in the fens. Even extensive modification of the course of a river combined with an enlargement of its channel often produces only a limited reduction in flood damage. Consequently, such floodworks are only commensurate with the expenditure involved where significant assets (such as a town) are under threat. Additionally, even when successful, such floodworks may simply move the problem further downstream and threaten some other town. Recent floodworks in Europe have included restoration of natural floodplains and winding courses, so that floodwater is held back and released more slowly. Human intervention sometimes inadvertently modifies the course or characteristics of a river, for example by introducing obstructions such as mining refuse, sluice gates for mills, fish-traps, unduly wide piers for bridges and solid weirs. By impeding flow these measures can raise the flood-level upstream. Regulations for the management of rivers may include stringent prohibitions with regard to pollution, requirements for enlarging sluice-ways and the compulsory raising of their gates for the passage of floods, the removal of fish traps, which are frequently blocked up by leaves and floating rubbish, reduction in the number and width of bridge piers when rebuilt, and the substitution of movable weirs for solid weirs. By installing gauges in a fairly large river and its tributaries at suitable points, and keeping continuous records for some time of the heights of the water at the various stations, the rise of the floods in the different tributaries, the periods they take in passing down to definite stations on the main river, and the influence they severally exercise on the height of the floods at these places, can be ascertained. With the help of these records, and by observing the times and heights of the maximum rise of a particular flood at the stations on the various tributaries, the time of arrival and height of the top of the flood at any station on the main river can be predicted with remarkable accuracy two or more days beforehand. By communicating these particulars about a high flood to places on the lower river, weir-keepers are enabled to fully open the movable weirs beforehand to permit the passage of the flood, and riparian inhabitants receive timely warning of the impending inundation. Where portions of a riverside town are situated below the maximum flood-level, or when it is important to protect land adjoining a river from inundations, the overflow of the river must be diverted into a flood-dam or confined within continuous embankments on both sides. By placing these embankments somewhat back from the margin of the river-bed, a wide flood-channel is provided for the discharge of the river as soon as it overflows its banks, while leaving the natural channel unaltered for the ordinary flow. Low embankments may be sufficient where only exceptional summer floods have to be excluded from meadows. Occasionally the embankments are raised high enough to retain the floods during most years, while provision is made for the escape of the rare, exceptionally high floods at special places in the embankments, where the scour of the issuing current is guarded against, and the inundation of the neighboring land is least injurious. In this manner, the increased cost of embankments raised above the highest flood-level of rare occurrence is avoided, as is the danger of breaches in the banks from an unusually high flood-rise and rapid flow, with their disastrous effects. == Embankments == A most serious objection to the formation of continuous, high embankments along rivers bringing down considerable quantities of detritus, especially near a place where their fall has been abruptly reduced by descending from mountain slopes onto alluvial plains, is the danger of their bed being raised by deposit, producing a rise in the flood-level, and necessitating a raising of the embankments if inundations are to be prevented. Longitudinal sections of the Po River, taken in 1874 and 1901, show that its bed was materially raised during this period from the confluence of the Ticino to below Caranella, despite the clearance of sediment effected by the rush through breaches. Therefore, the completion of the embankments, together with their raising, would only eventually aggravate the injuries of the inundations they have been designed to prevent, as the escape of floods from the raised river must occur sooner or later. Inadequate planning controls which have permitted development on floodplains have been blamed for the flooding of domestic properties. Channelization was done under the auspices or overall direction of engineers employed by the local authority or the national government. One of the most heavily channelized areas in the United States is West Tennessee, where every major stream with one exception (the Hatchie River) has been partially or completely channelized. Channelization of a stream may be undertaken for several reasons. One is to make a stream more suitable for navigation or for navigation by larger vessels with deep draughts. Another is to restrict water to a certain area of a stream's natural bottom lands so that the bulk of such lands can be made available for agriculture. A third reason is flood control, with the idea of giving a stream a sufficiently large and deep channel so that flooding beyond those limits will be minimal or nonexistent, at least on a routine basis. One major reason is to reduce natural erosion; as a natural waterway curves back and forth, it usually deposits sand and gravel on the inside of the corners where the water flows slowly, and cuts sand, gravel, subsoil, and precious topsoil from the outside corners where it flows rapidly due to a change in direction. Unlike sand and gravel, the topsoil that is eroded does not get deposited on the inside of the next corner of the river. It simply washes away. == Loss of wetlands == Channelization has several predictable and negative effects. One of them is loss of wetlands. Wetlands are an excellent habitat for multiple forms of wildlife, and additionally serve as a "filter" for much of the world's surface fresh water. Another is the fact that channelized streams are almost invariably straightened. For example, the channelization of Florida's Kissimmee River has been cited as a cause contributing to the loss of wetlands. This straightening causes the streams to flow more rapidly, which can, in some instances, vastly increase soil erosion. It can also increase flooding downstream from the channelized area, as larger volumes of water traveling more rapidly than normal can reach choke points over a shorter period of time than they otherwise would, with a net effect of flood control in one area coming at the expense of aggravated flooding in another. In addition, studies have shown that stream channelization results in declines of river fish populations.: 3-1ff A 1971 study of the Chariton River in northern Missouri, United States, found that the channelized section of the river contained only 13 species of fish, whereas the natural segment of the stream was home to 21 species of fish. The biomass of fish able to be caught in the dredged segments of the river was 80 percent less than in the natural parts of the same stream. This loss of fish diversity and abundance is thought to occur because of reduction in habitat, elimination of riffles and pools, greater fluctuation of stream levels and water temperature, and shifting substrates. The rate of recovery for a stream once it has been dredged is extremely slow, with multiple streams showing no significant recovery 30 to 40 years after the date of channelization. == Modern policy in the United States == For the reasons cited above, in recent years stream channelization has been curtailed in the U.S., and in some instances even partially reversed. In 1990 the United States Government published a "no net loss of wetlands" policy, whereby a stream channelization project in one place must be offset by the creation of new wetlands in another, a process known as "mitigation." The major agency involved in the enforcement of this policy is the same Army Corps of Engineers, which for a number of years was the primary promoter of wide-scale channelization. Often, in the instances where channelization is permitted, boulders may be installed in the bed of the new channel so that water velocity is slowed, and channels may be deliberately curved as well. In 1990 the U.S. Congress gave the Army Corps a specific mandate to include environmental protection in its mission, and in 1996 it authorized the Corps to undertake restoration projects. The U.S. Clean Water Act regulates certain aspects of channelization by requiring non-Federal entities (i.e. state and local governments, private parties) to obtain permits for dredging and filling operations. Permits are issued by the Army Corps with EPA participation. == Types of river canalization == Rivers whose discharge is liable to become quite small at their low stage, or which have a somewhat large fall, as is usual in the upper part of rivers, cannot be given an adequate depth for navigation purely by works which regulate the flow; their ordinary summer level has to be raised by impounding the flow with weirs at intervals across the channel, while a lock has to be provided alongside the weir, or in a side channel, to provide for the passage of vessels. A river is thereby converted into a succession of fairly level reaches rising in steps up-stream, providing still-water navigation comparable to a canal; but it differs from a canal in the introduction of weirs for keeping up the water-level, in the provision for the regular discharge of the river at the weirs, and in the two sills of the locks being laid at the same level instead of the upper sill being raised above the lower one to the extent of the rise at the lock, as usual on canals. Canalization secures a definite available depth for navigation; and the discharge of the river generally is amply sufficient for maintaining the impounded water level, as well as providing the necessary water for locking. Navigation, however, is liable to be stopped during the descent of high floods, which in a number of cases rise above the locks; and it is necessarily arrested in cold climates on all rivers by long, severe frosts, and especially by ice. Multiple small rivers, like the Thames above its tidal limit, have been rendered navigable by canalization, and several fairly large rivers have thereby provided a good depth for vessels for considerable distances inland. Thus the canalized Seine has secured a navigable depth of 101⁄2 feet (3.2 metres) from its tidal limit up to Paris, a distance of 135 miles, and a depth of 63⁄4 feet (2.06 metres) up to Montereau, 62 miles higher up. == River regulation works == As rivers flow onward towards the sea, they experience a considerable diminution in their fall, and a progressive increase in the basin which they drain, owing to the successive influx of their various tributaries. Thus, their current gradually becomes more gentle and their discharge larger in volume and less subject to abrupt variations; and, consequently, they become more suitable for navigation. Eventually, large rivers, under favorable conditions, often furnish important natural highways for inland navigation in the lower portion of their course, as, for instance, the Rhine, the Danube and the Mississippi. River engineering works are only required to prevent changes in the course of the stream, to regulate its depth, and especially to fix the low-water channel and concentrate the flow in it, so as to increase as far as practicable the navigable depth at the lowest stage of the water level. Engineering works to increase the navigability of rivers can only be advantageously undertaken in large rivers with a moderate fall and a fair discharge at their lowest stage, for with a large fall the current presents a great impediment to up-stream navigation, and there are generally variations in water level, and when the discharge becomes small in the dry season. It is impossible to maintain a sufficient depth of water in the low-water channel. The possibility to secure uniformity of depth in a river by lowering the shoals obstructing the channel depends on the nature of the shoals. A soft shoal in the bed of a river is due to deposit from a diminution in velocity of flow, produced by a reduction in fall and by a widening of the channel, or to a loss in concentration of the scour of the main current in passing over from one concave bank to the next on the opposite side. The lowering of such a shoal by dredging merely effects a temporary deepening, for it soon forms again from the causes which produced it. The removal, moreover, of the rocky obstructions at rapids, though increasing the depth and equalizing the flow at these places, produces a lowering of the river above the rapids by facilitating the efflux, which may result in the appearance of fresh shoals at the low stage of the river. Where, however, narrow rocky reefs or other hard shoals stretch across the bottom of a river and present obstacles to the erosion by the current of the soft materials forming the bed of the river above and below, their removal may result in permanent improvement by enabling the river to deepen its bed by natural scour. The capability of a river to provide a waterway for navigation during the summer or throughout the dry season depends on the depth that can be secured in the channel at the lowest stage. The problem in the dry season is the small discharge and deficiency in scour during this period. A typical solution is to restrict the width of the low-water channel, concentrate all of the flow in it, and also to fix its position so that it is scoured out every year by the floods which follow the deepest part of the bed along the line of the strongest current. This can be effected by closing subsidiary low-water channels with dikes across them, and narrowing the channel at the low stage by low-dipping cross dikes extending from the river banks down the slope and pointing slightly up-stream so as to direct the water flowing over them into a central channel. == Estuarine works == The needs of navigation may also require that a stable, continuous, navigable channel is prolonged from the navigable river to deep water at the mouth of the estuary. The interaction of river flow and tide needs to be modeled by computer or using scale models, moulded to the configuration of the estuary under consideration and reproducing in miniature the tidal ebb and flow and fresh-water discharge over a bed of fine sand, in which various lines of training walls can be successively inserted. The models should be capable of furnishing valuable indications of the respective effects and comparative merits of the different schemes proposed for works. == See also == Bridge scour Flood control == References == == External links == U.S. Army Corps of Engineers – Civil Works Program River morphology and stream restoration references - Wildland Hydrology at the Library of Congress Web Archives (archived 2002-08-13)
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https://en.wikipedia.org/wiki/River_engineering
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An audio engineer (also known as a sound engineer or recording engineer) helps to produce a recording or a live performance, balancing and adjusting sound sources using equalization, dynamics processing and audio effects, mixing, reproduction, and reinforcement of sound. Audio engineers work on the "technical aspect of recording—the placing of microphones, pre-amp knobs, the setting of levels. The physical recording of any project is done by an engineer…" Sound engineering is increasingly viewed as a creative profession and art form, where musical instruments and technology are used to produce sound for film, radio, television, music and video games. Audio engineers also set up, sound check and do live sound mixing using a mixing console and a sound reinforcement system for music concerts, theatre, sports games and corporate events. Alternatively, audio engineer can refer to a scientist or professional engineer who holds an engineering degree and designs, develops and builds audio or musical technology working under terms such as electronic/electrical engineering or (musical) signal processing. == Research and development == Research and development audio engineers invent new technologies, audio software, equipment and techniques, to enhance the process and art of audio engineering. They might design acoustical simulations of rooms, shape algorithms for audio signal processing, specify the requirements for public address systems, carry out research on audible sound for video game console manufacturers, and other advanced fields of audio engineering. They might also be referred to as acoustic engineers. === Education === Audio engineers working in research and development may come from backgrounds such as acoustics, computer science, broadcast engineering, physics, acoustical engineering, electrical engineering and electronics. Audio engineering courses at university or college fall into two rough categories: (i) training in the creative use of audio as a sound engineer, and (ii) training in science or engineering topics, which then allows students to apply these concepts while pursuing a career developing audio technologies. Audio training courses provide knowledge of technologies and their application to recording studios and sound reinforcement systems, but do not have sufficient mathematical and scientific content to allow someone to obtain employment in research and development in the audio and acoustic industry. Audio engineers in research and development usually possess a bachelor's degree, master's degree or higher qualification in acoustics, physics, computer science or another engineering discipline. They might work in acoustic consultancy, specializing in architectural acoustics. Alternatively they might work in audio companies (e.g. headphone manufacturer), or other industries that need audio expertise (e.g., automobile manufacturer), or carry out research in a university. Some positions, such as faculty (academic staff) require a Doctor of Philosophy. In Germany a Toningenieur is an audio engineer who designs, builds and repairs audio systems. === Sub-disciplines === The listed subdisciplines are based on PACS (Physics and Astronomy Classification Scheme) coding used by the Acoustical Society of America with some revision. ==== Audio signal processing ==== Audio engineers develop audio signal processing algorithms to allow the electronic manipulation of audio signals. These can be processed at the heart of much audio production such as reverberation, Auto-Tune or perceptual coding (e.g. MP3 or Opus). Alternatively, the algorithms might perform echo cancellation, or identify and categorize audio content through music information retrieval or acoustic fingerprint. ==== Architectural acoustics ==== Architectural acoustics is the science and engineering of achieving a good sound within a room. For audio engineers, architectural acoustics can be about achieving good speech intelligibility in a stadium or enhancing the quality of music in a theatre. Architectural Acoustic design is usually done by acoustic consultants. ==== Electroacoustics ==== Electroacoustics is concerned with the design of headphones, microphones, loudspeakers, sound reproduction systems and recording technologies. Examples of electroacoustic design include portable electronic devices (e.g. mobile phones, portable media players, and tablet computers), sound systems in architectural acoustics, surround sound and wave field synthesis in movie theater and vehicle audio. ==== Musical acoustics ==== Musical acoustics is concerned with researching and describing the science of music. In audio engineering, this includes the design of electronic instruments such as synthesizers; the human voice (the physics and neurophysiology of singing); physical modeling of musical instruments; room acoustics of concert venues; music information retrieval; music therapy, and the perception and cognition of music. ==== Psychoacoustics ==== Psychoacoustics is the scientific study of how humans respond to what they hear. At the heart of audio engineering are listeners who are the final arbitrator as to whether an audio design is successful, such as whether a binaural recording sounds immersive. ==== Speech ==== The production, computer processing and perception of speech is an important part of audio engineering. Ensuring speech is transmitted intelligibly, efficiently and with high quality; in rooms, through public address systems and through mobile telephone systems are important areas of study. == Practitioner == A variety of terms are used to describe audio engineers who install or operate sound recording, sound reinforcement, or sound broadcasting equipment, including large and small format consoles. Terms such as audio technician, sound technician, audio engineer, audio technologist, recording engineer, sound mixer, mixing engineer and sound engineer can be ambiguous; depending on the context they may be synonymous, or they may refer to different roles in audio production. Such terms can refer to a person working in sound and music production; for instance, a sound engineer or recording engineer is commonly listed in the credits of commercial music recordings (as well as in other productions that include sound, such as movies). These titles can also refer to technicians who maintain professional audio equipment. Certain jurisdictions specifically prohibit the use of the title engineer to any individual not a registered member of a professional engineering licensing body. In the recording studio environment, a sound engineer records, edits, manipulates, mixes, or masters sound by technical means to realize the creative vision of the artist and record producer. While usually associated with music production, an audio engineer deals with sound for a wide range of applications, including post-production for video and film, live sound reinforcement, advertising, multimedia, and broadcasting. In larger productions, an audio engineer is responsible for the technical aspects of a sound recording or other audio production, and works together with a record producer or director, although the engineer's role may also be integrated with that of the producer. In smaller productions and studios the sound engineer and producer are often the same person. In typical sound reinforcement applications, audio engineers often assume the role of producer, making artistic and technical decisions, and sometimes even scheduling and budget decisions. === Education and training === Audio engineers come from backgrounds or postsecondary training in fields such as audio, fine arts, broadcasting, music, or electrical engineering. Training in audio engineering and sound recording is offered by colleges and universities. Some audio engineers are autodidacts with no formal training, but who have attained professional skills in audio through extensive on-the-job experience. Audio engineers must have extensive knowledge of audio engineering principles and techniques. For instance, they must understand how audio signals travel, which equipment to use and when, how to mic different instruments and amplifiers, which microphones to use and how to position them to get the best quality recordings. In addition to technical knowledge, an audio engineer must have the ability to problem-solve quickly. The best audio engineers also have a high degree of creativity that allows them to stand out amongst their peers. In the music realm, an audio engineer must also understand the types of sounds and tones that are expected in musical ensembles across different genres—rock and pop music, for example. This knowledge of musical style is typically learned from years of experience listening to and mixing music in recording or live sound contexts. For education and training, there are audio engineering schools all over the world. === Role of women === According to Women's Audio Mission (WAM), a nonprofit organization based in San Francisco dedicated to the advancement of women in music production and the recording arts, less than 5% of the people working in the field of sound and media are women. "Only three women have ever been nominated for best producer at the Brits or the Grammys" and none won either award. According to Susan Rogers, audio engineer and professor at Berklee College of Music, women interested in becoming an audio engineer face "a boys' club, or a guild mentality". The UK "Music Producers' Guild says less than 4% of its members are women" and at the Liverpool Institute of Performing Arts, "only 6% of the students enrolled on its sound technology course are female." Women's Audio Mission was started in 2003 to address the lack of women in professional audio by training over 6,000 women and girls in the recording arts and is the only professional recording studio built and run by women. Notable recording projects include the Grammy Award-winning Kronos Quartet, Angelique Kidjo (2014 Grammy winner), author Salman Rushdie, the Academy Award-nominated soundtrack to "Dirty Wars", Van-Ahn Vo (NPR's top 50 albums of 2013), Grammy-nominated St. Lawrence Quartet, and world music artists Tanya Tagaq and Wu Man. There certainly are efforts to chronicle women's role and history in audio. Leslie Gaston-Bird wrote Women in Audio, which includes 100 profiles of women in audio through history. Sound Girls is an organization focused on the next generation of women in audio, but also has been building up resources and directories of women in audio. Women in Sound is another organization that has been working to highlight women and nonbinary people in all areas of live and recorded sound through an online zine and podcast featuring interviews of current audio engineers and producers. One of the first women to produce, engineer, arrange and promote music on her own rock and roll music label was Cordell Jackson (1923–2004). Trina Shoemaker is a mixer, record producer and sound engineer who became the first woman to win the Grammy Award for Best Engineered Album in 1998 for her work on The Globe Sessions. Gail Davies was the first female producer in country music, delivering a string of Top 10 hits in the 1970s and 1980s including "Someone Is Looking for Someone Like You", "Blue Heartache" and "I'll Be There (If You Ever Want Me)". When she moved to Nashville in 1976, men "didn't want to work for a woman" and she was told women in the city were "still barefoot, pregnant and [singing] in the vocal booth." When Jonell Polansky arrived in Nashville in 1994, with a degree in electrical engineering and recording experience in the Bay Area, she was told "You're a woman, and we already had one"—a reference to Wendy Waldman. KK Proffitt, a studio "owner and chief engineer", states that men in Nashville do not want to have women in the recording booth. At a meeting of the Audio Engineering Society, Proffitt was told to "shut up" by a male producer when she raised the issue of updating studio recording technologies. Proffitt said she "finds sexism rampant in the industry". Other notable women include: Sylvia Robinson, early hip hop music producer Susan Rogers, engineer for Purple Rain Genya Ravan, producer The Dead Boys' Young, Loud and Snotty; Delia Derbyshire, British electronics pioneer Lari White, a co-producer on Toby Keith's White Trash With Money Leslie Ann Jones, recording engineer Sylvia Massy, engineer and producer for Tool, System of a Down, and Johnny Cash Ethel Gabriel, producer and record executive RCA Victor === Sub-disciplines === There are four distinct steps to the commercial production of a recording: recording, editing, mixing, and mastering. Typically, each is performed by a sound engineer who specializes only in that part of the production. Studio engineer – an engineer working within a studio facility, either with a producer or independently. Recording engineer – the engineer who records sound. Assistant engineer – often employed in larger studios, allowing them to train to become full-time engineers. They often assist full-time engineers with microphone setups, session breakdowns and in some cases, rough mixes. Mixing engineer – a person who creates mixes of multi-track recordings. It is common to record a commercial record at one studio and have it mixed by different engineers in other studios. Mastering engineer – the person who masters the final mixed stereo tracks (or sometimes a series of audio stems, which consists in a mix of the main sections) that the mix engineer produces. The mastering engineer makes any final adjustments to the overall sound of the record in the final step before commercial duplication. Mastering engineers use principles of equalization, compression and limiting to fine-tune the sound timbre and dynamics and to achieve a louder recording. Sound designer – broadly an artist who produces soundtracks or sound effects content for media. Live sound engineer Front of House (FOH) engineer, or A1. – a person dealing with live sound reinforcement. This usually includes planning and installation of loudspeakers, cabling and equipment and mixing sound during the show. This may or may not include running the foldback sound. A live/sound reinforcement engineer hears source material and tries to correlate that sonic experience with system performance. Wireless microphone engineer, or A2. This position is responsible for wireless microphones during a theatre production, a sports event or a corporate event. Foldback or Monitor engineer – a person running foldback sound during a live event. The term foldback comes from the old practice of folding back audio signals from the front of house (FOH) mixing console to the stage so musicians can hear themselves while performing. Monitor engineers usually have a separate audio system from the FOH engineer and manipulate audio signals independently from what the audience hears so they can satisfy the requirements of each performer on stage. In-ear systems, digital and analog mixing consoles, and a variety of speaker enclosures are typically used by monitor engineers. In addition, most monitor engineers must be familiar with wireless or RF (radio-frequency) equipment and often must communicate personally with the artist(s) during each performance. Systems engineer – responsible for the design setup of modern PA systems, which are often very complex. A systems engineer is usually also referred to as a crew chief on tour and is responsible for the performance and day-to-day job requirements of the audio crew as a whole along with the FOH audio system. This is a sound-only position concerned with implementation, not to be confused with the interdisciplinary field of system engineering, which typically requires a college degree. Re-recording mixer – a person in post-production who mixes audio tracks for feature films or television programs. == Equipment == An audio engineer is proficient with different types of recording media, such as analog tape, digital multi-track recorders and workstations, plug-ins and computer knowledge. With the advent of the digital age, it is increasingly important for the audio engineer to understand software and hardware integration, from synchronization to analog to digital transfers. In their daily work, audio engineers use many tools, including: Tape machines Analog-to-digital converters Digital-to-analog converters Digital audio workstations (DAWs) Audio plug-ins Dynamic range compressors Audio data compressors Equalization (audio) Music sequencers Signal processors Headphones Microphones Preamplifiers Mixing consoles Amplifiers Loudspeakers == Notable audio engineers == === Recording === === Mastering === === Live sound === == See also == == References == == External links == Audio Engineering Society Audio engineering formulas and calculators Broadcast and Sound Engineering Technicians at the US Department of Labor Recording engineer video interviews A free collection of online audio tools for audio engineers Audio Engineering online course Archived 2008-11-21 at the Wayback Machine under Creative Commons Licence Audio White Papers, Articles and Books AES Pro Audio Reference
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Biological engineering or bioengineering is the application of principles of biology and the tools of engineering to create usable, tangible, economically viable products. Biological engineering employs knowledge and expertise from a number of pure and applied sciences, such as mass and heat transfer, kinetics, biocatalysts, biomechanics, bioinformatics, separation and purification processes, bioreactor design, surface science, fluid mechanics, thermodynamics, and polymer science. It is used in the design of medical devices, diagnostic equipment, biocompatible materials, renewable energy, ecological engineering, agricultural engineering, process engineering and catalysis, and other areas that improve the living standards of societies. Examples of bioengineering research include bacteria engineered to produce chemicals, new medical imaging technology, portable and rapid disease diagnostic devices, prosthetics, biopharmaceuticals, and tissue-engineered organs. Bioengineering overlaps substantially with biotechnology and the biomedical sciences in a way analogous to how various other forms of engineering and technology relate to various other sciences (such as aerospace engineering and other space technology to kinetics and astrophysics). Generally, biological engineers attempt to mimic biological systems to create products or modify and control biological systems. Working with doctors, clinicians, and researchers, bioengineers use traditional engineering principles and techniques to address biological processes, including ways to replace, augment, sustain, or predict chemical and mechanical processes. == History == Biological engineering is a science-based discipline founded upon the biological sciences in the same way that chemical engineering, electrical engineering, and mechanical engineering can be based upon chemistry, electricity and magnetism, and classical mechanics, respectively. Before WWII, biological engineering had begun being recognized as a branch of engineering and was a new concept to people. Post-WWII, it grew more rapidly, and the term "bioengineering" was coined by British scientist and broadcaster Heinz Wolff in 1954 at the National Institute for Medical Research. Wolff graduated that year and became the Division of Biological Engineering director at Oxford. This was the first time Bioengineering was recognized as its own branch at a university. The early focus of this discipline was electrical engineering due to the work with medical devices and machinery during this time. When engineers and life scientists started working together, they recognized that the engineers did not know enough about the actual biology behind their work. To resolve this problem, engineers who wanted to get into biological engineering devoted more time to studying the processes of biology, psychology, and medicine. More recently, the term biological engineering has been applied to environmental modifications such as surface soil protection, slope stabilization, watercourse and shoreline protection, windbreaks, vegetation barriers including noise barriers and visual screens, and the ecological enhancement of an area. Because other engineering disciplines also address living organisms, the term biological engineering can be applied more broadly to include agricultural engineering. The first biological engineering program in the United States was started at University of California, San Diego in 1966. More recent programs have been launched at MIT and Utah State University. Many old agricultural engineering departments in universities over the world have re-branded themselves as agricultural and biological engineering or agricultural and biosystems engineering. According to Professor Doug Lauffenburger of MIT, biological engineering has a broad base which applies engineering principles to an enormous range of size and complexities of systems, ranging from the molecular level (molecular biology, biochemistry, microbiology, pharmacology, protein chemistry, cytology, immunology, neurobiology and, neuroscience) to cellular and tissue-based systems (including devices and sensors), to whole macroscopic organisms (plants, animals), and even to biomes and ecosystems. == Education == The average length of study is three to five years, and the completed degree is signified as a bachelor of engineering (B.S. in engineering). Fundamental courses include thermodynamics, biomechanics, biology, genetic engineering, fluid and mechanical dynamics, chemical and enzyme kinetics, electronics, and materials properties. == Sub-disciplines == Depending on the institution and particular definitional boundaries employed, some major branches of bioengineering may be categorized as (note these may overlap): Biomedical engineering: application of engineering principles and design concepts to medicine and biology for healthcare purposes. Tissue engineering Neural engineering Pharmaceutical engineering Clinical engineering Biomechanics Biochemical engineering: fermentation engineering, application of engineering principles to microscopic biological systems that are used to create new products by synthesis, including the production of protein from suitable raw materials. Biological systems engineering: application of engineering principles and design concepts to agriculture, food sciences, and ecosystems. Bioprocess engineering: develop technology to monitor the conditions of where a particular process takes place, (Ex: bioprocess design, biocatalysis, bioseparation, bioenergy) Environmental health engineering: application of engineering principles to control the environment for the health, comfort, and safety of human beings. It includes the field of life-support systems for the exploration of outer space and the ocean. Human factors and ergonomics engineering: application of engineering, physiology, and psychology to the optimization of the human-machine relationship. (Ex: physical ergonomics, cognitive ergonomics, human–computer interaction) Biotechnology: the use of living systems and organisms to develop or make products. (Ex: pharmaceuticals, Bioinformatics, Genetic engineering.) Biomimetics: the imitation of models, systems, and elements of nature to solve complex human problems. (Ex: velcro, designed after George de Mestral noticed how easily burs stuck to a dog's hair.) Bioelectrical engineering Biomechanical engineering: is the application of mechanical engineering principles and biology to determine how these areas relate and how they can be integrated to potentially improve human health. Bionics: an integration of Biomedical, focused more on the robotics and assisted technologies. (Ex: prosthetics) Bioprinting: utilizing biomaterials to print cells, tissues and organs. Biorobotics: utilizing advanced electronics and sensors to make prosthetics or biohybrid robots. Systems biology: Molecules, cells, organs, and organisms are all investigated in terms of their interactions and behaviors. == Organizations == Accreditation Board for Engineering and Technology (ABET), the U.S.-based accreditation board for engineering B.S. programs, makes a distinction between biomedical engineering and biological engineering, though there is much overlap (see above). American Institute for Medical and Biological Engineering (AIMBE) is made up of 1,500 members. Their main goal is to educate the public about the value biological engineering has in our world, as well as invest in research and other programs to advance the field. They give out awards to those dedicated to innovation in the field, and awards of achievement in the field. (They do not have a direct contribution to biological engineering; they recognize those who do and encourage the public to continue that forward movement). Institute of Biological Engineering (IBE) is a non-profit organization that runs on donations alone. They aim to encourage the public to learn and to continue advancements in biological engineering. (Like AIMBE, they do not perform research directly; however, they offer scholarships to students who show promise in the field). Society for Biological Engineering (SBE) is a technological community associated with the American Institute of Chemical Engineers (AIChE). SBE hosts international conferences, and is a global organization of leading engineers and scientists dedicated to advancing the integration of biology with engineering. MediUnite Journal is a medical awareness campaign and newspaper that has often published biomedical findings and has cited biomedicine in various research papers. == References == == External links == Bioengineering Society Biomedical Engineering Society Institute of Biological Engineering Benjoe Institute of Systems Biological Engineering American Institute of Medical and Biological Engineering American Society of Agricultural and Biological Engineers Society for Biological Engineering part of AIChE Journal of Biological Engineering, JBE Biological Engineering Transactions Munich School of BioEngineering
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The following outline is provided as an overview of and topical guide to engineering: Engineering is the scientific discipline and profession that applies scientific theories, mathematical methods, and empirical evidence to design, create, and analyze technological solutions cognizant of safety, human factors, physical laws, regulations, practicality, and cost. == Branches of engineering == Applied engineering – application of management, design, and technical skills for the design and integration of systems, the execution of new product designs, the improvement of manufacturing processes, and the management and direction of physical and/or technical functions of a firm or organization. Packaging engineering Biological engineering Agricultural engineering Bionics Genetic engineering Biomedical engineering Metabolic engineering Neural engineering Tissue engineering Civil engineering Environmental engineering Architectural engineering Construction engineering Geotechnical engineering Transportation engineering Hydro engineering Structural engineering Urban engineering (municipal engineering) Architectonics Chemical engineering (outline) Molecular engineering Process engineering – also appears under industrial engineering Electrical engineering (outline) Broadcast engineering Computer engineering (outline) Power systems engineering Telecommunications engineering Electronic engineering (includes microelectronics engineering, microelectronics and semiconductor engineering) Optical engineering Electromechanical engineering Control engineering (outline) Mechatronics Electromechanics Instrumentation engineering Forensic engineering Geological engineering Green engineering Industrial engineering Engineering psychology Ergonomics Facilities engineering Logistic engineering Performance engineering Process engineering – also appears under chemical engineering Quality engineering (quality assurance engineering) Reliability engineering Safety engineering Security engineering Support engineering Information engineering Materials engineering Amorphous metals Biomaterials engineering Casting Ceramic engineering Composite materials Computational materials science Corrosion engineering Crystal engineering Electronic materials Forensic materials engineering Metal forming Metallurgical engineering Nanomaterials Polymer engineering Surface engineering Vitreous materials (glass) Welding Mechanical engineering Acoustical engineering – includes audio engineering Aerospace engineering – branch of engineering behind the design, construction and science of aircraft and spacecraft. It is broken into two major and overlapping branches: Aeronautical engineering – deals with craft that stay within Earth's atmosphere Astronautical engineering – deals with craft that operate outside of Earth's atmosphere Automotive engineering (automotive systems engineering) Manufacturing engineering Marine engineering Thermal engineering Naval architecture Sports engineering Vacuum engineering Military engineering Combat engineering Military technology Petroleum engineering Petroleum geology Drilling engineering Production engineering Reservoir engineering Well logging Well testing Radiation engineering Nuclear engineering Radiation protection engineering Planetary engineering – planetary engineering is the application of technology for the purpose of influencing the global properties of a planet. The goal of this theoretical task is usually to make other worlds habitable for life. Perhaps the best-known type of planetary engineering is terraforming, by which a planet's surface conditions are altered to be more like those of Earth. Climate engineering (geoengineering) Software engineering Computer-aided engineering Knowledge engineering Language engineering Release engineering Teletraffic engineering Usability engineering Sustainable engineering Systems engineering – analysis, design, and control of gigantic engineering systems. Ontology engineering == History of engineering == History of engineering Greatest Engineering Achievements of the 20th Century History of chemical engineering History of electrical engineering History of mechanical engineering History of software engineering History of structural engineering Roman engineering Roman military engineering == Engineering concepts == Design (outline) Drawings Computer-aided design (CAD) Drafting Engineering design process Earthworks Ecological engineering methods Engineering, procurement and construction Engineering economics Cost Manufacturing cost Value-driven design Engineering overhead Engineering society Environmental engineering science Exploratory engineering Fasteners Flexibility Freeze Gate Good engineering practice Hand tools Machine tools Punch Management Planning Teamwork Peopleware Materials Corrosion Crystallization Material science Measurement Model engineering Nanotechnology (outline) Non-recurring engineering Parts stress modelling Personalization Process Quality Quality control Validation Reverse engineering Risk analysis Structural analysis Structural element Beam Strut Tie Systems engineering process Tolerance Traction Yield == Engineering education and certification == Engineering education Bachelor of Engineering Bachelor of Applied Science Bachelor of Technology Bachelor of Biomedical Engineering Bachelor of Computer Science Bachelor of Electrical Engineering Bachelor of Software Engineering Master of Engineering Master of Science in Engineering Master of Technology Diplôme d'Ingénieur Master of Applied Science Master of Business Engineering Master of Engineering Management Engineering doctorate Engineer's degree Engineering science and mechanics Regulation and licensure in engineering Certified engineering technologist Fundamentals of Engineering exam Principles and Practice of Engineering examination Graduate Aptitude Test in Engineering == Engineering awards == Academy Scientific and Technical Award Award of Merit in Structural Engineering British Construction Industry Awards British Engineering Excellence Awards Charles Stark Draper Prize Engineering Heritage Awards Engineering Leadership Award Federal Engineer of the Year Award Gordon Prize IEEE Control Systems Award Louis Schwitzer Award Mondialogo Engineering Award NAS Award in Aeronautical Engineering Percy Nicholls Award Russ Prize Seymour Cray Computer Engineering Award Software Process Achievement Award Technology & Engineering Emmy Award The Science, Engineering & Technology Student of the Year Awards == Engineering publications == List of engineering journals and magazines == Persons influential in the field of engineering == Lists of engineers == Indices == Index of aerospace engineering articles Index of electrical engineering articles Index of genetic engineering articles Index of mechanical engineering articles Index of software engineering articles == See also == Outline of architecture Outline of construction Infrastructure Outline of science Outline of technology
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Engineering physics (EP), sometimes engineering science, is the field of study combining pure science disciplines (such as physics, mathematics, chemistry or biology) and engineering disciplines (computer, nuclear, electrical, aerospace, medical, materials, mechanical, etc.). In many languages, the term technical physics is also used. It has been used since 1861 by the German physics teacher J. Frick in his publications. == Terminology == In some countries, both what would be translated as "engineering physics" and what would be translated as "technical physics" are disciplines leading to academic degrees. In China, for example, with the former specializing in nuclear power research (i.e. nuclear engineering), and the latter closer to engineering physics. In some universities and their institutions, an engineering physics (or applied physics) major is a discipline or specialization within the scope of engineering science, or applied science. Several related names have existed since the inception of the interdisciplinary field. For example, some university courses are called or contain the phrase "physical technologies" or "physical engineering sciences" or "physical technics". In some cases, a program formerly called "physical engineering" has been renamed "applied physics" or has evolved into specialized fields such as "photonics engineering". == Expertise == Unlike traditional engineering disciplines, engineering science or engineering physics is not necessarily confined to a particular branch of science, engineering or physics. Instead, engineering science or engineering physics is meant to provide a more thorough grounding in applied physics for a selected specialty such as optics, quantum physics, materials science, applied mechanics, electronics, nanotechnology, microfabrication, microelectronics, computing, photonics, mechanical engineering, electrical engineering, nuclear engineering, biophysics, control theory, aerodynamics, energy, solid-state physics, etc. It is the discipline devoted to creating and optimizing engineering solutions through enhanced understanding and integrated application of mathematical, scientific, statistical, and engineering principles. The discipline is also meant for cross-functionality and bridges the gap between theoretical science and practical engineering with emphasis in research and development, design, and analysis. == Degrees == In many universities, engineering science programs may be offered at the levels of B.Tech., B.Sc., M.Sc. and Ph.D. Usually, a core of basic and advanced courses in mathematics, physics, chemistry, and biology forms the foundation of the curriculum, while typical elective areas may include fluid dynamics, quantum physics, economics, plasma physics, relativity, solid mechanics, operations research, quantitative finance, information technology and engineering, dynamical systems, bioengineering, environmental engineering, computational engineering, engineering mathematics and statistics, solid-state devices, materials science, electromagnetism, nanoscience, nanotechnology, energy, and optics. == Awards == There are awards for excellence in engineering physics. For example, Princeton University's Jeffrey O. Kephart '80 Prize is awarded annually to the graduating senior with the best record. Since 2002, the German Physical Society has awarded the Georg-Simon-Ohm-Preis for outstanding research in this field. == See also == Applied physics Engineering Engineering science and mechanics Environmental engineering science Index of engineering science and mechanics articles Industrial engineering == Notes and references == == External links == "Engineering Physics at Xavier" "The Engineering Physicist Profession" "Engineering Physicist Professional Profile" Society of Engineering Science Inc. Archived 2017-08-07 at the Wayback Machine
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Planetary engineering is the development and application of technology for the purpose of influencing the environment of a planet. Planetary engineering encompasses a variety of methods such as terraforming, seeding, and geoengineering. Widely discussed in the scientific community, terraforming refers to the alteration of other planets to create a habitable environment for terrestrial life. Seeding refers to the introduction of life from Earth to habitable planets. Geoengineering refers to the engineering of a planet's climate, and has already been applied on Earth. Each of these methods are composed of varying approaches and possess differing levels of feasibility and ethical concern. == Terraforming == Terraforming is the process of modifying the atmosphere, temperature, surface topography or ecology of a planet, moon, or other body in order to replicate the environment of Earth. === Technologies === A common object of discussion on potential terraforming is the planet Mars. To terraform Mars, humans would need to create a new atmosphere, due to the planet's high carbon dioxide concentration and low atmospheric pressure. This would be possible by introducing more greenhouse gases to below "freezing point from indigenous materials". To terraform Venus, carbon dioxide would need to be converted to graphite since Venus receives twice as much sunlight as Earth. This process is only possible if the greenhouse effect is removed with the use of "high-altitude absorbing fine particles" or a sun shield, creating a more habitable Venus. NASA has defined categories of habitability systems and technologies for terraforming to be feasible. These topics include creating power-efficient systems for preserving and packaging food for crews, preparing and cooking foods, dispensing water, and developing facilities for rest, trash and recycling, and areas for crew hygiene and rest. === Feasibility === A variety of planetary engineering challenges stand in the way of terraforming efforts. The atmospheric terraforming of Mars, for example, would require "significant quantities of gas" to be added to the Martian atmosphere. This gas has been thought to be stored in solid and liquid form within Mars' polar ice caps and underground reservoirs. It is unlikely, however, that enough CO2 for sufficient atmospheric change is present within Mars' polar deposits, and liquid CO2 could only be present at warmer temperatures "deep within the crust". Furthermore, sublimating the entire volume of Mars' polar caps would increase its current atmospheric pressure to 15 millibar, where an increase to around 1000 millibar would be required for habitability. For reference, Earth's average sea-level pressure is 1013.25 mbar. First formally proposed by astrophysicist Carl Sagan, the terraforming of Venus has since been discussed through methods such as organic molecule-induced carbon conversion, sun reflection, increasing planetary spin, and various chemical means. Due to the high presence of sulfuric acid and solar wind on Venus, which are harmful to organic environments, organic methods of carbon conversion have been found unfeasible. Other methods, such as solar shading, hydrogen bombardment, and magnesium-calcium bombardment are theoretically sound but would require large-scale resources and space technologies not yet available to humans. === Ethical considerations === While successful terraforming would allow life to prosper on other planets, philosophers have debated whether this practice is morally sound. Certain ethics experts suggest that planets like Mars hold an intrinsic value independent of their utility to humanity and should therefore be free from human interference. Also, some argue that through the steps that are necessary to make Mars habitable - such as fusion reactors, space-based solar-powered lasers, or spreading a thin layer of soot on Mars' polar ice caps - would deteriorate the current aesthetic value that Mars possesses. This calls into question humanity's intrinsic ethical and moral values, as it raises the question of whether humanity is willing to eradicate the current ecosystem of another planet for their benefit. Through this ethical framework, terraforming attempts on these planets could be seen to threaten their intrinsically valuable environments, rendering these efforts unethical. == Seeding == === Environmental considerations === Mars is the primary subject of discussion for seeding. Locations for seeding are chosen based on atmospheric temperature, air pressure, existence of harmful radiation, and availability of natural resources, such as water and other compounds essential to terrestrial life. === Developing microorganisms for seeding === Natural or engineered microorganisms must be created or discovered that can withstand the harsh environments of Mars. The first organisms used must be able to survive exposure to ionizing radiation and the high concentration of CO2 present in the Martian atmosphere. Later organisms such as multicellular plants must be able to withstand the freezing temperatures, withstand high CO2 levels, and produce significant amounts of O2. Microorganisms provide significant advantages over non-biological mechanisms. They are self-replicating, negating the needs to either transport or manufacture large machinery to the surface of Mars. They can also perform complicated chemical reactions with little maintenance to realize planet-scale terraforming. == Climate engineering == Climate engineering is a form of planetary engineering which involves the process of deliberate and large-scale alteration of the Earth's climate system to combat climate change. Examples of geoengineering are carbon dioxide removal (CDR), which removes carbon dioxide from the atmosphere, and solar radiation modification (SRM) to reflect solar energy to space. Carbon dioxide removal (CDR) has multiple practices, the simplest being reforestation, to more complex processes such as direct air capture. The latter is rather difficult to deploy on an industrial scale, for high costs and substantial energy usage would be some aspects to address. Examples of SRM include stratospheric aerosol injection (SAI) and marine cloud brightening (MCB). When a volcano erupts, small particles known as aerosols proliferate throughout the atmosphere, reflecting the sun's energy back into space. This results in a cooling effect, and humanity could conceivably inject these aerosols into the stratosphere, spurring large-scale cooling. One proposal for MCB involves spraying a vapor into low-laying sea clouds, creating more cloud condensation nuclei. This would in theory result in the cloud becoming whiter, and reflecting light more efficiently. == See also == Astroengineering Macro-engineering Megascale engineering Moving the Earth Virgin Earth Challenge == References == == Further reading == Angelo, Joseph A. Jr. (2006). "Planetary engineering". Encyclopedia of space and astronomy. New York: Facts On File. pp. 462–462. ISBN 978-1-4381-1018-9. Sagan, Carl (December 1973). "Planetary engineering on Mars". Icarus. 20 (4): 513–514. Bibcode:1973Icar...20..513S. doi:10.1016/0019-1035(73)90026-2. == External links == Geoengineering: A Worldchanging Retrospective – Overview of articles on geoengineering from the sustainability site Worldchanging
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Aerospace engineering is the primary field of engineering concerned with the development of aircraft and spacecraft. It has two major and overlapping branches: aeronautical engineering and astronautical engineering. Avionics engineering is similar, but deals with the electronics side of aerospace engineering. "Aeronautical engineering" was the original term for the field. As flight technology advanced to include vehicles operating in outer space, the broader term "aerospace engineering" has come into use. Aerospace engineering, particularly the astronautics branch, is often colloquially referred to as "rocket science". == Overview == Flight vehicles are subjected to demanding conditions such as those caused by changes in atmospheric pressure and temperature, with structural loads applied upon vehicle components. Consequently, they are usually the products of various technological and engineering disciplines including aerodynamics, air propulsion, avionics, materials science, structural analysis and manufacturing. The interaction between these technologies is known as aerospace engineering. Because of the complexity and number of disciplines involved, aerospace engineering is carried out by teams of engineers, each having their own specialized area of expertise. == History == The origin of aerospace engineering can be traced back to the aviation pioneers around the late 19th to early 20th centuries, although the work of Sir George Cayley dates from the last decade of the 18th to the mid-19th century. One of the most important people in the history of aeronautics and a pioneer in aeronautical engineering, Cayley is credited as the first person to separate the forces of lift and drag, which affect any atmospheric flight vehicle. Early knowledge of aeronautical engineering was largely empirical, with some concepts and skills imported from other branches of engineering. Some key elements, like fluid dynamics, were understood by 18th-century scientists. In December 1903, the Wright Brothers performed the first sustained, controlled flight of a powered, heavier-than-air aircraft, lasting 12 seconds. The 1910s saw the development of aeronautical engineering through the design of World War I military aircraft. === World War I === In 1914, Robert Goddard was granted two U.S. patents for rockets using solid fuel, liquid fuel, multiple propellant charges, and multi-stage designs. This would set the stage for future applications in multi-stage propulsion systems for outer space. On March 3, 1915, the U.S. Congress established the first aeronautical research administration, known then as the National Advisory Committee for Aeronautics, or NACA. It was the first government-sponsored organization to support aviation research. Though intended as an advisory board upon inception, the Langley Aeronautical Laboratory became its first sponsored research and testing facility in 1920. Between World Wars I and II, great leaps were made in the field, accelerated by the advent of mainstream civil aviation. Notable airplanes of this era include the Curtiss JN 4, Farman F.60 Goliath, and Fokker Trimotor. Notable military airplanes of this period include the Mitsubishi A6M Zero, Supermarine Spitfire and Messerschmitt Bf 109 from Japan, United Kingdom, and Germany respectively. A significant development came with the first operational Jet engine-powered airplane, the Messerschmitt Me 262 which entered service in 1944 towards the end of the Second World War. The first definition of aerospace engineering appeared in February 1958, considering the Earth's atmosphere and outer space as a single realm, thereby encompassing both aircraft (aero) and spacecraft (space) under the newly coined term aerospace. === Cold War === In response to the USSR launching the first satellite, Sputnik, into space on October 4, 1957, U.S. aerospace engineers launched the first American satellite on January 31, 1958. The National Aeronautics and Space Administration was founded in 1958 after the Sputnik crisis. In 1969, Apollo 11, the first human space mission to the Moon, took place. It saw three astronauts enter orbit around the Moon, with two, Neil Armstrong and Buzz Aldrin, visiting the lunar surface. The third astronaut, Michael Collins, stayed in orbit to rendezvous with Armstrong and Aldrin after their visit. An important innovation came on January 30, 1970, when the Boeing 747 made its first commercial flight from New York to London. This aircraft made history and became known as the "Jumbo Jet" or "Queen of the Skies" due to its ability to hold up to 480 passengers. === 1976: First passenger supersonic aircraft === Another significant development came in 1976, with the development of the first passenger supersonic aircraft, the Concorde. The development of this aircraft was agreed upon by the French and British on November 29, 1962. On December 21, 1988, the Antonov An-225 Mriya cargo aircraft commenced its first flight. It holds the records for the world's heaviest aircraft, heaviest airlifted cargo, and longest airlifted cargo of any aircraft in operational service. On October 25, 2007, the Airbus A380 made its maiden commercial flight from Singapore to Sydney, Australia. This aircraft was the first passenger plane to surpass the Boeing 747 in terms of passenger capacity, with a maximum of 853. Though development of this aircraft began in 1988 as a competitor to the 747, the A380 made its first test flight in April 2005. == Elements == Some of the elements of aerospace engineering are: Radar cross-section – the study of vehicle signature apparent to remote sensing by radar. Fluid mechanics – the study of fluid flow around objects. Specifically aerodynamics concerning the flow of air over bodies such as wings or through objects such as wind tunnels (see also lift and aeronautics). Astrodynamics – the study of orbital mechanics including prediction of orbital elements when given a select few variables. While few schools in the United States teach this at the undergraduate level, several have graduate programs covering this topic (usually in conjunction with the Physics department of said college or university). Statics and Dynamics (engineering mechanics) – the study of movement, forces, moments in mechanical systems. Mathematics – in particular, calculus, differential equations, and linear algebra. Electrotechnology – the study of electronics within engineering. Propulsion – the energy to move a vehicle through the air (or in outer space) is provided by internal combustion engines, jet engines and turbomachinery, or rockets (see also propeller and spacecraft propulsion). A more recent addition to this module is electric propulsion and ion propulsion. Control engineering – the study of mathematical modeling of the dynamic behavior of systems and designing them, usually using feedback signals, so that their dynamic behavior is desirable (stable, without large excursions, with minimum error). This applies to the dynamic behavior of aircraft, spacecraft, propulsion systems, and subsystems that exist on aerospace vehicles. Aircraft structures – design of the physical configuration of the craft to withstand the forces encountered during flight. Aerospace engineering aims to keep structures lightweight and low-cost while maintaining structural integrity. Materials science – related to structures, aerospace engineering also studies the materials of which the aerospace structures are to be built. New materials with very specific properties are invented, or existing ones are modified to improve their performance. Solid mechanics – Closely related to material science is solid mechanics which deals with stress and strain analysis of the components of the vehicle. Nowadays there are several Finite Element programs such as MSC Patran/Nastran which aid engineers in the analytical process. Aeroelasticity – the interaction of aerodynamic forces and structural flexibility, potentially causing flutter, divergence, etc. Avionics – the design and programming of computer systems on board an aircraft or spacecraft and the simulation of systems. Software – the specification, design, development, test, and implementation of computer software for aerospace applications, including flight software, ground control software, test & evaluation software, etc. Risk and reliability – the study of risk and reliability assessment techniques and the mathematics involved in the quantitative methods. Noise control – the study of the mechanics of sound transfer. Aeroacoustics – the study of noise generation via either turbulent fluid motion or aerodynamic forces interacting with surfaces. Flight testing – designing and executing flight test programs in order to gather and analyze performance and handling qualities data in order to determine if an aircraft meets its design and performance goals and certification requirements. The basis of most of these elements lies in theoretical physics, such as fluid dynamics for aerodynamics or the equations of motion for flight dynamics. There is also a large empirical component. Historically, this empirical component was derived from testing of scale models and prototypes, either in wind tunnels or in the free atmosphere. More recently, advances in computing have enabled the use of computational fluid dynamics to simulate the behavior of the fluid, reducing time and expense spent on wind-tunnel testing. Those studying hydrodynamics or hydroacoustics often obtain degrees in aerospace engineering. Additionally, aerospace engineering addresses the integration of all components that constitute an aerospace vehicle (subsystems including power, aerospace bearings, communications, thermal control, life support system, etc.) and its life cycle (design, temperature, pressure, radiation, velocity, lifetime). == Degree programs == Aerospace engineering may be studied at the advanced diploma, bachelor's, master's, and Ph.D. levels in aerospace engineering departments at many universities, and in mechanical engineering departments at others. A few departments offer degrees in space-focused astronautical engineering. Some institutions differentiate between aeronautical and astronautical engineering. Graduate degrees are offered in advanced or specialty areas for the aerospace industry. A background in chemistry, physics, computer science and mathematics is important for students pursuing an aerospace engineering degree. == In popular culture == The term "rocket scientist" is sometimes used to describe a person of great intelligence since rocket science is seen as a practice requiring great mental ability, especially technically and mathematically. The term is used ironically in the expression "It's not rocket science" to indicate that a task is simple. Strictly speaking, the use of "science" in "rocket science" is a misnomer since science is about understanding the origins, nature, and behavior of the universe; engineering is about using scientific and engineering principles to solve problems and develop new technology. The more etymologically correct version of this phrase would be "rocket engineer". However, "science" and "engineering" are often misused as synonyms. == See also == American Institute of Aeronautics and Astronautics American Helicopter Society International Flight test Glossary of aerospace engineering Index of aerospace engineering articles List of aerospace engineering schools List of aerospace engineers List of Russian aerospace engineers Sigma Gamma Tau – aerospace engineering honor society Space Power Facility Outline of rocketry == Footnotes == == References == == Further reading == Dharmahinder Singh Chand. Aero-Engineering Thermodynamics. Knowledge Curve, 2017. ISBN 978-93-84389-16-1. == External links == NDTAeroTech.com, The Online Community for Aerospace NDT Professionals Kroo, Ilan. "Aircraft Design: Synthesis and Analysis". Stanford University. Archived from the original on 23 February 2001. Retrieved 17 January 2015. Air Service Training Aviation Maintenance UK Question and Answer Archived 2021-11-14 at the Wayback Machine DTIC ADA032206: Chinese-English Aviation and Space Dictionary
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Chemical engineering is an engineering field which deals with the study of the operation and design of chemical plants as well as methods of improving production. Chemical engineers develop economical commercial processes to convert raw materials into useful products. Chemical engineering uses principles of chemistry, physics, mathematics, biology, and economics to efficiently use, produce, design, transport and transform energy and materials. The work of chemical engineers can range from the utilization of nanotechnology and nanomaterials in the laboratory to large-scale industrial processes that convert chemicals, raw materials, living cells, microorganisms, and energy into useful forms and products. Chemical engineers are involved in many aspects of plant design and operation, including safety and hazard assessments, process design and analysis, modeling, control engineering, chemical reaction engineering, nuclear engineering, biological engineering, construction specification, and operating instructions. Chemical engineers typically hold a degree in Chemical Engineering or Process Engineering. Practicing engineers may have professional certification and be accredited members of a professional body. Such bodies include the Institution of Chemical Engineers (IChemE) or the American Institute of Chemical Engineers (AIChE). A degree in chemical engineering is directly linked with all of the other engineering disciplines, to various extents. == Etymology == A 1996 article cites James F. Donnelly for mentioning an 1839 reference to chemical engineering in relation to the production of sulfuric acid. In the same paper, however, George E. Davis, an English consultant, was credited with having coined the term. Davis also tried to found a Society of Chemical Engineering, but instead, it was named the Society of Chemical Industry (1881), with Davis as its first secretary. The History of Science in United States: An Encyclopedia puts the use of the term around 1890. "Chemical engineering", describing the use of mechanical equipment in the chemical industry, became common vocabulary in England after 1850. By 1910, the profession, "chemical engineer," was already in common use in Britain and the United States. == History == === New concepts and innovations === In the 1940s, it became clear that unit operations alone were insufficient in developing chemical reactors. While the predominance of unit operations in chemical engineering courses in Britain and the United States continued until the 1960s, transport phenomena started to receive greater focus. Along with other novel concepts, such as process systems engineering (PSE), a "second paradigm" was defined. Transport phenomena gave an analytical approach to chemical engineering while PSE focused on its synthetic elements, such as those of a control system and process design. Developments in chemical engineering before and after World War II were mainly incited by the petrochemical industry; however, advances in other fields were made as well. Advancements in biochemical engineering in the 1940s, for example, found application in the pharmaceutical industry, and allowed for the mass production of various antibiotics, including penicillin and streptomycin. Meanwhile, progress in polymer science in the 1950s paved way for the "age of plastics". === Safety and hazard developments === Concerns regarding large-scale chemical manufacturing facilities' safety and environmental impact were also raised during this period. Silent Spring, published in 1962, alerted its readers to the harmful effects of DDT, a potent insecticide. The 1974 Flixborough disaster in the United Kingdom resulted in 28 deaths, as well as damage to a chemical plant and three nearby villages. 1984 Bhopal disaster in India resulted in almost 4,000 deaths. These incidents, along with other incidents, affected the reputation of the trade as industrial safety and environmental protection were given more focus. In response, the IChemE required safety to be part of every degree course that it accredited after 1982. By the 1970s, legislation and monitoring agencies were instituted in various countries, such as France, Germany, and the United States. In time, the systematic application of safety principles to chemical and other process plants began to be considered a specific discipline, known as process safety. === Recent progress === Advancements in computer science found applications for designing and managing plants, simplifying calculations and drawings that previously had to be done manually. The completion of the Human Genome Project is also seen as a major development, not only advancing chemical engineering but genetic engineering and genomics as well. Chemical engineering principles were used to produce DNA sequences in large quantities. == Concepts == Chemical engineering involves the application of several principles. Key concepts are presented below. === Plant design and construction === Chemical engineering design concerns the creation of plans, specifications, and economic analyses for pilot plants, new plants, or plant modifications. Design engineers often work in a consulting role, designing plants to meet clients' needs. Design is limited by several factors, including funding, government regulations, and safety standards. These constraints dictate a plant's choice of process, materials, and equipment. Plant construction is coordinated by project engineers and project managers, depending on the size of the investment. A chemical engineer may do the job of project engineer full-time or part of the time, which requires additional training and job skills or act as a consultant to the project group. In the USA the education of chemical engineering graduates from the Baccalaureate programs accredited by ABET do not usually stress project engineering education, which can be obtained by specialized training, as electives, or from graduate programs. Project engineering jobs are some of the largest employers for chemical engineers. === Process design and analysis === A unit operation is a physical step in an individual chemical engineering process. Unit operations (such as crystallization, filtration, drying and evaporation) are used to prepare reactants, purifying and separating its products, recycling unspent reactants, and controlling energy transfer in reactors. On the other hand, a unit process is the chemical equivalent of a unit operation. Along with unit operations, unit processes constitute a process operation. Unit processes (such as nitration, hydrogenation, and oxidation involve the conversion of materials by biochemical, thermochemical and other means. Chemical engineers responsible for these are called process engineers. Process design requires the definition of equipment types and sizes as well as how they are connected and the materials of construction. Details are often printed on a Process Flow Diagram which is used to control the capacity and reliability of a new or existing chemical factory. Education for chemical engineers in the first college degree 3 or 4 years of study stresses the principles and practices of process design. The same skills are used in existing chemical plants to evaluate the efficiency and make recommendations for improvements. === Transport phenomena === Modeling and analysis of transport phenomena is essential for many industrial applications. Transport phenomena involve fluid dynamics, heat transfer and mass transfer, which are governed mainly by momentum transfer, energy transfer and transport of chemical species, respectively. Models often involve separate considerations for macroscopic, microscopic and molecular level phenomena. Modeling of transport phenomena, therefore, requires an understanding of applied mathematics. == Applications and practice == Chemical engineers develop economic ways of using materials and energy. Chemical engineers use chemistry and engineering to turn raw materials into usable products, such as medicine, petrochemicals, and plastics on a large-scale, industrial setting. They are also involved in waste management and research. Both applied and research facets could make extensive use of computers. Chemical engineers may be involved in industry or university research where they are tasked with designing and performing experiments, by scaling up theoretical chemical reactions, to create better and safer methods for production, pollution control, and resource conservation. They may be involved in designing and constructing plants as a project engineer. Chemical engineers serving as project engineers use their knowledge in selecting optimal production methods and plant equipment to minimize costs and maximize safety and profitability. After plant construction, chemical engineering project managers may be involved in equipment upgrades, troubleshooting, and daily operations in either full-time or consulting roles. == See also == === Related topics === === Related fields and concepts === === Associations === == References == == Bibliography ==
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Rehabilitation engineering is the systematic application of engineering sciences to design, develop, adapt, test, evaluate, apply, and distribute technological solutions to problems confronted by individuals with disabilities. These individuals may have experienced a spinal cord injury, brain trauma, or any other debilitating injury or disease (such as multiple sclerosis, Parkinson's, West Nile, ALS, etc.). Functional areas addressed through rehabilitation engineering may include mobility, communications, hearing, vision, and cognition, and activities associated with employment, independent living, education, and integration into the community. Rehabilitation Engineering and Assistive Technology Society of North America, the association and certifying organization of professionals within the field of Rehabilitation Engineering and Assistive Technology in North America, defines the role of a Rehabilitation Engineer as well as the role of a Rehabilitation Technician, Assistive Technologist, and Rehabiltiation Technologist (not all the same) in the 2017 approved White Paper available online on their website. == Qualifications == While some rehabilitation engineers have master's degrees in rehabilitation engineering, usually a subspecialty of Biomedical engineering, most rehabilitation engineers have undergraduate or graduate degrees in biomedical engineering, mechanical engineering, or electrical engineering. A Portuguese university provides an undergraduate degree and a master's degree in Rehabilitation Engineering and Accessibility. In the UK, there are 3 recognised training routes into Rehabilitation Engineering: AHCS Practitioner Training Programme (PTP) higher/degree apprenticeship in Healthcare Science Practitioner (Clinical Engineering) at UWE Bristol or Healthcare Science (Rehabilitation Engineering) at Swansea University leading to RCT or AHCS registration as a Clinical Technologist/Healthcare Science Practitioner. The Scientist Training Programme (STP) leading to HCPC registration as a Clinical Scientist through the National School of Healthcare Science with applications open during January each year. Training centres around the UK are accredited to provide the IPEM Clinical Technologist Training Scheme leading to RCT registration as a Clinical Technologist. In the UK, there are 3 professional registration bodies for Rehabilitation Engineers: The Register of Clinical Technologists (RCT) and administered through the Institute of Physics and Engineering in Medicine (IPEM). The Healthcare Science Practitioner Register through the Academy for Healthcare Science (AHCS) The Health & Care Professions Council (HCPC) for IPEM, AHCS and ACS. == Professional, Scientific and Technical Associations == Many of the Rehabilitation Engineering professionals join multidisciplinary scientific and technical associations with a common interest in the field of Assistive Technology and Accessibility. Examples are RESNA - Rehabilitation Engineering and Assistive Technology Society of North America, RESJA - Rehabilitation Engineering Society of JAPAN, AAATE - Association for the Advancement of Assistive Technology in Europe, ARATA – Australian Rehabilitation & Assistive Technology Association, AITADIS - Asociación Iberoamericana de Tecnologías de Apoyo a la Discapacidad and SUPERA – Portuguese Society of Rehabilitation Engineering, Assistive Technologies and Accessibility. Other organizations, like RESMAG and the National Committee on Rehabilitation Engineering of Engineers Australia are also committed to developing and providing resources that support the practice of rehabilitation engineers. The Rehabilitation Engineering and Assistive Technology Society of North America (RESNA), whose mission is to "improve the potential of people with disabilities to achieve their goals through the use of technology", is one of the main professional societies for rehabilitation engineers. RESNA's annual conference is held in the Washington, D.C., area in July. UK Professional Bodies for Clinical Scientists in Rehabilitation Engineering: Association of Clinical Scientists (ACS) Institute of Physics and Engineering in Medicine (IPEM) Academy for Healthcare Science (AHCS) == Assistive Technology devices == The rehabilitation process for people with disabilities often entails mechanical design of assistive devices such as Walking aids intended to promote inclusion of their users into the mainstream of society, commerce, and recreation. Device development can range from purely mechanical to mechatronics and software. Within the National Health Service of the United Kingdom Rehabilitation Engineers are commonly involved with assessment and provision of wheelchairs and seating to promote good posture and independent mobility. This includes electrically powered wheelchairs, active user (lightweight) manual wheelchairs, and in more advanced clinics this may include assessments for specialist wheelchair control systems and/or bespoke seating solutions. The A-SET Mind Controlled Wheelchair has been invented by Diwakar Vaish, the head of Robotics and Research at A-SET Training and Research Institutes, India. It is of great importance to patients with locked-in syndrome, it uses neural signals to command the wheelchair. This is the world's first in production neurally controlled wheelchair. Many of these devices are not designed to be multi-functional or to be easy to use. == Ongoing research == Rehabilitation Engineering Research Centers conduct research in the rehabilitation engineering, each focusing on one general area or aspect of disability. For example, the Smith-Kettlewell Eye Research Institute conducts research for the blind and visually impaired. Many of the Veterans Administration Rehabilitation Research & Development Centers conduct rehabilitation engineering research. == See also == Rehabilitation Engineering and Assistive Technology Society of North America Rehabilitation Act of 1973 Disability Discrimination Act 1995 Medical engineering Prosthetics Mind Controlled Wheelchair == References ==
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Microwave engineering pertains to the study and design of microwave circuits, components, and systems. Fundamental principles are applied to analysis, design and measurement techniques in this field. The short wavelengths involved distinguish this discipline from electronic engineering. This is because there are different interactions with circuits, transmissions and propagation characteristics at microwave frequencies. Some theories and devices that pertain to this field are antennas, radar, transmission lines, space based systems (remote sensing), measurements, microwave radiation hazards and safety measures. During World War II, microwave engineering played a significant role in developing radar that could accurately locate enemy ships and planes with a focused beam of EM radiation. The foundations of this discipline are found in Maxwell's equations and the work of Heinrich Hertz, William Thomson's waveguide theory, J.C. Bose, the klystron from Russel and Varian Bross, as well as contributions from Perry Spencer, and others. == The microwave domain == Microwave is a term used to identify electromagnetic waves above 103 megahertz (1 Gigahertz) up to 300 Gigahertz because of the short physical wavelengths of these frequencies. Short wavelength energy offers distinct advantages in many applications. For instance, sufficient directivity can be obtained using relatively small antennas and low-power transmitters. These characteristics are ideal for use in both military and civilian radar and communication applications. Small antennas and other small components are made possible by microwave frequency applications. The size advantage can be considered as part of a solution to problems of space, or weight, or both. Microwave frequency usage is significant for the design of shipboard radar because it makes possible the detection of smaller targets. Microwave frequencies present special problems in transmission, generation, and circuit design that are not encountered at lower frequencies. Conventional circuit theory is based on voltages and currents, while microwave theory is based on electromagnetic fields. Apparatus and techniques may be described qualitatively as "microwave" when the wavelengths of signals are roughly the same as the dimensions of the equipment, so that the lumped-element model is inaccurate. As a consequence, practical microwave technique tends to move away from the discrete resistors, capacitors, and inductors used with lower frequency radio waves. Instead, the distributed-element model and transmission-line theory are more useful methods for design and analysis. Open-wire and coaxial transmission lines give way to waveguides and stripline, and lumped-element tuned circuits are replaced by cavity resonators or resonant lines. Effects of reflection, polarization, scattering, diffraction and atmospheric absorption usually associated with visible light are of practical significance in the study of microwave propagation. The same equations of electromagnetic theory apply at all frequencies. == Relevance == The microwave engineering discipline has become relevant as the microwave domain moves into the commercial sector, and no longer only applicable to 20th and 21st century military technologies. Inexpensive components and digital communications in the microwave domain have opened up areas pertinent to this discipline. Some of these areas are radar, satellite, wireless radio, optical communication, faster computer circuits, and collision avoidance radar. === Education === Many colleges and universities offer microwave engineering. A few examples follow. The University of Massachusetts Amherst provides research and educational programs in microwave remote sensing, antenna design and communications systems. Courses and project work are offered leading toward graduate degrees. Specialties include microwave and RF integrated circuit design, antenna engineering, computational electromagnetics, radiowave propagation, radar and remote sensing systems, image processing, and THz imaging. Tufts University offers a Microwave and Wireless Engineering certificate program as part of its graduate studies programs. It can be applied toward a master's degree in electrical engineering. The student must have an appropriate bachelor's degree to enroll in this program. Auburn University offers research for the microwave arena. Wireless Engineering Research and Education Center is one of three research centers. The university also offers a Bachelor of Wireless Engineering degree with a Wireless Electrical Engineering major. Bradley University offers an undergraduate and a graduate degree in its Microwave and Wireless Engineering Program. It has an Advanced Microwave Laboratory, a Wireless Communication Laboratory and other facilities related to research. === Societies === There are professional societies pertinent to this discipline: The IEEE Microwave Theory and Techniques Society (MTT-S) "promotes the advancement of microwave theory and its applications...". The society also publishes peer reviewed journals, and one magazine. === Journals and other scholarly periodicals === There are peer reviewed journals and other scholarly periodicals that cover topics that pertains to microwave engineering. Some of these are IEEE Transactions on Microwave Theory and Techniques, IEEE Microwave and Wireless Components Letters, Microwave Magazine, IET Microwaves, Antennas & Propagation, and Microwave Journal. == See also == Artificial dielectrics Microwave transmission Radio-frequency engineering Winston E. Kock == References == == Further reading == Dong, Junwei (2009). Microwave Lens Designs : Optimization, Fast simulation algorithms, and 360-degree scanning techniques (PhD thesis). Virginia Polytechnic Institute and State University. hdl:10919/29081. OCLC 469368809. Docket etd-09242009-195704. Retrieved September 26, 2020.
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An engineering drawing is a type of technical drawing that is used to convey information about an object. A common use is to specify the geometry necessary for the construction of a component and is called a detail drawing. Usually, a number of drawings are necessary to completely specify even a simple component. These drawings are linked together by a "master drawing." This "master drawing" is more commonly known as an assembly drawing. The assembly drawing gives the drawing numbers of the subsequent detailed components, quantities required, construction materials and possibly 3D images that can be used to locate individual items. Although mostly consisting of pictographic representations, abbreviations and symbols are used for brevity and additional textual explanations may also be provided to convey the necessary information. The process of producing engineering drawings is often referred to as technical drawing or drafting (draughting). Drawings typically contain multiple views of a component, although additional scratch views may be added of details for further explanation. Only the information that is a requirement is typically specified. Key information such as dimensions is usually only specified in one place on a drawing, avoiding redundancy and the possibility of inconsistency. Suitable tolerances are given for critical dimensions to allow the component to be manufactured and function. More detailed production drawings may be produced based on the information given in an engineering drawing. Drawings have an information box or title block containing who drew the drawing, who approved it, units of dimensions, meaning of views, the title of the drawing and the drawing number. == History == As a necessary means for visually conveying ideas, technical drawing has been in one form or another a part of human history since antiquity. The use of these early drawings was to express architectural and engineering concepts for large cultural structures: the temples, monuments, and public infrastructure. Basic forms of technical drawing were used by the Egyptians and Mesopotamians to create highly detailed irrigation systems, pyramids, and other such sophisticated structures. But their methods were, comparatively easy, yet needed a great deal of skill and accuracy. Even in their primitive form, they gave the construction a drawing for structures that would stand the test of time. With the invention of technical drawing in ancient Greece and Rome technical drawing, they have further evolved. Works by Vitruvius and other engineers and architects such as Vitruvius used drawings as a medium for the transmission of construction techniques, and the illustration of the basic principles of balance and proportion in architecture. Early examples of what would lead to more formal technical drawing practices included the drawings and geometric calculations used to construct aqueducts, bridges, and fortresses. Technical drawings also figured in the 12th-century design of cathedrals and castles, albeit such drawings were more typically produced by artisans and stonemasons, not formally trained engineers. The Renaissance was a period of great success for technical drawing. These inventive artists and inventors were starting to use sophisticated methods of visual representation within their work as well as a methodical adherence to accuracy. His notebooks contained drawings of mechanical devices anatomical studies, and engineering projects that demonstrated his advanced understanding of form, function, and proportion, as elucidated by his notebooks. Perhaps he was the first of the pioneers who combined the arts with engineering ability to produce technical drawings at once imaginative and instructive. It was an important foundation for future developments in technical drawing work. As the Industrial Revolution took hold, modern engineering drawing took shape with the emergence of strictly specified conventions like drawing in orthographic projection, exploding, and standard scales. Part of the movement towards standardization was somewhat triggered by the development of engineering education and uniform drawing techniques in France. During the same period, the French mathematician Gaspard Monge developed descriptive geometry, a means of representing three-dimensional objects in two-dimensional space, and contributed to technical drawing in a major way. His work set the ground for orthographic projection which is one of the core techniques to be used in technical drawing today. Monge's methods were disseminated initially as a military secret, then far and wide, and his methods shaped the future of engineering education, and also the engineering practice. Further contributions to the craft of technical drawing were made by pioneers like Marc Isambard Brunel. L. T. C. Rolt's biography of Isambard Kingdom Brunel, to whom Marc contributed in 1799 with his detailed drawings of block-making machinery, testified to the developing nature of British engineering methods. By applying what we now call mechanical drawing techniques to depict three-dimensional machinery on a two-dimensional plane more efficient manufacturing processes as well as greater precision were enabled. These innovations were essential as the world began to move toward mechanized production, and complex engineering projects, such as bridges, railways, and ships, required highly detailed and accurate technical representations to succeed. This increasing need for a degree of precision in technical drawings during the 19th century was a direct result of the Industrial Revolution. In this era, we have seen the development of large-scale engineering projects such as railways, steam engines, and iron structures which require a heightened degree of accuracy and standardization. New conventions and symbols were created by engineers; the use of which became standardized throughout industries, so that any person who could read a technical drawing could know the specifications of a component or structure. The standardization process helped engineer practices to become standardized, making it easier for engineers, manufacturers, and builders to work together. In the 20th century, technical drawing underwent yet another transformation with the introduction of drafting tools such as the T-square, compasses, and protractors. These tools helped drafters achieve the high degree of precision necessary for increasingly complex projects, such as skyscrapers, airplanes, and automobiles. The establishment of standards such as the American National Standards Institute (ANSI) and International Organization for Standardization (ISO) further formalized technical drawing conventions, ensuring consistency in engineering practices around the world. Today, technical drawing has largely transitioned from manual drafting to computer-aided design (CAD). CAD software has revolutionized the way technical drawings are created, allowing for faster, more precise, and easily modifiable drawings. Engineers can now visualize designs in three dimensions, simulate performance, and make adjustments before any physical prototype is built. This digital transformation has not only increased efficiency but also broadened the possibilities for innovation, enabling engineers to tackle challenges that were previously unimaginable. However, despite the advent of digital tools, the fundamental principles of technical drawing remain rooted in its history. Precision, clarity, and the ability to convey complex information visually are still at the core of technical drawing. The conventions established over centuries—from orthographic projection to the use of scale and dimension lines—continue to be essential in modern engineering and architectural practice. The evolution of technical drawing is a testament to human ingenuity, demonstrating how the ability to convey complex ideas visually has been pivotal in the advancement of civilization. == Standardization and disambiguation == Engineering drawings specify the requirements of a component or assembly which can be complicated. Standards provide rules for their specification and interpretation. Standardization also aids internationalization, because people from different countries who speak different languages can read the same engineering drawing, and interpret it the same way. One major set of engineering drawing standards is ASME Y14.5 and Y14.5M (most recently revised in 2018). These apply widely in the United States, although ISO 8015 (Geometrical product specifications (GPS) — Fundamentals — Concepts, principles and rules) is now also important. In 2018, ASME AED-1 was created to develop advanced practices unique to aerospace and other industries and supplement to Y14.5 Standards. In 2011, a new revision of ISO 8015 (Geometrical product specifications (GPS) — Fundamentals — Concepts, principles and rules) was published containing the Invocation Principle. This states that, "Once a portion of the ISO geometric product specification (GPS) system is invoked in a mechanical engineering product documentation, the entire ISO GPS system is invoked." It also goes on to state that marking a drawing "Tolerancing ISO 8015" is optional. The implication of this is that any drawing using ISO symbols can only be interpreted to ISO GPS rules. The only way not to invoke the ISO GPS system is to invoke a national or other standard. Britain, BS 8888 (Technical Product Specification) has undergone important updates in the 2010s. == Media == For centuries, until the 1970s, all engineering drawing was done manually by using pencil and pen on paper or other substrate (e.g., vellum, mylar). Since the advent of computer-aided design (CAD), engineering drawing has been done more and more in the electronic medium with each passing decade. Today most engineering drawing is done with CAD, but pencil and paper have not entirely disappeared. Some of the tools of manual drafting include pencils, pens and their ink, straightedges, T-squares, French curves, triangles, rulers, protractors, dividers, compasses, scales, erasers, and tacks or push pins. (Slide rules used to number among the supplies, too, but nowadays even manual drafting, when it occurs, benefits from a pocket calculator or its onscreen equivalent.) And of course the tools also include drawing boards (drafting boards) or tables. The English idiom "to go back to the drawing board", which is a figurative phrase meaning to rethink something altogether, was inspired by the literal act of discovering design errors during production and returning to a drawing board to revise the engineering drawing. Drafting machines are devices that aid manual drafting by combining drawing boards, straightedges, pantographs, and other tools into one integrated drawing environment. CAD provides their virtual equivalents. Producing drawings usually involves creating an original that is then reproduced, generating multiple copies to be distributed to the shop floor, vendors, company archives, and so on. The classic reproduction methods involved blue and white appearances (whether white-on-blue or blue-on-white), which is why engineering drawings were long called, and even today are still often called, "blueprints" or "bluelines", even though those terms are anachronistic from a literal perspective, since most copies of engineering drawings today are made by more modern methods (often inkjet or laser printing) that yield black or multicolour lines on white paper. The more generic term "print" is now in common usage in the US to mean any paper copy of an engineering drawing. In the case of CAD drawings, the original is the CAD file, and the printouts of that file are the "prints". == Systems of dimensioning and tolerancing == Almost all engineering drawings (except perhaps reference-only views or initial sketches) communicate not only geometry (shape and location) but also dimensions and tolerances for those characteristics. Several systems of dimensioning and tolerancing have evolved. The simplest dimensioning system just specifies distances between points (such as an object's length or width, or hole center locations). Since the advent of well-developed interchangeable manufacture, these distances have been accompanied by tolerances of the plus-or-minus or min-and-max-limit types. Coordinate dimensioning involves defining all points, lines, planes, and profiles in terms of Cartesian coordinates, with a common origin. Coordinate dimensioning was the sole best option until the post-World War II era saw the development of geometric dimensioning and tolerancing (GD&T), which departs from the limitations of coordinate dimensioning (e.g., rectangular-only tolerance zones, tolerance stacking) to allow the most logical tolerancing of both geometry and dimensions (that is, both form [shapes/locations] and sizes). == Common features == Drawings convey the following critical information: Geometry – the shape of the object; represented as views; how the object will look when it is viewed from various angles, such as front, top, side, etc. Dimensions – the size of the object is captured in accepted units. Tolerances – the allowable variations for each dimension. Material – represents what the item is made of. Finish – specifies the surface quality of the item, functional or cosmetic. For example, a mass-marketed product usually requires a much higher surface quality than, say, a component that goes inside industrial machinery. === Line styles and types === A variety of line styles graphically represent physical objects. Types of lines include the following: visible – are continuous lines used to depict edges directly visible from a particular angle. hidden – are short-dashed lines that may be used to represent edges that are not directly visible. center – are alternately long- and short-dashed lines that may be used to represent the axes of circular features. cutting plane – are thin, medium-dashed lines, or thick alternately long- and double short-dashed that may be used to define sections for section views. section – are thin lines in a pattern (pattern determined by the material being "cut" or "sectioned") used to indicate surfaces in section views resulting from "cutting". Section lines are commonly referred to as "cross-hatching". phantom – (not shown) are alternately long- and double short-dashed thin lines used to represent a feature or component that is not part of the specified part or assembly. E.g. billet ends that may be used for testing, or the machined product that is the focus of a tooling drawing. Lines can also be classified by a letter classification in which each line is given a letter. Type A lines show the outline of the feature of an object. They are the thickest lines on a drawing and done with a pencil softer than HB. Type B lines are dimension lines and are used for dimensioning, projecting, extending, or leaders. A harder pencil should be used, such as a 2H pencil. Type C lines are used for breaks when the whole object is not shown. These are freehand drawn and only for short breaks. 2H pencil Type D lines are similar to Type C, except these are zigzagged and only for longer breaks. 2H pencil Type E lines indicate hidden outlines of internal features of an object. These are dotted lines. 2H pencil Type F lines are Type E lines, except these are used for drawings in electrotechnology. 2H pencil Type G lines are used for centre lines. These are dotted lines, but a long line of 10–20 mm, then a 1 mm gap, then a small line of 2 mm. 2H pencil Type H lines are the same as type G, except that every second long line is thicker. These indicate the cutting plane of an object. 2H pencil Type K lines indicate the alternate positions of an object and the line taken by that object. These are drawn with a long line of 10–20 mm, then a small gap, then a small line of 2 mm, then a gap, then another small line. 2H pencil. === Multiple views and projections === In most cases, a single view is not sufficient to show all necessary features, and several views are used. Types of views include the following: ==== Multiview projection ==== A multiview projection is a type of orthographic projection that shows the object as it looks from the front, right, left, top, bottom, or back (e.g. the primary views), and is typically positioned relative to each other according to the rules of either first-angle or third-angle projection. The origin and vector direction of the projectors (also called projection lines) differs, as explained below. In first-angle projection, the parallel projectors originate as if radiated from behind the viewer and pass through the 3D object to project a 2D image onto the orthogonal plane behind it. The 3D object is projected into 2D "paper" space as if you were looking at a radiograph of the object: the top view is under the front view, the right view is at the left of the front view. First-angle projection is the ISO standard and is primarily used in Europe. In third-angle projection, the parallel projectors originate as if radiated from the far side of the object and pass through the 3D object to project a 2D image onto the orthogonal plane in front of it. The views of the 3D object are like the panels of a box that envelopes the object, and the panels pivot as they open up flat into the plane of the drawing. Thus the left view is placed on the left and the top view on the top; and the features closest to the front of the 3D object will appear closest to the front view in the drawing. Third-angle projection is primarily used in the United States and Canada, where it is the default projection system according to ASME standard ASME Y14.3M. Until the late 19th century, first-angle projection was the norm in North America as well as Europe; but circa the 1890s, third-angle projection spread throughout the North American engineering and manufacturing communities to the point of becoming a widely followed convention, and it was an ASA standard by the 1950s. Circa World War I, British practice was frequently mixing the use of both projection methods. As shown above, the determination of what surface constitutes the front, back, top, and bottom varies depending on the projection method used. Not all views are necessarily used. Generally only as many views are used as are necessary to convey all needed information clearly and economically. The front, top, and right-side views are commonly considered the core group of views included by default, but any combination of views may be used depending on the needs of the particular design. In addition to the six principal views (front, back, top, bottom, right side, left side), any auxiliary views or sections may be included as serve the purposes of part definition and its communication. View lines or section lines (lines with arrows marked "A-A", "B-B", etc.) define the direction and location of viewing or sectioning. Sometimes a note tells the reader in which zone(s) of the drawing to find the view or section. ==== Auxiliary views ==== An auxiliary view is an orthographic view that is projected into any plane other than one of the six primary views. These views are typically used when an object contains some sort of inclined plane. Using the auxiliary view allows for that inclined plane (and any other significant features) to be projected in their true size and shape. The true size and shape of any feature in an engineering drawing can only be known when the Line of Sight (LOS) is perpendicular to the plane being referenced. It is shown like a three-dimensional object. Auxiliary views tend to make use of axonometric projection. When existing all by themselves, auxiliary views are sometimes known as pictorials. ==== Isometric projection ==== An isometric projection shows the object from angles in which the scales along each axis of the object are equal. Isometric projection corresponds to rotation of the object by ± 45° about the vertical axis, followed by rotation of approximately ± 35.264° [= arcsin(tan(30°))] about the horizontal axis starting from an orthographic projection view. "Isometric" comes from the Greek for "same measure". One of the things that makes isometric drawings so attractive is the ease with which 60° angles can be constructed with only a compass and straightedge. Isometric projection is a type of axonometric projection. The other two types of axonometric projection are: Dimetric projection Trimetric projection ==== Oblique projection ==== An oblique projection is a simple type of graphical projection used for producing pictorial, two-dimensional images of three-dimensional objects: it projects an image by intersecting parallel rays (projectors) from the three-dimensional source object with the drawing surface (projection plan). In both oblique projection and orthographic projection, parallel lines of the source object produce parallel lines in the projected image. ==== Perspective projection ==== Perspective is an approximate representation on a flat surface, of an image as it is perceived by the eye. The two most characteristic features of perspective are that objects are drawn: Smaller as their distance from the observer increases Foreshortened: the size of an object's dimensions along the line of sight are relatively shorter than dimensions across the line of sight. ==== Section Views ==== Projected views (either Auxiliary or Multi view) which show a cross section of the source object along the specified cut plane. These views are commonly used to show internal features with more clarity than regular projections or hidden lines, it also helps reducing number of hidden lines.In assembly drawings, hardware components (e.g. nuts, screws, washers) are typically not sectioned. Section view is a half side view of object. === Scale === Plans are usually "scale drawings", meaning that the plans are drawn at specific ratio relative to the actual size of the place or object. Various scales may be used for different drawings in a set. For example, a floor plan may be drawn at 1:50 (1:48 or 1⁄4″ = 1′ 0″) whereas a detailed view may be drawn at 1:25 (1:24 or 1⁄2″ = 1′ 0″). Site plans are often drawn at 1:200 or 1:100. Scale is a nuanced subject in the use of engineering drawings. On one hand, it is a general principle of engineering drawings that they are projected using standardized, mathematically certain projection methods and rules. Thus, great effort is put into having an engineering drawing accurately depict size, shape, form, aspect ratios between features, and so on. And yet, on the other hand, there is another general principle of engineering drawing that nearly diametrically opposes all this effort and intent—that is, the principle that users are not to scale the drawing to infer a dimension not labeled. This stern admonition is often repeated on drawings, via a boilerplate note in the title block telling the user, "DO NOT SCALE DRAWING." The explanation for why these two nearly opposite principles can coexist is as follows. The first principle—that drawings will be made so carefully and accurately—serves the prime goal of why engineering drawing even exists, which is successfully communicating part definition and acceptance criteria—including "what the part should look like if you've made it correctly." The service of this goal is what creates a drawing that one even could scale and get an accurate dimension thereby. And thus the great temptation to do so, when a dimension is wanted but was not labeled. The second principle—that even though scaling the drawing will usually work, one should nevertheless never do it—serves several goals, such as enforcing total clarity regarding who has authority to discern design intent, and preventing erroneous scaling of a drawing that was never drawn to scale to begin with (which is typically labeled "drawing not to scale" or "scale: NTS"). When a user is forbidden from scaling the drawing, they must turn instead to the engineer (for the answers that the scaling would seek), and they will never erroneously scale something that is inherently unable to be accurately scaled. But in some ways, the advent of the CAD and MBD era challenges these assumptions that were formed many decades ago. When part definition is defined mathematically via a solid model, the assertion that one cannot interrogate the model—the direct analog of "scaling the drawing"—becomes ridiculous; because when part definition is defined this way, it is not possible for a drawing or model to be "not to scale". A 2D pencil drawing can be inaccurately foreshortened and skewed (and thus not to scale), yet still be a completely valid part definition as long as the labeled dimensions are the only dimensions used, and no scaling of the drawing by the user occurs. This is because what the drawing and labels convey is in reality a symbol of what is wanted, rather than a true replica of it. (For example, a sketch of a hole that is clearly not round still accurately defines the part as having a true round hole, as long as the label says "10mm DIA", because the "DIA" implicitly but objectively tells the user that the skewed drawn circle is a symbol representing a perfect circle.) But if a mathematical model—essentially, a vector graphic—is declared to be the official definition of the part, then any amount of "scaling the drawing" can make sense; there may still be an error in the model, in the sense that what was intended is not depicted (modeled); but there can be no error of the "not to scale" type—because the mathematical vectors and curves are replicas, not symbols, of the part features. Even in dealing with 2D drawings, the manufacturing world has changed since the days when people paid attention to the scale ratio claimed on the print, or counted on its accuracy. In the past, prints were plotted on a plotter to exact scale ratios, and the user could know that a line on the drawing 15 mm long corresponded to a 30 mm part dimension because the drawing said "1:2" in the "scale" box of the title block. Today, in the era of ubiquitous desktop printing, where original drawings or scaled prints are often scanned on a scanner and saved as a PDF file, which is then printed at any percent magnification that the user deems handy (such as "fit to paper size"), users have pretty much given up caring what scale ratio is claimed in the "scale" box of the title block. Which, under the rule of "do not scale drawing", never really did that much for them anyway. === Showing dimensions === The required sizes of features are conveyed through use of dimensions. Distances may be indicated with either of two standardized forms of dimension: linear and ordinate. With linear dimensions, two parallel lines, called "extension lines," spaced at the distance between two features, are shown at each of the features. A line perpendicular to the extension lines, called a "dimension line," with arrows at its endpoints, is shown between, and terminating at, the extension lines. The distance is indicated numerically at the midpoint of the dimension line, either adjacent to it, or in a gap provided for it. With ordinate dimensions, one horizontal and one vertical extension line establish an origin for the entire view. The origin is identified with zeroes placed at the ends of these extension lines. Distances along the x- and y-axes to other features are specified using other extension lines, with the distances indicated numerically at their ends. Sizes of circular features are indicated using either diametral or radial dimensions. Radial dimensions use an "R" followed by the value for the radius; Diametral dimensions use a circle with forward-leaning diagonal line through it, called the diameter symbol, followed by the value for the diameter. A radially-aligned line with arrowhead pointing to the circular feature, called a leader, is used in conjunction with both diametral and radial dimensions. All types of dimensions are typically composed of two parts: the nominal value, which is the "ideal" size of the feature, and the tolerance, which specifies the amount that the value may vary above and below the nominal. Geometric dimensioning and tolerancing is a method of specifying the functional geometry of an object. === Sizes of drawings === Sizes of drawings typically comply with either of two different standards, ISO (World Standard) or ANSI/ASME Y14.1 (American). The metric drawing sizes correspond to international paper sizes. These developed further refinements in the second half of the twentieth century, when photocopying became cheap. Engineering drawings could be readily doubled (or halved) in size and put on the next larger (or, respectively, smaller) size of paper with no waste of space. And the metric technical pens were chosen in sizes so that one could add detail or drafting changes with a pen width changing by approximately a factor of the square root of 2. A full set of pens would have the following nib sizes: 0.13, 0.18, 0.25, 0.35, 0.5, 0.7, 1.0, 1.5, and 2.0 mm. However, the International Organization for Standardization (ISO) called for four pen widths and set a colour code for each: 0.25 (white), 0.35 (yellow), 0.5 (brown), 0.7 (blue); these nibs produced lines that related to various text character heights and the ISO paper sizes. All ISO paper sizes have the same aspect ratio, one to the square root of 2, meaning that a document designed for any given size can be enlarged or reduced to any other size and will fit perfectly. Given this ease of changing sizes, it is of course common to copy or print a given document on different sizes of paper, especially within a series, e.g. a drawing on A3 may be enlarged to A2 or reduced to A4. The US customary "A-size" corresponds to "letter" size, and "B-size" corresponds to "ledger" or "tabloid" size. There were also once British paper sizes, which went by names rather than alphanumeric designations. American Society of Mechanical Engineers (ASME) ANSI/ASME Y14.1, Y14.2, Y14.3, and Y14.5 are commonly referenced standards in the US. === Technical lettering === Technical lettering is the process of forming letters, numerals, and other characters in technical drawing. It is used to describe, or provide detailed specifications for an object. With the goals of legibility and uniformity, styles are standardized and lettering ability has little relationship to normal writing ability. Engineering drawings use a Gothic sans-serif script, formed by a series of short strokes. Lower case letters are rare in most drawings of machines. ISO Lettering templates, designed for use with technical pens and pencils, and to suit ISO paper sizes, produce lettering characters to an international standard. The stroke thickness is related to the character height (for example, 2.5 mm high characters would have a stroke thickness - pen nib size - of 0.25 mm, 3.5 would use a 0.35 mm pen and so forth). The ISO character set (font) has a seriffed one, a barred seven, an open four, six, and nine, and a round topped three, that improves legibility when, for example, an A0 drawing has been reduced to A1 or even A3 (and perhaps enlarged back or reproduced/faxed/ microfilmed &c). When CAD drawings became more popular, especially using US software, such as AutoCAD, the nearest font to this ISO standard font was Romantic Simplex (RomanS) - a proprietary shx font) with a manually adjusted width factor (override) to make it look as near to the ISO lettering for the drawing board. However, with the closed four, and arced six and nine, romans.shx typeface could be difficult to read in reductions. In more recent revisions of software packages, the TrueType font ISOCPEUR reliably reproduces the original drawing board lettering stencil style, however, many drawings have switched to the ubiquitous Arial.ttf. == Conventional parts (areas) == === Title block === Every engineering drawing must have a title block. The title block (T/B, TB) is an area of the drawing that conveys header-type information about the drawing, such as: Drawing title (hence the name "title block") Drawing number Part number(s) Name of the design activity (corporation, government agency, etc.) Identifying code of the design activity (such as a CAGE code) Address of the design activity (such as city, state/province, country) Measurement units of the drawing (for example, inches, millimeters) Default tolerances for dimension callouts where no tolerance is specified Boilerplate callouts of general specs Intellectual property rights warning ISO 7200 specifies the data fields used in title blocks. It standardizes eight mandatory data fields: Title (hence the name "title block") Created by (name of drafter) Approved by Legal owner (name of company or organization) Document type Drawing number (same for every sheet of this document, unique for each technical document of the organization) Sheet number and number of sheets (for example, "Sheet 5/7") Date of issue (when the drawing was made) Traditional locations for the title block are the bottom right (most commonly) or the top right or center. === Revisions block === The revisions block (rev block) is a tabulated list of the revisions (versions) of the drawing, documenting the revision control. Traditional locations for the revisions block are the top right (most commonly) or adjoining the title block in some way. === Next assembly === The next assembly block, often also referred to as "where used" or sometimes "effectivity block", is a list of higher assemblies where the product on the current drawing is used. This block is commonly found adjacent to the title block. === Notes list === The notes list provides notes to the user of the drawing, conveying any information that the callouts within the field of the drawing did not. It may include general notes, flagnotes, or a mixture of both. Traditional locations for the notes list are anywhere along the edges of the field of the drawing. ==== General notes ==== General notes (G/N, GN) apply generally to the contents of the drawing, as opposed to applying only to certain part numbers or certain surfaces or features. ==== Flagnotes ==== Flagnotes or flag notes (FL, F/N) are notes that apply only where a flagged callout points, such as to particular surfaces, features, or part numbers. Typically the callout includes a flag icon. Some companies call such notes "delta notes", and the note number is enclosed inside a triangular symbol (similar to capital letter delta, Δ). "FL5" (flagnote 5) and "D5" (delta note 5) are typical ways to abbreviate in ASCII-only contexts. === Field of the drawing === The field of the drawing (F/D, FD) is the main body or main area of the drawing, excluding the title block, rev block, P/L and so on === List of materials, bill of materials, parts list === The list of materials (L/M, LM, LoM), bill of materials (B/M, BM, BoM), or parts list (P/L, PL) is a (usually tabular) list of the materials used to make a part, and the parts used to make an assembly. It may contain instructions for heat treatment, finishing, and other processes, for each part number. Sometimes such LoMs or PLs are separate documents from the drawing itself. Traditional locations for the LoM/BoM are above the title block, or in a separate document. === Parameter tabulations === Some drawings call out dimensions with parameter names (that is, variables, such a "A", "B", "C"), then tabulate rows of parameter values for each part number. Traditional locations for parameter tables, when such tables are used, are floating near the edges of the field of the drawing, either near the title block or elsewhere along the edges of the field. === Views and sections === Each view or section is a separate set of projections, occupying a contiguous portion of the field of the drawing. Usually views and sections are called out with cross-references to specific zones of the field. === Zones === Often a drawing is divided into zones by an alphanumeric grid, with zone labels along the margins, such as A, B, C, D up the sides and 1, 2, 3, 4, 5, 6 along the top and bottom. Names of zones are thus, for example, A5, D2, or B1. This feature greatly eases discussion of, and reference to, particular areas of the drawing. == Abbreviations and symbols == As in many technical fields, a wide array of abbreviations and symbols have been developed in engineering drawing during the 20th and 21st centuries. For example, cold rolled steel is often abbreviated as CRS, and diameter is often abbreviated as DIA, D, or ⌀. Most engineering drawings are language-independent—words are confined to the title block; symbols are used in place of words elsewhere. With the advent of computer generated drawings for manufacturing and machining, many symbols have fallen out of common use. This poses a problem when attempting to interpret an older hand-drawn document that contains obscure elements that cannot be readily referenced in standard teaching text or control documents such as ASME and ANSI standards. For example, ASME Y14.5M 1994 excludes a few elements that convey critical information as contained in older US Navy drawings and aircraft manufacturing drawings of World War 2 vintage. Researching the intent and meaning of some symbols can prove difficult. == Example == Here is an example of an engineering drawing (an isometric view of the same object is shown above). The different line types are colored for clarity. Black = object line and hatching Red = hidden line Blue = center line of piece or opening Magenta = phantom line or cutting plane line Sectional views are indicated by the direction of arrows, as in the example right side. == Legal instruments == An engineering drawing is a legal document (that is, a legal instrument), because it communicates all the needed information about "what is wanted" to the people who will expend resources turning the idea into a reality. It is thus a part of a contract; the purchase order and the drawing together, as well as any ancillary documents (engineering change orders [ECOs], called-out specs), constitute the contract. Thus, if the resulting product is wrong, the worker or manufacturer are protected from liability as long as they have faithfully executed the instructions conveyed by the drawing. If those instructions were wrong, it is the fault of the engineer. Because manufacturing and construction are typically very expensive processes (involving large amounts of capital and payroll), the question of liability for errors has legal implications. == Relationship to model-based definition (MBD/DPD) == For centuries, engineering drawing was the sole method of transferring information from design into manufacture. In recent decades another method has arisen, called model-based definition (MBD) or digital product definition (DPD). In MBD, the information captured by the CAD software app is fed automatically into a CAM app (computer-aided manufacturing), which (with or without postprocessing apps) creates code in other languages such as G-code to be executed by a CNC machine tool (computer numerical control), 3D printer, or (increasingly) a hybrid machine tool that uses both. Thus today it is often the case that the information travels from the mind of the designer into the manufactured component without having ever been codified by an engineering drawing. In MBD, the dataset, not a drawing, is the legal instrument. The term "technical data package" (TDP) is now used to refer to the complete package of information (in one medium or another) that communicates information from design to production (such as 3D-model datasets, engineering drawings, engineering change orders (ECOs), spec revisions and addenda, and so on). It still takes CAD/CAM programmers, CNC setup workers, and CNC operators to do manufacturing, as well as other people such as quality assurance staff (inspectors) and logistics staff (for materials handling, shipping-and-receiving, and front office functions). These workers often use drawings in the course of their work that have been produced from the MBD dataset. When proper procedures are being followed, a clear chain of precedence is always documented, such that when a person looks at a drawing, they are told by a note thereon that this drawing is not the governing instrument (because the MBD dataset is). In these cases, the drawing is still a useful document, although legally it is classified as "for reference only", meaning that if any controversies or discrepancies arise, it is the MBD dataset, not the drawing, that governs. == See also == == References == == Bibliography == French, Thomas E. (1918), A manual of engineering drawing for students and draftsmen (2nd ed.), New York, New York, USA: McGraw-Hill, LCCN 30018430. : Engineering Drawing (book) French, Thomas E.; Vierck, Charles J. (1953), A manual of engineering drawing for students and draftsmen (8th ed.), New York, New York, USA: McGraw-Hill, LCCN 52013455. : Engineering Drawing (book) Rolt, L.T.C. (1957), Isambard Kingdom Brunel: A Biography, Longmans Green, LCCN 57003475. == Further reading == Basant Agrawal and C M Agrawal (2013). Engineering Drawing. Second Edition, McGraw Hill Education India Pvt. Ltd., New Delhi. [1] Paige Davis, Karen Renee Juneau (2000). Engineering Drawing David A. Madsen, Karen Schertz, (2001) Engineering Drawing & Design. Delmar Thomson Learning. [2] Cecil Howard Jensen, Jay D. Helsel, Donald D. Voisinet Computer-aided engineering drawing using AutoCAD. Warren Jacob Luzadder (1959). Fundamentals of engineering drawing for technical students and professional. M.A. Parker, F. Pickup (1990) Engineering Drawing with Worked Examples. Colin H. Simmons, Dennis E. Maguire Manual of engineering drawing. Elsevier. Cecil Howard Jensen (2001). Interpreting Engineering Drawings. B. Leighton Wellman (1948). Technical Descriptive Geometry. McGraw-Hill Book Company, Inc. == External links == Examples of cubes drawn in different projections Animated presentation of drawing systems used in technical drawing (Flash animation) Archived 2011-07-06 at the Wayback Machine Design Handbook: Engineering Drawing and Sketching, by MIT OpenCourseWare
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Financial engineering is a multidisciplinary field involving financial theory, methods of engineering, tools of mathematics and the practice of programming. It has also been defined as the application of technical methods, especially from mathematical finance and computational finance, in the practice of finance. Financial engineering plays a key role in a bank's customer-driven derivatives business — delivering bespoke OTC-contracts and "exotics", and implementing various structured products — which encompasses quantitative modelling, quantitative programming and risk managing financial products in compliance with the regulations and Basel capital/liquidity requirements. An older use of the term "financial engineering" that is less common today is aggressive restructuring of corporate balance sheets. Mathematical finance is the application of mathematics to finance. Computational finance and mathematical finance are both subfields of financial engineering. Computational finance is a field in computer science and deals with the data and algorithms that arise in financial modeling. == Discipline == Financial engineering draws on tools from applied mathematics, computer science, statistics and economic theory. In the broadest sense, anyone who uses technical tools in finance could be called a financial engineer, for example any computer programmer in a bank or any statistician in a government economic bureau. However, most practitioners restrict the term to someone educated in the full range of tools of modern finance and whose work is informed by financial theory. It is sometimes restricted even further, to cover only those originating new financial products and strategies. Despite its name, financial engineering does not belong to any of the fields in traditional professional engineering even though many financial engineers have studied engineering beforehand and many universities offering a postgraduate degree in this field require applicants to have a background in engineering as well. In the United States, the Accreditation Board for Engineering and Technology (ABET) does not accredit financial engineering degrees. In the United States, financial engineering programs are accredited by the International Association of Quantitative Finance. Quantitative analyst ("Quant") is a broad term that covers any person who uses math for practical purposes, including financial engineers. Quant is often taken to mean "financial quant", in which case it is similar to financial engineer. The difference is that it is possible to be a theoretical quant, or a quant in only one specialized niche in finance, while "financial engineer" usually implies a practitioner with broad expertise. "Rocket scientist" (aerospace engineer) is an older term, first coined in the development of rockets in WWII (Wernher von Braun), and later, the NASA space program; it was adapted by the first generation of financial quants who arrived on Wall Street in the late 1970s and early 1980s. While basically synonymous with financial engineer, it implies adventurousness and fondness for disruptive innovation. Financial "rocket scientists" were usually trained in applied mathematics, statistics or finance and spent their entire careers in risk-taking. They were not hired for their mathematical talents, they either worked for themselves or applied mathematical techniques to traditional financial jobs. The later generation of financial engineers were more likely to have PhDs in mathematics, physics, electrical and computer engineering, and often started their careers in academics or non-financial fields. == Criticisms == One of the prominent critics of financial engineering is Nassim Taleb, a professor of financial engineering at Polytechnic Institute of New York University who argues that it replaces common sense and leads to disaster. A series of economic collapses has led many governments to argue a return to "real" engineering from financial engineering. A gentler criticism came from Emanuel Derman who heads a financial engineering degree program at Columbia University. He blames over-reliance on models for financial problems; see Financial Modelers' Manifesto. Many other authors have identified specific problems in financial engineering that caused catastrophes: Aaron Brown named confusion between quants and regulators over the meaning of "capital" Felix Salmon gently pointed to the Gaussian copula (see David X. Li § CDOs and Gaussian copula) Ian Stewart criticized the Black-Scholes formula Pablo Triana (along with others including Taleb and Brown) dislikes value at risk Scott Patterson accused quantitative traders and later high-frequency traders. Douglas W. Hubbard notes that the Black–Scholes formula, along with modern portfolio theory, makes no attempt to explain an underlying structure to price changes. James Rickards posits that the "key assumptions" underpinning financial risk management are flawed. The financial innovation often associated with financial engineers was mocked by former chairman of the Federal Reserve Paul Volcker in 2009 when he said it was a code word for risky securities, that brought no benefits to society. For most people, he said, the advent of the ATM was more crucial than any asset-backed bond. == Education == The first Master of Financial Engineering degree programs were set up in the early 1990s. The number and size of programs has grown rapidly, to the extent that some now use the term "financial engineer" to refer to a graduate in the field. The financial engineering program at New York University Polytechnic School of Engineering was the first curriculum to be certified by the International Association of Financial Engineers. The number, and variation, of these programs has grown over the decades subsequent (see Master of Quantitative Finance § History); and lately includes undergraduate study, as well as designations such as the Certificate in Quantitative Finance. == See also == == References == == Further reading == Beder, Tanya S.; Marshall, Cara M. (2011). Financial Engineering: The Evolution of a Profession. John Wiley & Sons.
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Electronic engineering is a sub-discipline of electrical engineering that emerged in the early 20th century and is distinguished by the additional use of active components such as semiconductor devices to amplify and control electric current flow. Previously electrical engineering only used passive devices such as mechanical switches, resistors, inductors, and capacitors. It covers fields such as analog electronics, digital electronics, consumer electronics, embedded systems and power electronics. It is also involved in many related fields, for example solid-state physics, radio engineering, telecommunications, control systems, signal processing, systems engineering, computer engineering, instrumentation engineering, electric power control, photonics and robotics. The Institute of Electrical and Electronics Engineers (IEEE) is one of the most important professional bodies for electronics engineers in the US; the equivalent body in the UK is the Institution of Engineering and Technology (IET). The International Electrotechnical Commission (IEC) publishes electrical standards including those for electronics engineering. == History and development == Electronics engineering as a profession emerged following Karl Ferdinand Braun´s development of the crystal detector, the first semiconductor device, in 1874 and the identification of the electron in 1897 and the subsequent invention of the vacuum tube which could amplify and rectify small electrical signals, that inaugurated the field of electronics. Practical applications started with the invention of the diode by Ambrose Fleming and the triode by Lee De Forest in the early 1900s, which made the detection of small electrical voltages such as radio signals from a radio antenna possible with a non-mechanical device. The growth of electronics was rapid. By the early 1920s, commercial radio broadcasting and communications were becoming widespread and electronic amplifiers were being used in such diverse applications as long-distance telephony and the music recording industry. The discipline was further enhanced by the large amount of electronic systems development during World War II in such as radar and sonar, and the subsequent peace-time consumer revolution following the invention of transistor by William Shockley, John Bardeen and Walter Brattain. == Specialist areas == Electronics engineering has many subfields. This section describes some of the most popular. Electronic signal processing deals with the analysis and manipulation of signals. Signals can be either analog, in which case the signal varies continuously according to the information, or digital, in which case the signal varies according to a series of discrete values representing the information. For analog signals, signal processing may involve the amplification and filtering of audio signals for audio equipment and the modulation and demodulation of radio frequency signals for telecommunications. For digital signals, signal processing may involve compression, error checking and error detection, and correction. Telecommunications engineering deals with the transmission of information across a medium such as a co-axial cable, an optical fiber, or free space. Transmissions across free space require information to be encoded in a carrier wave in order to be transmitted, this is known as modulation. Popular analog modulation techniques include amplitude modulation and frequency modulation. Once the transmission characteristics of a system are determined, telecommunication engineers design the transmitters and receivers needed for such systems. These two are sometimes combined to form a two-way communication device known as a transceiver. A key consideration in the design of transmitters is their power consumption as this is closely related to their signal strength. If the signal strength of a transmitter is insufficient the signal's information will be corrupted by noise. Aviation-electronics engineering and Aviation-telecommunications engineering, are concerned with aerospace applications. Aviation-telecommunication engineers include specialists who work on airborne avionics in the aircraft or ground equipment. Specialists in this field mainly need knowledge of computer, networking, IT, and sensors. These courses are offered at such as Civil Aviation Technology Colleges. Control engineering has a wide range of electronic applications from the flight and propulsion systems of commercial airplanes to the cruise control present in many modern cars. It also plays an important role in industrial automation. Control engineers often use feedback when designing control systems. Instrumentation engineering deals with the design of devices to measure physical quantities such as pressure, flow, and temperature. The design of such instrumentation requires a good understanding of electronics engineering and physics; for example, radar guns use the Doppler effect to measure the speed of oncoming vehicles. Similarly, thermocouples use the Peltier–Seebeck effect to measure the temperature difference between two points. Often instrumentation is not used by itself, but instead as the sensors of larger electrical systems. For example, a thermocouple might be used to help ensure a furnace's temperature remains constant. For this reason, instrumentation engineering is often viewed as the counterpart of control engineering. Computer engineering deals with the design of computers and computer systems. This may involve the design of new computer hardware, the design of PDAs or the use of computers to control an industrial plant. Development of embedded systems—systems made for specific tasks (e.g., mobile phones)—is also included in this field. This field includes the microcontroller and its applications. Computer engineers may also work on a system's software. However, the design of complex software systems is often the domain of software engineering which falls under computer science, which is usually considered a separate discipline. VLSI design engineering VLSI stands for very large-scale integration. It deals with fabrication of ICs and various electronic components. In designing an integrated circuit, electronics engineers first construct circuit schematics that specify the electrical components and describe the interconnections between them. When completed, VLSI engineers convert the schematics into actual layouts, which map the layers of various conductor and semiconductor materials needed to construct the circuit. == Education and training == Electronics is a subfield within the wider electrical engineering academic subject. Electronics engineers typically possess an academic degree with a major in electronics engineering. The length of study for such a degree is usually three or four years and the completed degree may be designated as a Bachelor of Engineering, Bachelor of Science, Bachelor of Applied Science, or Bachelor of Technology depending upon the university. Many UK universities also offer Master of Engineering (MEng) degrees at the graduate level. Some electronics engineers also choose to pursue a postgraduate degree such as a Master of Science, Doctor of Philosophy in Engineering, or an Engineering Doctorate. The master's degree is being introduced in some European and American Universities as a first degree and the differentiation of an engineer with graduate and postgraduate studies is often difficult. In these cases, experience is taken into account. The master's degree may consist of either research, coursework or a mixture of the two. The Doctor of Philosophy consists of a significant research component and is often viewed as the entry point to academia. In most countries, a bachelor's degree in engineering represents the first step towards certification and the degree program itself is certified by a professional body. Certification allows engineers to legally sign off on plans for projects affecting public safety. After completing a certified degree program, the engineer must satisfy a range of requirements, including work experience requirements, before being certified. Once certified the engineer is designated the title of Professional Engineer (in the United States, Canada, and South Africa), Chartered Engineer or Incorporated Engineer (in the United Kingdom, Ireland, India, and Zimbabwe), Chartered Professional Engineer (in Australia and New Zealand) or European Engineer (in much of the European Union). A degree in electronics generally includes units covering physics, chemistry, mathematics, project management and specific topics in electrical engineering. Initially, such topics cover most, if not all, of the subfields of electronics engineering. Students then choose to specialize in one or more subfields towards the end of the degree. Fundamental to the discipline are the sciences of physics and mathematics as these help to obtain both a qualitative and quantitative description of how such systems will work. Today, most engineering work involves the use of computers and it is commonplace to use computer-aided design and simulation software programs when designing electronic systems. Although most electronic engineers will understand basic circuit theory, the theories employed by engineers generally depend upon the work they do. For example, quantum mechanics and solid-state physics might be relevant to an engineer working on VLSI but are largely irrelevant to engineers working with embedded systems. Apart from electromagnetics and network theory, other items in the syllabus are particular to electronic engineering courses. Electrical engineering courses have other specialisms such as machines, power generation, and distribution. This list does not include the extensive engineering mathematics curriculum that is a prerequisite to a degree. === Supporting knowledge areas === The huge breadth of electronics engineering has led to the use of a large number of specialists supporting knowledge areas. Elements of vector calculus: divergence and curl; Gauss' and Stokes' theorems, Maxwell's equations: differential and integral forms. Wave equation, Poynting vector. Plane waves: propagation through various media; reflection and refraction; phase and group velocity; skin depth. Transmission lines: characteristic impedance; impedance transformation; Smith chart; impedance matching; pulse excitation. Waveguides: modes in rectangular waveguides; boundary conditions; cut-off frequencies; dispersion relations. Antennas: Dipole antennas; antenna arrays; radiation pattern; reciprocity theorem, antenna gain. Network graphs: matrices associated with graphs; incidence, fundamental cut set, and fundamental circuit matrices. Solution methods: nodal and mesh analysis. Network theorems: superposition, Thevenin and Norton's maximum power transfer, Wye-Delta transformation. Steady state sinusoidal analysis using phasors. Linear constant coefficient differential equations; time domain analysis of simple RLC circuits, Solution of network equations using Laplace transform: frequency domain analysis of RLC circuits. 2-port network parameters: driving point and transfer functions. State equations for networks. Electronic devices: Energy bands in silicon, intrinsic and extrinsic silicon. Carrier transport in silicon: diffusion current, drift current, mobility, resistivity. Generation and recombination of carriers. p-n junction diode, Zener diode, tunnel diode, BJT, JFET, MOS capacitor, MOSFET, LED, p-i-n and avalanche photo diode, LASERs. Device technology: integrated circuit fabrication process, oxidation, diffusion, ion implantation, photolithography, n-tub, p-tub and twin-tub CMOS process. Analog circuits: Equivalent circuits (large and small-signal) of diodes, BJT, JFETs, and MOSFETs. Simple diode circuits, clipping, clamping, rectifier. Biasing and bias stability of transistor and FET amplifiers. Amplifiers: single-and multi-stage, differential, operational, feedback and power. Analysis of amplifiers; frequency response of amplifiers. Simple op-amp circuits. Filters. Sinusoidal oscillators; criterion for oscillation; single-transistor and op-amp configurations. Function generators and wave-shaping circuits, Power supplies. Digital circuits: Boolean functions (NOT, AND, OR, XOR,...). Logic gates digital IC families (DTL, TTL, ECL, MOS, CMOS). Combinational circuits: arithmetic circuits, code converters, multiplexers, and decoders. Sequential circuits: latches and flip-flops, counters, and shift-registers. Sample and hold circuits, ADCs, DACs. Semiconductor memories. Microprocessor 8086: architecture, programming, memory, and I/O interfacing. Signals and systems: Definitions and properties of Laplace transform, continuous-time and discrete-time Fourier series, continuous-time and discrete-time Fourier Transform, z-transform. Sampling theorems. Linear Time-Invariant (LTI) Systems: definitions and properties; causality, stability, impulse response, convolution, poles and zeros frequency response, group delay and phase delay. Signal transmission through LTI systems. Random signals and noise: probability, random variables, probability density function, autocorrelation, power spectral density, and function analogy between vectors & functions. ==== Electronic Control systems ==== Basic control system components; block diagrammatic description, reduction of block diagrams — Mason's rule. Open loop and closed loop (negative unity feedback) systems and stability analysis of these systems. Signal flow graphs and their use in determining transfer functions of systems; transient and steady-state analysis of LTI control systems and frequency response. Analysis of steady-state disturbance rejection and noise sensitivity. Tools and techniques for LTI control system analysis and design: root loci, Routh–Hurwitz stability criterion, Bode and Nyquist plots. Control system compensators: elements of lead and lag compensation, elements of proportional–integral–derivative (PID) control. Discretization of continuous-time systems using zero-order hold and ADCs for digital controller implementation. Limitations of digital controllers: aliasing. State variable representation and solution of state equation of LTI control systems. Linearization of Nonlinear dynamical systems with state-space realizations in both frequency and time domains. Fundamental concepts of controllability and observability for MIMO LTI systems. State space realizations: observable and controllable canonical form. Ackermann's formula for state-feedback pole placement. Design of full order and reduced order estimators. ==== Communications ==== Analog communication systems: amplitude and angle modulation and demodulation systems, spectral analysis of these operations, superheterodyne noise conditions. Digital communication systems: pulse-code modulation (PCM), differential pulse-code modulation (DPCM), delta modulation (DM), digital modulation – amplitude, phase- and frequency-shift keying schemes (ASK, PSK, FSK), matched-filter receivers, bandwidth consideration and probability of error calculations for these schemes, GSM, TDMA. == Professional bodies == Professional bodies of note for electrical engineers USA's Institute of Electrical and Electronics Engineers (IEEE) and the UK's Institution of Engineering and Technology (IET). Members of the Institution of Engineering and Technology (MIET) are recognized professionally in Europe, as electrical and computer engineers. The IEEE claims to produce 30 percent of the world's literature in electrical and electronics engineering, has over 430,000 members, and holds more than 450 IEEE sponsored or cosponsored conferences worldwide each year. Senior membership of the IEEE is a recognised professional designation in the United States. == Project engineering == For most engineers not involved at the cutting edge of system design and development, technical work accounts for only a fraction of the work they do. A lot of time is also spent on tasks such as discussing proposals with clients, preparing budgets and determining project schedules. Many senior engineers manage a team of technicians or other engineers and for this reason, project management skills are important. Most engineering projects involve some form of documentation and strong written communication skills are therefore very important. The workplaces of electronics engineers are just as varied as the types of work they do. Electronics engineers may be found in the pristine laboratory environment of a fabrication plant, the offices of a consulting firm or in a research laboratory. During their working life, electronics engineers may find themselves supervising a wide range of individuals including scientists, electricians, programmers, and other engineers. Obsolescence of technical skills is a serious concern for electronics engineers. Membership and participation in technical societies, regular reviews of periodicals in the field, and a habit of continued learning are therefore essential to maintaining proficiency, which is even more crucial in the field of consumer electronics products. == See also == Comparison of EDA software Electrical engineering technology Glossary of electrical and electronics engineering Index of electrical engineering articles Information engineering List of electrical engineers Timeline of electrical and electronics engineering == References == == External links ==
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Explosives engineering is the field of science and engineering which is related to examining the behavior and usage of explosive materials. == Topics == Some of the topics that explosives engineers study, research, and work on include: Development and characterization of new explosive materials in various forms Analysis of the physical process of detonation Explosive generated shock waves and their effects on materials Safety testing of explosives Analysis and engineering of rock blasting for mining Design and analysis of shaped charges and reactive armor Design, analysis and application of military explosives such as grenades, mines, shells, aerial bombs, missile warheads, etc. Bomb disposal Drilling and blasting Demolition == Organizations == International Society of Explosives Engineers (ISEE) Missouri University of Science and Technology New Mexico Institute of Mining and Technology (New Mexico Tech) == In popular culture == The film The Hurt Locker follows an Iraq War Explosive Ordnance Disposal team who are targeted by insurgents and shows their psychological reactions to the stress of combat. == See also == Explosives Chapman–Jouguet condition Chemistry Civil engineer Chemical engineer Gurney equations Material science Physics Drilling and blasting == References == == External links == http://www.isee.org/ http://www.explosivesacademy.org/
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Control engineering, also known as control systems engineering and, in some European countries, automation engineering, is an engineering discipline that deals with control systems, applying control theory to design equipment and systems with desired behaviors in control environments. The discipline of controls overlaps and is usually taught along with electrical engineering, chemical engineering and mechanical engineering at many institutions around the world. The practice uses sensors and detectors to measure the output performance of the process being controlled; these measurements are used to provide corrective feedback helping to achieve the desired performance. Systems designed to perform without requiring human input are called automatic control systems (such as cruise control for regulating the speed of a car). Multi-disciplinary in nature, control systems engineering activities focus on implementation of control systems mainly derived by mathematical modeling of a diverse range of systems. == Overview == Modern day control engineering is a relatively new field of study that gained significant attention during the 20th century with the advancement of technology. It can be broadly defined or classified as practical application of control theory. Control engineering plays an essential role in a wide range of control systems, from simple household washing machines to high-performance fighter aircraft. It seeks to understand physical systems, using mathematical modelling, in terms of inputs, outputs and various components with different behaviors; to use control system design tools to develop controllers for those systems; and to implement controllers in physical systems employing available technology. A system can be mechanical, electrical, fluid, chemical, financial or biological, and its mathematical modelling, analysis and controller design uses control theory in one or many of the time, frequency and complex-s domains, depending on the nature of the design problem. Control engineering is the engineering discipline that focuses on the modeling of a diverse range of dynamic systems (e.g. mechanical systems) and the design of controllers that will cause these systems to behave in the desired manner.: 6 Although such controllers need not be electrical, many are and hence control engineering is often viewed as a subfield of electrical engineering. Electrical circuits, digital signal processors and microcontrollers can all be used to implement control systems. Control engineering has a wide range of applications from the flight and propulsion systems of commercial airliners to the cruise control present in many modern automobiles. In most cases, control engineers utilize feedback when designing control systems. This is often accomplished using a proportional–integral–derivative controller (PID controller) system. For example, in an automobile with cruise control the vehicle's speed is continuously monitored and fed back to the system, which adjusts the motor's torque accordingly. Where there is regular feedback, control theory can be used to determine how the system responds to such feedback. In practically all such systems stability is important and control theory can help ensure stability is achieved. Although feedback is an important aspect of control engineering, control engineers may also work on the control of systems without feedback. This is known as open loop control. A classic example of open loop control is a washing machine that runs through a pre-determined cycle without the use of sensors. == History == Automatic control systems were first developed over two thousand years ago. The first feedback control device on record is thought to be the ancient Ktesibios's water clock in Alexandria, Egypt, around the third century BCE. It kept time by regulating the water level in a vessel and, therefore, the water flow from that vessel. : 22 This certainly was a successful device as water clocks of similar design were still being made in Baghdad when the Mongols captured the city in 1258 CE. A variety of automatic devices have been used over the centuries to accomplish useful tasks or simply just to entertain. The latter includes the automata, popular in Europe in the 17th and 18th centuries, featuring dancing figures that would repeat the same task over and over again; these automata are examples of open-loop control. Milestones among feedback, or "closed-loop" automatic control devices, include the temperature regulator of a furnace attributed to Drebbel, circa 1620, and the centrifugal flyball governor used for regulating the speed of steam engines by James Watt: 22 in 1788. In his 1868 paper "On Governors", James Clerk Maxwell was able to explain instabilities exhibited by the flyball governor using differential equations to describe the control system. This demonstrated the importance and usefulness of mathematical models and methods in understanding complex phenomena, and it signaled the beginning of mathematical control and systems theory. Elements of control theory had appeared earlier but not as dramatically and convincingly as in Maxwell's analysis. Control theory made significant strides over the next century. New mathematical techniques, as well as advances in electronic and computer technologies, made it possible to control significantly more complex dynamical systems than the original flyball governor could stabilize. New mathematical techniques included developments in optimal control in the 1950s and 1960s followed by progress in stochastic, robust, adaptive, nonlinear control methods in the 1970s and 1980s. Applications of control methodology have helped to make possible space travel and communication satellites, safer and more efficient aircraft, cleaner automobile engines, and cleaner and more efficient chemical processes. Before it emerged as a unique discipline, control engineering was practiced as a part of mechanical engineering and control theory was studied as a part of electrical engineering since electrical circuits can often be easily described using control theory techniques. In the first control relationships, a current output was represented by a voltage control input. However, not having adequate technology to implement electrical control systems, designers were left with the option of less efficient and slow responding mechanical systems. A very effective mechanical controller that is still widely used in some hydro plants is the governor. Later on, previous to modern power electronics, process control systems for industrial applications were devised by mechanical engineers using pneumatic and hydraulic control devices, many of which are still in use today. === Mathematical modelling === David Quinn Mayne, (1930–2024) was among the early developers of a rigorous mathematical method for analysing Model predictive control algorithms (MPC). It is currently used in tens of thousands of applications and is a core part of the advanced control technology by hundreds of process control producers. MPC's major strength is its capacity to deal with nonlinearities and hard constraints in a simple and intuitive fashion. His work underpins a class of algorithms that are probably correct, heuristically explainable, and yield control system designs which meet practically important objectives. == Control systems == == Control theory == == Education == At many universities around the world, control engineering courses are taught primarily in electrical engineering and mechanical engineering, but some courses can be instructed in mechatronics engineering, and aerospace engineering. In others, control engineering is connected to computer science, as most control techniques today are implemented through computers, often as embedded systems (as in the automotive field). The field of control within chemical engineering is often known as process control. It deals primarily with the control of variables in a chemical process in a plant. It is taught as part of the undergraduate curriculum of any chemical engineering program and employs many of the same principles in control engineering. Other engineering disciplines also overlap with control engineering as it can be applied to any system for which a suitable model can be derived. However, specialised control engineering departments do exist, for example, in Italy there are several master in Automation & Robotics that are fully specialised in Control engineering or the Department of Automatic Control and Systems Engineering at the University of Sheffield or the Department of Robotics and Control Engineering at the United States Naval Academy and the Department of Control and Automation Engineering at the Istanbul Technical University. Control engineering has diversified applications that include science, finance management, and even human behavior. Students of control engineering may start with a linear control system course dealing with the time and complex-s domain, which requires a thorough background in elementary mathematics and Laplace transform, called classical control theory. In linear control, the student does frequency and time domain analysis. Digital control and nonlinear control courses require Z transformation and algebra respectively, and could be said to complete a basic control education. == Careers == A control engineer's career starts with a bachelor's degree and can continue through the college process. Control engineer degrees are typically paired with an electrical or mechanical engineering degree, but can also be paired with a degree in chemical engineering. According to a Control Engineering survey, most of the people who answered were control engineers in various forms of their own career. There are not very many careers that are classified as "control engineer", most of them are specific careers that have a small semblance to the overarching career of control engineering. A majority of the control engineers that took the survey in 2019 are system or product designers, or even control or instrument engineers. Most of the jobs involve process engineering or production or even maintenance, they are some variation of control engineering. Because of this, there are many job opportunities in aerospace companies, manufacturing companies, automobile companies, power companies, chemical companies, petroleum companies, and government agencies. Some places that hire Control Engineers include companies such as Rockwell Automation, NASA, Ford, Phillips 66, Eastman, and Goodrich. Control Engineers can possibly earn $66k annually from Lockheed Martin Corp. They can also earn up to $96k annually from General Motors Corporation. Process Control Engineers, typically found in Refineries and Specialty Chemical plants, can earn upwards of $90k annually. In India, control System Engineering is provided at different levels with a diploma, graduation and postgraduation. These programs require the candidate to have chosen physics, chemistry and mathematics for their secondary schooling or relevant bachelor's degree for postgraduate studies. == Recent advancement == Originally, control engineering was all about continuous systems. Development of computer control tools posed a requirement of discrete control system engineering because the communications between the computer-based digital controller and the physical system are governed by a computer clock.: 23 The equivalent to Laplace transform in the discrete domain is the Z-transform. Today, many of the control systems are computer controlled and they consist of both digital and analog components. Therefore, at the design stage either: Digital components are mapped into the continuous domain and the design is carried out in the continuous domain, or Analog components are mapped into discrete domain and design is carried out there. The first of these two methods is more commonly encountered in practice because many industrial systems have many continuous systems components, including mechanical, fluid, biological and analog electrical components, with a few digital controllers. Similarly, the design technique has progressed from paper-and-ruler based manual design to computer-aided design and now to computer-automated design or CAD which has been made possible by evolutionary computation. CAD can be applied not just to tuning a predefined control scheme, but also to controller structure optimisation, system identification and invention of novel control systems, based purely upon a performance requirement, independent of any specific control scheme. Resilient control systems extend the traditional focus of addressing only planned disturbances to frameworks and attempt to address multiple types of unexpected disturbance; in particular, adapting and transforming behaviors of the control system in response to malicious actors, abnormal failure modes, undesirable human action, etc. == See also == == References == == Further reading == D. Q. Mayne (1965). P. H. Hammond (ed.). A Gradient Method for Determining Optimal Control of Nonlinear Stochastic Systems in Proceedings of IFAC Symposium, Theory of Self-Adaptive Control Systems. Plenum Press. pp. 19–27. Bennett, Stuart (June 1986). A history of control engineering, 1800-1930. IET. ISBN 978-0-86341-047-5. Bennett, Stuart (1993). A history of control engineering, 1930-1955. IET. ISBN 978-0-86341-299-8. Christopher Kilian (2005). Modern Control Technology. Thompson Delmar Learning. ISBN 978-1-4018-5806-3. Arnold Zankl (2006). Milestones in Automation: From the Transistor to the Digital Factory. Wiley-VCH. ISBN 978-3-89578-259-6. Franklin, Gene F.; Powell, J. David; Emami-Naeini, Abbas (2014). Feedback control of dynamic systems (7th ed.). Stanford Cali. U.S.: Pearson. p. 880. ISBN 9780133496598. == External links == Control Labs Worldwide The Michigan Chemical Engineering Process Dynamics and Controls Open Textbook Control System Integrators Association List of control systems integrators Institution of Mechanical Engineers - Mechatronics, Informatics and Control Group (MICG) Systems Science & Control Engineering: An Open Access Journal
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Engineering psychology, also known as Human Factors Engineering or Human Factors Psychology, is the science of human behavior and capability, applied to the design and operation of systems and technology. As an applied field of psychology and an interdisciplinary part of ergonomics, it aims to improve the relationships between people and machines by redesigning equipment, interactions, or the environment in which they take place. The work of an engineering psychologist is often described as making the relationship more "user-friendly." == History == Engineering psychology was created from within experimental psychology. Engineering psychology started during World War I (1914). The reason why this subject was developed during this time was because many of America's weapons were failing; bombs not falling in the right place to weapons attacking normal marine life. The fault was traced back to human errors. One of the first designs to be built to restrain human error was the use of psychoacoustics by S.S. Stevens and L.L. Beranek were two of the first American psychologists called upon to help change how people and machinery worked together. One of their first assignments was to try and reduce noise levels in military aircraft. The work was directed at improving intelligibility of military communication systems and appeared to have been very successful. However it was not until after August 1945 that levels of research in engineering psychology began to increase significantly. This occurred because the research that started in 1940 now began to show. Lillian Gilbreth combined the talents of an engineer, psychologist and mother of twelve. Her appreciation of human factors made her successful in the implementation of time and motion studies and scientific management. She went on to pioneer ergonomics in the kitchen, inventing the pedal bin, for example. In Britain, the two world wars generated much formal study of human factors which affected the efficiency of munitions output and warfare. In World War I, the Health of Munitions Workers Committee was created in 1915. This made recommendations based upon studies of the effects of overwork on efficiency which resulted in policies of providing breaks and limiting hours of work, including avoidance of work on Sunday. The Industrial Fatigue Research Board was created in 1918 to take this work forward. In WW2, researchers at Cambridge University such as Frederic Bartlett and Kenneth Craik started work on the operation of equipment in 1939 and this resulted in the creation of the Unit for Research in Applied Psychology in 1944. == Related subjects == Cognitive ergonomics and cognitive engineering - studies cognition in work settings, in order to optimize human well-being and system performance. It is a subset of the larger field of human factors and ergonomics. Applied psychology - The use of psychological principles to overcome problems in other domains. It has been argued that engineering psychology is separate from applied (cognitive) psychology because advances in cognitive psychology have infrequently informed engineering psychology research. Surprisingly, work in engineering psychology often seems to inform developments in cognitive psychology. For example, engineering psychology research has enabled cognitive psychologists to explain why GUIs seem easier to use than character-based computer interfaces (such as DOS). === Engineering Psychology, Ergonomics and Human Factors === Although the comparability of these terms and many others have been a topic of debate, the differences of these fields can be seen in the applications of the respective fields. Engineering psychology is concerned with the adaptation of the equipment and environment to people, based upon their psychological capacities and limitations with the objective of improving overall system performance, involving human and machine elements Engineering psychologists strive to match equipment requirements with the capabilities of human operators by changing the design of the equipment. An example of this matching was the redesign of the mailbags used by letter carriers. Engineering psychologists discovered that mailbag with a waist-support strap, and a double bag that requires the use of both shoulders, reduces muscle fatigue. Another example involves the cumulative trauma disorders grocery checkout workers suffered as the result of repetitive wrist movements using electronic scanners. Engineering psychologists found that the optimal checkout station design would allow for workers to easily use either hand to distribute the workload between both wrists. The field of ergonomics is based on scientific studies of ordinary people in work situations and is applied to the design of processes and machines, to the layout of work places, to methods of work, and to the control of the physical environment, in order to achieve greater efficiency of both men and machines An example of an ergonomics study is the evaluation of the effects of screwdriver handle shape, surface material and workpiece orientation on torque performance, finger force distribution and muscle activity in a maximum screwdriving torque task. Another example of an ergonomics study is the effects of shoe traction and obstacle height on friction. Similarly, many topics in ergonomics deal with the actual science of matching man to equipment and encompasses narrower fields such as engineering psychology. At one point in time, the term human factors was used in place of ergonomics in Europe. Human factors involve interdisciplinary scientific research and studies to seek to realize greater recognition and understanding of the worker's characteristics, needs, abilities, and limitations when the procedures and products of technology are being designed. This field utilizes knowledge from several fields such as mechanical engineering, psychology, and industrial engineering to design instruments. Human factors is broader than engineering psychology, which is focused specifically on designing systems that accommodate the information-processing capabilities of the brain. Although the work in the respective fields differ, there are some similarities between these. These fields share the same objectives which are to optimize the effectiveness and efficiency with which human activities are conducted as well as to improve the general quality of life through increased safety, reduced fatigue and stress, increased comfort, and satisfaction. === Importance of Engineering Psychologists === Engineering psychologists contribute to the design of a variety of products, including dental and surgical tools, cameras, toothbrushes and car-seats. They have been involved in the re-design of the mailbags used by letter carriers. More than 20% of letter carriers suffer from musculoskeletal injury such as lower back pain from carrying mailbags slung over their shoulders. A mailbag with a waist-support strap, and a double bag that requires the use of both shoulders, has been shown to reduce muscle fatigue. Research by engineering psychologists has demonstrated that using cell-phones while driving degrades performance by increasing driver reaction time, particularly among older drivers, and can lead to higher accident risk among drivers of all ages. Research findings such as these have supported governmental regulation of cell-phone use. == References == == Bibliography == Stanley N. Roscoe (1997), The Adolescence of Engineering Psychology, Human Factors and Ergonomics Society, archived from the original on 28 September 2011, retrieved 2 July 2011 Francis Durso, Patricia DeLucia (2010), "Engineering Psychology", The Corsini Encyclopedia of Psychology, vol. 2, John Wiley and Sons, pp. 573–576, ISBN 978-0-470-17026-7 Wickens, Christopher D.; Hollands, J.G. (2000), Engineering Psychology and Human Performance, Prentice-Hall, ISBN 978-0-321-04711-3 Journal of Engineering Psychology Howell, William Carl (1971). Engineering Psychology: Current Perspectives in Research. New York: Appleton-Century-Crofts. ISBN 978-0-390-46456-9. Wickens, Christopher D. (1984). Engineering Psychology and Human Performance. Columbus: Merrill.
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https://en.wikipedia.org/wiki/Engineering_psychology
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Teenage Engineering is a Swedish consumer electronics company and manufacturer founded in 2005 by Jesper Kouthoofd, David Eriksson, Jens Rudberg and David Möllerstedt and based in Stockholm. Its products include electronics and synthesizers, with its core product being the OP-1, as well as instant cameras. == History == Teenage Engineering was founded in 2005 by Jesper Kouthoofd, Jens Rudberg and David Eriksson, the three of whom had previously led the computer games company Netbabyworld from 1999–2003. They were later joined by David Möllerstedt, who previously headed the audio department at EA DICE. Their first product, the OP-1, was introduced at the NAMM Show in 2010. Shortly after release, Teenage Engineering produced several "accessories", which could be used to manipulate the unit's input knobs. Following the success of the OP-1, the company began working with the Stig Carlsson Foundation to develop the OD-11 speaker, inspired by a speaker of the same name manufactured by Sonab and designed by Swedish designer Stig Carlsson in 1974. It was well received for its minimalist design, a faithful reproduction of the original, and for its sound quality. Despite two early appearances at the Consumer Electronics Show and an original release date of Summer 2013, it was not released until 2014. Teenage Engineering aimed to maintain Carlsson's goal of designing a speaker for use in a "regular home", rather than one designed to be used in an unrealistically ideal, noiseless environment. In 2013, the company collaborated with the Swedish clothing company Cheap Monday after ordering new work uniforms from them; Kouthoofd had previously collaborated with creative director, Ann-Sofie Back. The companies jointly announced the Pocket Operator (PO-10) synthesizer series in January 2015. The series includes three models: PO-12 rhythm, a drum machine; PO-14 sub, a bass synthesizer; and PO-16 factory, a lead synthesizer. Each model doubles as a 16-step sequencer. According to CEO Jesper Kouthoofd, Teenage Engineering sought to design synthesizers that would retail for US$49; however, each PO actually retails from US$59 to US$99. The POs target musicians seeking a less expensive alternative to the OP-1, which currently retails for US$1,399. The series uses a minimalist design, evoking pocket calculators and, according to Kouthoofd, Nintendo's Game & Watch games. Sonically, they emulate vintage synthesizers, in response to the contemporary surge in the popularity of retro style electronic music gear. The synthesizers debuted at the 2015 NAMM Show. The Pocket Operators were a success at NAMM, and sales were estimated by third parties to be as high as 40,000 units, which delayed shipments by up to three months. The PO-20 series of the Pocket Operators were introduced at the 2016 NAMM show. The PO-20 synthesizers have some additional effects and functionality that were not present in the original PO-10 series, but maintain the US$59 price point. The PO-30 series further elaborates upon the original Pocket operators by adding a drum synthesizer made in collaboration with MicroTonic, a sampler, and a voice synthesizer. These were released starting in late 2017 at a slightly increased price from previous series. PO-30 devices feature a microphone for use in recording audio samples and for transferring data. In 2018, Teenage Engineering announced a new line of audio equipment products, Frekvens, in collaboration with IKEA. The modular system takes visual cues from Bauhaus design. Founder Kouthoofd had previously collaborated with IKEA on Knäppa, a camera made of cardboard. On 22 May 2019, Panic announced Playdate, a new handheld video game console designed in collaboration with Teenage Engineering. The device features a mechanical crank which is specifically credited to Teenage Engineering. On 25 February 2021, Teenage Engineering announced that it will partner with the British electronics company, Nothing, to produce the design aesthetic of the brand and their products. Teenage Engineering later worked on the audio for the "ear (1)", Nothing's first product. On 9 January 2024, Rabbit Inc. announced the release of the Rabbit r1, co-designed with Teenage Engineering, a pocket assistant device that leverages a machine learning model to automate various tasks. == Awards and accolades == The OP-1 synthesizer won one of ten of Sweden's Design S Awards in 2012. The award committee described the OP-1 as "A technological product which through a clever colour scheme and fantastic graphics is intuitive, easily accessible and incredibly inviting. Music and machine in one". In 2014, the OP-1 was awarded second prize in Georgia Tech's Margaret Guthman Musical Instrument Competition. In 2017, the Pocket Operator series was awarded a Good Design Award by the Japan Institute of Design Promotion. The Institute noted that while the functions of the devices were not immediately clear, the format "inspires a desire to press the buttons". Musicians who have used the OP-1 include Bon Iver, Beck, Depeche Mode, Jean Michel Jarre, Caroline Rose, and Ivan Dorn. == Products == OP-1 synthesizer/sampler/sequencer (introduced January 2010) PX-0 earbuds (introduced 2011, collaboration with AIAIAI, discontinued) Oplab (introduced January 2012) OD-11 wireless loudspeaker (introduced January 2013) ortho remote remote controller (introduced January 2013) PO-12 Rhythm drum machine/sequencer, PO-14 Sub synthesizer/sequencer & PO-16 Factory synthesizer/sequencer (introduced January 2015; collaboration with Cheap Monday) Impossible I-1 (introduced May 2016; designed by teenage engineering for The Impossible Project) PO-20 Arcade synthesizer/sequencer, PO-24 Office drum machine/sequencer & PO-28 Robot synthesizer/sequencer (introduced January 2016; collaboration with Cheap Monday) PO-32 Tonic synthesizer and sequencer (introduced January 2017) H (introduced November 2017; designed by teenage engineering for Raven) R (introduced November 2017; designed by teenage engineering for Raven) PO-33 KO! & PO-35 speak (introduced January 2018) Frekvens collection (introduced April 2018; designed by teenage engineering for IKEA) OP-Z synthesizer and sequencer (introduced September 2018) pocket operator modular series (POM-16 keyboard/sequencer, POM-170 analog synthesizer/sequencer & POM-400 analog synthesizer) (introduced January 2019) PO-137 Rick and Morty (introduced July 2019; collaboration with Adult Swim (Rick and Morty)) Playdate game console (introduced May 2019; designed by teenage engineering for Panic Inc.) M-1 headphones (introduced December 2019) OB-4 radio (introduced September 2020) PO-128 Mega Man & PO-133 Streetfighter (introduced October 2020; collaboration with Capcom) ear (1) (introduced July 2021; designed by teenage engineering for Nothing) Mayku Multiplier (introduced September 2021; designed by teenage engineering for Mayku) computer-1 computer case (introduced October 2021) TX-6 field mixer (introduced April 2022) OP-1 Field synthesizer (introduced May 2022) PO-80 portable record player and engraver (introduced October 2022; collaboration with Yuri Suzuki) CH-8 singing wooden dolls (introduced November 2022) CM-15 microphone (introduced April 2023) TP-7 field recorder (introduced May 2023) EP-133 K.O. II sampler (introduced November 2023) Rabbit r1 (introduced January 2024; designed by teenage engineering for rabbit inc.) EP-1320 Medieval sampler (introduced August 2024) OP-XY sequencer/synthesizer (introduced November 2024) B-1 generative film deck (designed for live screenings of Eno (2024 film).) == References == == External links == Official website
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https://en.wikipedia.org/wiki/Teenage_Engineering
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Automotive engineering, along with aerospace engineering and naval architecture, is a branch of vehicle engineering, incorporating elements of mechanical, electrical, electronic, software, and safety engineering as applied to the design, manufacture and operation of motorcycles, automobiles, and trucks and their respective engineering subsystems. It also includes modification of vehicles. Manufacturing domain deals with the creation and assembling the whole parts of automobiles is also included in it. The automotive engineering field is research intensive and involves direct application of mathematical models and formulas. The study of automotive engineering is to design, develop, fabricate, and test vehicles or vehicle components from the concept stage to production stage. Production, development, and manufacturing are the three major functions in this field. == Disciplines == === Automobile engineering === Automobile engineering is a branch study of engineering which teaches manufacturing, designing, mechanical mechanisms as well as operations of automobiles. It is an introduction to vehicle engineering which deals with motorcycles, cars, buses, trucks, etc. It includes branch study of mechanical, electronic, software and safety elements. Some of the engineering attributes and disciplines that are of importance to the automotive engineer include: Safety engineering: Safety engineering is the assessment of various crash scenarios and their impact on the vehicle occupants. These are tested against very stringent governmental regulations. Some of these requirements include: seat belt and air bag functionality testing, front and side-impact testing, and tests of rollover resistance. Assessments are done with various methods and tools, including computer crash simulation (typically finite element analysis), crash-test dummy, and partial system sled and full vehicle crashes. Fuel economy/emissions: Fuel economy is the measured fuel efficiency of the vehicle in miles per gallon or kilometers per liter. Emissions-testing covers the measurement of vehicle emissions, including hydrocarbons, nitrogen oxides (NOx), carbon monoxide (CO), carbon dioxide (CO2), and evaporative emissions. NVH engineering (noise, vibration, and harshness): NVH involves customer feedback (both tactile [felt] and audible [heard]) concerning a vehicle. While sound can be interpreted as a rattle, squeal, or hot, a tactile response can be seat vibration or a buzz in the steering wheel. This feedback is generated by components either rubbing, vibrating, or rotating. NVH response can be classified in various ways: powertrain NVH, road noise, wind noise, component noise, and squeak and rattle. Note, there are both good and bad NVH qualities. The NVH engineer works to either eliminate bad NVH or change the "bad NVH" to good (i.e., exhaust tones). Vehicle electronics: Automotive electronics is an increasingly important aspect of automotive engineering. Modern vehicles employ dozens of electronic systems. These systems are responsible for operational controls such as the throttle, brake and steering controls; as well as many comfort-and-convenience systems such as the HVAC, infotainment, and lighting systems. It would not be possible for automobiles to meet modern safety and fuel-economy requirements without electronic controls. Performance: Performance is a measurable and testable value of a vehicle's ability to perform in various conditions. Performance can be considered in a wide variety of tasks, but it generally considers how quickly a car can accelerate (e.g. standing start 1/4 mile elapsed time, 0–60 mph, etc.), its top speed, how short and quickly a car can come to a complete stop from a set speed (e.g. 70-0 mph), how much g-force a car can generate without losing grip, recorded lap-times, cornering speed, brake fade, etc. Performance can also reflect the amount of control in inclement weather (snow, ice, rain). Shift quality: Shift quality is the driver's perception of the vehicle to an automatic transmission shift event. This is influenced by the powertrain (Internal combustion engine, transmission), and the vehicle (driveline, suspension, engine and powertrain mounts, etc.) Shift feel is both a tactile (felt) and audible (heard) response of the vehicle. Shift quality is experienced as various events: transmission shifts are felt as an upshift at acceleration (1–2), or a downshift maneuver in passing (4–2). Shift engagements of the vehicle are also evaluated, as in Park to Reverse, etc. Durability / corrosion engineering: Durability and corrosion engineering is the evaluation testing of a vehicle for its useful life. Tests include mileage accumulation, severe driving conditions, and corrosive salt baths. Drivability: Drivability is the vehicle's response to general driving conditions. Cold starts and stalls, RPM dips, idle response, launch hesitations and stumbles, and performance levels all contribute to the overall drivability of any given vehicle. Cost: The cost of a vehicle program is typically split into the effect on the variable cost of the vehicle, and the up-front tooling and fixed costs associated with developing the vehicle. There are also costs associated with warranty reductions and marketing. Program timing: To some extent programs are timed with respect to the market, and also to the production-schedules of assembly plants. Any new part in the design must support the development and manufacturing schedule of the model. Design for manufacturability (DFM): DFM refers to designing vehicular components in such a way that they are not only feasible to manufacture, but also such that they are cost-efficient to produce while resulting in acceptable quality that meets design specifications and engineering tolerances. This requires coördination between the design engineers and the assembly/manufacturing teams. Quality management: Quality control is an important factor within the production process, as high quality is needed to meet customer requirements and to avoid expensive recall campaigns. The complexity of components involved in the production process requires a combination of different tools and techniques for quality control. Therefore, the International Automotive Task Force (IATF), a group of the world's leading manufacturers and trade organizations, developed the standard ISO/TS 16949. This standard defines the design, development, production, and (when relevant) installation and service requirements. Furthermore, it combines the principles of ISO 9001 with aspects of various regional and national automotive standards such as AVSQ (Italy), EAQF (France), VDA6 (Germany) and QS-9000 (USA). In order to further minimize risks related to product failures and liability claims for automotive electric and electronic systems, the quality discipline functional safety according to ISO/IEC 17025 is applied. Since the 1950s, the comprehensive business approach total quality management (TQM) has operated to continuously improve the production process of automotive products and components. Some of the companies who have implemented TQM include Ford Motor Company, Motorola and Toyota Motor Company. == Job functions == === Development engineer === A development engineer has the responsibility for coordinating delivery of the engineering attributes of a complete automobile (bus, car, truck, van, SUV, motorcycle etc.) as dictated by the automobile manufacturer, governmental regulations, and the customer who buys the product. Much like the Systems engineer, the development engineer is concerned with the interactions of all systems in the complete automobile. While there are multiple components and systems in an automobile that have to function as designed, they must also work in harmony with the complete automobile. As an example, the brake system's main function is to provide braking functionality to the automobile. Along with this, it must also provide an acceptable level of: pedal feel (spongy, stiff), brake system "noise" (squeal, shudder, etc.), and interaction with the ABS (anti-lock braking system) Another aspect of the development engineer's job is a trade-off process required to deliver all of the automobile attributes at a certain acceptable level. An example of this is the trade-off between engine performance and fuel economy. While some customers are looking for maximum power from their engine, the automobile is still required to deliver an acceptable level of fuel economy. From the engine's perspective, these are opposing requirements. Engine performance is looking for maximum displacement (bigger, more power), while fuel economy is looking for a smaller displacement engine (ex: 1.4 L vs. 5.4 L). The engine size however, is not the only contributing factor to fuel economy and automobile performance. Different values come into play. Other attributes that involve trade-offs include: automobile weight, aerodynamic drag, transmission gearing, emission control devices, handling/roadholding, ride quality, and tires. The development engineer is also responsible for organizing automobile level testing, validation, and certification. Components and systems are designed and tested individually by the Product Engineer. The final evaluation is to be conducted at the automobile level to evaluate system to system interactions. As an example, the audio system (radio) needs to be evaluated at the automobile level. Interaction with other electronic components can cause interference. Heat dissipation of the system and ergonomic placement of the controls need to be evaluated. Sound quality in all seating positions needs to be provided at acceptable levels. === Manufacturing engineer === Manufacturing engineers are responsible for ensuring proper production of the automotive components or complete vehicles. While the development engineers are responsible for the function of the vehicle, manufacturing engineers are responsible for the safe and effective production of the vehicle. This group of engineers consist of process engineers, logistic coordinators, tooling engineers, robotics engineers, and assembly planners. In the automotive industry manufacturers are playing a larger role in the development stages of automotive components to ensure that the products are easy to manufacture. Design for manufacturability in the automotive world is crucial to make certain whichever design is developed in the Research and Development Stage of automotive design. Once the design is established, the manufacturing engineers take over. They design the machinery and tooling necessary to build the automotive components or vehicle and establish the methods of how to mass-produce the product. It is the manufacturing engineers job to increase the efficiency of the automotive plant and to implement lean manufacturing techniques such as Six Sigma and Kaizen. === Other automotive engineering roles === Other automotive engineers include those listed below: Aerodynamics engineers will often give guidance to the styling studio so that the shapes they design are aerodynamic, as well as attractive. Body engineers will also let the studio know if it is feasible to make the panels for their designs. Change control engineers make sure that all of the design and manufacturing changes that occur are organized, managed and implemented... NVH engineers perform sound and vibration testing to prevent loud cabin noises, detectable vibrations, and/or improve the sound quality while the vehicle is on the road. == The modern automotive product engineering process == Studies indicate that a substantial part of the modern vehicle's value comes from intelligent systems, and that these represent most of the current automotive innovation. To facilitate this, the modern automotive engineering process has to handle an increased use of mechatronics. Configuration and performance optimization, system integration, control, component, subsystem and system-level validation of the intelligent systems must become an intrinsic part of the standard vehicle engineering process, just as this is the case for the structural, vibro-acoustic and kinematic design. This requires a vehicle development process that is typically highly simulation-driven. === The V-approach === One way to effectively deal with the inherent multi-physics and the control systems development that is involved when including intelligent systems, is to adopt the V-Model approach to systems development, as has been widely used in the automotive industry for twenty years or more. In this V-approach, system-level requirements are propagated down the V via subsystems to component design, and the system performance is validated at increasing integration levels. Engineering of mechatronic systems requires the application of two interconnected "V-cycles": one focusing on the multi-physics system engineering (like the mechanical and electrical components of an electrically powered steering system, including sensors and actuators); and the other focuses on the controls engineering, the control logic, the software and realization of the control hardware and embedded software. == References ==
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https://en.wikipedia.org/wiki/Automotive_engineering
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Bioresource engineering is similar to biological engineering, except that it is based on biological and/or agricultural feedstocks. Bioresource engineering is more general and encompasses a wider range of technologies and various elements such as biomass, biological waste treatment, bioenergy, biotransformations, bioresource systems analysis, bioremediation and technologies associated with Thermochemical conversion technologies such as combustion, pyrolysis, gasification, catalysis, etc. Bioresource engineering also contains biochemical conversion technologies such as aerobic methods, anaerobic digestion, microbial growth processes, enzymatic methods, and composting. Products include fibre, fuels, feedstocks, fertilisers, building materials, polymers and other industrial products, and management products e.g. modelling, systems analysis, decisions, and support systems. Bioresource engineering is a discipline that is usually very similar to environmental engineering. The impact of urbanization and increasing demand for food, water and land presents bioresource engineers with the task of bridging the gap between the biological world and traditional engineering. Agricultural and bioresource engineers attempt to develop efficient and environmentally sensitive methods of producing food, fiber, timber, bio-based products and renewable energy sources for an ever-increasing world population. Some of the research in bioresource engineering include machine vision, vehicle modification, wastewater irrigation, irrigation water management, stormwater management, inside natural environment for animals and plants, sensors, non-point source pollution and animal manure management. == Accomplishments == A biosynthesis of silver nanoparticles (NPs) mediated by fungal proteins of Coriolus versicolor has been undertaken for the first time in 2008. Hydrogels have been used to separate As(V) from water. == ATCC == Founded in 1925, the ATCC (American Type Culture Collection) is a nonprofit and research organization, whose mission focuses on the acquisition, production, and development of standard reference microorganisms, cell lines and other materials for research in life sciences. ATCC has collected a wide range of biological items for research. Their holdings include molecular genomics tools, microorganisms and bioproducts. == See also == Environmentalist == References == == External links == Giles Shih, co-founder and CEO of BioResource International, briefly discusses some issues in bioresource engineering. Kauffman Foundation and Khan Academy, 2013.08.28 (about 3 min)
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https://en.wikipedia.org/wiki/Bioresource_engineering
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Systems engineering is an interdisciplinary field of engineering and engineering management that focuses on how to design, integrate, and manage complex systems over their life cycles. At its core, systems engineering utilizes systems thinking principles to organize this body of knowledge. The individual outcome of such efforts, an engineered system, can be defined as a combination of components that work in synergy to collectively perform a useful function. Issues such as requirements engineering, reliability, logistics, coordination of different teams, testing and evaluation, maintainability, and many other disciplines, aka "ilities", necessary for successful system design, development, implementation, and ultimate decommission become more difficult when dealing with large or complex projects. Systems engineering deals with work processes, optimization methods, and risk management tools in such projects. It overlaps technical and human-centered disciplines such as industrial engineering, production systems engineering, process systems engineering, mechanical engineering, manufacturing engineering, production engineering, control engineering, software engineering, electrical engineering, cybernetics, aerospace engineering, organizational studies, civil engineering and project management. Systems engineering ensures that all likely aspects of a project or system are considered and integrated into a whole. The systems engineering process is a discovery process that is quite unlike a manufacturing process. A manufacturing process is focused on repetitive activities that achieve high-quality outputs with minimum cost and time. The systems engineering process must begin by discovering the real problems that need to be resolved and identifying the most probable or highest-impact failures that can occur. Systems engineering involves finding solutions to these problems. == History == The term systems engineering can be traced back to Bell Telephone Laboratories in the 1940s. The need to identify and manipulate the properties of a system as a whole, which in complex engineering projects may greatly differ from the sum of the parts' properties, motivated various industries, especially those developing systems for the U.S. military, to apply the discipline. When it was no longer possible to rely on design evolution to improve upon a system and the existing tools were not sufficient to meet growing demands, new methods began to be developed that addressed the complexity directly. The continuing evolution of systems engineering comprises the development and identification of new methods and modeling techniques. These methods aid in a better comprehension of the design and developmental control of engineering systems as they grow more complex. Popular tools that are often used in the systems engineering context were developed during these times, including Universal Systems Language (USL), Unified Modeling Language (UML), Quality function deployment (QFD), and Integration Definition (IDEF). In 1990, a professional society for systems engineering, the National Council on Systems Engineering (NCOSE), was founded by representatives from a number of U.S. corporations and organizations. NCOSE was created to address the need for improvements in systems engineering practices and education. As a result of growing involvement from systems engineers outside of the U.S., the name of the organization was changed to the International Council on Systems Engineering (INCOSE) in 1995. Schools in several countries offer graduate programs in systems engineering, and continuing education options are also available for practicing engineers. == Concept == Systems engineering signifies only an approach and, more recently, a discipline in engineering. The aim of education in systems engineering is to formalize various approaches simply and in doing so, identify new methods and research opportunities similar to that which occurs in other fields of engineering. As an approach, systems engineering is holistic and interdisciplinary in flavor. === Origins and traditional scope === The traditional scope of engineering embraces the conception, design, development, production, and operation of physical systems. Systems engineering, as originally conceived, falls within this scope. "Systems engineering", in this sense of the term, refers to the building of engineering concepts. === Evolution to a broader scope === The use of the term "systems engineer" has evolved over time to embrace a wider, more holistic concept of "systems" and of engineering processes. This evolution of the definition has been a subject of ongoing controversy, and the term continues to apply to both the narrower and a broader scope. Traditional systems engineering was seen as a branch of engineering in the classical sense, that is, as applied only to physical systems, such as spacecraft and aircraft. More recently, systems engineering has evolved to take on a broader meaning especially when humans were seen as an essential component of a system. Peter Checkland, for example, captures the broader meaning of systems engineering by stating that 'engineering' "can be read in its general sense; you can engineer a meeting or a political agreement.": 10 Consistent with the broader scope of systems engineering, the Systems Engineering Body of Knowledge (SEBoK) has defined three types of systems engineering: Product Systems Engineering (PSE) is the traditional systems engineering focused on the design of physical systems consisting of hardware and software. Enterprise Systems Engineering (ESE) pertains to the view of enterprises, that is, organizations or combinations of organizations, as systems. Service Systems Engineering (SSE) has to do with the engineering of service systems. Checkland defines a service system as a system which is conceived as serving another system. Most civil infrastructure systems are service systems. === Holistic view === Systems engineering focuses on analyzing and eliciting customer needs and required functionality early in the development cycle, documenting requirements, then proceeding with design synthesis and system validation while considering the complete problem, the system lifecycle. This includes fully understanding all of the stakeholders involved. Oliver et al. claim that the systems engineering process can be decomposed into: A Systems Engineering Technical Process A Systems Engineering Management Process Within Oliver's model, the goal of the Management Process is to organize the technical effort in the lifecycle, while the Technical Process includes assessing available information, defining effectiveness measures, to create a behavior model, create a structure model, perform trade-off analysis, and create sequential build & test plan. Depending on their application, although there are several models that are used in the industry, all of them aim to identify the relation between the various stages mentioned above and incorporate feedback. Examples of such models include the Waterfall model and the VEE model (also called the V model). === Interdisciplinary field === System development often requires contribution from diverse technical disciplines. By providing a systems (holistic) view of the development effort, systems engineering helps mold all the technical contributors into a unified team effort, forming a structured development process that proceeds from concept to production to operation and, in some cases, to termination and disposal. In an acquisition, the holistic integrative discipline combines contributions and balances tradeoffs among cost, schedule, and performance while maintaining an acceptable level of risk covering the entire life cycle of the item. This perspective is often replicated in educational programs, in that systems engineering courses are taught by faculty from other engineering departments, which helps create an interdisciplinary environment. === Managing complexity === The need for systems engineering arose with the increase in complexity of systems and projects, in turn exponentially increasing the possibility of component friction, and therefore the unreliability of the design. When speaking in this context, complexity incorporates not only engineering systems but also the logical human organization of data. At the same time, a system can become more complex due to an increase in size as well as with an increase in the amount of data, variables, or the number of fields that are involved in the design. The International Space Station is an example of such a system. The development of smarter control algorithms, microprocessor design, and analysis of environmental systems also come within the purview of systems engineering. Systems engineering encourages the use of tools and methods to better comprehend and manage complexity in systems. Some examples of these tools can be seen here: System architecture System model, modeling, and simulation Mathematical optimization System dynamics Systems analysis Statistical analysis Reliability engineering Decision making Taking an interdisciplinary approach to engineering systems is inherently complex since the behavior of and interaction among system components is not always immediately well defined or understood. Defining and characterizing such systems and subsystems and the interactions among them is one of the goals of systems engineering. In doing so, the gap that exists between informal requirements from users, operators, marketing organizations, and technical specifications is successfully bridged. === Scope === The principles of systems engineering – holism, emergent behavior, boundary, et al. – can be applied to any system, complex or otherwise, provided systems thinking is employed at all levels. Besides defense and aerospace, many information and technology-based companies, software development firms, and industries in the field of electronics & communications require systems engineers as part of their team. An analysis by the INCOSE Systems Engineering Center of Excellence (SECOE) indicates that optimal effort spent on systems engineering is about 15–20% of the total project effort. At the same time, studies have shown that systems engineering essentially leads to a reduction in costs among other benefits. However, no quantitative survey at a larger scale encompassing a wide variety of industries has been conducted until recently. Such studies are underway to determine the effectiveness and quantify the benefits of systems engineering. Systems engineering encourages the use of modeling and simulation to validate assumptions or theories on systems and the interactions within them. Use of methods that allow early detection of possible failures, in safety engineering, are integrated into the design process. At the same time, decisions made at the beginning of a project whose consequences are not clearly understood can have enormous implications later in the life of a system, and it is the task of the modern systems engineer to explore these issues and make critical decisions. No method guarantees today's decisions will still be valid when a system goes into service years or decades after first conceived. However, there are techniques that support the process of systems engineering. Examples include soft systems methodology, Jay Wright Forrester's System dynamics method, and the Unified Modeling Language (UML)—all currently being explored, evaluated, and developed to support the engineering decision process. == Education == Education in systems engineering is often seen as an extension to the regular engineering courses, reflecting the industry attitude that engineering students need a foundational background in one of the traditional engineering disciplines (e.g. aerospace engineering, civil engineering, electrical engineering, mechanical engineering, manufacturing engineering, industrial engineering, chemical engineering)—plus practical, real-world experience to be effective as systems engineers. Undergraduate university programs explicitly in systems engineering are growing in number but remain uncommon, the degrees including such material are most often presented as a BS in Industrial Engineering. Typically programs (either by themselves or in combination with interdisciplinary study) are offered beginning at the graduate level in both academic and professional tracks, resulting in the grant of either a MS/MEng or Ph.D./EngD degree. INCOSE, in collaboration with the Systems Engineering Research Center at Stevens Institute of Technology maintains a regularly updated directory of worldwide academic programs at suitably accredited institutions. As of 2017, it lists over 140 universities in North America offering more than 400 undergraduate and graduate programs in systems engineering. Widespread institutional acknowledgment of the field as a distinct subdiscipline is quite recent; the 2009 edition of the same publication reported the number of such schools and programs at only 80 and 165, respectively. Education in systems engineering can be taken as systems-centric or domain-centric: Systems-centric programs treat systems engineering as a separate discipline and most of the courses are taught focusing on systems engineering principles and practice. Domain-centric programs offer systems engineering as an option that can be exercised with another major field in engineering. Both of these patterns strive to educate the systems engineer who is able to oversee interdisciplinary projects with the depth required of a core engineer. == Systems engineering topics == Systems engineering tools are strategies, procedures, and techniques that aid in performing systems engineering on a project or product. The purpose of these tools varies from database management, graphical browsing, simulation, and reasoning, to document production, neutral import/export, and more. === System === There are many definitions of what a system is in the field of systems engineering. Below are a few authoritative definitions: ANSI/EIA-632-1999: "An aggregation of end products and enabling products to achieve a given purpose." DAU Systems Engineering Fundamentals: "an integrated composite of people, products, and processes that provide a capability to satisfy a stated need or objective." IEEE Std 1220-1998: "A set or arrangement of elements and processes that are related and whose behavior satisfies customer/operational needs and provides for life cycle sustainment of the products." INCOSE Systems Engineering Handbook: "homogeneous entity that exhibits predefined behavior in the real world and is composed of heterogeneous parts that do not individually exhibit that behavior and an integrated configuration of components and/or subsystems." INCOSE: "A system is a construct or collection of different elements that together produce results not obtainable by the elements alone. The elements, or parts, can include people, hardware, software, facilities, policies, and documents; that is, all things required to produce systems-level results. The results include system-level qualities, properties, characteristics, functions, behavior, and performance. The value added by the system as a whole, beyond that contributed independently by the parts, is primarily created by the relationship among the parts; that is, how they are interconnected." ISO/IEC 15288:2008: "A combination of interacting elements organized to achieve one or more stated purposes." NASA Systems Engineering Handbook: "(1) The combination of elements that function together to produce the capability to meet a need. The elements include all hardware, software, equipment, facilities, personnel, processes, and procedures needed for this purpose. (2) The end product (which performs operational functions) and enabling products (which provide life-cycle support services to the operational end products) that make up a system." === Systems engineering processes === Systems engineering processes encompass all creative, manual, and technical activities necessary to define the product and which need to be carried out to convert a system definition to a sufficiently detailed system design specification for product manufacture and deployment. Design and development of a system can be divided into four stages, each with different definitions: Task definition (informative definition) Conceptual stage (cardinal definition) Design stage (formative definition) Implementation stage (manufacturing definition) Depending on their application, tools are used for various stages of the systems engineering process: === Using models === Models play important and diverse roles in systems engineering. A model can be defined in several ways, including: An abstraction of reality designed to answer specific questions about the real world An imitation, analog, or representation of a real-world process or structure; or A conceptual, mathematical, or physical tool to assist a decision-maker. Together, these definitions are broad enough to encompass physical engineering models used in the verification of a system design, as well as schematic models like a functional flow block diagram and mathematical (i.e. quantitative) models used in the trade study process. This section focuses on the last. The main reason for using mathematical models and diagrams in trade studies is to provide estimates of system effectiveness, performance or technical attributes, and cost from a set of known or estimable quantities. Typically, a collection of separate models is needed to provide all of these outcome variables. The heart of any mathematical model is a set of meaningful quantitative relationships among its inputs and outputs. These relationships can be as simple as adding up constituent quantities to obtain a total, or as complex as a set of differential equations describing the trajectory of a spacecraft in a gravitational field. Ideally, the relationships express causality, not just correlation. Furthermore, key to successful systems engineering activities are also the methods with which these models are efficiently and effectively managed and used to simulate the systems. However, diverse domains often present recurring problems of modeling and simulation for systems engineering, and new advancements are aiming to cross-fertilize methods among distinct scientific and engineering communities, under the title of 'Modeling & Simulation-based Systems Engineering'. === Modeling formalisms and graphical representations === Initially, when the primary purpose of a systems engineer is to comprehend a complex problem, graphic representations of a system are used to communicate a system's functional and data requirements. Common graphical representations include: Functional flow block diagram (FFBD) Model-based design Data flow diagram (DFD) N2 chart IDEF0 diagram Use case diagram Sequence diagram Block diagram Signal-flow graph USL function maps and type maps Enterprise architecture frameworks A graphical representation relates the various subsystems or parts of a system through functions, data, or interfaces. Any or each of the above methods is used in an industry based on its requirements. For instance, the N2 chart may be used where interfaces between systems are important. Part of the design phase is to create structural and behavioral models of the system. Once the requirements are understood, it is now the responsibility of a systems engineer to refine them and to determine, along with other engineers, the best technology for a job. At this point starting with a trade study, systems engineering encourages the use of weighted choices to determine the best option. A decision matrix, or Pugh method, is one way (QFD is another) to make this choice while considering all criteria that are important. The trade study in turn informs the design, which again affects graphic representations of the system (without changing the requirements). In an SE process, this stage represents the iterative step that is carried out until a feasible solution is found. A decision matrix is often populated using techniques such as statistical analysis, reliability analysis, system dynamics (feedback control), and optimization methods. === Other tools === ==== Systems Modeling Language ==== Systems Modeling Language (SysML), a modeling language used for systems engineering applications, supports the specification, analysis, design, verification and validation of a broad range of complex systems. ==== Lifecycle Modeling Language ==== Lifecycle Modeling Language (LML), is an open-standard modeling language designed for systems engineering that supports the full lifecycle: conceptual, utilization, support, and retirement stages. == Related fields and sub-fields == Many related fields may be considered tightly coupled to systems engineering. The following areas have contributed to the development of systems engineering as a distinct entity: === Cognitive systems engineering === Cognitive systems engineering (CSE) is a specific approach to the description and analysis of human-machine systems or sociotechnical systems. The three main themes of CSE are how humans cope with complexity, how work is accomplished by the use of artifacts, and how human-machine systems and socio-technical systems can be described as joint cognitive systems. CSE has since its beginning become a recognized scientific discipline, sometimes also referred to as cognitive engineering. The concept of a Joint Cognitive System (JCS) has in particular become widely used as a way of understanding how complex socio-technical systems can be described with varying degrees of resolution. The more than 20 years of experience with CSE has been described extensively. === Configuration management === Like systems engineering, configuration management as practiced in the defense and aerospace industry is a broad systems-level practice. The field parallels the taskings of systems engineering; where systems engineering deals with requirements development, allocation to development items and verification, configuration management deals with requirements capture, traceability to the development item, and audit of development item to ensure that it has achieved the desired functionality and outcomes that systems engineering and/or Test and Verification Engineering have obtained and proven through objective testing. === Control engineering === Control engineering and its design and implementation of control systems, used extensively in nearly every industry, is a large sub-field of systems engineering. The cruise control on an automobile and the guidance system for a ballistic missile are two examples. Control systems theory is an active field of applied mathematics involving the investigation of solution spaces and the development of new methods for the analysis of the control process. === Industrial engineering === Industrial engineering is a branch of engineering that concerns the development, improvement, implementation, and evaluation of integrated systems of people, money, knowledge, information, equipment, energy, material, and process. Industrial engineering draws upon the principles and methods of engineering analysis and synthesis, as well as mathematical, physical, and social sciences together with the principles and methods of engineering analysis and design to specify, predict, and evaluate results obtained from such systems. === Production Systems Engineering === Production Systems Engineering (PSE) is an emerging branch of Engineering intended to uncover fundamental principles of production systems and utilize them for analysis, continuous improvement, and design. === Interface design === Interface design and its specification are concerned with assuring that the pieces of a system connect and inter-operate with other parts of the system and with external systems as necessary. Interface design also includes assuring that system interfaces are able to accept new features, including mechanical, electrical, and logical interfaces, including reserved wires, plug-space, command codes, and bits in communication protocols. This is known as extensibility. Human-Computer Interaction (HCI) or Human-Machine Interface (HMI) is another aspect of interface design and is a critical aspect of modern systems engineering. Systems engineering principles are applied in the design of communication protocols for local area networks and wide area networks. === Mechatronic engineering === Mechatronic engineering, like systems engineering, is a multidisciplinary field of engineering that uses dynamic systems modeling to express tangible constructs. In that regard, it is almost indistinguishable from Systems Engineering, but what sets it apart is the focus on smaller details rather than larger generalizations and relationships. As such, both fields are distinguished by the scope of their projects rather than the methodology of their practice. === Operations research === Operations research supports systems engineering. Operations research, briefly, is concerned with the optimization of a process under multiple constraints. === Performance engineering === Performance engineering is the discipline of ensuring a system meets customer expectations for performance throughout its life. Performance is usually defined as the speed with which a certain operation is executed or the capability of executing a number of such operations in a unit of time. Performance may be degraded when operations queued to execute are throttled by limited system capacity. For example, the performance of a packet-switched network is characterized by the end-to-end packet transit delay or the number of packets switched in an hour. The design of high-performance systems uses analytical or simulation modeling, whereas the delivery of high-performance implementation involves thorough performance testing. Performance engineering relies heavily on statistics, queueing theory, and probability theory for its tools and processes. === Program management and project management === Program management (or project management) has many similarities with systems engineering, but has broader-based origins than the engineering ones of systems engineering. Project management is also closely related to both program management and systems engineering. Both include scheduling as engineering support tool in assessing interdisciplinary concerns under management process. In particular, the direct relationship of resources, performance features, and risk to the duration of a task or the dependency links among tasks and impacts across the system lifecycle are systems engineering concerns. === Proposal engineering === Proposal engineering is the application of scientific and mathematical principles to design, construct, and operate a cost-effective proposal development system. Basically, proposal engineering uses the "systems engineering process" to create a cost-effective proposal and increase the odds of a successful proposal. === Reliability engineering === Reliability engineering is the discipline of ensuring a system meets customer expectations for reliability throughout its life (i.e. it does not fail more frequently than expected). Next to the prediction of failure, it is just as much about the prevention of failure. Reliability engineering applies to all aspects of the system. It is closely associated with maintainability, availability (dependability or RAMS preferred by some), and integrated logistics support. Reliability engineering is always a critical component of safety engineering, as in failure mode and effects analysis (FMEA) and hazard fault tree analysis, and of security engineering. === Risk management === Risk management, the practice of assessing and dealing with risk is one of the interdisciplinary parts of Systems Engineering. In development, acquisition, or operational activities, the inclusion of risk in tradeoffs with cost, schedule, and performance features, involves the iterative complex configuration management of traceability and evaluation to the scheduling and requirements management across domains and for the system lifecycle that requires the interdisciplinary technical approach of systems engineering. Systems Engineering has Risk Management define, tailor, implement, and monitor a structured process for risk management which is integrated into the overall effort. === Safety engineering === The techniques of safety engineering may be applied by non-specialist engineers in designing complex systems to minimize the probability of safety-critical failures. The "System Safety Engineering" function helps to identify "safety hazards" in emerging designs and may assist with techniques to "mitigate" the effects of (potentially) hazardous conditions that cannot be designed out of systems. === Security engineering === Security engineering can be viewed as an interdisciplinary field that integrates the community of practice for control systems design, reliability, safety, and systems engineering. It may involve such sub-specialties as authentication of system users, system targets, and others: people, objects, and processes. === Software engineering === From its beginnings, software engineering has helped shape modern systems engineering practice. The techniques used in the handling of the complexities of large software-intensive systems have had a major effect on the shaping and reshaping of the tools, methods, and processes of Systems Engineering. == See also == == References == == Further reading == Madhavan, Guru (2024). Wicked Problems: How to Engineer a Better World. New York: W.W. Norton & Company. ISBN 978-0-393-65146-1 Blockley, D. Godfrey, P. Doing it Differently: Systems for Rethinking Infrastructure, Second Edition, ICE Publications, London, 2017. Buede, D.M., Miller, W.D. The Engineering Design of Systems: Models and Methods, Third Edition, John Wiley and Sons, 2016. Chestnut, H., Systems Engineering Methods. Wiley, 1967. Gianni, D. et al. (eds.), Modeling and Simulation-Based Systems Engineering Handbook, CRC Press, 2014 at CRC Goode, H.H., Robert E. Machol System Engineering: An Introduction to the Design of Large-scale Systems, McGraw-Hill, 1957. Hitchins, D. (1997) World Class Systems Engineering at hitchins.net. Lienig, J., Bruemmer, H., Fundamentals of Electronic Systems Design, Springer, 2017 ISBN 978-3-319-55839-4. Malakooti, B. (2013). Operations and Production Systems with Multiple Objectives. John Wiley & Sons.ISBN 978-1-118-58537-5 MITRE, The MITRE Systems Engineering Guide(pdf) NASA (2007) Systems Engineering Handbook, NASA/SP-2007-6105 Rev1, December 2007. NASA (2013) NASA Systems Engineering Processes and Requirements Archived 27 December 2016 at the Wayback Machine NPR 7123.1B, April 2013 NASA Procedural Requirements Oliver, D.W., et al. Engineering Complex Systems with Models and Objects. McGraw-Hill, 1997. Parnell, G.S., Driscoll, P.J., Henderson, D.L. (eds.), Decision Making in Systems Engineering and Management, 2nd. ed., Hoboken, NJ: Wiley, 2011. This is a textbook for undergraduate students of engineering. Ramo, S., St.Clair, R.K. The Systems Approach: Fresh Solutions to Complex Problems Through Combining Science and Practical Common Sense, Anaheim, CA: KNI, Inc, 1998. Sage, A.P., Systems Engineering. Wiley IEEE, 1992. ISBN 0-471-53639-3. Sage, A.P., Olson, S.R., Modeling and Simulation in Systems Engineering, 2001. SEBOK.org, Systems Engineering Body of Knowledge (SEBoK) Shermon, D. Systems Cost Engineering, Gower Publishing, 2009 Shishko, R., et al. (2005) NASA Systems Engineering Handbook. NASA Center for AeroSpace Information, 2005. Stevens, R., et al. Systems Engineering: Coping with Complexity. Prentice Hall, 1998. US Air Force, SMC Systems Engineering Primer & Handbook, 2004 US DoD Systems Management College (2001) Systems Engineering Fundamentals. Defense Acquisition University Press, 2001 US DoD Guide for Integrating Systems Engineering into DoD Acquisition Contracts Archived 29 August 2017 at the Wayback Machine, 2006 US DoD MIL-STD-499 System Engineering Management == External links == ICSEng homepage INCOSE homepage INCOSE UK homepage PPI SE Goldmine homepage Systems Engineering Body of Knowledge Systems Engineering Tools AcqNotes DoD Systems Engineering Overview NDIA Systems Engineering Division
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The World Wide Web has become a major delivery platform for a variety of complex and sophisticated enterprise applications in several domains. In addition to their inherent multifaceted functionality, these Web applications exhibit complex behaviour and place some unique demands on their usability, performance, security, and ability to grow and evolve. However, a vast majority of these applications continue to be developed in an ad hoc way, contributing to problems of usability, maintainability, quality and reliability. While Web development can benefit from established practices from other related disciplines, it has certain distinguishing characteristics that demand special considerations. In recent years, there have been developments towards addressing these considerations. Web engineering focuses on the methodologies, techniques, and tools that are the foundation of Web application development and which support their design, development, evolution, and evaluation. Web application development has certain characteristics that make it different from traditional software, information systems, or computer application development. Web engineering is multidisciplinary and encompasses contributions from diverse areas: systems analysis and design, software engineering, hypermedia/hypertext engineering, requirements engineering, human-computer interaction, user interface, data engineering, information science, information indexing and retrieval, testing, modelling and simulation, project management, and graphic design and presentation. Web engineering is neither a clone nor a subset of software engineering, although both involve programming and software development. While Web Engineering uses software engineering principles, it encompasses new approaches, methodologies, tools, techniques, and guidelines to meet the unique requirements of Web-based applications. == As a discipline == Proponents of Web engineering supported the establishment of Web engineering as a discipline at an early stage of Web. Major arguments for Web engineering as a new discipline are: Web-based Information Systems (WIS) development process is different and unique. Web engineering is multi-disciplinary; no single discipline (such as software engineering) can provide a complete theory basis, body of knowledge and practices to guide WIS development. Issues of evolution and lifecycle management when compared to more 'traditional' applications. Web-based information systems and applications are pervasive and non-trivial. The prospect of Web as a platform will continue to grow and it is worth being treated specifically. However, it has been controversial, especially for people in other traditional disciplines such as software engineering, to recognize Web engineering as a new field. The issue is how different and independent Web engineering is, compared with other disciplines. Main topics of Web engineering include, but are not limited to, the following areas: === Modeling disciplines === Business Processes for Applications on the Web Process Modelling of Web applications Requirements Engineering for Web applications B2B applications === Design disciplines, tools, and methods === UML and the Web Conceptual Modeling of Web Applications (aka. Web modeling) Prototyping Methods and Tools Web design methods CASE Tools for Web Applications Web Interface Design Data Models for Web Information Systems === Implementation disciplines === Integrated Web Application Development Environments Code Generation for Web Applications Software Factories for/on the Web Web 2.0, AJAX, E4X, ASP.NET, PHP and Other New Developments Web Services Development and Deployment === Testing disciplines === Testing and Evaluation of Web systems and Applications. Testing Automation, Methods, and Tools. === Applications categories disciplines === Semantic Web applications Document centric Web sites Transactional Web applications Interactive Web applications Workflow-based Web applications Collaborative Web applications Portal-oriented Web applications Ubiquitous and Mobile Web Applications Device Independent Web Delivery Localization and Internationalization of Web Applications Personalization of Web Applications == Attributes == === Web quality === Web Metrics, Cost Estimation, and Measurement Personalisation and Adaptation of Web applications Web Quality Usability of Web Applications Web accessibility Performance of Web-based applications === Content-related === Web Content Management Content Management System (CMS) Multimedia Authoring Tools and Software Authoring of adaptive hypermedia == Education == Master of Science: Web Engineering as a branch of study within the MSc program Web Sciences at the Johannes Kepler University Linz, Austria Diploma in Web Engineering: Web Engineering as a study program at the International Webmasters College (iWMC), Germany == See also == DevOps Web developer Web modeling == References == == Sources == Robert L. Glass, "Who's Right in the Web Development Debate?" Cutter IT Journal, July 2001, Vol. 14, No.7, pp 6–0. S. Ceri, P. Fraternali, A. Bongio, M. Brambilla, S. Comai, M. Matera. "Designing Data-Intensive Web Applications". Morgan Kaufmann Publisher, Dec 2002, ISBN 1-55860-843-5 === Web engineering resources === Organizations International Society for Web Engineering e.V.: http://www.iswe-ev.de/ Web Engineering Community: http://www.webengineering.org WISE Society: http://www.wisesociety.org/ ACM SIGWEB: http://www.acm.org/sigweb World Wide Web Consortium: http://www.w3.org Books "Engineering Web Applications", by Sven Casteleyn, Florian Daniel, Peter Dolog and Maristella Matera, Springer, 2009, ISBN 978-3-540-92200-1 "Web Engineering: Modelling and Implementing Web Applications", edited by Gustavo Rossi, Oscar Pastor, Daniel Schwabe and Luis Olsina, Springer Verlag HCIS, 2007, ISBN 978-1-84628-922-4 "Cost Estimation Techniques for Web Projects", Emilia Mendes, IGI Publishing, ISBN 978-1-59904-135-3 "Web Engineering - The Discipline of Systematic Development of Web Applications", edited by Gerti Kappel, Birgit Pröll, Siegfried Reich, and Werner Retschitzegger, John Wiley & Sons, 2006 "Web Engineering", edited by Emilia Mendes and Nile Mosley, Springer-Verlag, 2005 "Web Engineering: Principles and Techniques", edited by Woojong Suh, Idea Group Publishing, 2005 "Form-Oriented Analysis -- A New Methodology to Model Form-Based Applications", by Dirk Draheim, Gerald Weber, Springer, 2005 "Building Web Applications with UML" (2nd edition), by Jim Conallen, Pearson Education, 2003 "Information Architecture for the World Wide Web" (2nd edition), by Peter Morville and Louis Rosenfeld, O'Reilly, 2002 "Web Site Engineering: Beyond Web Page Design", by Thomas A. Powell, David L. Jones and Dominique C. Cutts, Prentice Hall, 1998 "Designing Data-Intensive Web Applications", by S. Ceri, P. Fraternali, A. Bongio, M. Brambilla, S. Comai, M. Matera. Morgan Kaufmann Publisher, Dec 2002, ISBN 1-55860-843-5 Conferences World Wide Web Conference (by IW3C2, since 1994): http://www.iw3c2.org International Conference on Web Engineering (ICWE) (since 2000) 2018: http://icwe2018.webengineering.org/ (Caceres, Spain) 2017: http://icwe2017.webengineering.org/ (Rome, Italy) 2016: http://icwe2016.webengineering.org/ (Lugano, Switzerland) 2007: http://www.icwe2007.org/ 2006: http://www.icwe2006.org 2005: http://www.icwe2005.org 2004: http://www.icwe2004.org ICWE Conference Proceedings ICWE2007: LNCS 4607 https://www.springer.com/computer/database+management+&+information+retrieval/book/978-3-540-73596-0 ICWE2005: LNCS 3579 https://www.springer.com/east/home/generic/search/results?SGWID=5-40109-22-58872076-0 ICWE2004: LNCS 3140 https://www.springer.com/east/home/generic/search/results?SGWID=5-40109-22-32445543-0 ICWE2003: LNCS 2722 https://www.springer.com/east/home/generic/search/results?SGWID=5-40109-22-3092664-0 Web Information Systems Engineering Conference (by WISE Society, since 2000): http://www.wisesociety.org/ International Conference on Web Information Systems and Technologies (Webist) (since 2005): http://www.webist.org/ International Workshop on Web Site Evolution (WSE): http://www.websiteevolution.org/ International Conference on Software Engineering: http://www.icse-conferences.org/ Book chapters and articles Pressman, R.S., 'Applying Web Engineering', Part 3, Chapters 16–20, in Software Engineering: A Practitioner's Perspective, Sixth Edition, McGraw-Hill, New York, 2004. http://www.rspa.com/' Journals Journal of Web Engineering: http://www.rintonpress.com/journals/jwe/ International Journal of Web Engineering and Technology: http://www.inderscience.com/browse/index.php?journalID=48 ACM Transactions on Internet Technology: http://toit.acm.org/ World Wide Web (Springer): https://link.springer.com/journal/11280 Web coding journal: http://www.web-code.org/ Web Reference: https://www.kevi.my/ Special issues Web Engineering, IEEE MultiMedia, Jan.–Mar. 2001 (Part 1) and April–June 2001 (Part 2). http://csdl2.computer.org/persagen/DLPublication.jsp?pubtype=m&acronym=mu Usability Engineering, IEEE Software, January–February 2001. Web Engineering, Cutter IT Journal, 14(7), July 2001.* Testing E-business Applications, Cutter IT Journal, September 2001. Engineering Internet Software, IEEE Software, March–April 2002. Usability and the Web, IEEE Internet Computing, March–April 2002. Citations [1]
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In the context of information security, social engineering is the use of psychological influence of people into performing actions or divulging confidential information. This differs from psychological manipulation in that it doesn't need to be controlling, negative or a one-way transaction. Manipulation involves a zero-sum game where one party wins and the other loses while social engineering can be win-win for both parties. A type of confidence trick for the purpose of information gathering, fraud, or system access, it differs from a traditional "con" in the sense that it is often one of the many steps in a more complex fraud scheme. It has also been defined as "any act that influences a person to take an action that may or may not be in their best interests." Research done in 2020 has indicated that social engineering will be one of the most prominent challenges of the upcoming decade. Having proficiency in social engineering will be increasingly important for organizations and countries, due to the impact on geopolitics as well. Social engineering raises the question of whether our decisions will be accurately informed if our primary information is engineered and biased. Social engineering attacks have been increasing in intensity and number, cementing the need for novel detection techniques and cyber security educational programs. == Techniques and terms == All social engineering techniques are based on exploitable weaknesses in human decision-making known as cognitive biases. One example of social engineering is an individual who walks into a building and posts an official-looking announcement to the company bulletin that says the number for the help desk has changed. So, when employees call for help the individual asks them for their passwords and IDs thereby gaining the ability to access the company's private information. Another example of social engineering would be that the hacker contacts the target on a social networking site and starts a conversation with the target. Gradually the hacker gains the trust of the target and then uses that trust to get access to sensitive information like password or bank account details. === Pretexting === Pretexting (adj. pretextual), also known in the UK as blagging, is the act of creating and using an invented scenario (the pretext) to engage a targeted victim in a manner that increases the chance the victim will divulge information or perform actions that would be unlikely in ordinary circumstances. An elaborate lie, it most often involves some prior research or setup and the use of this information for impersonation (e.g., date of birth, Social Security number, last bill amount) to establish legitimacy in the mind of the target. === Water holing === Water holing is a targeted social engineering strategy that capitalizes on the trust users have in websites they regularly visit. The victim feels safe to do things they would not do in a different situation. A wary person might, for example, purposefully avoid clicking a link in an unsolicited email, but the same person would not hesitate to follow a link on a website they often visit. So, the attacker prepares a trap for the unwary prey at a favored watering hole. This strategy has been successfully used to gain access to some (supposedly) very secure systems. === Baiting === Baiting is like the real-world Trojan horse that uses physical media and relies on the curiosity or greed of the victim. In this attack, attackers leave malware-infected floppy disks, CD-ROMs, or USB flash drives in locations people will find them (bathrooms, elevators, sidewalks, parking lots, etc.), give them legitimate and curiosity-piquing labels, and wait for victims. Unless computer controls block infections, insertion compromises PCs "auto-running" media. Hostile devices can also be used. For instance, a "lucky winner" is sent a free digital audio player compromising any computer it is plugged to. A "road apple" (the colloquial term for horse manure, suggesting the device's undesirable nature) is any removable media with malicious software left in opportunistic or conspicuous places. It may be a CD, DVD, or USB flash drive, among other media. Curious people take it and plug it into a computer, infecting the host and any attached networks. Again, hackers may give them enticing labels, such as "Employee Salaries" or "Confidential". One study published in 2016 had researchers drop 297 USB drives around the campus of the University of Illinois. The drives contained files on them that linked to webpages owned by the researchers. The researchers were able to see how many of the drives had files on them opened, but not how many were inserted into a computer without having a file opened. Of the 297 drives that were dropped, 290 (98%) of them were picked up and 135 (45%) of them "called home". === Quid Pro Quo === An attacker offers to provide sensitive information (e.g. login credentials) or pay some amount of money in exchange for a favor. The attacker may pose as an expert offering free IT help, whereby they need login credentials from the user. === Scareware === The victim is bombarded with multiple messages about fake threats and alerts, making them think that the system is infected with malware. Thus, attackers force them to install remote login software or other malicious software. Or directly extort a ransom, such as offering to send a certain amount of money in cryptocurrency in exchange for the safety of confidential videos that the criminal has, as he claims. === Tailgating (piggybacking) === An attacker pretends to be a company employee or other person with access rights in order to enter an office or other restricted area. Deception and social engineering tools are actively used. For example, the intruder pretends to be a courier or loader carrying something in his hands and asks an employee who is walking outside to hold the door, gaining access to the building. == Law == In common law, pretexting is an invasion of privacy tort of appropriation. === Pretexting of telephone records === In December 2006, United States Congress approved a Senate sponsored bill making the pretexting of telephone records a federal felony with fines of up to $250,000 and ten years in prison for individuals (or fines of up to $500,000 for companies). It was signed by President George W. Bush on 12 January 2007. === Federal legislation === The 1999 Gramm-Leach-Bliley Act (GLBA) is a U.S. Federal law that specifically addresses pretexting of banking records as an illegal act punishable under federal statutes. When a business entity such as a private investigator, SIU insurance investigator, or an adjuster conducts any type of deception, it falls under the authority of the Federal Trade Commission (FTC). This federal agency has the obligation and authority to ensure that consumers are not subjected to any unfair or deceptive business practices. US Federal Trade Commission Act, Section 5 of the FTCA states, in part: "Whenever the Commission shall have reason to believe that any such person, partnership, or corporation has been or is using any unfair method of competition or unfair or deceptive act or practice in or affecting commerce, and if it shall appear to the Commission that a proceeding by it in respect thereof would be to the interest of the public, it shall issue and serve upon such person, partnership, or corporation a complaint stating its charges in that respect." The statute states that when someone obtains any personal, non-public information from a financial institution or the consumer, their action is subject to the statute. It relates to the consumer's relationship with the financial institution. For example, a pretexter using false pretenses either to get a consumer's address from the consumer's bank, or to get a consumer to disclose the name of their bank, would be covered. The determining principle is that pretexting only occurs when information is obtained through false pretenses. While the sale of cell telephone records has gained significant media attention, and telecommunications records are the focus of the two bills currently before the United States Senate, many other types of private records are being bought and sold in the public market. Alongside many advertisements for cell phone records, wireline records and the records associated with calling cards are advertised. As individuals shift to VoIP telephones, it is safe to assume that those records will be offered for sale as well. Currently, it is legal to sell telephone records, but illegal to obtain them. === 1st Source Information Specialists === U.S. Rep. Fred Upton (R-Kalamazoo, Michigan), chairman of the Energy and Commerce Subcommittee on Telecommunications and the Internet, expressed concern over the easy access to personal mobile phone records on the Internet during a House Energy & Commerce Committee hearing on "Phone Records For Sale: Why Aren't Phone Records Safe From Pretexting?" Illinois became the first state to sue an online records broker when Attorney General Lisa Madigan sued 1st Source Information Specialists, Inc. A spokeswoman for Madigan's office said. The Florida-based company operates several Web sites that sell mobile telephone records, according to a copy of the suit. The attorneys general of Florida and Missouri quickly followed Madigan's lead, filing suits respectively, against 1st Source Information Specialists and, in Missouri's case, one other records broker – First Data Solutions, Inc. Several wireless providers, including T-Mobile, Verizon, and Cingular filed earlier lawsuits against records brokers, with Cingular winning an injunction against First Data Solutions and 1st Source Information Specialists. U.S. Senator Charles Schumer (D-New York) introduced legislation in February 2006 aimed at curbing the practice. The Consumer Telephone Records Protection Act of 2006 would create felony criminal penalties for stealing and selling the records of mobile phone, landline, and Voice over Internet Protocol (VoIP) subscribers. === Hewlett Packard === Patricia Dunn, former chairwoman of Hewlett Packard, reported that the HP board hired a private investigation company to delve into who was responsible for leaks within the board. Dunn acknowledged that the company used the practice of pretexting to solicit the telephone records of board members and journalists. Chairman Dunn later apologized for this act and offered to step down from the board if it was desired by board members. Unlike Federal law, California law specifically forbids such pretexting. The four felony charges brought on Dunn were dismissed. == Notable social engineering incidents == === 2017 Equifax breach help websites === Following the 2017 Equifax data breach linked to China's People's Liberation Army in which over 150 million private records were leaked (including Social Security numbers, and drivers license numbers, birthdates, etc.), warnings were sent out regarding the dangers of impending security risks. In the day after the establishment of a legitimate help website (equifaxsecurity2017.com) dedicated to people potentially victimized by the breach, 194 malicious domains were reserved from small variations on the URL, capitalizing on the likelihood of people mistyping. === 2017 Google and Facebook phishing emails === Two tech giants—Google and Facebook—were phished out of $100 million by a Lithuanian fraudster. He impersonated a hardware supplier to falsely invoice both companies over two years. Despite their technological sophistication, the companies lost the money, although they were later able to recuperate the majority of the funds stolen. === 2016 United States Elections leaks === During the 2016 United States Elections, hackers associated with Russian Military Intelligence (GRU) sent phishing emails directed to members of Hillary Clinton's campaign, disguised as a Google alert. Many members, including the chairman of the campaign, John Podesta, had entered their passwords thinking it would be reset, causing their personal information, and thousands of private emails and documents to be leaked. With this information, they hacked into other computers in the Democratic Congressional Campaign Committee, implanting malware in them, which caused their computer activities to be monitored and leaked. === 2015 Ubiquiti Networks scam === In 2015, specialized Wi-Fi hardware and software maker Ubiquiti lost nearly $47 million to hackers. Attackers sent Ubiquiti's accounting department a phishing email from a Hong Kong branch with instructions to change payment account details. Upon discovering the theft, the company began cooperating with law enforcement, but was only able to recover $8 million of the stolen funds, although they had hoped for $15 million. === 2014 Sony pictures leak === On 24 November 2014, the hacker group "Guardians of Peace" (probably linked to North Korea) leaked confidential data from the film studio Sony Pictures Entertainment. The data included emails, executive salaries, and employees' personal and family information. The phishers pretended to be high up employees to install malware on workers' computers. === 2013 Department of Labor watering hole attack === In 2013, a U.S. Department of Labor server was hacked and used to host malware and redirect some visitors to a site using a zero-day Internet Explorer exploit to install a remote access trojan called Poison Ivy. Watering hole attacks were used, with the attackers creating pages related to toxic nuclear substances overseen by the Department of Energy. The targets were likely DoL and DOE employees with access to sensitive nuclear data. === 2011 RSA SecurID phishing attack === In 2011, hackers broke into the сryptographic corporation RSA and obtained information about SecurID two-factor authentication fobs. Using this data, the hackers later tried to infiltrate the network of defense contractor Lockheed Martin. The hackers gained access to the key fob data by sending emails to four employees of the parent corporation from an alleged recruitment site. The emails contained an Excel attachment titled 2011 Recruitment Plan. The spreadsheet contained a zero-day Flash exploit that provided backdoor access to the work computers. == Notable social engineers == === Susan Headley === Susan Headley became involved in phreaking with Kevin Mitnick and Lewis de Payne in Los Angeles, but later framed them for erasing the system files at US Leasing after a falling out, leading to Mitnick's first conviction. She retired to professional poker. === Mike Ridpath === Mike Ridpath is a security consultant, published author, speaker and previous member of w00w00. He is well known for developing techniques and tactics for social engineering through cold calling. He became well known for live demonstrations as well as playing recorded calls after talks where he explained his thought process on what he was doing to get passwords through the phone. As a child, Ridpath was connected with Badir Brothers and was widely known within the phreaking and hacking community for his articles with popular underground ezines, such as, Phrack, B4B0 and 9x on modifying Oki 900s, blueboxing, satellite hacking and RCMAC. === Badir Brothers === Brothers Ramy, Muzher, and Shadde Badir—all of whom were blind from birth—managed to set up an extensive phone and computer fraud scheme in Israel in the 1990s using social engineering, voice impersonation, and Braille-display computers. === Christopher J. Hadnagy === Christopher J. Hadnagy is an American social engineer and information technology security consultant. He is best known as an author of 4 books on social engineering and cyber security and founder of Innocent Lives Foundation, an organization that helps tracking and identifying child trafficking by seeking the assistance of information security specialists, using data from open-source intelligence (OSINT) and collaborating with law enforcement. == See also == Advance-fee scam Phishing Pretexting == References == == Further reading == == External links == Social Engineering Fundamentals – Securityfocus.com. Retrieved 3 August 2009. "Social Engineering, the USB Way". Light Reading Inc. 7 June 2006. Archived from the original on 13 July 2006. Retrieved 23 April 2014. Should Social Engineering be a part of Penetration Testing? – Darknet.org.uk. Retrieved 3 August 2009. "Protecting Consumers' Phone Records", Electronic Privacy Information Center US Committee on Commerce, Science, and Transportation. Retrieved 8 February 2006. Plotkin, Hal. Memo to the Press: Pretexting is Already Illegal. Retrieved 9 September 2006.
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https://en.wikipedia.org/wiki/Social_engineering_(security)
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In engineering, deformation (the change in size or shape of an object) may be elastic or plastic. If the deformation is negligible, the object is said to be rigid. == Main concepts == Occurrence of deformation in engineering applications is based on the following background concepts: Displacements are any change in position of a point on the object, including whole-body translations and rotations (rigid transformations). Deformation are changes in the relative position between internals points on the object, excluding rigid transformations, causing the body to change shape or size. Strain is the relative internal deformation, the dimensionless change in shape of an infinitesimal cube of material relative to a reference configuration. Mechanical strains are caused by mechanical stress, see stress-strain curve. The relationship between stress and strain is generally linear and reversible up until the yield point and the deformation is elastic. Elasticity in materials occurs when applied stress does not surpass the energy required to break molecular bonds, allowing the material to deform reversibly and return to its original shape once the stress is removed. The linear relationship for a material is known as Young's modulus. Above the yield point, some degree of permanent distortion remains after unloading and is termed plastic deformation. The determination of the stress and strain throughout a solid object is given by the field of strength of materials and for a structure by structural analysis. In the above figure, it can be seen that the compressive loading (indicated by the arrow) has caused deformation in the cylinder so that the original shape (dashed lines) has changed (deformed) into one with bulging sides. The sides bulge because the material, although strong enough to not crack or otherwise fail, is not strong enough to support the load without change. As a result, the material is forced out laterally. Internal forces (in this case at right angles to the deformation) resist the applied load. == Types of deformation == Depending on the type of material, size and geometry of the object, and the forces applied, various types of deformation may result. The image to the right shows the engineering stress vs. strain diagram for a typical ductile material such as steel. Different deformation modes may occur under different conditions, as can be depicted using a deformation mechanism map. Permanent deformation is irreversible; the deformation stays even after removal of the applied forces, while the temporary deformation is recoverable as it disappears after the removal of applied forces. Temporary deformation is also called elastic deformation, while the permanent deformation is called plastic deformation. === Elastic deformation === The study of temporary or elastic deformation in the case of engineering strain is applied to materials used in mechanical and structural engineering, such as concrete and steel, which are subjected to very small deformations. Engineering strain is modeled by infinitesimal strain theory, also called small strain theory, small deformation theory, small displacement theory, or small displacement-gradient theory where strains and rotations are both small. For some materials, e.g. elastomers and polymers, subjected to large deformations, the engineering definition of strain is not applicable, e.g. typical engineering strains greater than 1%, thus other more complex definitions of strain are required, such as stretch, logarithmic strain, Green strain, and Almansi strain. Elastomers and shape memory metals such as Nitinol exhibit large elastic deformation ranges, as does rubber. However, elasticity is nonlinear in these materials. Normal metals, ceramics and most crystals show linear elasticity and a smaller elastic range. Linear elastic deformation is governed by Hooke's law, which states: σ = E ε {\displaystyle \sigma =E\varepsilon } where σ is the applied stress; E is a material constant called Young's modulus or elastic modulus; ε is the resulting strain. This relationship only applies in the elastic range and indicates that the slope of the stress vs. strain curve can be used to find Young's modulus (E). Engineers often use this calculation in tensile tests. The area under this elastic region is known as resilience. Note that not all elastic materials undergo linear elastic deformation; some, such as concrete, gray cast iron, and many polymers, respond in a nonlinear fashion. For these materials Hooke's law is inapplicable. === Plastic deformation === This type of deformation is not undone simply by removing the applied force. An object in the plastic deformation range, however, will first have undergone elastic deformation, which is undone simply by removing the applied force, so the object will return part way to its original shape. Soft thermoplastics have a rather large plastic deformation range as do ductile metals such as copper, silver, and gold. Steel does, too, but not cast iron. Hard thermosetting plastics, rubber, crystals, and ceramics have minimal plastic deformation ranges. An example of a material with a large plastic deformation range is wet chewing gum, which can be stretched to dozens of times its original length. Under tensile stress, plastic deformation is characterized by a strain hardening region and a necking region and finally, fracture (also called rupture). During strain hardening the material becomes stronger through the movement of atomic dislocations. The necking phase is indicated by a reduction in cross-sectional area of the specimen. Necking begins after the ultimate strength is reached. During necking, the material can no longer withstand the maximum stress and the strain in the specimen rapidly increases. Plastic deformation ends with the fracture of the material. == Failure == === Compressive failure === Usually, compressive stress applied to bars, columns, etc. leads to shortening. Loading a structural element or specimen will increase the compressive stress until it reaches its compressive strength. According to the properties of the material, failure modes are yielding for materials with ductile behavior (most metals, some soils and plastics) or rupturing for brittle behavior (geomaterials, cast iron, glass, etc.). In long, slender structural elements — such as columns or truss bars — an increase of compressive force F leads to structural failure due to buckling at lower stress than the compressive strength. === Fracture === A break occurs after the material has reached the end of the elastic, and then plastic, deformation ranges. At this point forces accumulate until they are sufficient to cause a fracture. All materials will eventually fracture, if sufficient forces are applied. == Types of stress and strain == Engineering stress and engineering strain are approximations to the internal state that may be determined from the external forces and deformations of an object, provided that there is no significant change in size. When there is a significant change in size, the true stress and true strain can be derived from the instantaneous size of the object. === Engineering stress and strain === Consider a bar of original cross sectional area A0 being subjected to equal and opposite forces F pulling at the ends so the bar is under tension. The material is experiencing a stress defined to be the ratio of the force to the cross sectional area of the bar, as well as an axial elongation: Subscript 0 denotes the original dimensions of the sample. The SI derived unit for stress is newtons per square metre, or pascals (1 pascal = 1 Pa = 1 N/m2), and strain is unitless. The stress–strain curve for this material is plotted by elongating the sample and recording the stress variation with strain until the sample fractures. By convention, the strain is set to the horizontal axis and stress is set to vertical axis. Note that for engineering purposes we often assume the cross-section area of the material does not change during the whole deformation process. This is not true since the actual area will decrease while deforming due to elastic and plastic deformation. The curve based on the original cross-section and gauge length is called the engineering stress–strain curve, while the curve based on the instantaneous cross-section area and length is called the true stress–strain curve. Unless stated otherwise, engineering stress–strain is generally used. === True stress and strain === In the above definitions of engineering stress and strain, two behaviors of materials in tensile tests are ignored: the shrinking of section area compounding development of elongation True stress and true strain are defined differently than engineering stress and strain to account for these behaviors. They are given as Here the dimensions are instantaneous values. Assuming volume of the sample conserves and deformation happens uniformly, A 0 L 0 = A L {\displaystyle A_{0}L_{0}=AL} The true stress and strain can be expressed by engineering stress and strain. For true stress, σ t = F A = F A 0 A 0 A = F A 0 L L 0 = σ ( 1 + ε ) {\displaystyle \sigma _{\mathrm {t} }={\frac {F}{A}}={\frac {F}{A_{0}}}{\frac {A_{0}}{A}}={\frac {F}{A_{0}}}{\frac {L}{L_{0}}}=\sigma (1+\varepsilon )} For the strain, δ ε t = δ L L {\displaystyle \delta \varepsilon _{\mathrm {t} }={\frac {\delta L}{L}}} Integrate both sides and apply the boundary condition, ε t = ln ( L L 0 ) = ln ( 1 + ε ) {\displaystyle \varepsilon _{\mathrm {t} }=\ln \left({\frac {L}{L_{0}}}\right)=\ln(1+\varepsilon )} So in a tension test, true stress is larger than engineering stress and true strain is less than engineering strain. Thus, a point defining true stress–strain curve is displaced upwards and to the left to define the equivalent engineering stress–strain curve. The difference between the true and engineering stresses and strains will increase with plastic deformation. At low strains (such as elastic deformation), the differences between the two is negligible. As for the tensile strength point, it is the maximal point in engineering stress–strain curve but is not a special point in true stress–strain curve. Because engineering stress is proportional to the force applied along the sample, the criterion for necking formation can be set as δ F = 0. {\displaystyle \delta F=0.} δ F = σ t δ A + A δ σ t = 0 − δ A A = δ σ t σ t {\displaystyle {\begin{aligned}&\delta F=\sigma _{\text{t}}\,\delta A+A\,\delta \sigma _{\text{t}}=0\\&-{\frac {\delta A}{A}}={\frac {\delta \sigma _{\mathrm {t} }}{\sigma _{\mathrm {t} }}}\end{aligned}}} This analysis suggests nature of the ultimate tensile strength (UTS) point. The work strengthening effect is exactly balanced by the shrinking of section area at UTS point. After the formation of necking, the sample undergoes heterogeneous deformation, so equations above are not valid. The stress and strain at the necking can be expressed as: σ t = F A n e c k ε t = ln ( A 0 A n e c k ) {\displaystyle {\begin{aligned}\sigma _{\mathrm {t} }&={\frac {F}{A_{\mathrm {neck} }}}\\\varepsilon _{\mathrm {t} }&=\ln \left({\frac {A_{0}}{A_{\mathrm {neck} }}}\right)\end{aligned}}} An empirical equation is commonly used to describe the relationship between true stress and true strain. σ t = K ( ε t ) n {\displaystyle \sigma _{\mathrm {t} }=K(\varepsilon _{\mathrm {t} })^{n}} Here, n is the strain-hardening exponent and K is the strength coefficient. n is a measure of a material's work hardening behavior. Materials with a higher n have a greater resistance to necking. Typically, metals at room temperature have n ranging from 0.02 to 0.5. ==== Discussion ==== Since we disregard the change of area during deformation above, the true stress and strain curve should be re-derived. For deriving the stress strain curve, we can assume that the volume change is 0 even if we deformed the materials. We can assume that: A i × ε i = A f × ε f {\displaystyle A_{i}\times \varepsilon _{i}=A_{f}\times \varepsilon _{f}} Then, the true stress can be expressed as below: σ T = F A f = F A i × A i A f = σ e × l f l i = σ E × l i + δ l l i = σ E ( 1 + ε E ) {\displaystyle {\begin{aligned}\sigma _{T}={\frac {F}{A_{f}}}&={\frac {F}{A_{i}}}\times {\frac {A_{i}}{A_{f}}}\\&=\sigma _{e}\times {\frac {l_{f}}{l_{i}}}\\[2pt]&=\sigma _{E}\times {\frac {l_{i}+\delta l}{l_{i}}}\\[2pt]&=\sigma _{E}(1+\varepsilon _{E})\end{aligned}}} Additionally, the true strain εT can be expressed as below: ε T = d l l 0 + d l l 1 + d l l 2 + ⋯ = ∑ i d l l i {\displaystyle \varepsilon _{T}={\frac {dl}{l_{0}}}+{\frac {dl}{l_{1}}}+{\frac {dl}{l_{2}}}+\cdots =\sum _{i}{\frac {dl}{l_{i}}}} Then, we can express the value as ∫ l 0 l i d l l d x = ln ( l i l 0 ) = ln ( 1 + ε E ) {\displaystyle \int _{l_{0}}^{l_{i}}{\frac {dl}{l}}\,dx=\ln \left({\frac {l_{i}}{l_{0}}}\right)=\ln(1+\varepsilon _{E})} Thus, we can induce the plot in terms of σ T {\displaystyle \sigma _{T}} and ε E {\displaystyle \varepsilon _{E}} as right figure. Additionally, based on the true stress-strain curve, we can estimate the region where necking starts to happen. Since necking starts to appear after ultimate tensile stress where the maximum force applied, we can express this situation as below: d F = 0 = σ T d A i + A i d σ T {\displaystyle dF=0=\sigma _{T}dA_{i}+A_{i}d\sigma _{T}} so this form can be expressed as below: d σ T σ T = − d A i A i {\displaystyle {\frac {d\sigma _{T}}{\sigma _{T}}}=-{\frac {dA_{i}}{A_{i}}}} It indicates that the necking starts to appear where reduction of area becomes much significant compared to the stress change. Then the stress will be localized to specific area where the necking appears. Additionally, we can induce various relation based on true stress-strain curve. 1) True strain and stress curve can be expressed by the approximate linear relationship by taking a log on true stress and strain. The relation can be expressed as below: σ T = K × ( ε T ) n {\displaystyle \sigma _{T}=K\times (\varepsilon _{T})^{n}} Where K {\displaystyle K} is stress coefficient and n {\displaystyle n} is strain-hardening coefficient. Usually, the value of n {\displaystyle n} has range around 0.02 to 0.5 at room temperature. If n {\displaystyle n} is 1, we can express this material as perfect elastic material. 2) In reality, stress is also highly dependent on the rate of strain variation. Thus, we can induce the empirical equation based on the strain rate variation. σ T = K ′ × ( ε T ˙ ) m {\displaystyle \sigma _{T}=K'\times ({\dot {\varepsilon _{T}}})^{m}} Where K ′ {\displaystyle K'} is constant related to the material flow stress. ε T ˙ {\displaystyle {\dot {\varepsilon _{T}}}} indicates the derivative of strain by the time, which is also known as strain rate. m {\displaystyle m} is the strain-rate sensitivity. Moreover, value of m {\displaystyle m} is related to the resistance toward the necking. Usually, the value of m {\displaystyle m} is at the range of 0-0.1 at room temperature and as high as 0.8 when the temperature is increased. By combining the 1) and 2), we can create the ultimate relation as below: σ T = K ″ × ( ε T ) n ( ε T ˙ ) m {\displaystyle \sigma _{T}=K''\times (\varepsilon _{T})^{n}({\dot {\varepsilon _{T}}})^{m}} Where K ″ {\displaystyle K''} is the global constant for relating strain, strain rate and stress. 3) Based on the true stress-strain curve and its derivative form, we can estimate the strain necessary to start necking. This can be calculated based on the intersection between true stress-strain curve as shown in right. This figure also shows the dependency of the necking strain at different temperature. In case of FCC metals, both of the stress-strain curve at its derivative are highly dependent on temperature. Therefore, at higher temperature, necking starts to appear even under lower strain value. All of these properties indicate the importance of calculating the true stress-strain curve for further analyzing the behavior of materials in sudden environment. 4) A graphical method, so-called "Considere construction", can help determine the behavior of stress-strain curve whether necking or drawing happens on the sample. By setting λ = L / L 0 {\displaystyle \lambda =L/L_{0}} as determinant, the true stress and strain can be expressed with engineering stress and strain as below: σ T = σ e × λ , ε T = ln λ . {\displaystyle \sigma _{T}=\sigma _{e}\times \lambda ,\qquad \varepsilon _{T}=\ln \lambda .} Therefore, the value of engineering stress can be expressed by the secant line from made by true stress and λ {\displaystyle \lambda } value where λ = 0 {\displaystyle \lambda =0} to λ = 1 {\displaystyle \lambda =1} . By analyzing the shape of σ T − λ {\displaystyle \sigma _{T}-\lambda } diagram and secant line, we can determine whether the materials show drawing or necking. On the figure (a), there is only concave upward Considere plot. It indicates that there is no yield drop so the material will be suffered from fracture before it yields. On the figure (b), there is specific point where the tangent matches with secant line at point where λ = λ Y {\displaystyle \lambda =\lambda _{Y}} . After this value, the slope becomes smaller than the secant line where necking starts to appear. On the figure (c), there is point where yielding starts to appear but when λ = λ d {\displaystyle \lambda =\lambda _{d}} , the drawing happens. After drawing, all the material will stretch and eventually show fracture. Between λ Y {\displaystyle \lambda _{Y}} and λ d {\displaystyle \lambda _{d}} , the material itself does not stretch but rather, only the neck starts to stretch out. == Misconceptions == A popular misconception is that all materials that bend are "weak" and those that do not are "strong". In reality, many materials that undergo large elastic and plastic deformations, such as steel, are able to absorb stresses that would cause brittle materials, such as glass, with minimal plastic deformation ranges, to break. == See also == == References ==
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https://en.wikipedia.org/wiki/Deformation_(engineering)
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Capgemini Engineering (previously known as Altran Technologies, SA) is a global innovation and engineering consulting firm founded in 1982 in France by Alexis Kniazeff and Hubert Martigny. Altran Technologies operated primarily in high technology and innovation industries, which accounted for nearly 75% of its turnover. Administrative and information consultancy accounted for 20% of its turnover with strategy and management consulting making up the rest. The firm is active in most engineering domains, particularly electronics and IT technology. In 2018, Altran generated €2.916 billion in revenues and employed over 46,693 people around the world. Altran was acquired by Capgemini in 2019 and was renamed as "Capgemini Engineering" on 8 April 2021 due to its merge with Capgemini's Engineering and R&D services. == History == === 1980s === In 1982, Alexis Kniazeff and Hubert Martigny, ex-consultants of Peat Marwick (today known as KPMG), founded CGS Informatique, which would later become Altran. By 1985, the firm counted a staff of 50 engineers. The company expanded through small business units that would later generally range from 10 to 200 employees. Business units operated semi-independently and were given the autonomy to choose their own growth strategy and investment programs while still getting assistance from central management. This allowed business units to give each other support and share ideas. Managers’ compensation was decided based on the units’ performance. One of Altran's first major projects was developing the on-board communications network in 1987 for France's high-speed TGV trains that allowed French lines to be connected to other European rail lines. In 1987, the company was listed on the Secondary Market of the Paris Stock Exchange. By 1989, Altran's sales had neared the equivalent of 48 million euros. That same year, Altran bought Ségur Informatique, an aeronautics simulation and modeling company. The number of the company's employees grew to approximately 1,000 by 1990, as well as its range of expertise, moving into the transportation, telecommunications, and energy sectors, with a strong information technology component. === 1990s === In the early 1990s the company adopted a new business model. While much of the company's work during the previous decade had been performed in-house, at the beginning of the 1990s the company developed a new operational concept, that of a temp agency for the high-technology sector. The firm's staff started to work directly with its clients' projects, adding their specialized expertise to projects. By the end of the decade, the company had more than 50 subsidiaries in France, and had taken the lead of that market's technology consulting sector. The company was helped by the long-lasting recession affecting France and much of Europe at the beginning of the decade, as companies began outsourcing parts of their research and development operations. Altran was also expanding by acquisition, buying up a number of similar consultancies in France, such as the 1992 acquisition of GERPI, based in Rennes. By the end of that year, Altran's revenues had reached 76.5 million euros. With the elimination of border controls within the European Community in 1992, the company's clients began operations in other European countries. At first Altran turned to foreign partnerships in order to accommodate its clients. Yet this approach quickly proved unsatisfactory, and Altran put into place an aggressive acquisition plan in order to establish its own foreign operations. Altran targeted the Benelux countries, the first to lower their trade barriers, acquiring a Belgian company in 1992. By the end of the decade, the firm's network in these countries' markets was composed of 12 companies and 1,000 consultants. When an acquisition took place, Altran kept on existing management and in general the acquired firms retained their names. The acquisition policy was based on paying an initial fee for an acquisition, then on subsequent annual payments based on the acquired unit's performance. In 1992, Altran created Altran Conseil to work in the automobile equipment, nuclear and consumer electronic industries. Altran's operations in Spain began with the acquisition in 1993 of SDB España, a leading telecommunications consultant in that country, and later grew with the acquisitions of STE Consulting, Norma Consulting, Insert Sistemas, Strategy Consultors, Inad, Siev and Consultrans. Spain remained one of the company's top three markets into the new century, becoming a group of nine companies and more than 2,000 consultants operating under the Altran brand. By 1995, Altran's sales had topped 155 million euros, and its total number of employees had grown to nearly 2,400 (mostly engineers). The company recognized that the majority of engineers lacked a background in management, thus a training program called IMA (Institut pour le management Altran) was launched capable of training 200 candidates per year. In 1995 the company invested in the United Kingdom and acquired High Integrity Systems, a consulting firm focused on assisting companies that were transitioning into new-generation computer and network systems, and DCE Consultants, which operated from offices in Oxford and Manchester. In 1997, Altran also acquired Praxis Critical Systems, founded in Bath in 1983 to provide software and safety-engineering services. In order to supplement the activities of its acquisitions, the company also opened new subsidiary offices, such as Altran Technologies UK, a multi-disciplinary and cross-industry engineering consultancy. In the second half of the 1990s the company was acquiring an average of 15 companies per year. Italy became a target for growth in 1996, when Altran established subsidiary Altran Italy, before making its first acquisition in that country in 1997. In 1998, Altran added four new Italian acquisitions, EKAR, RSI Sistemi, CCS and Pool. In 1999, the company added an office in Turin as well as two new companies, ASP and O&I. Germany was also a primary target for Altran during this period, starting with the 1997 establishment of Altran Technologies GmbH and the acquisition of Europspace Technische Entwicklungen, a company that had been formed in 1993 and specialized in aeronautics. In 1998, the company added consulting group Berata and, the following year, Askon Consulting joined the group, which then expanded with a second component, Askon Beratung. Other European countries joined the Altran network in the late 1990s as well, including Portugal and Luxembourg in 1998 and Austria in 1999. In 1998, Altran deployed a telecommunications network in Portugal. By the end of 1999, the company's sales had climbed to EUR 614 million; significantly, international sales already accounted for more than one-third of the company's total revenues. Similar progress was made in Switzerland, a market Altran entered in 1997 with the purchase of D1B2. The Berate Germany purchase brought Altran that company's Swiss office as well in 1998; that same year, Altran launched its own Swiss startup, Altran Technologies Switzerland. In 1999, the company added three new Swiss companies, Net@rchitects, Innovatica, and Cerri. Significant projects during the decade included the design of the Météor autopilot system for the first automated subway line for the Paris Metro (Line 14) and the attitude control system for the European Space Agency's Ariane 5 rocket. === Early 21st century === In 2000, the company's Italian branch expanded to 10 subsidiaries with the opening of offices in Lombardy and Lazio and the acquisition of CEDATI. Also in 2000, Altran's presence in Switzerland grew with two new subsidiaries (Infolearn and De Simone & Osswald). In Germany, Altran acquired I&K Beratung. The United States became a primary target for the company's expansion with the acquisition of a company that was renamed Altran Corporation. Altran began building its operations in South America as well, especially in Brazil. By the end of 2001, Altran's revenues had jumped to more than 1.2 billion euros, while its ranks of consultants now topped 15,000. Altran become involved in a couple of new PR initiatives at the beginning of the decade, including a partnership with the Renault F1 racing team and a commitment to the Solar Impulse project with the goal of circumnavigating the Earth powered by only solar power. In 2002, Askon Beratung was spun off from Askon consulting as a separate, independently operating company within Altran, and the company's Swiss network had added a new component with the purchase of Sigma. This year a full-scale entry into the United States was made. After providing $56 million to back a management buyout of the European, Asian, and Latin American operations of bankrupt Arthur D. Little (the US-based consulting firm founded in 1886), Altran itself acquired the Arthur D. Little brand and trademark. This acquisition was seen as an important step in achieving the company's next growth target. Sales grew to 2 billion euros by 2003 and the company had more than 40,000 engineers by 2005. In 2004, Altran established operations in Asia and created Altran Pr[i]me [sic], a consulting outfit specialized in large-scale innovation projects. On 29 December 2006, all subsidiaries based in Ile de France were merged under the name of Altran Technologies SA, a technology consultant, which was organized into four business lines (as well as brand names): Altran TEM: Telecommunications, Electronics and Multimedia. Altran AIT: Automobiles, Infrastructure and Transportation. Altran Eilis: Energy, Industry and Life Science. Altran ASD: Aeronautics, Space and Defence. In 2009, Altran launched its Altran Research program. The program is centered around three main themes: designing tools, research and proof-of-concepts, and research on how to organize and improve practices. In 2012, as part its Performance Plan 2012, PSA Peugeot Citroën chose Altran as its strategic partner. In early 2013, Altran group finalised the acquisition of 100% of IndustrieHansa, an engineering and consulting group based in Germany, placing it among the top five in the market of Technical Consultancy, Innovation, Research and Development. Altran continued to acquire innovation consultancies in other countries as part of its expansion strategy. In February 2015, it acquired Nspyre, a Dutch R&D and high-technology firm. In July 2015, it bought SiConTech, an Indian engineering company specializing in semiconductors. Altran's revenues reached €1.945 billion in 2015. At that time, it had over 25,000 employees operating in over 20 countries. In November 2015, Dominique Cerutti announced his five-year strategic plan, "Altran 2020. Ignition." The plan aimed for the firm to reach 3 billion euros in revenue in five years and a big increase in profitability. In December 2015, Altran announced the acquisition of Tessella, in analytical and data science consulting. In 2016, the company acquired two other American companies: Synapse, specializing in the development of innovative products, and Lohika, a software engineering firm. This transatlantic expansion is one of the principal approaches to development supported by Altran in the Ignition 2020 strategic plan. Additionally, Altran announced in October 2016 the acquisition of two automobile industry companies: Swell, an engineering services and research and development firm based in the Czech Republic, as well as Benteler Engineering, a German firm specializing in conception and engineering services. Dominique Cerutti is noted for establishing several strategic partnerships, notably with Divergent, an American holding that integrates 3D printing in the automobile production process, and the Chinese digital mapping holding EMG (eMapgo). 22 December 2016 Acquisition: Altran acquires Pricol Technologies, an India-based engineering firm. In July and September 2017, Altran finalized two acquisitions: Information Risk Management, and GlobalEdge. The acquisition of IRM enabled Altran to enhance its presence and offers in the domain of cyber security. The buying of GlobalEdge, an Indian software product engineering firm, aimed at helping Altran to develop its presence in India as well as in the US, where Global Edge has an office in California. In November 2017, the company also acquired Aricent, a global digital design and engineering company headquartered in Santa Clara, California. The $2.0 billion transaction enabled the company to become the global leader in engineering and R&D services, completing its "Altran 2020. Ignition" strategic plan as early as 2018. The acquisition was completed on 22 March 2018, bringing the overall turnover of the new structure close to €3 billion. On 28 June 2018, Altran announced the plan "The High Road, Altran 2022". This plan aimed for a 14.5% margin and a 4 billion euros turnover in 2022 by betting on technological breakthroughs. === Takeover by Capgemini === On 1 April 2020, Capgemini's friendly takeover bid for Altran was finalized. Capgemini reached the squeeze-out threshold of 90% of Altran's capital, which was delisted from stock markets on 15 April 2020. == Organization and activities == The company covers the entire project life-cycle, from the planning stages (technological monitoring, technical feasibility studies, strategy planning, etc.) to final realization (design, implementation, and testing.) == Worldwide presences == Altran is headquartered on the avenue Charles de Gaulle in Neuilly-sur-Seine, France. The group is present in Belgium, Brazil, Canada, China, Colombia, Germany, Spain, Ukraine, France, Italy, India, Luxembourg, Malaysia, Mexico, Tunisia, Morocco, the Netherlands, Norway, Austria, Portugal, Romania, Sweden, Switzerland, the Middle East, the United Kingdom and the United States. Geographical breakdown of revenues: France (43.3%), Europe (51.6%) and other (5.1%). == Research and Innovation == === Altran Research === Altran Research, headed by Fabrice Mariaud, is Altran's internal R&D department in France. Scientific experts, each without their domain of expertise, plan and put in place research and innovation projects in collaboration with Altran Lab, academic partners and industrial actors. Current research areas include e-health, space & aeronautics, energy, complex systems, transportation and mobility, industry, and the services of the future. === Altran Lab === Altran Lab is made up of an incubator, an innovation hub and Altran Pr[i]me, created in 2004 and focused on innovation management. === Altran Foundation for Innovation === The Altran Foundation for Innovation is an international scientific competition run by the company. The competition's theme is selected each year addressing a major issue in society. The entries are judged by a panel containing scientific, political or academic experts. A prize of a year's technological support for the project is awarded to the winner and Altran's consultant teams will also follow up the awarded project. == Pro bono work == Altran France does pro bono work in areas relating to culture, civic engagement and innovation. In particular, Altran aids the Musée des Arts et Métiers of Paris, the Quai Branly Museum and the Arab World Institute with their digital strategy and management of their digital cultural assets. == Financial data == Altran first appeared on the Paris stock market on 20 October 1987. Stock valued on the Paris stock market (Euronext) Member of the CAC All Shares index ISIN Code: FR0000034639 Number of outstanding shares as of 30 October 2015: 175,536,188 Market capitalization as of 10 April 2019: 2.5 billion euros Primary stockholders as of 10 April 2019: Altrafin Participations: 8.4% Alexis Kniazeff: 1.4% Hubert Martigny: 1.4% === Financial data table === == See also == List of IT consulting firms Frog Design Inc. Tessella Cambridge Consultants == References ==
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https://en.wikipedia.org/wiki/Capgemini_Engineering
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Industrial engineering (IE) is concerned with the design, improvement and installation of integrated systems of people, materials, information, equipment and energy. It draws upon specialized knowledge and skill in the mathematical, physical, and social sciences together with the principles and methods of engineering analysis and design, to specify, predict, and evaluate the results to be obtained from such systems. Industrial engineering is a branch of engineering that focuses on optimizing complex processes, systems, and organizations by improving efficiency, productivity, and quality. It combines principles from engineering, mathematics, and business to design, analyze, and manage systems that involve people, materials, information, equipment, and energy. Industrial engineers aim to reduce waste, streamline operations, and enhance overall performance across various industries, including manufacturing, healthcare, logistics, and service sectors. Industrial engineers are employed in numerous industries, such as automobile manufacturing, aerospace, healthcare, forestry, finance, leisure, and education. Industrial engineering combines the physical and social sciences together with engineering principles to improve processes and systems. Several industrial engineering principles are followed to ensure the effective flow of systems, processes, and operations. Industrial engineers work to improve quality and productivity while simultaneously cutting waste. They use principles such as lean manufacturing, six sigma, information systems, process capability, and more. These principles allow the creation of new systems, processes or situations for the useful coordination of labor, materials and machines. Depending on the subspecialties involved, industrial engineering may also overlap with, operations research, systems engineering, manufacturing engineering, production engineering, supply chain engineering, management science, engineering management, financial engineering, ergonomics or human factors engineering, safety engineering, logistics engineering, quality engineering or other related capabilities or fields. == History == === Origins === ==== Industrial engineering ==== The origins of industrial engineering are generally traced back to the Industrial Revolution with the rise of factory systems and mass production. The fundamental concepts began to emerge through ideas like Adam Smith's division of labor and the implementation of interchangeable parts by Eli Whitney. The term "industrial engineer" is credited to James Gunn who proposed the need for such an engineer focused on production and cost analysis in 1901. However, Frederick Taylor is widely credited as the "father of industrial engineering" for his focus on scientific management, emphasizing time studies and standardized work methods, with his principles being published in 1911. Notably, Taylor established the first department dedicated to industrial engineering work, called "Elementary Rate Fixing," in 1885 with the goal of process improvement and productivity increase. Frank and Lillian Gilbreth further contributed significantly with their development of motion studies and therbligs for analyzing manual labor in the early 20th century. The early focus of the field was heavily on improving efficiency and productivity within manufacturing environments, driven in part by the call for cost reduction by engineering professionals, as highlighted by the first president of ASME in 1880. The formalization of the discipline continued with the founding of the American Institute of Industrial Engineering (AIIE) in 1948. In more recent years, industrial engineering has expanded beyond manufacturing to include areas like healthcare, project management, and supply chain optimization. ==== Systems Engineering ==== The origins of systems engineering as a recognized discipline can be traced back to World War II, where its principles began to emerge to manage the complexities of new war technologies. Although systems thinking predates this period, the analysis of the RAF Fighter Command C2 System during the Battle of Britain (even though the term wasn't yet invented) is considered an early example of high-caliber systems engineering. The first known public use of the term "systems engineering" occurred in March 1950 by Mervin J. Kelly of Bell Telephone Laboratories, who described it as crucial for defining new systems and guiding the application of research in creating new services. The first published paper specifically on the subject appeared in 1956 by Kenneth Schlager, who noted the growing importance of systems engineering due to increasing technological complexity and the formation of dedicated systems engineering groups. In 1957, E.W. Engstrom further elaborated on the concept, emphasizing the determination of objectives and the thorough consideration of all influencing factors as requirements for successful systems engineering. That same year also saw the publication of the first textbook on the subject, "Systems Engineering: An Introduction to the Design of Large-Scale Systems" by Goode and Mahol. Early practices of systems engineering were generally informal, transdisciplinary, and deeply rooted in the application domain. Following these initial mentions and publications, the field saw further development in the 1960s and 1970s, with figures like Arthur Hall defining traits of a systems engineer and viewing it as a comprehensive process. Despite its informal nature, systems engineering played a vital role in major achievements like the 1969 Apollo moon landing. A significant step towards formalization occurred in July 1969 with the introduction of the first formal systems engineering process, Military Standard (MIL-STD)-499: System Engineering Management, by the U.S. Air Force. This standard aimed to provide guidance for managing the systems engineering process and was later extended and updated. The need for formally trained systems engineers led to the formation of the National Council on Systems Engineering (NCOSE) in the late 1980s, which evolved into the International Council on Systems Engineering (INCOSE). INCOSE further contributed to the formalization of the field through publications like its journal "Systems Engineering" starting in 1994 and the first edition of the "Systems Engineering Handbook" in 1997. Additionally, organizations like NASA published their own systems engineering handbooks. In the 21st century, international standardization became a key aspect, with the International Standards Organization (ISO) publishing its first standard defining systems engineering application and management in 2005, further solidifying its standing as a formal discipline. === Pioneers === Frederick Taylor (1856–1915) is generally credited as the father of the industrial engineering discipline. He earned a degree in mechanical engineering from Stevens Institute of Technology and earned several patents from his inventions. Taylor is the author of many well-known works, including a book, The Principles of Scientific Management, which became a classic of management literature. It is considered one of the most influential management books of the 20th century. The book laid our three goals: to illustrate how the country loses through inefficiency, to show that the solution to inefficiency is systematic management, and to show that the best management rests on defined laws, rules, and principles that can be applied to all kinds of human activity. Taylor is remembered for developing the stopwatch time study. Taylor's findings set the foundation for industrial engineering. Frank Gilbreth (1868-1924), along with his wife Lillian Gilbreth (1878-1972), also had a significant influence on the development of Industrial Engineering. Their work is housed at Purdue University. In 1907, Frank Gilbreth met Frederick Taylor, and he learned tremendously from Taylor’s work. Frank and Lillian created 18 kinds of elemental motions that make up a set of fundamental motions required for a worker to perform a manual operation or task. They named the elements therbligs, which are used in the study of motion in the workplace. These developments were the beginning of a much broader field known as human factors or ergonomics. Through the efforts of Hugo Diemer, the first course on industrial engineering was offered as an elective at Pennsylvania State University in 1908. The first doctoral degree in industrial engineering was awarded in 1933 by Cornell University. Henry Gantt (1861-1919) immersed himself in the growing movement of Taylorism. Gantt is best known for creating a management tool, the Gantt chart. Gantt charts display dependencies pictorially, which allows project managers to keep everything organized. They are studied in colleges and used by project managers around the world. In addition to the creation of the Gannt chart, Gantt had many other significant contributions to scientific management. He cared about worker incentives and the impact businesses had on society. Today, the American Society of Mechanical Engineers awards a Gantt Medal for “distinguished achievement in management and for service to the community.” Henry Ford (1863-1947) further revolutionized factory production with the first installation of a moving assembly line. This innovation reduced the time it took to build a car from more than 12 hours to one hour and 33 minutes. This continuous-flow inspired production method introduced a new way of automobile manufacturing. Ford is also known for transforming the workweek schedule. He cut the typical six-day workweek to five and doubled the daily pay. Thus, creating the typical 40-hour workweek. Total quality management (TQM) emerged in the 1940s and gained momentum after World War II. The term was coined to describe its Japanese-style management approach to quality improvement. Total quality management can be described as a management system for a customer-focused organization that engages all employees in continual improvement of the organization. Joseph Juran is credited with being a pioneer of TQM by teaching the concepts of controlling quality and managerial breakthrough. The American Institute of Industrial Engineering was formed in 1948. The early work by F. W. Taylor and the Gilbreths was documented in papers presented to the American Society of Mechanical Engineers as interest grew from merely improving machine performance to the performance of the overall manufacturing process, most notably starting with the presentation by Henry R. Towne (1844–1924) of his paper The Engineer as An Economist (1886). === Modern practice === From 1960 to 1975, with the development of decision support systems in supply such as material requirements planning (MRP), one can emphasize the timing issue (inventory, production, compounding, transportation, etc.) of industrial organization. Israeli scientist Dr. Jacob Rubinovitz installed the CMMS program developed in IAI and Control-Data (Israel) in 1976 in South Africa and worldwide. In the 1970s, with the penetration of Japanese management theories such as Kaizen and Kanban, Japan realized very high levels of quality and productivity. These theories improved issues of quality, delivery time, and flexibility. Companies in the west realized the great impact of Kaizen and started implementing their own continuous improvement programs. W. Edwards Deming made significant contributions in the minimization of variance starting in the 1950s and continuing to the end of his life. In the 1990s, following the global industry globalization process, the emphasis was on supply chain management and customer-oriented business process design. The theory of constraints, developed by Israeli scientist Eliyahu M. Goldratt (1985), is also a significant milestone in the field. In recent years (late 2000s to 2025), the traditional skills of industrial engineering, such as system optimization, process improvement, and efficiency management, remain essential. However, these foundational abilities are increasingly complemented by a deeper understanding of emerging technologies, such as artificial intelligence, machine learning, and IoT (Internet of Things). Proficiency in data analytics has become crucial, as it allows engineers to harness big data and derive insights that inform decision-making and innovation. Additionally, knowledge in fields such as cybersecurity, software development, and sustainable practices is becoming integral to the industrial engineering scope. As we navigate beyond 2025, it is imperative for professionals across various industries to stay abreast of these advancements. The ongoing evolution of industrial engineering will undoubtedly open new career pathways and reshape existing roles. Companies and individuals must be proactive in adapting to these changes to harness the full potential of this dynamic field. == Etymology == While originally applied to manufacturing, the use of industrial in industrial engineering can be somewhat misleading, since it has grown to encompass any methodical or quantitative approach to optimizing how a process, system, or organization operates. In fact, the industrial in industrial engineering means the industry in its broadest sense. People have changed the term industrial to broader terms such as industrial and manufacturing engineering, industrial and systems engineering, industrial engineering and operations research, or industrial engineering and management. == Sub-disciplines == There are numerous sub-disciplines associated with industrial engineering, including the following a non-exhaustive list. While some industrial engineers focus exclusively on one of these sub-disciplines, many deal with a combination of sub-disciplines. The first 14 of these sub-disciplines come from the IISE Body of Knowledge. These are considered knowledge areas, and many of them contain an overlap of content. Work design and measurement Operations research and analysis Engineering economic analysis Facilities engineering and energy management Quality engineering and reliability engineering Ergonomics and human factors in engineering and design Operations engineering and operations management Supply chain management Engineering management Safety Information engineering Design and manufacturing engineering Product design and product development Systems design and systems engineering Facilities engineering Logistics Systems engineering Healthcare engineering Project management Financial engineering == Education == Industrial engineering students take courses in work analysis and design, process design, human factors, facilities planning and layout, engineering economic analysis, production planning and control, systems engineering, computer utilization and simulation, operations research, quality control, automation, robotics, and productivity engineering. Various universities offer Industrial Engineering degrees across the world. The Edwardson School of Industrial Engineering at Purdue University, the H. Milton Stewart School of Industrial and Systems Engineering at Georgia Institute of Technology, and the Department of Industrial and Operations Engineering at the University of Michigan are all named industrial engineering departments in the United States. Other universities include: Virginia Tech, Texas A&M, Northwestern University, University of Wisconsin–Madison, and the University of Southern California, and NC State University. It is important to attend accredited universities because ABET accreditation ensures that graduates have met the educational requirements necessary to enter the profession. This quality of education is recognized internationally and prepares students for successful careers. Internationally, industrial engineering degrees accredited within any member country of the Washington Accord enjoy equal accreditation within all other signatory countries, thus allowing engineers from one country to practice engineering professionally in any other. Universities offer degrees at the bachelor, master, and doctoral levels. === Undergraduate curriculum === In the United States, the undergraduate degree earned is either a bachelor of science (BS) or a bachelor of science and engineering (BSE) in industrial engineering (IE). In South Africa, the undergraduate degree is a bachelor of engineering (BEng). Variations of the title include Industrial & Operations Engineering (IOE), and Industrial & Systems Engineering (ISE or ISyE). The typical curriculum includes a broad math and science foundation spanning chemistry, physics, mechanics (i.e., statics, kinematics, and dynamics), materials science, computer science, electronics/circuits, engineering design, and the standard range of engineering mathematics (i.e., calculus, linear algebra, differential equations, statistics). For any engineering undergraduate program to be accredited, regardless of concentration, it must cover a largely similar span of such foundational work, which also overlaps heavily with the content tested on one or more engineering licensure exams in most jurisdictions. The coursework specific to IE entails specialized courses in areas such as optimization, applied probability, stochastic modeling, design of experiments, statistical process control, simulation, manufacturing engineering, ergonomics/safety engineering, and engineering economics. Industrial engineering elective courses typically cover more specialized topics in areas such as manufacturing, supply chains and logistics, analytics and machine learning, production systems, human factors and industrial design, and service systems. Certain business schools may offer programs with some overlapping relevance to IE, but the engineering programs are distinguished by a much more intensely quantitative focus, required engineering science electives, and the core math and science courses required of all engineering programs. === Graduate curriculum === The usual graduate degree earned is the master of science (MS), master of science and engineering (MSE) or master of engineering (MEng) in industrial engineering or various alternative related concentration titles. Typical MS curricula may cover: == See also == === Notable Associations and Professional Organizations === Institute of Industrial Engineers (IISE) Human Factors and Ergonomics Society (HFES) Society of Manufacturing Engineers (SME) American Production and Inventory Control Society (APICS) Institute for Operations Research and the Management Sciences (INFORMS) American Society for Quality (ASQ) The International Council on Systems Engineering (INSCOE) === Notable Universities === List of Universities with Industrial Engineering Programs === Notable Conferences === International Conference on Mechanical Industrial & Energy Engineering IISE Annual Conference INFORMS Annual Conference === Related topics === == Notes == == Further reading == Badiru, A. (Ed.) (2005). Handbook of industrial and systems engineering. CRC Press. ISBN 0-8493-2719-9. B. S. Blanchard and Fabrycky, W. (2005). Systems Engineering and Analysis (4th Edition). Prentice-Hall. ISBN 0-13-186977-9. Salvendy, G. (Ed.) (2001). Handbook of industrial engineering: Technology and operations management. Wiley-Interscience. ISBN 0-471-33057-4. Turner, W. et al. (1992). Introduction to industrial and systems engineering (Third edition). Prentice Hall. ISBN 0-13-481789-3. Eliyahu M. Goldratt, Jeff Cox (1984). The Goal North River Press; 2nd Rev edition (1992). ISBN 0-88427-061-0; 20th Anniversary edition (2004) ISBN 0-88427-178-1 Miller, Doug, Towards Sustainable Labour Costing in UK Fashion Retail (February 5, 2013). doi:10.2139/ssrn.2212100 Malakooti, B. (2013). Operations and Production Systems with Multiple Objectives. John Wiley & Sons.ISBN 978-1-118-58537-5 Systems Engineering Body of Knowledge (SEBoK) Traditional Engineering Master of Engineering Administration (MEA) Kambhampati, Venkata Satya Surya Narayana Rao (2017). "Principles of Industrial Engineering" IIE Annual Conference. Proceedings; Norcross (2017): 890-895.Principles of Industrial Engineering - ProQuest IISE Body of Knowledge == External links == Media related to Industrial engineering at Wikimedia Commons
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https://en.wikipedia.org/wiki/Industrial_engineering
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Margaret Elaine Hamilton (née Heafield; born August 17, 1936) is an American computer scientist. She directed the Software Engineering Division at the MIT Instrumentation Laboratory, where she led the development of the on-board flight software for NASA's Apollo Guidance Computer for the Apollo program. She later founded two software companies, Higher Order Software in 1976 and Hamilton Technologies in 1986, both in Cambridge, Massachusetts. Hamilton has published more than 130 papers, proceedings, and reports, about sixty projects, and six major programs. She coined the term "software engineering", stating "I began to use the term 'software engineering' to distinguish it from hardware and other kinds of engineering, yet treat each type of engineering as part of the overall systems engineering process." On November 22, 2016, Hamilton received the Presidential Medal of Freedom from president Barack Obama for her work leading to the development of on-board flight software for NASA's Apollo Moon missions. == Early life and education == Margaret Elaine Heafield was born August 17, 1936, in Paoli, Indiana, to Kenneth Heafield and Ruth Esther Heafield (née Partington). The family later moved to Michigan, where Margaret graduated from Hancock High School in 1954. She studied mathematics at the University of Michigan in 1955 before transferring to Earlham College, where her mother had been a student. She earned a BA in mathematics with a minor in philosophy in 1958. She cites Florence Long, the head of the math department at Earlham, as helping with her desire to pursue abstract mathematics and become a mathematics professor. She says her poet father and headmaster grandfather inspired her to include a minor in philosophy in her studies. == Career == In Boston, Hamilton initially intended to enroll in graduate study in abstract mathematics at Brandeis University. However, in mid-1959, Hamilton began working for Edward Norton Lorenz, in the meteorology department at Massachusetts Institute of Technology (MIT). She developed software for predicting weather, programming on the LGP-30 and the PDP-1 computers at Marvin Minsky's Project MAC. Her work contributed to Lorenz's publications on chaos theory. At the time, computer science and software engineering were not yet established disciplines; instead, programmers learned on the job with hands-on experience. She moved on to another project in the summer of 1961, and hired and trained Ellen Fetter as her replacement. === SAGE Project === From 1961 to 1963, Hamilton worked on the Semi-Automatic Ground Environment (SAGE) Project at the MIT Lincoln Lab, where she was one of the programmers who wrote software for the prototype AN/FSQ-7 computer (the XD-1), used by the U.S. Air Force to search for possibly unfriendly aircraft. She also wrote software for a satellite tracking project at the Air Force Cambridge Research Laboratories. The SAGE Project was an extension of Project Whirlwind, started by MIT to create a computer system that could predict weather systems and track their movements using simulators. SAGE was soon developed for military use in anti-aircraft air defense. Hamilton said: What they used to do when you came into this organization as a beginner, was to assign you this program which nobody was able to ever figure out or get to run. When I was the beginner they gave it to me as well. And what had happened was it was tricky programming, and the person who wrote it took delight in the fact that all of his comments were in Greek and Latin. So I was assigned this program and I actually got it to work. It even printed out its answers in Latin and Greek. I was the first one to get it to work. It was her efforts on this project that made her a candidate for the position at NASA as the lead developer for Apollo flight software. === MIT Instrumentation Laboratory and the Apollo Guidance Computer === Hamilton learned of the Apollo project in 1965 and wanted to get involved due to it being "very exciting" as a Moon program. She joined the MIT Instrumentation Laboratory, which developed the Apollo Guidance Computer for the Apollo lunar exploration program. Hamilton was the first programmer hired for the Apollo project at MIT and the first female programmer in the project, and later became Director of the Software Engineering Division. She was responsible for the team writing and testing all on-board in-flight software for the Apollo spacecraft's Command and Lunar Module and for the subsequent Skylab space station. Another part of her team designed and developed the systems software. This included error detection and recovery software such as restarts and the Display Interface Routines (also known as the Priority Displays), which Hamilton designed and developed. She worked to gain hands-on experience during a time when computer science courses were uncommon and software engineering courses did not exist. Her areas of expertise include systems design and software development, enterprise and process modeling, development paradigm, formal systems modeling languages, system-oriented objects for systems modeling and development, automated life-cycle environments, methods for maximizing software reliability and reuse, domain analysis, correctness by built-in language properties, open-architecture techniques for robust systems, full life-cycle automation, quality assurance, seamless integration, error detection and recovery techniques, human-machine interface systems, operating systems, end-to-end testing techniques, and life-cycle management techniques. These techniques are intended to make code more reliable because they help programmers identify and fix errors sooner in the development process. ==== Apollo 11 landing ==== In one of the critical moments of the Apollo 11 mission, the Apollo Guidance Computer, together with the on-board flight software, averted an abort of the landing on the Moon. Three minutes before the lunar lander reached the Moon's surface, several computer alarms were triggered. According to software engineer Robert Wills, Buzz Aldrin entered the codes to request that the computer display altitude and other data on the computer’s screen. The system was designed to support seven simultaneous programs running, but Aldrin’s request was the eighth. This action was something he requested many times whilst working in the simulator. The result was a series of unexpected error codes during the live descent. The on-board flight software captured these alarms with the "never supposed to happen displays" interrupting the astronauts with priority alarm displays. Hamilton had prepared for just this situation years before: There was one other failsafe that Hamilton likes to remember. Her "priority display" innovation had created a knock-on risk that astronaut and computer would slip out of synch just when it mattered most. As the alarms went off and priority displays replaced normal ones, the actual switchover to new programmes behind the screens was happening "a step slower" than it would today. Hamilton had thought long and hard about this. It meant that if Aldrin, say, hit a button on the priority display too quickly, he might still get a "normal" response. Her solution: when you see a priority display, first count to five. By some accounts, the astronauts had inadvertently left the rendezvous radar switch on, causing these alarms to be triggered (the claim that the radar was left on inadvertently by the astronauts is disputed by Robert Wills with the National Museum of Computing). The computer was overloaded with interrupts caused by incorrectly phased power supplied to the lander's rendezvous radar. The program alarms indicated "executive overflows", meaning the guidance computer could not complete all of its tasks in real time and had to postpone some of them. The asynchronous executive designed by J. Halcombe Laning was used by Hamilton's team to develop asynchronous flight software: Because of the flight software's system-software's error detection and recovery techniques that included its system-wide "kill and recompute" from a "safe place" restart approach to its snapshot and rollback techniques, the Display Interface Routines (AKA the priority displays) together with its man-in-the-loop capabilities were able to be created in order to have the capability to interrupt the astronauts' normal mission displays with priority displays of critical alarms in case of an emergency. This depended on our assigning a unique priority to every process in the software in order to ensure that all of its events would take place in the correct order and at the right time relative to everything else that was going on. Hamilton's priority alarm displays interrupted the astronauts' normal displays to warn them that there was an emergency "giving the astronauts a go/no-go decision (to land or not to land)". Jack Garman, a NASA computer engineer in mission control, recognized the meaning of the errors that were presented to the astronauts by the priority displays and shouted, "Go, go!" and they continued. Paul Curto, a senior technologist who nominated Hamilton for a NASA Space Act Award, called Hamilton's work "the foundation for ultra-reliable software design". Hamilton later wrote of the incident: The computer (or rather the software in it) was smart enough to recognize that it was being asked to perform more tasks than it should be performing. It then sent out an alarm, which meant to the astronaut, 'I'm overloaded with more tasks than I should be doing at this time and I'm going to keep only the more important tasks'; i.e., the ones needed for landing ... Actually, the computer was programmed to do more than recognize error conditions. A complete set of recovery programs was incorporated into the software. The software's action, in this case, was to eliminate lower priority tasks and re-establish the more important ones ... If the computer hadn't recognized this problem and taken recovery action, I doubt if Apollo 11 would have been the successful Moon landing it was. === Businesses === In 1976, Hamilton co-founded with Saydean Zeldin a company called Higher Order Software (HOS) to further develop ideas about error prevention and fault tolerance emerging from their experience at MIT working on the Apollo program. They created a product called USE.IT, based on the HOS methodology they developed at MIT. It was successfully used in numerous government programs including a project to formalize and implement C-IDEF, an automated version of IDEF, a modeling language developed by the U.S. Air Force in the Integrated Computer-Aided Manufacturing (ICAM) project. In 1980, British-Israeli computer scientist David Harel published a proposal for a structured programming language derived from HOS from the viewpoint of and/or subgoals. Others have used HOS to formalize the semantics of linguistic quantifiers, and to formalize the design of reliable real-time embedded systems. Hamilton was the CEO of HOS through 1984 and left the company in 1985. In March 1986, she founded Hamilton Technologies, Inc. in Cambridge, Massachusetts. The company was developed around the Universal Systems Language (USL) and its associated automated environment, the 001 Tool Suite, based on her paradigm of development before the fact for systems design and software development. == Legacy == Hamilton has been credited with naming the discipline of "software engineering". Hamilton details how she came to make up the term "software engineering": When I first came up with the term, no one had heard of it before, at least in our world. It was an ongoing joke for a long time. They liked to kid me about my radical ideas. It was a memorable day when one of the most respected hardware gurus explained to everyone in a meeting that he agreed with me that the process of building software should also be considered an engineering discipline, just like with hardware. Not because of his acceptance of the new 'term' per se, but because we had earned his and the acceptance of the others in the room as being in an engineering field in its own right. When Hamilton started using the term "software engineering" during the early Apollo missions, software development was not taken seriously compared to other engineering, nor was it regarded as a science. Hamilton was concerned with legitimizing software development as an engineering discipline. Over time the term "software engineering" gained the same respect as any other technical discipline. The IEEE Software September/October 2018 issue celebrates the 50th anniversary of software engineering. Hamilton talks about "Errors" and how they influenced her work related to software engineering and how her language, USL, could be used to prevent the majority of "Errors" in a system. With USL, rather than continuing to test for errors, her program was designed to keep most errors out of the system from the beginning. USL was created after her knowledge and experience from the Apollo mission, in which she determined a mathematical theory for systems and software. This method was then, and still is, highly impactful to the field of software engineering. Writing in Wired, Robert McMillan noted: "At MIT she assisted in the creation of the core principles in computer programming as she worked with her colleagues in writing code for the world's first portable computer". Hamilton's innovations go beyond the feats of playing an important role in getting humans to the Moon. According to Wired's Karen Tegan Padir: "She, along with that other early programming pioneer, COBOL inventor Grace Hopper, also deserve tremendous credit for helping to open the door for more women to enter and succeed in STEM fields like software." === Tributes === In 2017, a "Women of NASA" LEGO set went on sale featuring minifigures of Hamilton, Mae Jemison, Sally Ride, and Nancy Grace Roman. The set was initially proposed by Maia Weinstock as a tribute to the women's contributions to NASA history, and Hamilton's section of the set features a recreation of her famous 1969 photo posing with a stack of her software listings. In 2019, to celebrate 50 years after the Apollo landing, Google decided to make a tribute to Hamilton. The mirrors at the Ivanpah Solar Power Facility were configured to create a picture of Hamilton and the Apollo 11 by moonlight. Margo Madison, a fictional NASA engineer in the alternate history series For All Mankind, was inspired by Hamilton. == Awards == In 1986, Hamilton received the Augusta Ada Lovelace Award by the Association for Women in Computing. In 2003, she was given the NASA Exceptional Space Act Award for scientific and technical contributions. The award included $37,200, the largest amount awarded to any individual in NASA's history. In 2009, she received the Outstanding Alumni Award from Earlham College. In 2016, she received the Presidential Medal of Freedom from Barack Obama, the highest civilian honor in the United States. On April 28, 2017, she received the Computer History Museum Fellow Award, which honors exceptional men and women whose computing ideas have changed the world. In 2018, she was awarded an honorary doctorate degree by the Polytechnic University of Catalonia. In 2019, she was awarded The Washington Award. In 2019, she was awarded an honorary doctorate degree by Bard College. In 2019, she was awarded the Intrepid Lifetime Achievement Award. In 2022, she was inducted into the National Aviation Hall of Fame in Dayton, Ohio. == Publications == Hamilton, M.; Zeldin, S. (March 1976). "Higher Order Software—A Methodology for Defining Software". IEEE Transactions on Software Engineering. SE-2 (1): 9–32. doi:10.1109/TSE.1976.233798. S2CID 7799553. Hamilton, M.; Zeldin, S. (January 1, 1979). "The relationship between design and verification". Journal of Systems and Software. 1: 29–56. doi:10.1016/0164-1212(79)90004-9. Hamilton, M. (April 1994). "Inside Development Before the Fact". (Cover story). Special Editorial Supplement. 8ES-24ES. Electronic Design. Hamilton, M. (June 1994). "001: A Full Life Cycle Systems Engineering and Software Development Environment". (Cover story). Special Editorial Supplement. 22ES-30ES. Electronic Design. Hamilton, M.; Hackler, W. R. (2004). "Deeply Integrated Guidance Navigation Unit (DI-GNU) Common Software Architecture Principles". (Revised December 29, 2004). DAAAE30-02-D-1020 and DAAB07-98-D-H502/0180, Picatinny Arsenal, NJ, 2003–2004. Hamilton, M.; Hackler, W. R. (2007). "Universal Systems Language for Preventative Systems Engineering", Proc. 5th Ann. Conf. Systems Eng. Res. (CSER), Stevens Institute of Technology, Mar. 2007, paper #36. Hamilton, Margaret H.; Hackler, William R. (2007). "8.3.2 a Formal Universal Systems Semantics for SysML". Incose International Symposium. 17 (1). Wiley: 1333–1357. doi:10.1002/j.2334-5837.2007.tb02952.x. ISSN 2334-5837. S2CID 57214708. Hamilton, Margaret H.; Hackler, William R. (2008). "Universal Systems Language: Lessons Learned from Apollo". Computer. 41 (12). Institute of Electrical and Electronics Engineers (IEEE): 34–43. doi:10.1109/mc.2008.541. ISSN 0018-9162. Hamilton, M. H. (September 2018). "What the Errors Tell Us". IEEE Software. 35 (5): 32–37. doi:10.1109/MS.2018.290110447. S2CID 52896962. == Personal life == Hamilton has a sister, Kathryn Heafield. She met her first husband, James Cox Hamilton, in the mid-1950s while attending college. They were married on June 15, 1958, the summer after she graduated from Earlham. She briefly taught high school mathematics and French at a public school in Boston, Indiana. The couple then moved to Boston, Massachusetts, where they had a daughter, Lauren, born on November 10, 1959. They divorced in 1967 and Margaret married Dan Lickly two years later. == See also == List of pioneers in computer science == References == == Further reading == Steafel, Eleanor (July 20, 2019). "One woman in a room full of men". The Telegraph Magazine. London: Daily Telegraph plc. pp. 56–59, 61. OCLC 69022829. == External links == Hamilton Technologies, Inc. MIT News Margaret Hamilton Archived September 5, 2017, at the Wayback Machine Video produced by Makers: Women Who Make America Margaret Hamilton ’58 – Presidential Medal of Freedom Recipient Archived July 30, 2019, at the Wayback Machine: Earlham College profile
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https://en.wikipedia.org/wiki/Margaret_Hamilton_(software_engineer)
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Reverse engineering (also known as backwards engineering or back engineering) is a process or method through which one attempts to understand through deductive reasoning how a previously made device, process, system, or piece of software accomplishes a task with very little (if any) insight into exactly how it does so. Depending on the system under consideration and the technologies employed, the knowledge gained during reverse engineering can help with repurposing obsolete objects, doing security analysis, or learning how something works. Although the process is specific to the object on which it is being performed, all reverse engineering processes consist of three basic steps: information extraction, modeling, and review. Information extraction is the practice of gathering all relevant information for performing the operation. Modeling is the practice of combining the gathered information into an abstract model, which can be used as a guide for designing the new object or system. Review is the testing of the model to ensure the validity of the chosen abstract. Reverse engineering is applicable in the fields of computer engineering, mechanical engineering, design, electrical and electronic engineering, civil engineering, nuclear engineering, aerospace engineering,software engineering, chemical engineering, systems biology and more. == Overview == There are many reasons for performing reverse engineering in various fields. Reverse engineering has its origins in the analysis of hardware for commercial or military advantage.: 13 However, the reverse engineering process may not always be concerned with creating a copy or changing the artifact in some way. It may be used as part of an analysis to deduce design features from products with little or no additional knowledge about the procedures involved in their original production.: 15 In some cases, the goal of the reverse engineering process can simply be a redocumentation of legacy systems.: 15 Even when the reverse-engineered product is that of a competitor, the goal may not be to copy it but to perform competitor analysis. Reverse engineering may also be used to create interoperable products and despite some narrowly-tailored United States and European Union legislation, the legality of using specific reverse engineering techniques for that purpose has been hotly contested in courts worldwide for more than two decades. Software reverse engineering can help to improve the understanding of the underlying source code for the maintenance and improvement of the software, relevant information can be extracted to make a decision for software development and graphical representations of the code can provide alternate views regarding the source code, which can help to detect and fix a software bug or vulnerability. Frequently, as some software develops, its design information and improvements are often lost over time, but that lost information can usually be recovered with reverse engineering. The process can also help to cut down the time required to understand the source code, thus reducing the overall cost of the software development. Reverse engineering can also help to detect and to eliminate a malicious code written to the software with better code detectors. Reversing a source code can be used to find alternate uses of the source code, such as detecting the unauthorized replication of the source code where it was not intended to be used, or revealing how a competitor's product was built. That process is commonly used for "cracking" software and media to remove their copy protection,: 7 or to create a possibly-improved copy or even a knockoff, which is usually the goal of a competitor or a hacker.: 8 Malware developers often use reverse engineering techniques to find vulnerabilities in an operating system to build a computer virus that can exploit the system vulnerabilities.: 5 Reverse engineering is also being used in cryptanalysis to find vulnerabilities in substitution cipher, symmetric-key algorithm or public-key cryptography.: 6 There are other uses to reverse engineering: Games. Reverse engineering in the context of games and game engines is often used to understand underlying mechanics, data structures, and proprietary protocols, allowing developers to create mods, custom tools, or to enhance compatibility. This practice is particularly useful when interfacing with existing systems to improve interoperability between different game components, engines, or platforms. Platforms like Reshax provide tools and resources that assist in analyzing game binaries, dissecting game engine behavior, thus contributing to a deeper understanding of game technology and enabling community-driven enhancements. Interfacing. Reverse engineering can be used when a system is required to interface to another system and how both systems would negotiate is to be established. Such requirements typically exist for interoperability. Military or commercial espionage. Learning about an enemy's or competitor's latest research by stealing or capturing a prototype and dismantling it may result in the development of a similar product or a better countermeasure against it. Obsolescence. Integrated circuits are often designed on proprietary systems and built on production lines, which become obsolete in only a few years. When systems using those parts can no longer be maintained since the parts are no longer made, the only way to incorporate the functionality into new technology is to reverse-engineer the existing chip and then to redesign it using newer tools by using the understanding gained as a guide. Another obsolescence originated problem that can be solved by reverse engineering is the need to support (maintenance and supply for continuous operation) existing legacy devices that are no longer supported by their original equipment manufacturer. The problem is particularly critical in military operations. Product security analysis. That examines how a product works by determining the specifications of its components and estimate costs and identifies potential patent infringement. Also part of product security analysis is acquiring sensitive data by disassembling and analyzing the design of a system component. Another intent may be to remove copy protection or to circumvent access restrictions. Competitive technical intelligence. That is to understand what one's competitor is actually doing, rather than what it says that it is doing. Saving money. Finding out what a piece of electronics can do may spare a user from purchasing a separate product. Repurposing. Obsolete objects are then reused in a different-but-useful manner. Design. Production and design companies applied Reverse Engineering to practical craft-based manufacturing process. The companies can work on "historical" manufacturing collections through 3D scanning, 3D re-modeling and re-design. In 2013 Italian manufactures Baldi and Savio Firmino together with University of Florence optimized their innovation, design, and production processes. == Common uses == === Machines === As computer-aided design (CAD) has become more popular, reverse engineering has become a viable method to create a 3D virtual model of an existing physical part for use in 3D CAD, CAM, CAE, or other software. The reverse-engineering process involves measuring an object and then reconstructing it as a 3D model. The physical object can be measured using 3D scanning technologies like CMMs, laser scanners, structured light digitizers, or industrial CT scanning (computed tomography). The measured data alone, usually represented as a point cloud, lacks topological information and design intent. The former may be recovered by converting the point cloud to a triangular-faced mesh. Reverse engineering aims to go beyond producing such a mesh and to recover the design intent in terms of simple analytical surfaces where appropriate (planes, cylinders, etc.) as well as possibly NURBS surfaces to produce a boundary-representation CAD model. Recovery of such a model allows a design to be modified to meet new requirements, a manufacturing plan to be generated, etc. Hybrid modeling is a commonly used term when NURBS and parametric modeling are implemented together. Using a combination of geometric and freeform surfaces can provide a powerful method of 3D modeling. Areas of freeform data can be combined with exact geometric surfaces to create a hybrid model. A typical example of this would be the reverse engineering of a cylinder head, which includes freeform cast features, such as water jackets and high-tolerance machined areas. Reverse engineering is also used by businesses to bring existing physical geometry into digital product development environments, to make a digital 3D record of their own products, or to assess competitors' products. It is used to analyze how a product works, what it does, what components it has; estimate costs; identify potential patent infringement; etc. Value engineering, a related activity that is also used by businesses, involves deconstructing and analyzing products. However, the objective is to find opportunities for cost-cutting. === Printed circuit boards === Reverse engineering of printed circuit boards involves recreating fabrication data for a particular circuit board. This is done primarily to identify a design, and learn the functional and structural characteristics of a design. It also allows for the discovery of the design principles behind a product, especially if this design information is not easily available. Outdated PCBs are often subject to reverse engineering, especially when they perform highly critical functions such as powering machinery, or other electronic components. Reverse engineering these old parts can allow the reconstruction of the PCB if it performs some crucial task, as well as finding alternatives which provide the same function, or in upgrading the old PCB. Reverse engineering PCBs largely follow the same series of steps. First, images are created by drawing, scanning, or taking photographs of the PCB. Then, these images are ported to suitable reverse engineering software in order to create a rudimentary design for the new PCB. The quality of these images that is necessary for suitable reverse engineering is proportional to the complexity of the PCB itself. More complicated PCBs require well lighted photos on dark backgrounds, while fairly simple PCBs can be recreated simply with just basic dimensioning. Each layer of the PCB is carefully recreated in the software with the intent of producing a final design as close to the initial. Then, the schematics for the circuit are finally generated using an appropriate tool. === Software === In 1990, the Institute of Electrical and Electronics Engineers (IEEE) defined (software) reverse engineering (SRE) as "the process of analyzing a subject system to identify the system's components and their interrelationships and to create representations of the system in another form or at a higher level of abstraction" in which the "subject system" is the end product of software development. Reverse engineering is a process of examination only, and the software system under consideration is not modified, which would otherwise be re-engineering or restructuring. Reverse engineering can be performed from any stage of the product cycle, not necessarily from the functional end product. There are two components in reverse engineering: redocumentation and design recovery. Redocumentation is the creation of new representation of the computer code so that it is easier to understand. Meanwhile, design recovery is the use of deduction or reasoning from general knowledge or personal experience of the product to understand the product's functionality fully. It can also be seen as "going backwards through the development cycle". In this model, the output of the implementation phase (in source code form) is reverse-engineered back to the analysis phase, in an inversion of the traditional waterfall model. Another term for this technique is program comprehension. The Working Conference on Reverse Engineering (WCRE) has been held yearly to explore and expand the techniques of reverse engineering. Computer-aided software engineering (CASE) and automated code generation have contributed greatly in the field of reverse engineering. Software anti-tamper technology like obfuscation is used to deter both reverse engineering and re-engineering of proprietary software and software-powered systems. In practice, two main types of reverse engineering emerge. In the first case, source code is already available for the software, but higher-level aspects of the program, which are perhaps poorly documented or documented but no longer valid, are discovered. In the second case, there is no source code available for the software, and any efforts towards discovering one possible source code for the software are regarded as reverse engineering. The second usage of the term is more familiar to most people. Reverse engineering of software can make use of the clean room design technique to avoid copyright infringement. On a related note, black box testing in software engineering has a lot in common with reverse engineering. The tester usually has the API but has the goals to find bugs and undocumented features by bashing the product from outside. Other purposes of reverse engineering include security auditing, removal of copy protection ("cracking"), circumvention of access restrictions often present in consumer electronics, customization of embedded systems (such as engine management systems), in-house repairs or retrofits, enabling of additional features on low-cost "crippled" hardware (such as some graphics card chip-sets), or even mere satisfaction of curiosity. ==== Binary software ==== Binary reverse engineering is performed if source code for a software is unavailable. This process is sometimes termed reverse code engineering, or RCE. For example, decompilation of binaries for the Java platform can be accomplished by using Jad. One famous case of reverse engineering was the first non-IBM implementation of the PC BIOS, which launched the historic IBM PC compatible industry that has been the overwhelmingly-dominant computer hardware platform for many years. Reverse engineering of software is protected in the US by the fair use exception in copyright law. The Samba software, which allows systems that do not run Microsoft Windows systems to share files with systems that run it, is a classic example of software reverse engineering since the Samba project had to reverse-engineer unpublished information about how Windows file sharing worked so that non-Windows computers could emulate it. The Wine project does the same thing for the Windows API, and OpenOffice.org is one party doing that for the Microsoft Office file formats. The ReactOS project is even more ambitious in its goals by striving to provide binary (ABI and API) compatibility with the current Windows operating systems of the NT branch, which allows software and drivers written for Windows to run on a clean-room reverse-engineered free software (GPL) counterpart. WindowsSCOPE allows for reverse-engineering the full contents of a Windows system's live memory including a binary-level, graphical reverse engineering of all running processes. ===== Binary software techniques ===== Reverse engineering of software can be accomplished by various methods. The three main groups of software reverse engineering are Analysis through observation of information exchange, most prevalent in protocol reverse engineering, which involves using bus analyzers and packet sniffers, such as for accessing a computer bus or computer network connection and revealing the traffic data thereon. Bus or network behavior can then be analyzed to produce a standalone implementation that mimics that behavior. That is especially useful for reverse engineering device drivers. Sometimes, reverse engineering on embedded systems is greatly assisted by tools deliberately introduced by the manufacturer, such as JTAG ports or other debugging means. In Microsoft Windows, low-level debuggers such as SoftICE are popular. Disassembly using a disassembler, meaning the raw machine language of the program is read and understood in its own terms, only with the aid of machine-language mnemonics. It works on any computer program but can take quite some time, especially for those who are not used to machine code. The Interactive Disassembler is a particularly popular tool. Decompilation using a decompiler, a process that tries, with varying results, to recreate the source code in some high-level language for a program only available in machine code or bytecode. ==== Software classification ==== Software classification is the process of identifying similarities between different software binaries (such as two different versions of the same binary) used to detect code relations between software samples. The task was traditionally done manually for several reasons (such as patch analysis for vulnerability detection and copyright infringement), but it can now be done somewhat automatically for large numbers of samples. This method is being used mostly for long and thorough reverse engineering tasks (complete analysis of a complex algorithm or big piece of software). In general, statistical classification is considered to be a hard problem, which is also true for software classification, and so few solutions/tools that handle this task well. === Source code === A number of UML tools refer to the process of importing and analysing source code to generate UML diagrams as "reverse engineering". See List of UML tools. Although UML is one approach in providing "reverse engineering" more recent advances in international standards activities have resulted in the development of the Knowledge Discovery Metamodel (KDM). The standard delivers an ontology for the intermediate (or abstracted) representation of programming language constructs and their interrelationships. An Object Management Group standard (on its way to becoming an ISO standard as well), KDM has started to take hold in industry with the development of tools and analysis environments that can deliver the extraction and analysis of source, binary, and byte code. For source code analysis, KDM's granular standards' architecture enables the extraction of software system flows (data, control, and call maps), architectures, and business layer knowledge (rules, terms, and process). The standard enables the use of a common data format (XMI) enabling the correlation of the various layers of system knowledge for either detailed analysis (such as root cause, impact) or derived analysis (such as business process extraction). Although efforts to represent language constructs can be never-ending because of the number of languages, the continuous evolution of software languages, and the development of new languages, the standard does allow for the use of extensions to support the broad language set as well as evolution. KDM is compatible with UML, BPMN, RDF, and other standards enabling migration into other environments and thus leverage system knowledge for efforts such as software system transformation and enterprise business layer analysis. === Protocols === Protocols are sets of rules that describe message formats and how messages are exchanged: the protocol state machine. Accordingly, the problem of protocol reverse-engineering can be partitioned into two subproblems: message format and state-machine reverse-engineering. The message formats have traditionally been reverse-engineered by a tedious manual process, which involved analysis of how protocol implementations process messages, but recent research proposed a number of automatic solutions. Typically, the automatic approaches group observe messages into clusters by using various clustering analyses, or they emulate the protocol implementation tracing the message processing. There has been less work on reverse-engineering of state-machines of protocols. In general, the protocol state-machines can be learned either through a process of offline learning, which passively observes communication and attempts to build the most general state-machine accepting all observed sequences of messages, and online learning, which allows interactive generation of probing sequences of messages and listening to responses to those probing sequences. In general, offline learning of small state-machines is known to be NP-complete, but online learning can be done in polynomial time. An automatic offline approach has been demonstrated by Comparetti et al. and an online approach by Cho et al. Other components of typical protocols, like encryption and hash functions, can be reverse-engineered automatically as well. Typically, the automatic approaches trace the execution of protocol implementations and try to detect buffers in memory holding unencrypted packets. === Integrated circuits/smart cards === Reverse engineering is an invasive and destructive form of analyzing a smart card. The attacker uses chemicals to etch away layer after layer of the smart card and takes pictures with a scanning electron microscope (SEM). That technique can reveal the complete hardware and software part of the smart card. The major problem for the attacker is to bring everything into the right order to find out how everything works. The makers of the card try to hide keys and operations by mixing up memory positions, such as by bus scrambling. In some cases, it is even possible to attach a probe to measure voltages while the smart card is still operational. The makers of the card employ sensors to detect and prevent that attack. That attack is not very common because it requires both a large investment in effort and special equipment that is generally available only to large chip manufacturers. Furthermore, the payoff from this attack is low since other security techniques are often used such as shadow accounts. It is still uncertain whether attacks against chip-and-PIN cards to replicate encryption data and then to crack PINs would provide a cost-effective attack on multifactor authentication. Full reverse engineering proceeds in several major steps. The first step after images have been taken with a SEM is stitching the images together, which is necessary because each layer cannot be captured by a single shot. A SEM needs to sweep across the area of the circuit and take several hundred images to cover the entire layer. Image stitching takes as input several hundred pictures and outputs a single properly-overlapped picture of the complete layer. Next, the stitched layers need to be aligned because the sample, after etching, cannot be put into the exact same position relative to the SEM each time. Therefore, the stitched versions will not overlap in the correct fashion, as on the real circuit. Usually, three corresponding points are selected, and a transformation applied on the basis of that. To extract the circuit structure, the aligned, stitched images need to be segmented, which highlights the important circuitry and separates it from the uninteresting background and insulating materials. Finally, the wires can be traced from one layer to the next, and the netlist of the circuit, which contains all of the circuit's information, can be reconstructed. === Military applications === Reverse engineering is often used by people to copy other nations' technologies, devices, or information that have been obtained by regular troops in the fields or by intelligence operations. It was often used during the Second World War and the Cold War. Here are well-known examples from the Second World War and later: Jerry can: British and American forces in WW2 noticed that the Germans had gasoline cans with an excellent design. They reverse-engineered copies of those cans, which were popularly known as "Jerry cans". Nakajima G5N: In 1939, the U.S. Douglas Aircraft Company sold its DC-4E airliner prototype to Imperial Japanese Airways, which was secretly acting as a front for the Imperial Japanese Navy, which wanted a long-range strategic bomber but had been hindered by the Japanese aircraft industry's inexperience with heavy long-range aircraft. The DC-4E was transferred to the Nakajima Aircraft Company and dismantled for study; as a cover story, the Japanese press reported that it had crashed in Tokyo Bay. The wings, engines, and landing gear of the G5N were copied directly from the DC-4E. Panzerschreck: The Germans captured an American bazooka during the Second World War and reverse engineered it to create the larger Panzerschreck. Tupolev Tu-4: In 1944, three American B-29 bombers on missions over Japan were forced to land in the Soviet Union. The Soviets, who did not have a similar strategic bomber, decided to copy the B-29. Within three years, they had developed the Tu-4, a nearly-perfect copy. SCR-584 radar: copied by the Soviet Union after the Second World War, it is known for a few modifications - СЦР-584, Бинокль-Д. V-2 rocket: Technical documents for the V-2 and related technologies were captured by the Western Allies at the end of the war. The Americans focused their reverse engineering efforts via Operation Paperclip, which led to the development of the PGM-11 Redstone rocket. The Soviets used captured German engineers to reproduce technical documents and plans and worked from captured hardware to make their clone of the rocket, the R-1. Thus began the postwar Soviet rocket program, which led to the R-7 and the beginning of the space race. K-13/R-3S missile (NATO reporting name AA-2 Atoll), a Soviet reverse-engineered copy of the AIM-9 Sidewinder, was made possible after a Taiwanese (ROCAF) AIM-9B hit a Chinese PLA MiG-17 without exploding in September 1958. The missile became lodged within the airframe, and the pilot returned to base with what Soviet scientists would describe as a university course in missile development. Toophan missile: In May 1975, negotiations between Iran and Hughes Missile Systems on co-production of the BGM-71 TOW and Maverick missiles stalled over disagreements in the pricing structure, the subsequent 1979 revolution ending all plans for such co-production. Iran was later successful in reverse-engineering the missile and now produces its own copy, the Toophan. China has reverse engineered many examples of Western and Russian hardware, from fighter aircraft to missiles and HMMWV cars, such as the MiG-15,17,19,21 (which became the J-2,5,6,7) and the Su-33 (which became the J-15). During the Second World War, Polish and British cryptographers studied captured German "Enigma" message encryption machines for weaknesses. Their operation was then simulated on electromechanical devices, "bombes", which tried all the possible scrambler settings of the "Enigma" machines that helped the breaking of coded messages that had been sent by the Germans. Also during the Second World War, British scientists analyzed and defeated a series of increasingly-sophisticated radio navigation systems used by the Luftwaffe to perform guided bombing missions at night. The British countermeasures to the system were so effective that in some cases, German aircraft were led by signals to land at RAF bases since they believed that they had returned to German territory. === Gene networks === Reverse engineering concepts have been applied to biology as well, specifically to the task of understanding the structure and function of gene regulatory networks. They regulate almost every aspect of biological behavior and allow cells to carry out physiological processes and responses to perturbations. Understanding the structure and the dynamic behavior of gene networks is therefore one of the paramount challenges of systems biology, with immediate practical repercussions in several applications that are beyond basic research. There are several methods for reverse engineering gene regulatory networks by using molecular biology and data science methods. They have been generally divided into six classes: Coexpression methods are based on the notion that if two genes exhibit a similar expression profile, they may be related although no causation can be simply inferred from coexpression. Sequence motif methods analyze gene promoters to find specific transcription factor binding domains. If a transcription factor is predicted to bind a promoter of a specific gene, a regulatory connection can be hypothesized. Chromatin ImmunoPrecipitation (ChIP) methods investigate the genome-wide profile of DNA binding of chosen transcription factors to infer their downstream gene networks. Orthology methods transfer gene network knowledge from one species to another. Literature methods implement text mining and manual research to identify putative or experimentally-proven gene network connections. Transcriptional complexes methods leverage information on protein-protein interactions between transcription factors, thus extending the concept of gene networks to include transcriptional regulatory complexes. Often, gene network reliability is tested by genetic perturbation experiments followed by dynamic modelling, based on the principle that removing one network node has predictable effects on the functioning of the remaining nodes of the network. Applications of the reverse engineering of gene networks range from understanding mechanisms of plant physiology to the highlighting of new targets for anticancer therapy. === Overlap with patent law === Reverse engineering applies primarily to gaining understanding of a process or artifact in which the manner of its construction, use, or internal processes has not been made clear by its creator. Patented items do not of themselves have to be reverse-engineered to be studied, for the essence of a patent is that inventors provide a detailed public disclosure themselves, and in return receive legal protection of the invention that is involved. However, an item produced under one or more patents could also include other technology that is not patented and not disclosed. Indeed, one common motivation of reverse engineering is to determine whether a competitor's product contains patent infringement or copyright infringement. == Legality == === United States === In the United States, even if an artifact or process is protected by trade secrets, reverse-engineering the artifact or process is often lawful if it has been legitimately obtained. Reverse engineering of computer software often falls under both contract law as a breach of contract as well as any other relevant laws. That is because most end-user license agreements specifically prohibit it, and US courts have ruled that if such terms are present, they override the copyright law that expressly permits it (see Bowers v. Baystate Technologies). According to Section 103(f) of the Digital Millennium Copyright Act (17 U.S.C. § 1201 (f)), a person in legal possession of a program may reverse-engineer and circumvent its protection if that is necessary to achieve "interoperability", a term that broadly covers other devices and programs that can interact with it, make use of it, and to use and transfer data to and from it in useful ways. A limited exemption exists that allows the knowledge thus gained to be shared and used for interoperability purposes. === European Union === EU Directive 2009/24 on the legal protection of computer programs, which superseded an earlier (1991) directive, governs reverse engineering in countries of the European Union. == See also == == Notes == == References == == Sources ==
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Kansei engineering (Japanese: 感性工学 kansei kougaku, emotional or affective engineering) aims at the development or improvement of products and services by translating the customer's psychological feelings and needs into the domain of product design (i.e. parameters). It was founded by Mitsuo Nagamachi, professor emeritus of Hiroshima University (also former Dean of Hiroshima International University and CEO of International Kansei Design Institute). Kansei engineering parametrically links the customer's emotional responses (i.e. physical and psychological) to the properties and characteristics of a product or service. In consequence, products can be designed to bring forward the intended feeling. It has been adopted as one of the topics for professional development by the Royal Statistical Society. == Introduction == Product design has become increasingly complex as products contain more functions and have to meet increasing demands such as user-friendliness, manufacturability and ecological considerations. With a shortened product lifecycle, development costs are likely to increase. Since errors in the estimations of market trends can be very expensive, companies therefore perform benchmarking studies that compare with competitors on strategic, process, marketing, and product levels. However, success in a certain market segment not only requires knowledge about the competitors and the performance of competing products, but also about the impressions which a product leaves to the customer. The latter requirement becomes much more important as products and companies are becoming mature. Customers purchase products based on subjective terms such as brand image, reputation, design, impression etc.. A large number of manufacturers have started to consider such subjective properties and develop their products in a way that conveys the company image. A reliable instrument is therefore needed: an instrument which can predict the reception of a product on the market before the development costs become too large. This demand has triggered the research dealing with the translation of the customer's subjective, hidden needs into concrete products. Research is done foremost in Asia, including Japan and Korea. In Europe, a network has been forged under the 6th EU framework. This network refers to the new research field as "emotional design" or "affective engineering". == History == People want to use products that are functional at the physical level, usable at the psychological level and attractive at the emotional level. Affective engineering is the study of the interactions between the customer and the product at that third level. It focuses on the relationships between the physical traits of a product and its affective influence on the user. Thanks to this field of research, it is possible to gain knowledge on how to design more attractive products and make the customers satisfied. Methods in affective engineering (or Kansei engineering) is one of the major areas of ergonomics (human factor engineering). The study of integrating affective values in artifacts is not new at all. Already in the 18th century philosophers such as Baumgarten and Kant established the area of aesthetics. In addition to pure practical values, artifacts always also had an affective component. One example is jewellery found in excavations from the Stone Ages. The period of Renaissance is also a good example. In the middle of the 20th century, the idea of aesthetics was deployed in scientific contexts. Charles E. Osgood developed his semantic differential method in which he quantified the peoples' perceptions of artifacts. Some years later, in 1960, Professors Shigeru Mizuno and Yoji Akao developed an engineering approach in order to connect peoples' needs to product properties. This method was called quality function deployment (QFD). Another method, the Kano model, was developed in the field of quality in the early 1980s by Professor Noriaki Kano, of Tokyo University. Kano's model is used to establish the importance of individual product features for the customer's satisfaction and hence it creates the optimal requirement for process oriented product development activities. A pure marketing technique is conjoint analysis. Conjoint analysis estimates the relative importance of a product's attributes by analysing the consumer's overall judgment of a product or service. A more artistic method is called Semantic description of environments. It is mainly a tool for examining how a single person or a group of persons experience a certain (architectural) environment. Although all of these methods are concerned with subjective impact, none of them can translate this impact to design parameters sufficiently. This can, however, be accomplished by Kansei engineering. Kansei engineering (KE) has been used as a tool for affective engineering. It was developed in the early 70s in Japan and is now widely spread among Japanese companies. In the middle of the 90s, the method spread to the United States, but cultural differences may have prevented the method to enfold its whole potential. == Procedure == As mentioned above, Kansei engineering can be considered as a methodology within the research field of 'affective engineering'. Some researchers have identified the content of the methodology. Shimizu et al. state that 'Kansei Engineering is used as a tool for product development and the basic principles behind it are the following: identification of product properties and correlation between those properties and the design characteristics'. According to Nagasawa, one of the forerunners of Kansei engineering, there are three focal points in the method: How to accurately understand consumer Kansei How to reflect and translate Kansei understanding into product design How to create a system and organization for Kansei orientated design == A model on methodology == Source: Different types of Kansei engineering are identified and applied in various contexts. Schütte examined different types of Kansei engineering and developed a general model covering the contents of Kansei engineering. Choice of Domain Domain in this context describes the overall idea behind an assembly of products, i.e. the product type in general. Choosing the domain includes the definition of the intended target group and user type, market-niche and type, and the product group in question. Choosing and defining the domain are carried out on existing products, concepts and on design solutions yet unknown. From this, a domain description is formulated, serving as the basis for further evaluation. The process is necessary and has been described by Schütte in detail in a couple of publications. Span the Semantic Space The expression Semantic space was addressed for the first time by Osgood et al.. He posed that every artifact can be described in a certain vector space defined by semantic expressions (words). This is done by collecting a large number of words that describe the domain. Suitable sources are pertinent literature, commercials, manuals, specification list, experts etc. The number of the words gathered varies according to the product, typically between 100 and 1000 words. In a second step the words are grouped using manual (e.g. Affinity diagram) or mathematical methods (e.g. factor and/or cluster analysis). Finally a few representing words are selected from this spanning the Semantic Space. These words are called "Kansei words" or "Kansei Engineering words". Span the Space of Properties The next step is to span the Space of Product Properties, which is similar to the Semantic Space. The Space of Product Properties collects products representing the domain, identifies key features and selects product properties for further evaluation. The collection of products representing the domain is done from different sources such as existing products, customer suggestions, possible technical solutions and design concepts etc. The key features are found using specification lists for the products in question. To select properties for further evaluation, a Pareto-diagram can assist the decision between important and less important features. Synthesis In the synthesis step, the Semantic Space and the Space of Properties are linked together, as displayed in Figure 3. Compared to other methods in Affective Engineering, Kansei engineering is the only method that can establish and quantify connections between abstract feelings and technical specifications. For every Kansei word a number of product properties are found, affecting the Kansei word. Synthesis The research into constructing these links has been a core part of Nagamachi's work with Kansei engineering in the last few years. Nowadays, a number of different tools is available. Some of the most common tools are : Category Identification Regression Analysis /Quantification Theory Type I Rough Sets Theory Genetic Algorithm Fuzzy Sets Theory Model building and Test of Validity After doing the necessary stages, the final step of validation remains. This is done in order to check if the prediction model is reliable and realistic. However, in case of prediction model failure, it is necessary to update the Space of Properties and the Semantic Space, and consequently refine the model. The process of refinement is difficult due to the shortage of methods. This shows the need of new tools to be integrated. The existing tools can partially be found in the previously mentioned methods for the synthesis. == Software tools == Kansei engineering has always been a statistically and mathematically advanced methodology. Most types require good expert knowledge and a reasonable amount of experience to carry out the studies sufficiently. This has also been the major obstacle for a widespread application of Kansei engineering. In order to facilitate application some software packages have been developed in the recent years, most of them in Japan. There are two different types of software packages available: User consoles and data collection and analysis tools. User consoles are software programs that calculate and propose a product design based on the users' subjective preferences (Kanseis). However, such software requires a database that quantifies the connections between Kanseis and the combination of product attributes. For building such databases, data collection and analysis tools can be used. This part of the paper demonstrates some of the tools. There are many more tools used in companies and universities, which might not be available to the public. User consoles == Software == As described above, Kansei data collection and analysis is often complex and connected with statistical analysis. Depending on which synthesis method is used, different computer software is used. Kansei Engineering Software (KESo) uses QT1 for linear analysis. The concept of Kansei Engineering Software (KESo) Linköping University in Sweden. The software generates online questionnaires for collection of Kansei raw-data Another software package (Kn6) was developed at the Polytechnic University of Valencia in Spain. Both software packages improve the collection and evaluation of Kansei data. In this way even users with no specialist competence in advanced statistics can use Kansei engineering. == See also == Affective computing Fahrvergnügen Japanese quality == References == == External links == Conference on Kansei Engineering and Emotional Research KEER KANSEI Innovation (Hiroshima, JAPAN) European Kansei Engineering group Ph.D thesis on Kansei Engineering (europe) Ph.D thesis on Website Emotional UX and Kansei Engineering Archived 2017-07-01 at the Wayback Machine The Japan Society of Kansei Engineering The Malaysian Research Intensive Group for Kansei/Affective Engineering International Conference on Kansei Engineering & Intelligent Systems KEIS
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https://en.wikipedia.org/wiki/Kansei_engineering
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Maintenance Engineering is the discipline and profession of applying engineering concepts for the optimization of equipment, procedures, and departmental budgets to achieve better maintainability, reliability, and availability of equipment. Maintenance, and hence maintenance engineering, is increasing in importance due to rising amounts of equipment, systems, machineries and infrastructure. Since the Industrial Revolution, devices, equipment, machinery and structures have grown increasingly complex, requiring a host of personnel, vocations and related systems needed to maintain them. Prior to 2006, the United States spent approximately US$300 billion annually on plant maintenance and operations alone. Maintenance is to ensure a unit is fit for purpose, with maximum availability at minimum costs. A person practicing maintenance engineering is known as a maintenance engineer. == Maintenance engineer's description == A maintenance engineer should possess significant knowledge of statistics, probability, and logistics, and in the fundamentals of the operation of the equipment and machinery he or she is responsible for. A maintenance engineer should also possess high interpersonal, communication, and management skills, as well as the ability to make decisions quickly. Typical responsibilities include: Assure optimization of the maintenance organization structure Analysis of repetitive equipment failures Estimation of maintenance costs and evaluation of alternatives Forecasting of spare parts Assessing the needs for equipment replacements and establish replacement programs when due Application of scheduling and project management principles to replacement programs Assessing required maintenance tools and skills required for efficient maintenance of equipment Assessing required skills for maintenance personnel Reviewing personnel transfers to and from maintenance organizations Assessing and reporting safety hazards associated with maintenance of equipment == Maintenance engineering education == Institutions across the world have recognised the need for maintenance engineering. Maintenance engineers usually hold a degree in mechanical engineering, industrial engineering, or other engineering disciplines. In recent years specialised bachelor and master courses have developed. The bachelor degree program in maintenance engineering at the German-Jordanian University in Amman is addressing the need, as well as the master's program in maintenance engineering at Luleå University of Technology. With an increased demand for Chartered Engineers, The University of Central Lancashire in United Kingdom has developed a MSc in maintenance engineering currently under accreditation with the Institution of Engineering and Technology and a top-up Bachelor of Engineering with honour degree for technicians holding a Higher National Diploma and seeking a progression in their professional career. == See also == Aircraft maintenance engineering Asset management Auto mechanic Civil engineer Computerized maintenance management system Computer repair technician Electrician Electrical Technologist Industrial Engineering Marine fuel management Mechanic Millwright (machinery maintenance) Maintenance, repair and operations (MRO) Reliability centered maintenance (RCM) Reliability engineering Preventive maintenance Product lifecycle management Stationary engineer Total productive maintenance (TPM) Six Sigma for maintenance Associations INFORMS Institute of Industrial Engineers == References == School of Applied Technical Sciences - Maintenance Engineering
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https://en.wikipedia.org/wiki/Maintenance_engineering
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Usability engineering is a professional discipline that focuses on improving the usability of interactive systems. It draws on theories from computer science and psychology to define problems that occur during the use of such a system. Usability Engineering involves the testing of designs at various stages of the development process, with users or with usability experts. The history of usability engineering in this context dates back to the 1980s. In 1988, authors John Whiteside and John Bennett—of Digital Equipment Corporation and IBM, respectively—published material on the subject, isolating the early setting of goals, iterative evaluation, and prototyping as key activities. The usability expert Jakob Nielsen is a leader in the field of usability engineering. In his 1993 book Usability Engineering, Nielsen describes methods to use throughout a product development process—so designers can ensure they take into account the most important barriers to learnability, efficiency, memorability, error-free use, and subjective satisfaction before implementing the product. Nielsen’s work describes how to perform usability tests and how to use usability heuristics in the usability engineering lifecycle. Ensuring good usability via this process prevents problems in product adoption after release. Rather than focusing on finding solutions for usability problems—which is the focus of a UX or interaction designer—a usability engineer mainly concentrates on the research phase. In this sense, it is not strictly a design role, and many usability engineers have a background in computer science because of this. Despite this point, its connection to the design trade is absolutely crucial, not least as it delivers the framework by which designers can work so as to be sure that their products will connect properly with their target usership. == International standards == Usability engineers sometimes work to shape an interface such that it adheres to accepted operational definitions of user requirements documentation. For example, the International Organization for Standardization approved definitions (see e.g., ISO 9241 part 11) usability are held by some to be a context, efficiency, and satisfaction with which specific users should be able to perform tasks. Advocates of this approach engage in task analysis, then prototype interface design, and usability testing on those designs. On the basis of such tests, the technology is potentially redesigned if necessary. The National Institute of Standards and Technology has collaborated with industry to develop the Common Industry Specification for Usability – Requirements, which serves as a guide for many industry professionals. The specifications for successful usability in biometrics were also developed by the NIST. Usability.gov, a no-longer maintained website formerly operated by the US General Services Administration, provided a tutorial and wide general reference for the design of usable websites. Usability, especially with the goal of Universal Usability, encompasses the standards and guidelines of design for accessibility. The aim of these guidelines is to facilitate the use of a software application for people with disabilities. Some guidelines for web accessibility are: The Web Accessibility Initiative Guidelines. The Section 508 government guidelines applicable to all public-sector websites. The ADA Guidelines for accessibility of state and local government websites. The IBM Guidelines for accessibility of websites. == Errors == In usability engineering, it's important target and identify human errors when interacting with the product of interest because if a user is expected to engage with a product, interface, or service in some way, the very introduction of a human in that engagement increases the potential of encountering human error. Error should be reduced as much as possible in order to avoid frustration or injury. There are two main types of human errors which are categorized as slips and mistakes. Slips are a very common kind of error involving automatic behaviors (i.e. typos, hitting the wrong menu item). When we experience slips, we have the correct goal in mind, but execute the wrong action. Mistakes on the other hand involve conscious deliberation that result in the incorrect conclusion. When we experience mistakes, we have the wrong goal in mind and thereby execute the wrong action. Even though slips are the more common type of error, they are no less dangerous. A certain type of slip error, a mode error, can be especially dangerous if a user is executing a high-risk task. For instance, if a user is operating a vehicle and does not realize they are in the wrong mode (i.e. reverse), they might step on the gas intending to drive, but instead accelerate into a garage wall or another car. In order to avoid modal errors, designers often employ modeless states in which users do not have to choose a mode at all, or they must execute a continuous action while intending to execute a certain mode (i.e. pressing a key continuously in order to activate "lasso" mode in Photoshop). == Evaluation methods == Usability engineers conduct usability evaluations of existing or proposed interfaces and their findings are fed back to the designer for use in design or redesign. Common usability evaluation methods include: Card sorting Cognitive task analysis Cognitive walkthroughs Contextual inquiry Focus groups Heuristic evaluations Interviews Questionnaires RITE method Surveys Think aloud protocol Usability testing == Software applications and development tools == There are a variety of online resources that make the job of a usability engineer a little easier. Online tools are only a useful tool, and do not substitute for a complete usability engineering analysis. Some examples of these include: === The Web Metrics Tool Suite === This is a product of the National Institute of Standards and Technology. This toolkit is focused on evaluating the HTML of a website versus a wide range of usability guidelines and includes: Web Static Analyzer Tool (WebSAT) – checks web page HTML against typical usability guidelines Web Category Analysis Tool (WebCAT) – lets the usability engineer construct and conduct a web category analysis Web Variable Instrumenter Program (WebVIP) – instruments a website to capture a log of user interaction Framework for Logging Usability Data (FLUD) – a file format and parser for representation of user interaction logs FLUDViz Tool – produces a 2D visualization of a single user session VisVIP Tool – produces a 3D visualization of user navigation paths through a website TreeDec – adds navigation aids to the pages of a website === The Usability Testing Environment (UTE) === This tool is produced by Mind Design Systems is available freely to federal government employees. According to the official company website this tool consists of two tightly-integrated applications. The first is the UTE Manager, which helps a tester set up test scenarios (tasks) as well as survey and demographic questions. The UTE Manager also compiles the test results and produces customized reports and summary data, which can be used as quantitative measures of usability observations and recommendations. The second UTE application is the UTE Runner. The UTE Runner presents the test participants with the test scenarios (tasks) as well as any demographic and survey questions. In addition, the UTE Runner tracks the actions of the subject throughout the test including clicks, keystrokes, and scrolling. === The UsableNet Liftmachine === This tool is a product of UsableNet.com and implements the section 508 Usability and Accessibility guidelines as well as the W3C Web Accessibility Initiative Guidelines. == Notable practitioners == Deborah Mayhew Donald Norman Alan Cooper Jakob Nielsen John M. Carroll Larry Constantine Mary Beth Rossen Steve Krug == Bibliography == Nielsen, Jakob (1993). Usability engineering (2nd ed.). Boston: AP Professional. ISBN 0-12-518405-0. Carroll, John M. (2000). Making use : scenario-based design of human–computer interactions. Cambridge, Mass.: MIT Press. ISBN 0-262-03279-1. Rosson, Mary Beth; John Millar Carroll (2002). Usability Engineering: Scenario-Based Development of Human-Computer Interaction. Morgan Kaufmann. ISBN 1-55860-712-9. Nielsen, Jakob (1993). Usability engineering. Morgan Kaufmann. ISBN 978-0-12-518406-9. Spool, Jared; Tara Scanlon; Carolyn Snyder; Terri DeAngelo (1998). Web Site Usability: A Designer's Guide. Morgan Kaufmann. ISBN 978-1-55860-569-5. Mayhew, Deborah (1999). The Usability Engineering Lifecycle: A Practitioner's Handbook. Morgan Kaufmann. ISBN 978-1-55860-561-9. Faulkner, Xristine (2000). Usability Engineering. Palgrave. ISBN 978-0-333-77321-5. Smith, Michael J. (2001). Usability Evaluation and Interface Design: Cognitive Engineering, Intelligent Agents, and Virtual Reality, Volume 1 (Human Factors and Ergonomics). CRC Press. ISBN 978-0-8058-3607-3. Rosson, Mary Beth; John Millar Carroll (2002). Usability Engineering: Scenario-Based Development of Human-Computer Interaction. Morgan Kaufmann. Jacko, Julie (2012). Human-Computer Interaction Handbook: Fundamentals, Evolving Technologies, and Emerging Applications. CRC Press. ISBN 978-1-4398-2943-1. Leventhal, Laura (2007). Usability Engineering: Process, Products & Examples. Prentice Hall. ISBN 978-0-13-157008-5. Sears, Andrew; Julie A. Jacko (2007). The Human-Computer Interaction Handbook: Fundamentals, Evolving Technologies and Emerging Applications. CRC Press. ISBN 978-0-8058-5870-9. == External links == Digital.gov Usability.gov The National Institute of Standards and Technology The Web Accessibility Initiative Guidelines == References ==
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https://en.wikipedia.org/wiki/Usability_engineering
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In engineering and materials science, necking is a mode of tensile deformation where relatively large amounts of strain localize disproportionately in a small region of the material. The resulting prominent decrease in local cross-sectional area provides the basis for the name "neck". Because the local strains in the neck are large, necking is often closely associated with yielding, a form of plastic deformation associated with ductile materials, often metals or polymers. Once necking has begun, the neck becomes the exclusive location of yielding in the material, as the reduced area gives the neck the largest local stress. == Formation == Necking results from an instability during tensile deformation when the cross-sectional area of the sample decreases by a greater proportion than the material strain hardens. Armand Considère published the basic criterion for necking in 1885, in the context of the stability of large scale structures such as bridges. Three concepts provide the framework for understanding neck formation. Before deformation, all real materials have heterogeneities such as flaws or local variations in dimensions or composition that cause local fluctuations in stresses and strains. To determine the location of the incipient neck, these fluctuations need only be infinitesimal in magnitude. During plastic tensile deformation the material decreases in cross-sectional area due to the incompressibility of plastic flow. (Not due to the Poisson effect, which is linked to elastic behaviour.) During plastic tensile deformation the material strain hardens. The amount of hardening varies with extent of deformation. The latter two effects determine the stability while the first effect determines the neck's location. === The Considère treatment === Instability (onset of necking) is expected to occur when an increase in the (local) strain produces no net increase in the load, F. This will happen when Δ F = 0 {\displaystyle \Delta F=0} This leads to F = A σ T ⟹ d F = A d σ T + σ T d A = 0 ⟹ d σ T σ T = − d A A = d L L = d ε T ⟹ σ T = d σ T d ε T {\displaystyle {\begin{aligned}&F=A\sigma _{T}\\[4pt]\implies &dF=Ad\sigma _{T}+\sigma _{T}dA=0\\[4pt]\implies &{\frac {d\sigma _{T}}{\sigma _{T}}}=-{\frac {dA}{A}}={\frac {dL}{L}}=d\varepsilon _{T}\\\implies &\sigma _{T}={\frac {d\sigma _{T}}{d\varepsilon _{T}}}\end{aligned}}} with the T subscript being used to emphasize that these stresses and strains must be true values. Necking is thus predicted to start when the slope of the true stress / true strain curve falls to a value equal to the true stress at that point. === Application to metals === Necking commonly arises in both metals and polymers. However, while the phenomenon is caused by the same basic effect in both materials, they tend to have different types of (true) stress-strain curve, such that they should be considered separately in terms of necking behaviour. For metals, the (true) stress tends to rise monotonically with increasing strain, although the gradient (work hardening rate) tends to fall off progressively. This is primarily due to a progressive fall in dislocation mobility, caused by interactions between them. With polymers, on the other hand, the curve can be more complex. For example, the gradient can in some cases rise sharply with increasing strain, due to the polymer chains becoming aligned as they reorganise during plastic deformation. This can lead to a stable neck. No effect of this type is possible in metals. The figure shows a screenshot from an interactive simulation available on the DoITPoMS educational website. The construction is shown for a (true) stress-strain curve represented by a simple analytical expression (Ludwik-Hollomon). The condition can also be expressed in terms of the nominal strain: d σ T d ε T = d σ T d ε N d ε N d ε T = d σ T d ε N d L / L 0 d L / L = d σ T d ε N L L 0 = d σ T d ε N ( 1 + ε N ) {\displaystyle {\begin{aligned}{\frac {d\sigma _{T}}{d\varepsilon _{T}}}&={\frac {d\sigma _{T}}{d\varepsilon _{N}}}{\frac {d\varepsilon _{N}}{d\varepsilon _{T}}}\\[4pt]&={\frac {d\sigma _{T}}{d\varepsilon _{N}}}{\frac {dL/L_{0}}{dL/L}}\\[4pt]&={\frac {d\sigma _{T}}{d\varepsilon _{N}}}{\frac {L}{L_{0}}}\\[4pt]&={\frac {d\sigma _{T}}{d\varepsilon _{N}}}(1+\varepsilon _{\mathrm {N} })\end{aligned}}} Therefore, at the instability point: σ T = d σ T d ε N ( 1 + ε N ) {\displaystyle \sigma _{T}={\frac {d\sigma _{T}}{d\varepsilon _{N}}}(1+\varepsilon _{N})} It can therefore also be formulated in terms of a plot of true stress against nominal strain. On such a plot, necking will start where a line from the point εN = –1 forms a tangent to the curve. This is shown in the next figure, which was obtained using the same Ludwik-Hollomon representation of the true stress – true strain relationship as that of the previous figure. Importantly, the condition also corresponds to a peak (plateau) in the nominal stress – nominal strain plot. This can be seen on obtaining the gradient of such a plot by differentiating the expression for σN with respect to εN. σ N = σ T 1 + ε N ∴ d σ N d ε N = d σ T d ε N 1 1 + ε N − σ T ( 1 + ε N ) 2 {\displaystyle {\begin{aligned}\sigma _{N}&={\frac {\sigma _{T}}{1+\varepsilon _{N}}}\\[4pt]\therefore {\frac {d\sigma _{N}}{d\varepsilon _{N}}}&={\frac {d\sigma _{T}}{d\varepsilon _{N}}}{\frac {1}{1+\varepsilon _{N}}}-{\frac {\sigma _{T}}{(1+\varepsilon _{N})^{2}}}\end{aligned}}} Substituting for the true stress – nominal strain gradient (at the onset of necking): d σ N d ε N = σ T 1 + ε N 1 1 + ε N − σ T ( 1 + ε N ) 2 = 0 {\displaystyle {\frac {d\sigma _{N}}{d\varepsilon _{N}}}={\frac {\sigma _{T}}{1+\varepsilon _{N}}}{\frac {1}{1+\varepsilon _{N}}}-{\frac {\sigma _{T}}{(1+\varepsilon _{N})^{2}}}=0} This condition can also be seen in the two figures. Since many stress-strain curves are presented as nominal plots, and this is a simple condition that can be identified by visual inspection, it is in many ways the easiest criterion to use to establish the onset of necking. It also corresponds to the “strength” (ultimate tensile stress), at least for metals that do neck (which covers the majority of “engineering” metals). On the other hand, the peak in a nominal stress-strain curve is commonly a fairly flat plateau, rather than a sharp maximum, so accurate assessment of the strain at the onset of necking may be difficult. Nevertheless, this strain is a meaningful indication of the “ductility” of the metal – more so than the commonly-used “nominal strain at fracture”, which depends on the aspect ratio of the gauge length of the tensile test-piece – see the article on ductility. === Application to polymers === The tangent construction shown above is rarely used in interpreting the stress-strain curves of metals. However, it is popular for analysis of the tensile drawing of polymers. (since it allows study of the regime of stable necking). It may be noted that, for polymers, the strain is commonly expressed as a “draw ratio”, rather than a strain: in this case, extrapolation of the tangent is carried out to a draw ratio of zero, rather than a strain of -1. The plots relate (top) to a material that forms a stable neck and (bottom) a material that deforms homogeneously at all draw ratios. As deformation proceeds, the geometric instability causes strain to continue concentrating in the neck until the material either ruptures or the necked material hardens enough, as indicated by the second tangent point in the top diagram, to cause other regions of the material to deform instead. The amount of strain in the stable neck is called the natural draw ratio because it is determined by the material's hardening characteristics, not the amount of drawing imposed on the material. Ductile polymers often exhibit stable necks because molecular orientation provides a mechanism for hardening that predominates at large strains. == See also == Stress–strain curve Trace necking Universal testing machine == References ==
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https://en.wikipedia.org/wiki/Necking_(engineering)
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Telecommunications engineering is a subfield of electronics engineering which seeks to design and devise systems of communication at a distance. The work ranges from basic circuit design to strategic mass developments. A telecommunication engineer is responsible for designing and overseeing the installation of telecommunications equipment and facilities, such as complex electronic switching system, and other plain old telephone service facilities, optical fiber cabling, IP networks, and microwave transmission systems. Telecommunications engineering also overlaps with broadcast engineering. Telecommunication is a diverse field of engineering connected to electronic, civil and systems engineering. Ultimately, telecom engineers are responsible for providing high-speed data transmission services. They use a variety of equipment and transport media to design the telecom network infrastructure; the most common media used by wired telecommunications today are twisted pair, coaxial cables, and optical fibers. Telecommunications engineers also provide solutions revolving around wireless modes of communication and information transfer, such as wireless telephony services, radio and satellite communications, internet, Wi-Fi and broadband technologies. == History == Telecommunication systems are generally designed by telecommunication engineers which sprang from technological improvements in the telegraph industry in the late 19th century and the radio and the telephone industries in the early 20th century. Today, telecommunication is widespread and devices that assist the process, such as the television, radio and telephone, are common in many parts of the world. There are also many networks that connect these devices, including computer networks, public switched telephone network (PSTN), radio networks, and television networks. Computer communication across the Internet is one of many examples of telecommunication. Telecommunication plays a vital role in the world economy, and the telecommunication industry's revenue has been placed at just under 3% of the gross world product. === Telegraph and telephone === Samuel Morse independently developed a version of the electrical telegraph that he unsuccessfully demonstrated on 2 September 1837. Soon after he was joined by Alfred Vail who developed the register — a telegraph terminal that integrated a logging device for recording messages to paper tape. This was demonstrated successfully over three miles (five kilometres) on 6 January 1838 and eventually over forty miles (sixty-four kilometres) between Washington, D.C. and Baltimore on 24 May 1844. The patented invention proved lucrative and by 1851 telegraph lines in the United States spanned over 20,000 miles (32,000 kilometres). The first successful transatlantic telegraph cable was completed on 27 July 1866, allowing transatlantic telecommunication for the first time. Earlier transatlantic cables installed in 1857 and 1858 only operated for a few days or weeks before they failed. The international use of the telegraph has sometimes been dubbed the "Victorian Internet". The first commercial telephone services were set up in 1878 and 1879 on both sides of the Atlantic in the cities of New Haven and London. Alexander Graham Bell held the master patent for the telephone that was needed for such services in both countries. The technology grew quickly from this point, with inter-city lines being built and telephone exchanges in every major city of the United States by the mid-1880s. Despite this, transatlantic voice communication remained impossible for customers until January 7, 1927, when a connection was established using radio. However no cable connection existed until TAT-1 was inaugurated on September 25, 1956, providing 36 telephone circuits. In 1880, Bell and co-inventor Charles Sumner Tainter conducted the world's first wireless telephone call via modulated lightbeams projected by photophones. The scientific principles of their invention would not be utilized for several decades, when they were first deployed in military and fiber-optic communications. === Radio and television === Over several years starting in 1894, the Italian inventor Guglielmo Marconi built the first complete, commercially successful wireless telegraphy system based on airborne electromagnetic waves (radio transmission). In December 1901, he would go on to established wireless communication between Britain and Newfoundland, earning him the Nobel Prize in physics in 1909 (which he shared with Karl Braun). In 1900, Reginald Fessenden was able to wirelessly transmit a human voice. On March 25, 1925, Scottish inventor John Logie Baird publicly demonstrated the transmission of moving silhouette pictures at the London department store Selfridges. In October 1925, Baird was successful in obtaining moving pictures with halftone shades, which were by most accounts the first true television pictures. This led to a public demonstration of the improved device on 26 January 1926 again at Selfridges. Baird's first devices relied upon the Nipkow disk and thus became known as the mechanical television. It formed the basis of semi-experimental broadcasts done by the British Broadcasting Corporation beginning September 30, 1929. === Satellite === The first U.S. satellite to relay communications was Project SCORE in 1958, which used a tape recorder to store and forward voice messages. It was used to send a Christmas greeting to the world from U.S. President Dwight D. Eisenhower. In 1960 NASA launched an Echo satellite; the 100-foot (30 m) aluminized PET film balloon served as a passive reflector for radio communications. Courier 1B, built by Philco, also launched in 1960, was the world's first active repeater satellite. Satellites these days are used for many applications such as uses in GPS, television, internet and telephone uses. Telstar was the first active, direct relay commercial communications satellite. Belonging to AT&T as part of a multi-national agreement between AT&T, Bell Telephone Laboratories, NASA, the British General Post Office, and the French National PTT (Post Office) to develop satellite communications, it was launched by NASA from Cape Canaveral on July 10, 1962, the first privately sponsored space launch. Relay 1 was launched on December 13, 1962, and became the first satellite to broadcast across the Pacific on November 22, 1963. The first and historically most important application for communication satellites was in intercontinental long distance telephony. The fixed Public Switched Telephone Network relays telephone calls from land line telephones to an earth station, where they are then transmitted a receiving satellite dish via a geostationary satellite in Earth orbit. Improvements in submarine communications cables, through the use of fiber-optics, caused some decline in the use of satellites for fixed telephony in the late 20th century, but they still exclusively service remote islands such as Ascension Island, Saint Helena, Diego Garcia, and Easter Island, where no submarine cables are in service. There are also some continents and some regions of countries where landline telecommunications are rare to nonexistent, for example Antarctica, plus large regions of Australia, South America, Africa, Northern Canada, China, Russia and Greenland. After commercial long distance telephone service was established via communication satellites, a host of other commercial telecommunications were also adapted to similar satellites starting in 1979, including mobile satellite phones, satellite radio, satellite television and satellite Internet access. The earliest adaption for most such services occurred in the 1990s as the pricing for commercial satellite transponder channels continued to drop significantly. === Computer networks and the Internet === On 11 September 1940, George Stibitz was able to transmit problems using teleprinter to his Complex Number Calculator in New York and receive the computed results back at Dartmouth College in New Hampshire. This configuration of a centralized computer or mainframe computer with remote "dumb terminals" remained popular throughout the 1950s and into the 1960s. However, it was not until the 1960s that researchers started to investigate packet switching — a technology that allows chunks of data to be sent between different computers without first passing through a centralized mainframe. A four-node network emerged on 5 December 1969. This network soon became the ARPANET, which by 1981 would consist of 213 nodes. ARPANET's development centered around the Request for Comment process and on 7 April 1969, RFC 1 was published. This process is important because ARPANET would eventually merge with other networks to form the Internet, and many of the communication protocols that the Internet relies upon today were specified through the Request for Comment process. In September 1981, RFC 791 introduced the Internet Protocol version 4 (IPv4) and RFC 793 introduced the Transmission Control Protocol (TCP) — thus creating the TCP/IP protocol that much of the Internet relies upon today. === Optical fiber === Optical fiber can be used as a medium for telecommunication and computer networking because it is flexible and can be bundled into cables. It is especially advantageous for long-distance communications, because light propagates through the fiber with little attenuation compared to electrical cables. This allows long distances to be spanned with few repeaters. In 1966 Charles K. Kao and George Hockham proposed optical fibers at STC Laboratories (STL) at Harlow, England, when they showed that the losses of 1000 dB/km in existing glass (compared to 5-10 dB/km in coaxial cable) was due to contaminants, which could potentially be removed. Optical fiber was successfully developed in 1970 by Corning Glass Works, with attenuation low enough for communication purposes (about 20dB/km), and at the same time GaAs (Gallium arsenide) semiconductor lasers were developed that were compact and therefore suitable for transmitting light through fiber optic cables for long distances. After a period of research starting from 1975, the first commercial fiber-optic communications system was developed, which operated at a wavelength around 0.8 μm and used GaAs semiconductor lasers. This first-generation system operated at a bit rate of 45 Mbps with repeater spacing of up to 10 km. Soon on 22 April 1977, General Telephone and Electronics sent the first live telephone traffic through fiber optics at a 6 Mbit/s throughput in Long Beach, California. The first wide area network fibre optic cable system in the world seems to have been installed by Rediffusion in Hastings, East Sussex, UK in 1978. The cables were placed in ducting throughout the town, and had over 1000 subscribers. They were used at that time for the transmission of television channels, not available because of local reception problems. The first transatlantic telephone cable to use optical fiber was TAT-8, based on Desurvire optimized laser amplification technology. It went into operation in 1988. In the late 1990s through 2000, industry promoters, and research companies such as KMI, and RHK predicted massive increases in demand for communications bandwidth due to increased use of the Internet, and commercialization of various bandwidth-intensive consumer services, such as video on demand, Internet Protocol data traffic was increasing exponentially, at a faster rate than integrated circuit complexity had increased under Moore's Law. == Concepts == === Basic elements of a telecommunication system === ==== Transmitter ==== Transmitter (information source) that takes information and converts it to a signal for transmission. In electronics and telecommunications a transmitter or radio transmitter is an electronic device which, with the aid of an antenna, produces radio waves. In addition to their use in broadcasting, transmitters are necessary component parts of many electronic devices that communicate by radio, such as cell phones, ==== Transmission medium ==== Transmission medium over which the signal is transmitted. For example, the transmission medium for sounds is usually air, but solids and liquids may also act as transmission media for sound. Many transmission media are used as communications channel. One of the most common physical media used in networking is copper wire. Copper wire is used to carry signals to long distances using relatively low amounts of power. Another example of a physical medium is optical fiber, which has emerged as the most commonly used transmission medium for long-distance communications. Optical fiber is a thin strand of glass that guides light along its length. The absence of a material medium in vacuum may also constitute a transmission medium for electromagnetic waves such as light and radio waves. ==== Receiver ==== Receiver (information sink) that receives and converts the signal back into required information. In radio communications, a radio receiver is an electronic device that receives radio waves and converts the information carried by them to a usable form. It is used with an antenna. The information produced by the receiver may be in the form of sound (an audio signal), images (a video signal) or digital data. === Wired communication === Wired communications make use of underground communications cables (less often, overhead lines), electronic signal amplifiers (repeaters) inserted into connecting cables at specified points, and terminal apparatus of various types, depending on the type of wired communications used. === Wireless communication === Wireless communication involves the transmission of information over a distance without help of wires, cables or any other forms of electrical conductors. Wireless operations permit services, such as long-range communications, that are impossible or impractical to implement with the use of wires. The term is commonly used in the telecommunications industry to refer to telecommunications systems (e.g. radio transmitters and receivers, remote controls etc.) which use some form of energy (e.g. radio waves, acoustic energy, etc.) to transfer information without the use of wires. Information is transferred in this manner over both short and long distances. == Roles == === Telecom equipment engineer === A telecom equipment engineer is an electronics engineer that designs equipment such as routers, switches, multiplexers, and other specialized computer/electronics equipment designed to be used in the telecommunication network infrastructure. === Network engineer === A network engineer is a computer engineer who is in charge of designing, deploying and maintaining computer networks. In addition, they oversee network operations from a network operations center, designs backbone infrastructure, or supervises interconnections in a data center. === Central-office engineer === A central-office engineer is responsible for designing and overseeing the implementation of telecommunications equipment in a central office (CO for short), also referred to as a wire center or telephone exchange A CO engineer is responsible for integrating new technology into the existing network, assigning the equipment's location in the wire center, and providing power, clocking (for digital equipment), and alarm monitoring facilities for the new equipment. The CO engineer is also responsible for providing more power, clocking, and alarm monitoring facilities if there are currently not enough available to support the new equipment being installed. Finally, the CO engineer is responsible for designing how the massive amounts of cable will be distributed to various equipment and wiring frames throughout the wire center and overseeing the installation and turn up of all new equipment. ==== Sub-roles ==== As structural engineers, CO engineers are responsible for the structural design and placement of racking and bays for the equipment to be installed in as well as for the plant to be placed on. As electrical engineers, CO engineers are responsible for the resistance, capacitance, and inductance (RCL) design of all new plant to ensure telephone service is clear and crisp and data service is clean as well as reliable. Attenuation or gradual loss in intensity and loop loss calculations are required to determine cable length and size required to provide the service called for. In addition, power requirements have to be calculated and provided to power any electronic equipment being placed in the wire center. Overall, CO engineers have seen new challenges emerging in the CO environment. With the advent of Data Centers, Internet Protocol (IP) facilities, cellular radio sites, and other emerging-technology equipment environments within telecommunication networks, it is important that a consistent set of established practices or requirements be implemented. Installation suppliers or their sub-contractors are expected to provide requirements with their products, features, or services. These services might be associated with the installation of new or expanded equipment, as well as the removal of existing equipment. Several other factors must be considered such as: Regulations and safety in installation Removal of hazardous material Commonly used tools to perform installation and removal of equipment === Outside-plant engineer === Outside plant (OSP) engineers are also often called field engineers, because they frequently spend much time in the field taking notes about the civil environment, aerial, above ground, and below ground. OSP engineers are responsible for taking plant (copper, fiber, etc.) from a wire center to a distribution point or destination point directly. If a distribution point design is used, then a cross-connect box is placed in a strategic location to feed a determined distribution area. The cross-connect box, also known as a serving area interface, is then installed to allow connections to be made more easily from the wire center to the destination point and ties up fewer facilities by not having dedication facilities from the wire center to every destination point. The plant is then taken directly to its destination point or to another small closure called a terminal, where access can also be gained to the plant, if necessary. These access points are preferred as they allow faster repair times for customers and save telephone operating companies large amounts of money. The plant facilities can be delivered via underground facilities, either direct buried or through conduit or in some cases laid under water, via aerial facilities such as telephone or power poles, or via microwave radio signals for long distances where either of the other two methods is too costly. ==== Sub-roles ==== As structural engineers, OSP engineers are responsible for the structural design and placement of cellular towers and telephone poles as well as calculating pole capabilities of existing telephone or power poles onto which new plant is being added. Structural calculations are required when boring under heavy traffic areas such as highways or when attaching to other structures such as bridges. Shoring also has to be taken into consideration for larger trenches or pits. Conduit structures often include encasements of slurry that needs to be designed to support the structure and withstand the environment around it (soil type, high traffic areas, etc.). As electrical engineers, OSP engineers are responsible for the resistance, capacitance, and inductance (RCL) design of all new plant to ensure telephone service is clear and crisp and data service is clean as well as reliable. Attenuation or gradual loss in intensity and loop loss calculations are required to determine cable length and size required to provide the service called for. In addition power requirements have to be calculated and provided to power any electronic equipment being placed in the field. Ground potential has to be taken into consideration when placing equipment, facilities, and plant in the field to account for lightning strikes, high voltage intercept from improperly grounded or broken power company facilities, and from various sources of electromagnetic interference. As civil engineers, OSP engineers are responsible for drafting plans, either by hand or using Computer-aided design (CAD) software, for how telecom plant facilities will be placed. Often when working with municipalities trenching or boring permits are required and drawings must be made for these. Often these drawings include about 70% or so of the detailed information required to pave a road or add a turn lane to an existing street. Structural calculations are required when boring under heavy traffic areas such as highways or when attaching to other structures such as bridges. As civil engineers, telecom engineers provide the modern communications backbone for all technological communications distributed throughout civilizations today. Unique to telecom engineering is the use of air-core cable which requires an extensive network of air handling equipment such as compressors, manifolds, regulators and hundreds of miles of air pipe per system that connects to pressurized splice cases all designed to pressurize this special form of copper cable to keep moisture out and provide a clean signal to the customer. As political and social ambassador, the OSP engineer is a telephone operating company's face and voice to the local authorities and other utilities. OSP engineers often meet with municipalities, construction companies and other utility companies to address their concerns and educate them about how the telephone utility works and operates. Additionally, the OSP engineer has to secure real estate in which to place outside facilities, such as an easement to place a cross-connect box. == See also == == References == == Further reading == Dahlman, Erik; Parkvall, Stefan; Beming, Per; Bovik, Alan C.; Fette, Bruce A.; Jack, Keith; Skold, Johan; Dowla, Farid; Chou, Philip A.; DeCusatis, Casimer (2009). Communications engineering desk reference. Academic Press. p. 544. ISBN 978-0-12-374648-1. == External links == Media related to Communication engineering at Wikimedia Commons
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https://en.wikipedia.org/wiki/Telecommunications_engineering
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ST Engineering, is a global technology, defence and engineering group with a diverse portfolio of businesses across the aerospace, smart city, defence and public security segments. Headquartered in Singapore, the group reported a revenue of over S$11 billion in 2024 and ranks among the largest companies listed on the Singapore Exchange. It is a component stock of MSCI Singapore, FTSE Straits Times Index and Dow Jones Best-in-Class Asia Pacific Index. The Group harnesses technology and innovation to solve real-world problems, enabling a more secure and sustainable world. It leverages synergies across the group and strategic partnerships externally to accelerate innovation, its strategic AI pillars, and its core technological and engineering capabilities. ST Engineering has more than 27,000 employees with diverse background and skills, including over 19,000 engineering and technical talents. == History == ST Engineering's history began with its precursor, the Chartered Industries of Singapore, which was established in 1967 by the newly independent Singaporean government as an ammunition manufacturer. Businesses related to aerospace and shipbuilding were later created and put under the ST umbrella. The ST group of companies went commercial in 1990, setting up its first commercial airframe manufacturing, repair and overhaul facilities in Singapore and the United States. ST Engineering was created in December 1997 as a merger of four listed companies: ST Aerospace, ST Electronics, ST Automative and ST Marine. Its shares debuted on the Singapore Exchange on 8 December 1997. Since then, ST Engineering has grown to become one of Asia's largest defence and engineering groups for commercial and defence organisations across multiple industries. In Mar 2007, ST Engineering was ranked 19th in the aerospace & defence industry and 1,661th of 2,000 of the world's largest public companies by Forbes. In 2018, the Group harmonised all brands by using "ST Engineering" as a Masterbrand while in 2020, the Group reorganised as Commercial and Defence & Public Security clusters, replacing the sector-structure of Aerospace, Electronics, Land Systems and Marine. == Areas of business == ST Engineering has a diverse portfolio of businesses and a global network of subsidiaries and associated companies across Asia, Europe, the Middle East and the U.S. Its Commercial Aerospace arm is the world’s largest third-party airframe MRO solution provider and a Premier MRO for CFM LEAP engines. The businesses support aircraft operations and OEM partners with aviation lifecycle solutions or holistic offerings for practically every stage of an aircraft's lifecycle. In 2024, its Urban Solutions business was awarded a S$60m contract to design, build and operate a state-of-the-art smart city platform with citywide network connectivity for Lusail City, Qatar. Powered by AI, machine learning and data analytics, ST Engineering Urban Solution’s Agil Smart City Operating System will serve as the digital backbone of Lusail. ST Engineering is a major player in the defence and military industries. It was ranked Number 58 in the Stockholm International Peace Research Institute's list of the world's top 100 defence manufacturers in 2023. Outside of Singapore, it has sold defence products to over 100 countries, including United States, United Kingdom, Indonesia, Philippines, United Arab Emirates, Brazil, Sweden, India, Thailand and Finland. ST Engineering do not design, produce or sell anti-personnel mines, cluster munitions, white phosphorus munitions and its related key components. On December 12, 2024, ST Engineering signed a strategic agreement with Kazakhstan Paramount Engineering to set up in-country production capability for a new 8x8 armored vehicle. ST Engineering expanded to the United States in 2001, locating its U.S. headquarters in Herndon, Virginia. It now operates in 52 cities across 21 states. It was known as VT Systems (VTS; formerly known as Vision Technologies Systems) until 1 July 2019, when VTS was changed to ST Engineering North America as part of the Group’s brand harmonization exercise in 2018. == Core capabilities == ST Engineering's businesses span across the aerospace, smart city, defence and public security sectors. === Aerospace === ST Engineering's Aerospace arm provides aviation asset management to commercial airlines, airfreight operators and military operators. It is the world's largest airframe maintenance, repair, and operations (MRO) company, and one of the few with in-house engineering design and development capabilities. On top of MRO capabilities, ST Engineering also has expertise as an OEM specialising in engine nacelle and composite panels. It is the only company in the world offering Airbus freighter conversions using OEM data. ST Engineering is a major investor in Skyports to provide drone services for Singapore’s Public Utilities Board. === Smart City === ST Engineering's capabilities for Smart City addresses the connectivity, mobility, security, infrastructure and environmental needs of cities. Its products span over rail and road, autonomous and electric vehicles, mobility payment systems, building access and security systems, as well as IoT products for lighting, water and energy management. In March 2022, ST Engineering completed its acquisition of Transcore to enhance its Smart City products through TransCore’s tolling and congestion pricing businesses. === Defence & Public Security === ST Engineering's defence business provides integrated defence technologies and critical systems spanning the digital, air, land and sea domains. It has over four decades of activity in the development of military technology, from aircraft and avionics upgrades, to designing and building battlefield mobility platforms, soldier systems, ammunition and naval vessels. Its capabilities in Public Security cover critical infrastructure, intelligence operations, homeland security applications and maritime system, which have been implemented in more than 100 cities worldwide. == Corruption for ship-repair contracts == In 2014, ST Engineering and its subsidiaries ST Engineering Marine and ST Engineering Aerospace were hit by one of the largest corruption scandals in Singapore history following investigations by the Corrupt Practices Investigation Bureau. In December 2014, former ST Engineering Marine and ST Engineering Aerospace president, Chang Cheow Teck, was charged with conspiring with two subordinates to offer bribes in return for ship-repair contracts between 2004 and 2010. The corruption charges were eventually withdrawn and in January 2017, Chang pleaded guilty to "failing to use reasonable diligence in performing his duties" and was given a short detention order of 14 days. Former ST Marine CEO and president See Leong Teck was also charged with seven counts of corruption. In December 2016, See was sentenced to 10 months' jail and a $100,000 fine. Since then, six other former ST Engineering Marine senior executives were implicated in the corruption scandal, including former financial controller and senior vice-president of finance Ong Tek Liam who pleaded guilty to ten out of 118 charges in relating to the falsification of accounts, former senior vice-president Mok Kim Whang who pleaded guilty to 49 out of 826 corruption charges, ex-chief operating officer Han Yew Kwang who pleaded guilty to 50 out of 407 charges and was sentenced to six months' jail and fined $80,000, former president of commercial business Tan Mong Seng who faced 445 corruption charges and was sentenced to 16 weeks' jail, and ex-financial controller Patrick Lee Swee Ching who pled guilty to seven of 38 charges of conspiring with others between 2004 and 2007 to make false entries in petty cash vouchers, and was given the maximum fine of $210,000. In June 2017, Ong Teck Liam was sentenced to a fine of SGD300,000 ($217,200), in default 30 weeks’ imprisonment. Ong was the last to be sentenced. == References ==
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https://en.wikipedia.org/wiki/ST_Engineering
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The Institute of Electrical and Electronics Engineers (IEEE) is an American 501(c)(3) public charity professional organization for electrical engineering, electronics engineering, and other related disciplines. The IEEE has a corporate office in New York City and an operations center in Piscataway, New Jersey. The IEEE was formed in 1963 as an amalgamation of the American Institute of Electrical Engineers and the Institute of Radio Engineers. == History == The IEEE traces its founding to 1884 and the American Institute of Electrical Engineers. In 1912, the rival Institute of Radio Engineers was formed. Although the AIEE was initially larger, the IRE attracted more students and was larger by the mid-1950s. The AIEE and IRE merged in 1963. The IEEE is headquartered in New York City, but most business is done at the IEEE Operations Center in Piscataway, New Jersey, opened in 1975. The Australian Section of the IEEE existed between 1972 and 1985, after which it split into state- and territory-based sections. As of 2023, IEEE has over 460,000 members in 190 countries, with more than 66 percent from outside the United States. == Publications == IEEE claims to produce over 30% of the world's literature in the electrical, electronics, and computer engineering fields, publishing approximately 200 peer-reviewed journals and magazines. IEEE publishes more than 1,700 conference proceedings every year. The published content in these journals as well as the content from several hundred annual conferences sponsored by the IEEE are available in the IEEE Electronic Library (IEL) available through IEEE Xplore platform, for subscription-based access and individual publication purchases. In addition to journals and conference proceedings, the IEEE also publishes tutorials and standards that are produced by its standardization committees. The organization also has its own IEEE paper format. === Publishing standards === IEEE provides IEEE Editorial Style Manual for Authors style guide for article's authors and basic templates in Microsoft Word and LaTeX file formats . It's based on The Chicago Manual of Style and doesn't cover "Grammar" and "Usage" styles which are provided by Chicago style guideline. In April 2024 IEEE banned Lenna test images, and stated that they would decline papers containing them. == Technical societies == IEEE has 39 technical societies, each focused on a certain knowledge area, which provide specialized publications, conferences, business networking and other services. == Other bodies == === IEEE Global History Network === In September 2008, the IEEE History Committee founded the IEEE Global History Network, which now redirects to Engineering and Technology History Wiki. === IEEE Foundation === The IEEE Foundation is a charitable foundation established in 1973 to support and promote technology education, innovation, and excellence. It is incorporated separately from the IEEE, although it has a close relationship to it. Members of the Board of Directors of the foundation are required to be active members of IEEE, and one third of them must be current or former members of the IEEE Board of Directors. Initially, the role of the IEEE Foundation was to accept and administer donations for the IEEE Awards program, but donations increased beyond what was necessary for this purpose, and the scope was broadened. In addition to soliciting and administering unrestricted funds, the foundation also administers donor-designated funds supporting particular educational, humanitarian, historical preservation, and peer recognition programs of the IEEE. As of the end of 2014, the foundation's total assets were nearly $45 million, split equally between unrestricted and donor-designated funds. == Controversies == === Huawei ban === In May 2019, IEEE restricted Huawei employees from peer reviewing papers or handling papers as editors due to the "severe legal implications" of U.S. government sanctions against Huawei. As members of its standard-setting body, Huawei employees could continue to exercise their voting rights, attend standards development meetings, submit proposals and comment in public discussions on new standards. The ban sparked outrage among Chinese scientists on social media. Some professors in China decided to cancel their memberships. On June 3, 2019, IEEE lifted restrictions on Huawei's editorial and peer review activities after receiving clearance from the United States government. === Position on the Russian invasion of Ukraine === On February 26, 2022, the chair of the IEEE Ukraine Section, Ievgen Pichkalov, publicly appealed to the IEEE members to "freeze [IEEE] activities and membership in Russia" and requested "public reaction and strict disapproval of Russia's aggression" from the IEEE and IEEE Region 8. On March 17, 2022, an article in the form of Q&A interview with IEEE Russia (Siberia) senior member Roman Gorbunov titled "A Russian Perspective on the War in Ukraine" was published in IEEE Spectrum to demonstrate "the plurality of views among IEEE members" and the "views that are at odds with international reporting on the war in Ukraine". On March 30, 2022, activist Anna Rohrbach created an open letter to the IEEE in an attempt to have them directly address the article, stating that the article used "common narratives in Russian propaganda" on the 2022 Russian invasion of Ukraine and requesting the IEEE Spectrum to acknowledge "that they have unwittingly published a piece furthering misinformation and Russian propaganda." A few days later a note from the editors was added on April 6 with an apology "for not providing adequate context at the time of publication", though the editors did not revise the original article. == See also == Certified Software Development Professional (CSDP) program of the IEEE Computer Society Glossary of electrical and electronics engineering Engineering and Technology History Wiki Eta Kappa Nu – IEEE HKN Honor society (merged into IEEE in 2010) IEEE Standards Association Institution of Engineering and Technology (UK) International Electrotechnical Commission (IEC) List of IEEE awards List of IEEE conferences List of IEEE fellows == Notes == == References == == External links == Official website IEEE Xplore – Research database and online digital library archive IEEE History Center
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https://en.wikipedia.org/wiki/Institute_of_Electrical_and_Electronics_Engineers
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Feature engineering is a preprocessing step in supervised machine learning and statistical modeling which transforms raw data into a more effective set of inputs. Each input comprises several attributes, known as features. By providing models with relevant information, feature engineering significantly enhances their predictive accuracy and decision-making capability. Beyond machine learning, the principles of feature engineering are applied in various scientific fields, including physics. For example, physicists construct dimensionless numbers such as the Reynolds number in fluid dynamics, the Nusselt number in heat transfer, and the Archimedes number in sedimentation. They also develop first approximations of solutions, such as analytical solutions for the strength of materials in mechanics. == Clustering == One of the applications of feature engineering has been clustering of feature-objects or sample-objects in a dataset. Especially, feature engineering based on matrix decomposition has been extensively used for data clustering under non-negativity constraints on the feature coefficients. These include Non-Negative Matrix Factorization (NMF), Non-Negative Matrix-Tri Factorization (NMTF), Non-Negative Tensor Decomposition/Factorization (NTF/NTD), etc. The non-negativity constraints on coefficients of the feature vectors mined by the above-stated algorithms yields a part-based representation, and different factor matrices exhibit natural clustering properties. Several extensions of the above-stated feature engineering methods have been reported in literature, including orthogonality-constrained factorization for hard clustering, and manifold learning to overcome inherent issues with these algorithms. Other classes of feature engineering algorithms include leveraging a common hidden structure across multiple inter-related datasets to obtain a consensus (common) clustering scheme. An example is Multi-view Classification based on Consensus Matrix Decomposition (MCMD), which mines a common clustering scheme across multiple datasets. MCMD is designed to output two types of class labels (scale-variant and scale-invariant clustering), and: is computationally robust to missing information, can obtain shape- and scale-based outliers, and can handle high-dimensional data effectively. Coupled matrix and tensor decompositions are popular in multi-view feature engineering. == Predictive modelling == Feature engineering in machine learning and statistical modeling involves selecting, creating, transforming, and extracting data features. Key components include feature creation from existing data, transforming and imputing missing or invalid features, reducing data dimensionality through methods like Principal Components Analysis (PCA), Independent Component Analysis (ICA), and Linear Discriminant Analysis (LDA), and selecting the most relevant features for model training based on importance scores and correlation matrices. Features vary in significance. Even relatively insignificant features may contribute to a model. Feature selection can reduce the number of features to prevent a model from becoming too specific to the training data set (overfitting). Feature explosion occurs when the number of identified features is too large for effective model estimation or optimization. Common causes include: Feature templates - implementing feature templates instead of coding new features Feature combinations - combinations that cannot be represented by a linear system Feature explosion can be limited via techniques such as: regularization, kernel methods, and feature selection. == Automation == Automation of feature engineering is a research topic that dates back to the 1990s. Machine learning software that incorporates automated feature engineering has been commercially available since 2016. Related academic literature can be roughly separated into two types: Multi-relational decision tree learning (MRDTL) uses a supervised algorithm that is similar to a decision tree. Deep Feature Synthesis uses simpler methods. === Multi-relational decision tree learning (MRDTL) === Multi-relational Decision Tree Learning (MRDTL) extends traditional decision tree methods to relational databases, handling complex data relationships across tables. It innovatively uses selection graphs as decision nodes, refined systematically until a specific termination criterion is reached. Most MRDTL studies base implementations on relational databases, which results in many redundant operations. These redundancies can be reduced by using techniques such as tuple id propagation. === Open-source implementations === There are a number of open-source libraries and tools that automate feature engineering on relational data and time series: featuretools is a Python library for transforming time series and relational data into feature matrices for machine learning. MCMD: An open-source feature engineering algorithm for joint clustering of multiple datasets . OneBM or One-Button Machine combines feature transformations and feature selection on relational data with feature selection techniques. [OneBM] helps data scientists reduce data exploration time allowing them to try and error many ideas in short time. On the other hand, it enables non-experts, who are not familiar with data science, to quickly extract value from their data with a little effort, time, and cost. getML community is an open source tool for automated feature engineering on time series and relational data. It is implemented in C/C++ with a Python interface. It has been shown to be at least 60 times faster than tsflex, tsfresh, tsfel, featuretools or kats. tsfresh is a Python library for feature extraction on time series data. It evaluates the quality of the features using hypothesis testing. tsflex is an open source Python library for extracting features from time series data. Despite being 100% written in Python, it has been shown to be faster and more memory efficient than tsfresh, seglearn or tsfel. seglearn is an extension for multivariate, sequential time series data to the scikit-learn Python library. tsfel is a Python package for feature extraction on time series data. kats is a Python toolkit for analyzing time series data. === Deep feature synthesis === The deep feature synthesis (DFS) algorithm beat 615 of 906 human teams in a competition. == Feature stores == The feature store is where the features are stored and organized for the explicit purpose of being used to either train models (by data scientists) or make predictions (by applications that have a trained model). It is a central location where you can either create or update groups of features created from multiple different data sources, or create and update new datasets from those feature groups for training models or for use in applications that do not want to compute the features but just retrieve them when it needs them to make predictions. A feature store includes the ability to store code used to generate features, apply the code to raw data, and serve those features to models upon request. Useful capabilities include feature versioning and policies governing the circumstances under which features can be used. Feature stores can be standalone software tools or built into machine learning platforms. == Alternatives == Feature engineering can be a time-consuming and error-prone process, as it requires domain expertise and often involves trial and error. Deep learning algorithms may be used to process a large raw dataset without having to resort to feature engineering. However, deep learning algorithms still require careful preprocessing and cleaning of the input data. In addition, choosing the right architecture, hyperparameters, and optimization algorithm for a deep neural network can be a challenging and iterative process. == See also == Covariate Data transformation Feature extraction Feature learning Hashing trick Instrumental variables estimation Kernel method List of datasets for machine learning research Scale co-occurrence matrix Space mapping == References == == Further reading ==
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https://en.wikipedia.org/wiki/Feature_engineering
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In computer science, information science and systems engineering, ontology engineering is a field which studies the methods and methodologies for building ontologies, which encompasses a representation, formal naming and definition of the categories, properties and relations between the concepts, data and entities of a given domain of interest. In a broader sense, this field also includes a knowledge construction of the domain using formal ontology representations such as OWL/RDF. A large-scale representation of abstract concepts such as actions, time, physical objects and beliefs would be an example of ontological engineering. Ontology engineering is one of the areas of applied ontology, and can be seen as an application of philosophical ontology. Core ideas and objectives of ontology engineering are also central in conceptual modeling. Ontology engineering aims at making explicit the knowledge contained within software applications, and within enterprises and business procedures for a particular domain. Ontology engineering offers a direction towards solving the inter-operability problems brought about by semantic obstacles, i.e. the obstacles related to the definitions of business terms and software classes. Ontology engineering is a set of tasks related to the development of ontologies for a particular domain. Automated processing of information not interpretable by software agents can be improved by adding rich semantics to the corresponding resources, such as video files. One of the approaches for the formal conceptualization of represented knowledge domains is the use of machine-interpretable ontologies, which provide structured data in, or based on, RDF, RDFS, and OWL. Ontology engineering is the design and creation of such ontologies, which can contain more than just the list of terms (controlled vocabulary); they contain terminological, assertional, and relational axioms to define concepts (classes), individuals, and roles (properties) (TBox, ABox, and RBox, respectively). Ontology engineering is a relatively new field of study concerning the ontology development process, the ontology life cycle, the methods and methodologies for building ontologies, and the tool suites and languages that support them. A common way to provide the logical underpinning of ontologies is to formalize the axioms with description logics, which can then be translated to any serialization of RDF, such as RDF/XML or Turtle. Beyond the description logic axioms, ontologies might also contain SWRL rules. The concept definitions can be mapped to any kind of resource or resource segment in RDF, such as images, videos, and regions of interest, to annotate objects, persons, etc., and interlink them with related resources across knowledge bases, ontologies, and LOD datasets. This information, based on human experience and knowledge, is valuable for reasoners for the automated interpretation of sophisticated and ambiguous contents, such as the visual content of multimedia resources. Application areas of ontology-based reasoning include, but are not limited to, information retrieval, automated scene interpretation, and knowledge discovery. == Languages == An ontology language is a formal language used to encode the ontology. There are a number of such languages for ontologies, both proprietary and standards-based: Common logic is ISO standard 24707, a specification for a family of ontology languages that can be accurately translated into each other. The Cyc project has its own ontology language called CycL, based on first-order predicate calculus with some higher-order extensions. The Gellish language includes rules for its own extension and thus integrates an ontology with an ontology language. IDEF5 is a software engineering method to develop and maintain usable, accurate, domain ontologies. KIF is a syntax for first-order logic that is based on S-expressions. Rule Interchange Format (RIF), F-Logic and its successor ObjectLogic combine ontologies and rules. OWL is a language for making ontological statements, developed as a follow-on from RDF and RDFS, as well as earlier ontology language projects including OIL, DAML and DAML+OIL. OWL is intended to be used over the World Wide Web, and all its elements (classes, properties and individuals) are defined as RDF resources, and identified by URIs. OntoUML is a well-founded language for specifying reference ontologies. SHACL (RDF SHapes Constraints Language) is a language for describing structure of RDF data. It can be used together with RDFS and OWL or it can be used independently from them. XBRL (Extensible Business Reporting Language) is a syntax for expressing business semantics. == Methodologies and tools == DOGMA KAON OntoClean HOZO Protégé (software) Large language models == In life sciences == Life sciences is flourishing with ontologies that biologists use to make sense of their experiments. For inferring correct conclusions from experiments, ontologies have to be structured optimally against the knowledge base they represent. The structure of an ontology needs to be changed continuously so that it is an accurate representation of the underlying domain. Recently, an automated method was introduced for engineering ontologies in life sciences such as Gene Ontology (GO), one of the most successful and widely used biomedical ontology. Based on information theory, it restructures ontologies so that the levels represent the desired specificity of the concepts. Similar information theoretic approaches have also been used for optimal partition of Gene Ontology. Given the mathematical nature of such engineering algorithms, these optimizations can be automated to produce a principled and scalable architecture to restructure ontologies such as GO. Open Biomedical Ontologies (OBO), a 2006 initiative of the U.S. National Center for Biomedical Ontology, provides a common 'foundry' for various ontology initiatives, amongst which are: The Generic Model Organism Project (GMOD) Gene Ontology Consortium Sequence Ontology Ontology Lookup Service The Plant Ontology Consortium Standards and Ontologies for Functional Genomics and more == See also == ISO/IEC 21838 Ontology (information science) Ontology components Ontology double articulation Ontology learning Ontology modularization Semantic decision table Semantic integration Semantic technology Semantic Web Linked data == References == This article incorporates public domain material from the National Institute of Standards and Technology == Further reading == Kotis, K., A. Papasalouros, G. A. Vouros, N. Pappas, and K. Zoumpatianos, "Enhancing the Collective Knowledge for the Engineering of Ontologies in Open and Socially Constructed Learning Spaces", Journal of Universal Computer Science, vol. 17, issue 12, pp. 1710–1742, 08/2011 Kotis, K., and A. Papasalouros, "Learning useful kick-off ontologies from Query Logs: HCOME revised", 4th International Conference on Complex, Intelligent and Software Intensive Systems (CISIS-2010), Kracow, IEEE Computer Society Press, 2010. John Davies (Ed.) (2006). Semantic Web Technologies: Trends and Research in Ontology-based Systems. Wiley. ISBN 978-0-470-02596-3 Asunción Gómez-Pérez, Mariano Fernández-López, Oscar Corcho (2004). Ontological Engineering: With Examples from the Areas of Knowledge Management, E-commerce and the Semantic Web. Springer, 2004. Jarrar, Mustafa (2006). "Position paper". Proceedings of the 15th international conference on World Wide Web - WWW '06. pp. 497–503. doi:10.1145/1135777.1135850. ISBN 978-1-59593-323-2. S2CID 14184354. Mustafa Jarrar and Robert Meersman (2008). "Ontology Engineering -The DOGMA Approach". Book Chapter (Chapter 3). In Advances in Web Semantics I. Volume LNCS 4891, Springer. Riichiro Mizoguchi (2004). "Tutorial on ontological engineering: part 3: Advanced course of ontological engineering" Archived 2013-03-09 at the Wayback Machine. In: New Generation Computing. Ohmsha & Springer-Verlag, 22(2):198-220. Elena Paslaru Bontas Simperl and Christoph Tempich (2006). "Ontology Engineering: A Reality Check" Devedzić, Vladan (2002). "Understanding ontological engineering". Communications of the ACM. 45 (4): 136–144. CiteSeerX 10.1.1.218.7546. doi:10.1145/505248.506002. S2CID 5352880. Sure, York, Staab, Steffen and Studer, Rudi (2009). Ontology Engineering Methodology. In Staab, Steffen & Studer, Rudi (eds.) Handbook on Ontologies (2nd edition), Springer-Verlag, Heidelberg. ISBN 978-3-540-70999-2 == External links == Ontopia.net: Metadata? Thesauri? Taxonomies? Topic Maps! Making Sense of it All, by Lars Marius Garshol, 2004. OntologyEngineering.org: Ontology Engineering With Diagrams
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Engineering is the discipline and profession that applies scientific theories, mathematical methods, and empirical evidence to design, create, and analyze technological solutions, balancing technical requirements with concerns or constraints on safety, human factors, physical limits, regulations, practicality, and cost, and often at an industrial scale. In the contemporary era, engineering is generally considered to consist of the major primary branches of biomedical engineering, chemical engineering, civil engineering, electrical engineering, materials engineering and mechanical engineering. There are numerous other engineering sub-disciplines and interdisciplinary subjects that may or may not be grouped with these major engineering branches. == Biomedical engineering == Biomedical engineering is the application of engineering principles and design concepts to medicine and biology for healthcare applications (e.g., diagnostic or therapeutic purposes). == Chemical engineering == Chemical engineering is the application of chemical, physical, and biological sciences to developing technological solutions from raw materials or chemicals. == Civil engineering == Civil engineering comprises the design, construction, and maintenance of the physical and natural built environments. == Electrical engineering == Electrical engineering comprises the study and application of electricity, electronics and electromagnetism. == Material engineering == Materials engineering is the application of material science and engineering principles to understand the properties of materials. Material science emerged in the mid-20th century, grouping together fields which had previously been considered unrelated. Materials engineering is thus much more interdisciplinary than the other major engineering branches. == Mechanical engineering == Mechanical engineering comprises the design and analysis of heat and mechanical power for the operation of machines and mechanical systems. == Interdisciplinary == == See also == Outline of engineering History of engineering Glossary of engineering: A–L Glossary of engineering: M–Z Category:Engineering disciplines Engineering techniques: Computer-aided engineering Model-driven engineering Concurrent engineering Engineering analysis Engineering design process (engineering method) Engineering mathematics Engineering notation Engineering optimization Engineering statistics Front-end engineering Knowledge engineering Life-cycle engineering Redundancy (engineering) Reverse engineering Sustainable engineering Traditional engineering Value engineering Non-technical fields: Cost engineering Demographic engineering Engineering management Financial engineering Market engineering Memetic engineering Political engineering Sales engineering Social engineering (political science) Social engineering (security) Tariff engineering Exploratory engineering – the design and analysis of hypothetical models of systems not feasible with current technologies Astronomical engineering Megascale engineering Planetary engineering Stellar engineering Engineering studies – the study of engineers Engineering economics Engineering ethics Engineering law Engineering psychology Philosophy of engineering == References ==
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Ceramic engineering is the science and technology of creating objects from inorganic, non-metallic materials. This is done either by the action of heat, or at lower temperatures using precipitation reactions from high-purity chemical solutions. The term includes the purification of raw materials, the study and production of the chemical compounds concerned, their formation into components and the study of their structure, composition and properties. Ceramic materials may have a crystalline or partly crystalline structure, with long-range order on atomic scale. Glass-ceramics may have an amorphous or glassy structure, with limited or short-range atomic order. They are either formed from a molten mass that solidifies on cooling, formed and matured by the action of heat, or chemically synthesized at low temperatures using, for example, hydrothermal or sol-gel synthesis. The special character of ceramic materials gives rise to many applications in materials engineering, electrical engineering, chemical engineering and mechanical engineering. As ceramics are heat resistant, they can be used for many tasks for which materials like metal and polymers are unsuitable. Ceramic materials are used in a wide range of industries, including mining, aerospace, medicine, refinery, food and chemical industries, packaging science, electronics, industrial and transmission electricity, and guided lightwave transmission. == History == The word "ceramic" is derived from the Greek word κεραμικός (keramikos) meaning pottery. It is related to the older Indo-European language root "to burn". "Ceramic" may be used as a noun in the singular to refer to a ceramic material or the product of ceramic manufacture, or as an adjective. Ceramics is the making of things out of ceramic materials. Ceramic engineering, like many sciences, evolved from a different discipline by today's standards. Materials science engineering is grouped with ceramics engineering to this day. Abraham Darby first used coke in 1709 in Shropshire, England, to improve the yield of a smelting process. Coke is now widely used to produce carbide ceramics. Potter Josiah Wedgwood opened the first modern ceramics factory in Stoke-on-Trent, England, in 1759. Austrian chemist Carl Josef Bayer, working for the textile industry in Russia, developed a process to separate alumina from bauxite ore in 1888. The Bayer process is still used to purify alumina for the ceramic and aluminium industries. Brothers Pierre and Jacques Curie discovered piezoelectricity in Rochelle salt c. 1880. Piezoelectricity is one of the key properties of electroceramics. E.G. Acheson heated a mixture of coke and clay in 1893, and invented carborundum, or synthetic silicon carbide. Henri Moissan also synthesized SiC and tungsten carbide in his electric arc furnace in Paris about the same time as Acheson. Karl Schröter used liquid-phase sintering to bond or "cement" Moissan's tungsten carbide particles with cobalt in 1923 in Germany. Cemented (metal-bonded) carbide edges greatly increase the durability of hardened steel cutting tools. W.H. Nernst developed cubic-stabilized zirconia in the 1920s in Berlin. This material is used as an oxygen sensor in exhaust systems. The main limitation on the use of ceramics in engineering is brittleness. === Military === The military requirements of World War II encouraged developments, which created a need for high-performance materials and helped speed the development of ceramic science and engineering. Throughout the 1960s and 1970s, new types of ceramics were developed in response to advances in atomic energy, electronics, communications, and space travel. The discovery of ceramic superconductors in 1986 has spurred intense research to develop superconducting ceramic parts for electronic devices, electric motors, and transportation equipment. There is an increasing need in the military sector for high-strength, robust materials which have the capability to transmit light around the visible (0.4–0.7 micrometers) and mid-infrared (1–5 micrometers) regions of the spectrum. These materials are needed for applications requiring transparent armour. Transparent armour is a material or system of materials designed to be optically transparent, yet protect from fragmentation or ballistic impacts. The primary requirement for a transparent armour system is to not only defeat the designated threat but also provide a multi-hit capability with minimized distortion of surrounding areas. Transparent armour windows must also be compatible with night vision equipment. New materials that are thinner, lightweight, and offer better ballistic performance are being sought. Such solid-state components have found widespread use for various applications in the electro-optical field including: optical fibres for guided lightwave transmission, optical switches, laser amplifiers and lenses, hosts for solid-state lasers and optical window materials for gas lasers, and infrared (IR) heat seeking devices for missile guidance systems and IR night vision. == Modern industry == Now a multibillion-dollar a year industry, ceramic engineering and research has established itself as an important field of science. Applications continue to expand as researchers develop new kinds of ceramics to serve different purposes. Zirconium dioxide ceramics are used in the manufacture of knives. The blade of the ceramic knife will stay sharp for much longer than that of a steel knife, although it is more brittle and can be snapped by dropping it on a hard surface. Ceramics such as alumina, boron carbide and silicon carbide have been used in bulletproof vests to repel small arms rifle fire. Such plates are known commonly as ballistic plates. Similar material is used to protect cockpits of some military aircraft, because of the low weight of the material. Silicon nitride parts are used in ceramic ball bearings. Their higher hardness means that they are much less susceptible to wear and can offer more than triple lifetimes. They also deform less under load meaning they have less contact with the bearing retainer walls and can roll faster. In very high speed applications, heat from friction during rolling can cause problems for metal bearings; problems which are reduced by the use of ceramics. Ceramics are also more chemically resistant and can be used in wet environments where steel bearings would rust. The major drawback to using ceramics is a significantly higher cost. In many cases their electrically insulating properties may also be valuable in bearings. In the early 1980s, Toyota researched production of an adiabatic ceramic engine which can run at a temperature of over 6000 °F (3300 °C). Ceramic engines do not require a cooling system and hence allow a major weight reduction and therefore greater fuel efficiency. Fuel efficiency of the engine is also higher at high temperature, as shown by Carnot's theorem. In a conventional metallic engine, much of the energy released from the fuel must be dissipated as waste heat in order to prevent a meltdown of the metallic parts. Despite all of these desirable properties, such engines are not in production because the manufacturing of ceramic parts in the requisite precision and durability is difficult. Imperfection in the ceramic leads to cracks, which can lead to potentially dangerous equipment failure. Such engines are possible in laboratory settings, but mass-production is not feasible with current technology. Work is being done in developing ceramic parts for gas turbine engines. Currently, even blades made of advanced metal alloys used in the engines' hot section require cooling and careful limiting of operating temperatures. Turbine engines made with ceramics could operate more efficiently, giving aircraft greater range and payload for a set amount of fuel. Recently, there have been advances in ceramics which include bio-ceramics, such as dental implants and synthetic bones. Hydroxyapatite, the natural mineral component of bone, has been made synthetically from a number of biological and chemical sources and can be formed into ceramic materials. Orthopedic implants made from these materials bond readily to bone and other tissues in the body without rejection or inflammatory reactions. Because of this, they are of great interest for gene delivery and tissue engineering scaffolds. Most hydroxyapatite ceramics are very porous and lack mechanical strength and are used to coat metal orthopedic devices to aid in forming a bond to bone or as bone fillers. They are also used as fillers for orthopedic plastic screws to aid in reducing the inflammation and increase absorption of these plastic materials. Work is being done to make strong, fully dense nano crystalline hydroxyapatite ceramic materials for orthopedic weight bearing devices, replacing foreign metal and plastic orthopedic materials with a synthetic, but naturally occurring, bone mineral. Ultimately these ceramic materials may be used as bone replacements or with the incorporation of protein collagens, synthetic bones. Durable actinide-containing ceramic materials have many applications such as in nuclear fuels for burning excess Pu and in chemically-inert sources of alpha irradiation for power supply of unmanned space vehicles or to produce electricity for microelectronic devices. Both use and disposal of radioactive actinides require their immobilization in a durable host material. Nuclear waste long-lived radionuclides such as actinides are immobilized using chemically-durable crystalline materials based on polycrystalline ceramics and large single crystals. Alumina ceramics are widely utilized in the chemical industry due to their excellent chemical stability and high resistance to corrosion. It is used as acid-resistant pump impellers and pump bodies, ensuring long-lasting performance in transferring aggressive fluids. They are also used in acid-carrying pipe linings to prevent contamination and maintain fluid purity, which is crucial in industries like pharmaceuticals and food processing. Valves made from alumina ceramics demonstrate exceptional durability and resistance to chemical attack, making them reliable for controlling the flow of corrosive liquids. == Glass-ceramics == Glass-ceramic materials share many properties with both glasses and ceramics. Glass-ceramics have an amorphous phase and one or more crystalline phases and are produced by a so-called "controlled crystallization", which is typically avoided in glass manufacturing. Glass-ceramics often contain a crystalline phase which constitutes anywhere from 30% [m/m] to 90% [m/m] of its composition by volume, yielding an array of materials with interesting thermomechanical properties. In the processing of glass-ceramics, molten glass is cooled down gradually before reheating and annealing. In this heat treatment the glass partly crystallizes. In many cases, so-called 'nucleation agents' are added in order to regulate and control the crystallization process. Because there is usually no pressing and sintering, glass-ceramics do not contain the volume fraction of porosity typically present in sintered ceramics. The term mainly refers to a mix of lithium and aluminosilicates which yields an array of materials with interesting thermomechanical properties. The most commercially important of these have the distinction of being impervious to thermal shock. Thus, glass-ceramics have become extremely useful for countertop cooking. The negative thermal expansion coefficient (TEC) of the crystalline ceramic phase can be balanced with the positive TEC of the glassy phase. At a certain point (~70% crystalline) the glass-ceramic has a net TEC near zero. This type of glass-ceramic exhibits excellent mechanical properties and can sustain repeated and quick temperature changes up to 1000 °C. == Processing steps == The traditional ceramic process generally follows this sequence: Milling → Batching → Mixing → Forming → Drying → Firing → Assembly. Milling is the process by which materials are reduced from a large size to a smaller size. Milling may involve breaking up cemented material (in which case individual particles retain their shape) or pulverization (which involves grinding the particles themselves to a smaller size). Milling is generally done by mechanical means, including attrition (which is particle-to-particle collision that results in agglomerate break up or particle shearing), compression (which applies a forces that results in fracturing), and impact (which employs a milling medium or the particles themselves to cause fracturing). Attrition milling equipment includes the wet scrubber (also called the planetary mill or wet attrition mill), which has paddles in water creating vortexes in which the material collides and break up. Compression mills include the jaw crusher, roller crusher and cone crusher. Impact mills include the ball mill, which has media that tumble and fracture the material, or the ResonantAcoustic mixer. Shaft impactors cause particle-to particle attrition and compression. Batching is the process of weighing the oxides according to recipes, and preparing them for mixing and drying. Mixing occurs after batching and is performed with various machines, such as dry mixing ribbon mixers (a type of cement mixer), ResonantAcoustic mixers, Mueller mixers, and pug mills. Wet mixing generally involves the same equipment. Forming is making the mixed material into shapes, ranging from toilet bowls to spark plug insulators. Forming can involve: (1) Extrusion, such as extruding "slugs" to make bricks, (2) Pressing to make shaped parts, (3) Slip casting, as in making toilet bowls, wash basins and ornamentals like ceramic statues. Forming produces a "green" part, ready for drying. Green parts are soft, pliable, and over time will lose shape. Handling the green product will change its shape. For example, a green brick can be "squeezed", and after squeezing it will stay that way. Drying is removing the water or binder from the formed material. Spray drying is widely used to prepare powder for pressing operations. Other dryers are tunnel dryers and periodic dryers. Controlled heat is applied in this two-stage process. First, heat removes water. This step needs careful control, as rapid heating causes cracks and surface defects. The dried part is smaller than the green part, and is brittle, necessitating careful handling, since a small impact will cause crumbling and breaking. Sintering is where the dried parts pass through a controlled heating process, and the oxides are chemically changed to cause bonding and densification. The fired part will be smaller than the dried part. == Forming methods == Ceramic forming techniques include throwing, slipcasting, tape casting, freeze-casting, injection molding, dry pressing, isostatic pressing, hot isostatic pressing (HIP), 3D printing and others. Methods for forming ceramic powders into complex shapes are desirable in many areas of technology. Such methods are required for producing advanced, high-temperature structural parts such as heat engine components and turbines. Materials other than ceramics which are used in these processes may include: wood, metal, water, plaster and epoxy—most of which will be eliminated upon firing. A ceramic-filled epoxy, such as Martyte, is sometimes used to protect structural steel under conditions of rocket exhaust impingement. These forming techniques are well known for providing tools and other components with dimensional stability, surface quality, high (near theoretical) density and microstructural uniformity. The increasing use and diversity of specialty forms of ceramics adds to the diversity of process technologies to be used. Thus, reinforcing fibers and filaments are mainly made by polymer, sol-gel, or CVD processes, but melt processing also has applicability. The most widely used specialty form is layered structures, with tape casting for electronic substrates and packages being pre-eminent. Photo-lithography is of increasing interest for precise patterning of conductors and other components for such packaging. Tape casting or forming processes are also of increasing interest for other applications, ranging from open structures such as fuel cells to ceramic composites. The other major layer structure is coating, where thermal spraying is very important, but chemical and physical vapor deposition and chemical (e.g., sol-gel and polymer pyrolysis) methods are all seeing increased use. Besides open structures from formed tape, extruded structures, such as honeycomb catalyst supports, and highly porous structures, including various foams, for example, reticulated foam, are of increasing use. Densification of consolidated powder bodies continues to be achieved predominantly by (pressureless) sintering. However, the use of pressure sintering by hot pressing is increasing, especially for non-oxides and parts of simple shapes where higher quality (mainly microstructural homogeneity) is needed, and larger size or multiple parts per pressing can be an advantage. == The sintering process == The principles of sintering-based methods are simple ("sinter" has roots in the English "cinder"). The firing is done at a temperature below the melting point of the ceramic. Once a roughly-held-together object called a "green body" is made, it is fired in a kiln, where atomic and molecular diffusion processes give rise to significant changes in the primary microstructural features. This includes the gradual elimination of porosity, which is typically accompanied by a net shrinkage and overall densification of the component. Thus, the pores in the object may close up, resulting in a denser product of significantly greater strength and fracture toughness. Another major change in the body during the firing or sintering process will be the establishment of the polycrystalline nature of the solid. Significant grain growth tends to occur during sintering, with this growth depending on temperature and duration of the sintering process. The growth of grains will result in some form of grain size distribution, which will have a significant impact on the ultimate physical properties of the material. In particular, abnormal grain growth in which certain grains grow very large in a matrix of finer grains will significantly alter the physical and mechanical properties of the obtained ceramic. In the sintered body, grain sizes are a product of the thermal processing parameters as well as the initial particle size, or possibly the sizes of aggregates or particle clusters which arise during the initial stages of processing. The ultimate microstructure (and thus the physical properties) of the final product will be limited by and subject to the form of the structural template or precursor which is created in the initial stages of chemical synthesis and physical forming. Hence the importance of chemical powder and polymer processing as it pertains to the synthesis of industrial ceramics, glasses and glass-ceramics. There are numerous possible refinements of the sintering process. Some of the most common involve pressing the green body to give the densification a head start and reduce the sintering time needed. Sometimes organic binders such as polyvinyl alcohol are added to hold the green body together; these burn out during the firing (at 200–350 °C). Sometimes organic lubricants are added during pressing to increase densification. It is common to combine these, and add binders and lubricants to a powder, then press. (The formulation of these organic chemical additives is an art in itself. This is particularly important in the manufacture of high performance ceramics such as those used by the billions for electronics, in capacitors, inductors, sensors, etc.) A slurry can be used in place of a powder, and then cast into a desired shape, dried and then sintered. Indeed, traditional pottery is done with this type of method, using a plastic mixture worked with the hands. If a mixture of different materials is used together in a ceramic, the sintering temperature is sometimes above the melting point of one minor component – a liquid phase sintering. This results in shorter sintering times compared to solid state sintering. Such liquid phase sintering involves in faster diffusion processes and may result in abnormal grain growth. == Strength of ceramics == A material's strength is dependent on its microstructure. The engineering processes to which a material is subjected can alter its microstructure. The variety of strengthening mechanisms that alter the strength of a material include the mechanism of grain boundary strengthening. Thus, although yield strength is maximized with decreasing grain size, ultimately, very small grain sizes make the material brittle. Considered in tandem with the fact that the yield strength is the parameter that predicts plastic deformation in the material, one can make informed decisions on how to increase the strength of a material depending on its microstructural properties and the desired end effect. The relation between yield stress and grain size is described mathematically by the Hall-Petch equation which is σ y = σ 0 + k y d {\displaystyle \sigma _{y}=\sigma _{0}+{k_{y} \over {\sqrt {d}}}} where ky is the strengthening coefficient (a constant unique to each material), σo is a materials constant for the starting stress for dislocation movement (or the resistance of the lattice to dislocation motion), d is the grain diameter, and σy is the yield stress. Theoretically, a material could be made infinitely strong if the grains are made infinitely small. This is, unfortunately, impossible because the lower limit of grain size is a single unit cell of the material. Even then, if the grains of a material are the size of a single unit cell, then the material is in fact amorphous, not crystalline, since there is no long range order, and dislocations can not be defined in an amorphous material. It has been observed experimentally that the microstructure with the highest yield strength is a grain size of about 10 nanometers, because grains smaller than this undergo another yielding mechanism, grain boundary sliding. Producing engineering materials with this ideal grain size is difficult because of the limitations of initial particle sizes inherent to nanomaterials and nanotechnology. == Faber-Evans model == The Faber-Evans model, developed by Katherine Faber and Anthony G. Evans, was developed to predict the increase in fracture toughness in ceramics due to crack deflection around second-phase particles that are prone to microcracking in a matrix. The model considers particle morphology, aspect ratio, spacing, and volume fraction of the second phase, as well as the reduction in local stress intensity at the crack tip when the crack is deflected or the crack plane bows. Actual crack tortuosity is obtained through imaging techniques, which allows for the direct input of deflection and bowing angles into the model. The model calculates the average strain energy release rate and compares the resulting increase in fracture toughness to that of a flat crack through the plain matrix. The magnitude of the toughening is determined by the mismatch strain caused by thermal contraction incompatibility and the microfracture resistance of the particle/matrix interface. The toughening becomes noticeable with a narrow size distribution of appropriately sized particles, and researchers typically accept that deflection effects in materials with roughly equiaxial grains may increase the fracture toughness by about twice the grain boundary value. The model reveals that the increase in toughness is dependent on particle shape and the volume fraction of the second phase, with the most effective morphology being the rod of high aspect ratio, which can account for a fourfold increase in fracture toughness. The toughening arises primarily from the twist of the crack front between particles, as indicated by deflection profiles. Disc-shaped particles and spheres are less effective in toughening. Fracture toughness, regardless of morphology, is determined by the twist of the crack front at its most severe configuration, rather than the initial tilt of the crack front. Only for disc-shaped particles does the initial tilting of the crack front provide significant toughening; however, the twist component still overrides the tilt-derived toughening. Additional important features of the deflection analysis include the appearance of asymptotic toughening for the three morphologies at volume fractions in excess of 0.2. It is also noted that a significant influence on the toughening by spherical particles is exerted by the interparticle spacing distribution; greater toughening is afforded when spheres are nearly contacting such that twist angles approach π/2. These predictions provide the basis for the design of high-toughness two-phase ceramic materials. The ideal second phase, in addition to maintaining chemical compatibility, should be present in amounts of 10 to 20 volume percent. Greater amounts may diminish the toughness increase due to overlapping particles. Particles with high aspect ratios, especially those with rod-shaped morphologies, are most suitable for maximum toughening. This model is often used to determine the factors that contribute to the increase in fracture toughness in ceramics which is ultimately useful in the development of advanced ceramic materials with improved performance. == Theory of chemical processing == === Microstructural uniformity === In the processing of fine ceramics, the irregular particle sizes and shapes in a typical powder often lead to non-uniform packing morphologies that result in packing density variations in the powder compact. Uncontrolled agglomeration of powders due to attractive van der Waals forces can also give rise to in microstructural inhomogeneities. Differential stresses that develop as a result of non-uniform drying shrinkage are directly related to the rate at which the solvent can be removed, and thus highly dependent upon the distribution of porosity. Such stresses have been associated with a plastic-to-brittle transition in consolidated bodies, and can yield to crack propagation in the unfired body if not relieved. In addition, any fluctuations in packing density in the compact as it is prepared for the kiln are often amplified during the sintering process, yielding inhomogeneous densification. Some pores and other structural defects associated with density variations have been shown to play a detrimental role in the sintering process by growing and thus limiting end-point densities. Differential stresses arising from inhomogeneous densification have also been shown to result in the propagation of internal cracks, thus becoming the strength-controlling flaws. It would therefore appear desirable to process a material in such a way that it is physically uniform with regard to the distribution of components and porosity, rather than using particle size distributions which will maximize the green density. The containment of a uniformly dispersed assembly of strongly interacting particles in suspension requires total control over particle-particle interactions. Monodisperse colloids provide this potential. Monodisperse powders of colloidal silica, for example, may therefore be stabilized sufficiently to ensure a high degree of order in the colloidal crystal or polycrystalline colloidal solid which results from aggregation. The degree of order appears to be limited by the time and space allowed for longer-range correlations to be established. Such defective polycrystalline colloidal structures would appear to be the basic elements of sub-micrometer colloidal materials science, and, therefore, provide the first step in developing a more rigorous understanding of the mechanisms involved in microstructural evolution in inorganic systems such as polycrystalline ceramics. === Self-assembly === Self-assembly is the most common term in use in the modern scientific community to describe the spontaneous aggregation of particles (atoms, molecules, colloids, micelles, etc.) without the influence of any external forces. Large groups of such particles are known to assemble themselves into thermodynamically stable, structurally well-defined arrays, quite reminiscent of one of the 7 crystal systems found in metallurgy and mineralogy (e.g. face-centered cubic, body-centered cubic, etc.). The fundamental difference in equilibrium structure is in the spatial scale of the unit cell (or lattice parameter) in each particular case. Thus, self-assembly is emerging as a new strategy in chemical synthesis and nanotechnology. Molecular self-assembly has been observed in various biological systems and underlies the formation of a wide variety of complex biological structures. Molecular crystals, liquid crystals, colloids, micelles, emulsions, phase-separated polymers, thin films and self-assembled monolayers all represent examples of the types of highly ordered structures which are obtained using these techniques. The distinguishing feature of these methods is self-organization in the absence of any external forces. In addition, the principal mechanical characteristics and structures of biological ceramics, polymer composites, elastomers, and cellular materials are being re-evaluated, with an emphasis on bioinspired materials and structures. Traditional approaches focus on design methods of biological materials using conventional synthetic materials. This includes an emerging class of mechanically superior biomaterials based on microstructural features and designs found in nature. The new horizons have been identified in the synthesis of bioinspired materials through processes that are characteristic of biological systems in nature. This includes the nanoscale self-assembly of the components and the development of hierarchical structures. == Ceramic composites == Substantial interest has arisen in recent years in fabricating ceramic composites. While there is considerable interest in composites with one or more non-ceramic constituents, the greatest attention is on composites in which all constituents are ceramic. These typically comprise two ceramic constituents: a continuous matrix, and a dispersed phase of ceramic particles, whiskers, or short (chopped) or continuous ceramic fibers. The challenge, as in wet chemical processing, is to obtain a uniform or homogeneous distribution of the dispersed particle or fiber phase. Consider first the processing of particulate composites. The particulate phase of greatest interest is tetragonal zirconia because of the toughening that can be achieved from the phase transformation from the metastable tetragonal to the monoclinic crystalline phase, aka transformation toughening. There is also substantial interest in dispersion of hard, non-oxide phases such as SiC, TiB, TiC, boron, carbon and especially oxide matrices like alumina and mullite. There is also interest too incorporating other ceramic particulates, especially those of highly anisotropic thermal expansion. Examples include Al2O3, TiO2, graphite, and boron nitride. In processing particulate composites, the issue is not only homogeneity of the size and spatial distribution of the dispersed and matrix phases, but also control of the matrix grain size. However, there is some built-in self-control due to inhibition of matrix grain growth by the dispersed phase. Particulate composites, though generally offer increased resistance to damage, failure, or both, are still quite sensitive to inhomogeneities of composition as well as other processing defects such as pores. Thus they need good processing to be effective. Particulate composites have been made on a commercial basis by simply mixing powders of the two constituents. Although this approach is inherently limited in the homogeneity that can be achieved, it is the most readily adaptable for existing ceramic production technology. However, other approaches are of interest. From the technological standpoint, a particularly desirable approach to fabricating particulate composites is to coat the matrix or its precursor onto fine particles of the dispersed phase with good control of the starting dispersed particle size and the resultant matrix coating thickness. One should in principle be able to achieve the ultimate in homogeneity of distribution and thereby optimize composite performance. This can also have other ramifications, such as allowing more useful composite performance to be achieved in a body having porosity, which might be desired for other factors, such as limiting thermal conductivity. There are also some opportunities to utilize melt processing for fabrication of ceramic, particulate, whisker and short-fiber, and continuous-fiber composites. Both particulate and whisker composites are conceivable by solid-state precipitation after solidification of the melt. This can also be obtained in some cases by sintering, as for precipitation-toughened, partially stabilized zirconia. Similarly, it is known that one can directionally solidify ceramic eutectic mixtures and hence obtain uniaxially aligned fiber composites. Such composite processing has typically been limited to very simple shapes and thus suffers from serious economic problems due to high machining costs. There is a possibility for melt casting to be used for many of these approaches. Potentially even more desirable is using melt-derived particles. In this method, quenching is done in a solid solution or in a fine eutectic structure, in which the particles are then processed by more typical ceramic powder processing methods into a useful body. There have also been preliminary attempts to use melt spraying as a means of forming composites by introducing the dispersed particulate, whisker, or fiber phase in conjunction with the melt spraying process. Other methods besides melt infiltration to manufacture ceramic composites with long fiber reinforcement are chemical vapor infiltration and the infiltration of fiber preforms with organic precursor, which after pyrolysis yield an amorphous ceramic matrix, initially with a low density. With repeated cycles of infiltration and pyrolysis one of those types of ceramic matrix composites is produced. Chemical vapor infiltration is used to manufacture carbon/carbon and silicon carbide reinforced with carbon or silicon carbide fibers. Besides many process improvements, the first of two major needs for fiber composites is lower fiber costs. The second major need is fiber compositions or coatings, or composite processing, to reduce degradation that results from high-temperature composite exposure under oxidizing conditions. == Applications == The products of technical ceramics include tiles used in the Space Shuttle program, gas burner nozzles, ballistic protection, nuclear fuel uranium oxide pellets, bio-medical implants, jet engine turbine blades, and missile nose cones. Its products are often made from materials other than clay, chosen for their particular physical properties. These may be classified as follows: Oxides: silica, alumina, zirconia Non-oxides: carbides, borides, nitrides, silicides Composites: particulate or whisker reinforced matrices, combinations of oxides and non-oxides (e.g. polymers). Ceramics can be used in many technological industries. One application is the ceramic tiles on NASA's Space Shuttle, used to protect it and the future supersonic space planes from the searing heat of re-entry into the Earth's atmosphere. They are also used widely in electronics and optics. In addition to the applications listed here, ceramics are also used as a coating in various engineering cases. An example would be a ceramic bearing coating over a titanium frame used for an aircraft. Recently the field has come to include the studies of single crystals or glass fibers, in addition to traditional polycrystalline materials, and the applications of these have been overlapping and changing rapidly. === Aerospace === Engines: shielding a hot running aircraft engine from damaging other components. Airframes: used as a high-stress, high-temp and lightweight bearing and structural component. Missile nose-cones: shielding the missile internals from heat. Space Shuttle tiles Space-debris ballistic shields: ceramic fiber woven shields offer better protection to hypervelocity (~7 km/s) particles than aluminum shields of equal weight. Rocket nozzles: focusing high-temperature exhaust gases from the rocket booster. Unmanned Air Vehicles: ceramic engine utilization in aeronautical applications (such as Unmanned Air Vehicles) may result in enhanced performance characteristics and less operational costs. === Biomedical === Artificial bone; Dentistry applications, teeth. Biodegradable splints; Reinforcing bones recovering from osteoporosis Implant material === Electronics === Capacitors Integrated circuit packages Transducers Insulators === Optical === Optical fibers, guided light wave transmission Switches Laser amplifiers Lenses Infrared heat-seeking devices === Automotive === Heat shield Exhaust heat management == Biomaterials == Silicification is quite common in the biological world and occurs in bacteria, single-celled organisms, plants, and animals (invertebrates and vertebrates). Crystalline minerals formed in such environment often show exceptional physical properties (e.g. strength, hardness, fracture toughness) and tend to form hierarchical structures that exhibit microstructural order over a range of length or spatial scales. The minerals are crystallized from an environment that is undersaturated with respect to silicon, and under conditions of neutral pH and low temperature (0–40 °C). Formation of the mineral may occur either within or outside of the cell wall of an organism, and specific biochemical reactions for mineral deposition exist that include lipids, proteins and carbohydrates. Most natural (or biological) materials are complex composites whose mechanical properties are often outstanding, considering the weak constituents from which they are assembled. These complex structures, which have risen from hundreds of million years of evolution, are inspiring the design of novel materials with exceptional physical properties for high performance in adverse conditions. Their defining characteristics such as hierarchy, multifunctionality, and the capacity for self-healing, are currently being investigated. The basic building blocks begin with the 20 amino acids and proceed to polypeptides, polysaccharides, and polypeptides–saccharides. These, in turn, compose the basic proteins, which are the primary constituents of the 'soft tissues' common to most biominerals. With well over 1000 proteins possible, current research emphasizes the use of collagen, chitin, keratin, and elastin. The 'hard' phases are often strengthened by crystalline minerals, which nucleate and grow in a bio-mediated environment that determines the size, shape and distribution of individual crystals. The most important mineral phases have been identified as hydroxyapatite, silica, and aragonite. Using the classification of Wegst and Ashby, the principal mechanical characteristics and structures of biological ceramics, polymer composites, elastomers, and cellular materials have been presented. Selected systems in each class are being investigated with emphasis on the relationship between their microstructure over a range of length scales and their mechanical response. Thus, the crystallization of inorganic materials in nature generally occurs at ambient temperature and pressure. Yet the vital organisms through which these minerals form are capable of consistently producing extremely precise and complex structures. Understanding the processes in which living organisms control the growth of crystalline minerals such as silica could lead to significant advances in the field of materials science, and open the door to novel synthesis techniques for nanoscale composite materials, or nanocomposites. High-resolution scanning electron microscope (SEM) observations were performed of the microstructure of the mother-of-pearl (or nacre) portion of the abalone shell. Those shells exhibit the highest mechanical strength and fracture toughness of any non-metallic substance known. The nacre from the shell of the abalone has become one of the more intensively studied biological structures in materials science. Clearly visible in these images are the neatly stacked (or ordered) mineral tiles separated by thin organic sheets along with a macrostructure of larger periodic growth bands which collectively form what scientists are currently referring to as a hierarchical composite structure. (The term hierarchy simply implies that there are a range of structural features which exist over a wide range of length scales). Future developments reside in the synthesis of bio-inspired materials through processing methods and strategies that are characteristic of biological systems. These involve nanoscale self-assembly of the components and the development of hierarchical structures. == See also == == References == == External links == The American Ceramic Society Ceramic Tile Institute of America
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https://en.wikipedia.org/wiki/Ceramic_engineering
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Food engineering is a scientific, academic, and professional field that interprets and applies principles of engineering, science, and mathematics to food manufacturing and operations, including the processing, production, handling, storage, conservation, control, packaging and distribution of food products. Given its reliance on food science and broader engineering disciplines such as electrical, mechanical, civil, chemical, industrial and agricultural engineering, food engineering is considered a multidisciplinary and narrow field. Due to the complex nature of food materials, food engineering also combines the study of more specific chemical and physical concepts such as biochemistry, microbiology, food chemistry, thermodynamics, transport phenomena, rheology, and heat transfer. Food engineers apply this knowledge to the cost-effective design, production, and commercialization of sustainable, safe, nutritious, healthy, appealing, affordable and high-quality ingredients and foods, as well as to the development of food systems, machinery, and instrumentation. == History == Although food engineering is a relatively recent and evolving field of study, it is based on long-established concepts and activities. The traditional focus of food engineering was preservation, which involved stabilizing and sterilizing foods, preventing spoilage, and preserving nutrients in food for prolonged periods of time. More specific traditional activities include food dehydration and concentration, protective packaging, canning and freeze-drying . The development of food technologies were greatly influenced and urged by wars and long voyages, including space missions, where long-lasting and nutritious foods were essential for survival. Other ancient activities include milling, storage, and fermentation processes. Although several traditional activities remain of concern and form the basis of today’s technologies and innovations, the focus of food engineering has recently shifted to food quality, safety, taste, health and sustainability. == Application and practices == The following are some of the applications and practices used in food engineering to produce safe, healthy, tasty, and sustainable food: === Refrigeration and freezing === The main objective of food refrigeration and/or freezing is to preserve the quality and safety of food materials. Refrigeration and freezing contribute to the preservation of perishable foods, and to the conservation some food quality factors such as visual appearance, texture, taste, flavor and nutritional content. Freezing food slows the growth of bacteria that could potentially harm consumers. === Evaporation === Evaporation is used to pre-concentrate, increase the solid content, change the color, and reduce the water content of food and liquid products. This process is mostly seen when processing milk, starch derivatives, coffee, fruit juices, vegetable pastes and concentrates, seasonings, sauces, sugar, and edible oil. Evaporation is also used in food dehydration processes. The purpose of dehydration is to prevent the growth of molds in food, which only build when moisture is present. This process can be applied to vegetables, fruits, meats, and fish, for example. === Packaging === Food packaging technologies are used to extend the shelf-life of products, to stabilize food (preserve taste, appearance, and quality), and to maintain the food clean, protected, and appealing to the consumer. This can be achieved, for example, by packaging food in cans and jars. Because food production creates large amounts of waste, many companies are transitioning to eco-friendly packaging to preserve the environment and attract the attention of environmentally conscious consumers. Some types of environmentally friendly packaging include plastics made from corn or potato, bio-compostable plastic and paper products which disintegrate, and recycled content. Even though transitioning to eco-friendly packaging has positive effects on the environment, many companies are finding other benefits such as reducing excess packaging material, helping to attract and retain customers, and showing that companies care about the environment. === Energy for food processing === To increase sustainability of food processing there is a need for energy efficiency and waste heat recovery. The replacement of conventional energy-intensive food processes with new technologies like thermodynamic cycles and non-thermal heating processes provide another potential to reduce energy consumption, reduce production costs, and improve the sustainability in food production. === Heat transfer in food processing === Heat transfer is important in the processing of almost every commercialized food product and is important to preserve the hygienic, nutritional and sensory qualities of food. Heat transfer methods include induction, convection, and radiation. These methods are used to create variations in the physical properties of food when freezing, baking, or deep frying products, and also when applying ohmic heating or infrared radiation to food. These tools allow food engineers to innovate in the creation and transformation of food products. === Food Safety Management Systems (FSMS) === A Food Safety Management System (FSMS) is "a systematic approach to controlling food safety hazards within a business in order to ensure that the food product is safe to consume." In some countries FSMS is a legal requirement, which obliges all food production businesses to use and maintain a FSMS based on the principles of Hazard Analysis Critical Control Point (HACCP). HACCP is a management system that addresses food safety through the analysis and control of biological, chemical, and physical hazards in all stages of the food supply chain. The ISO 22000 standard specifies the requirements for FSMS. == Emerging technologies == The following technologies, which continue to evolve, have contributed to the innovation and advancement of food engineering practices: === Three-dimensional printing of food === Three-dimensional (3D) printing, also known as additive manufacturing, is the process of using digital files to create three dimensional objects. In the food industry, 3D printing of food is used for the processing of food layers using computer equipment. The process of 3D printing is slow, but is improving over time with the goal of reducing costs and processing times. Some of the successful food items that have been printed through 3D technology are: chocolate, cheese, cake frosting, turkey, pizza, celery, among others. This technology is continuously improving, and has the potential of providing cost-effective, energy efficient food that meets nutritional stability, safety and variety. === Biosensors === Biosensors can be used for quality control in laboratories and in different stages of food processing. Biosensor technology is one way in which farmers and food processors have adapted to the worldwide increase in demand for food, while maintaining their food production and quality high. Furthermore, since millions of people are affected by food-borne diseases caused by bacteria and viruses, biosensors are becoming an important tool to ensure the safety of food. They help track and analyze food quality during several parts of the supply chain: in food processing, shipping and commercialization. Biosensors can also help with the detection of genetically modified organisms (GMOs), to help regulate GMO products. With the advancement of technologies, like nanotechnology, the quality and uses of biosensors are constantly being improved. === Milk pasteurization by microwave === When storage conditions of milk are controlled, milk tends to have a very good flavor. However, oxidized flavor is a problem that affects the taste and safety of milk in a negative way. To prevent the growth of pathogenic bacteria and extend the shelf life of milk, pasteurization processes were developed. Microwaved milk has been studied and developed to prevent oxidation compared to traditional pasteurized milk methods, and it has been concluded that milk has a better quality when it has microwaved milk pasteurization. == Education and training == In the 1950s, food engineering emerged as an academic discipline, when several U.S. universities included food science and food technology in their curricula, and important works on food engineering appeared. Today, educational institutions throughout the world offer bachelors, masters, and doctoral degrees in food engineering. However, due to the unique character of food engineering, its training is more often offered as a branch of broader programs on food science, food technology, biotechnology, or agricultural and chemical engineering. In other cases, institutions offer food engineering education through concentrations, specializations, or minors. Food engineering candidates receive multidisciplinary training in areas like mathematics, chemistry, biochemistry, physics, microbiology, nutrition, and law. Food engineering is still growing and developing as a field of study, and academic curricula continue to evolve. Future food engineering programs are subject to change due to the current challenges in the food industry, including bio-economics, food security, population growth, food safety, changing eating behavior, globalization, climate change, energy cost and change in value chain, fossil fuel prices, and sustainability. To address these challenges, which require the development of new products, services, and processes, academic programs are incorporating innovative and practical forms of training. For example, innovation laboratories, research programs, and projects with food companies and equipment manufacturers are being adopted by some universities. In addition, food engineering competitions and competitions from other scientific disciplines are appearing. With the growing demand for safe, sustainable, and healthy food, and for environmentally friendly processes and packaging, there is a large job market for food engineering prospective employees. Food engineers are typically employed by the food industry, academia, government agencies, research centers, consulting firms, pharmaceutical companies, healthcare firms, and entrepreneurial projects. Job descriptions include but are not limited to food engineer, food microbiologist, bioengineering/biotechnology, nutrition, traceability, food safety and quality management. == Challenges == === Sustainability === Food engineering has negative impacts on the environment such as the emission of large quantities of waste and the pollution of water and air, which must be addressed by food engineers in the future development of food production and processing operations. Scientists and engineers are experimenting in different ways to create improved processes that reduce pollution, but these must continue to be improved in order to achieve a sustainable food supply chain. Food engineers must reevaluate current practices and technologies to focus on increasing productivity and efficiency while reducing the consumption of water and energy, and decreasing the amount of waste produced. === Population growth === Even though food supply expands yearly, there has also been an increase in the number of hungry people. The world population is expected to reach 9-10 billion people by 2050 and the problem of malnutrition remains a priority. To achieve food security, food engineers are required to address land and water scarcity to provide enough growth and food for undernourished people. In addition, food production depends on land and water supply, which are under stress as the population size increases. There is a growing pressure on land resources driven by expanding populations, leading to expansions of croplands; this usually involves the destruction of forests and exploitation of arable land. Food engineers face the challenge of finding sustainable ways to produce to adapt to the growing population. === Human health === Food engineers must adapt food technologies and operations to the recent consumer trend toward the consumption of healthy and nutritious food. To supply foods with these qualities, and for the benefit of human health, food engineers must work collaboratively with professionals in other domains such as medicine, biochemistry, chemistry, and consumerism. New technologies and practices must be developed to increase the production of foods that have a positive impact on human health. == See also == == References ==
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https://en.wikipedia.org/wiki/Food_engineering
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In engineering, a process is a series of interrelated tasks that, together, transform inputs into a given output. These tasks may be carried out by people, nature or machines using various resources; an engineering process must be considered in the context of the agents carrying out the tasks and the resource attributes involved. Systems engineering normative documents and those related to Maturity Models are typically based on processes, for example, systems engineering processes of the EIA-632 and processes involved in the Capability Maturity Model Integration (CMMI) institutionalization and improvement approach. Constraints imposed on the tasks and resources required to implement them are essential for executing the tasks mentioned. == Semiconductor industry == Semiconductor process engineers face the unique challenge of transforming raw materials into high-tech devices. Common semiconductor devices include Integrated Circuits (ICs), Light-Emitting Diodes (LEDs), solar cells, and solid-state lasers. To produce these and other semiconductor devices, semiconductor process engineers rely heavily on interconnected physical and chemical processes. A prominent example of these combined processes is the use of ultra-violet photolithography which is then followed by wet etching, the process of creating an IC pattern that is transferred onto an organic coating and etched onto the underlying semiconductor chip. Other examples include the ion implantation of dopant species to tailor the electrical properties of a semiconductor chip and the electrochemical deposition of metallic interconnects (e.g. electroplating). Process Engineers are generally involved in the development, scaling, and quality control of new semiconductor processes from lab bench to manufacturing floor. == Chemical engineering == A chemical process is a series of unit operations used to produce a material in large quantities. In the chemical industry, chemical engineers will use the following to define or illustrate a process: Process flow diagram (PFD) Piping and instrumentation diagram (P&ID) Simplified process description Detailed process description Project management Process simulation == CPRET == The Association Française d'Ingénierie Système has developed a process definition dedicated to Systems engineering (SE), but open to all domains. The CPRET representation integrates the process Mission and Environment in order to offer an external standpoint. Several models may correspond to a single definition depending on the language used (UML or another language). Note: process definition and modeling are interdependent notions but different the one from the other. Process A process is a set of transformations of input elements into products: respecting constraints, requiring resources, meeting a defined mission, corresponding to a specific purpose adapted to a given environment. Environment Natural conditions and external factors impacting a process. Mission Purpose of the process tailored to a given environment. This definition requires a process description to include the Constraints, Products, Resources, Input Elements and Transformations. This leads to the CPRET acronym to be used as name and mnemonic for this definition. Constraints Imposed conditions, rules or regulations. Products All whatever is generated by transformations. The products can be of the desired or not desired type (e.g., the software system and bugs, the defined products and waste). Resources Human resources, energy, time and other means required to carry out the transformations. Elements as inputs Elements submitted to transformations for producing the products. Transformations Operations organized according to a logic aimed at optimizing the attainment of specific products from the input elements, with the allocated resources and on compliance with the imposed constraints. === CPRET through examples === The purpose of the following examples is to illustrate the definitions with concrete cases. These examples come from the Engineering field but also from other fields to show that the CPRET definition of processes is not limited to the System Engineering context. Examples of processes An engineering (EIA-632, ISO/IEC 15288, etc.) A concert A polling campaign A certification Examples of environment Various levels of maturity, technicality, equipment An audience A political system Practices Examples of mission Supply better quality products Satisfy the public, critics Have candidates elected Obtain the desired approval Examples of constraints Imposed technologies Correct acoustics Speaking times A reference model (ISO, CMMI, etc.) Examples of products A mobile telephone network A show Vote results A quality label Examples of resources Development teams An orchestra and its instruments An organization An assessment team Examples of elements as inputs Specifications Scores Candidates A company and its practices Examples of transformations Define an architecture Play the scores Make people vote for a candidate Audit the organization == Conclusions == The CPRET formalized definition systematically addresses the input Elements, Transformations, and Products but also the other essential components of a Process, namely the Constraints and Resources. Among the resources, note the specificity of the Resource-Time component which passes inexorably and irreversibly, with problems of synchronization and sequencing. This definition states that environment is an external factor which cannot be avoided: as a matter of fact, a process is always interdependent with other phenomena including other processes. == References == == Bibliography ==
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https://en.wikipedia.org/wiki/Process_(engineering)
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Chaos engineering is the discipline of experimenting on a system in order to build confidence in the system's capability to withstand turbulent conditions in production. == Concept == In software development, the ability of a given software to tolerate failures while still ensuring adequate quality of service—often termed resilience—is typically specified as a requirement. However, development teams may fail to meet this requirement due to factors such as short deadlines or lack of domain knowledge. Chaos engineering encompasses techniques aimed at meeting resilience requirements. Chaos engineering can be used to achieve resilience against infrastructure failures, network failures, and application failures. == Operational readiness using chaos engineering == Calculating how much confidence we have in the interconnected complex systems that are put into production environments requires operational readiness metrics. Operational readiness can be evaluated using chaos engineering simulations. Solutions for increasing the resilience and operational readiness of a platform include strengthening the backup, restore, network file transfer, failover capabilities and overall security of the environment. An evaluation to induce chaos in a Kubernetes environment terminated random pods receiving data from edge devices in data centers while processing analytics on a big data network. The pods' recovery time was a resiliency metric that estimated the response time. == History == 1983 – Apple While MacWrite and MacPaint were being developed for the first Apple Macintosh computer, Steve Capps created "Monkey", a desk accessory which randomly generated user interface events at high speed, simulating a monkey frantically banging the keyboard and moving and clicking the mouse. It was promptly put to use for debugging by generating errors for programmers to fix, because automated testing was not possible; the first Macintosh had too little free memory space for anything more sophisticated. 1992 – Prologue While ABAL2 and SING were being developed for the first graphical versions of the PROLOGUE operating system, Iain James Marshall created "La Matraque", a desk accessory which randomly generated random sequences of both legal and invalid graphical interface events, at high speed, thus testing the critical edge behaviour of the underlying graphics libraries. This program would be launched prior to production delivery, for days on end, thus ensuring the required degree of total resilience. This tool was subsequently extended to include the Database and other File Access instructions of the ABAL language to check and ensure their subsequent resiliance. A variation, of this tool, is currently employed for the qualification of the modern day version known as OPENABAL. 2003 – Amazon While working to improve website reliability at Amazon, Jesse Robbins created "Game day", an initiative that increases reliability by purposefully creating major failures on a regular basis. Robbins has said it was inspired by firefighter training and research in other fields lessons in complex systems, reliability engineering. 2006 – Google While at Google, Kripa Krishnan created a similar program to Amazon's Game day (see above) called "DiRT". Jason Cahoon, a Site Reliability Engineer at Google, contributed a chapter on Google DiRT in the "Chaos Engineering" book and described the system at the GOTOpia 2021 conference. 2011 – Netflix While overseeing Netflix's migration to the cloud in 2011 Nora Jones, Casey Rosenthal, and Greg Orzell expanded the discipline while working together at Netflix by setting up a tool that would cause breakdowns in their production environment, the environment used by Netflix customers. The intent was to move from a development model that assumed no breakdowns to a model where breakdowns were considered to be inevitable, driving developers to consider built-in resilience to be an obligation rather than an option: "At Netflix, our culture of freedom and responsibility led us not to force engineers to design their code in a specific way. Instead, we discovered that we could align our teams around the notion of infrastructure resilience by isolating the problems created by server neutralization and pushing them to the extreme. We have created Chaos Monkey, a program that randomly chooses a server and disables it during its usual hours of activity. Some will find that crazy, but we could not depend on the random occurrence of an event to test our behavior in the face of the very consequences of this event. Knowing that this would happen frequently has created a strong alignment among engineers to build redundancy and process automation to survive such incidents, without impacting the millions of Netflix users. Chaos Monkey is one of our most effective tools to improve the quality of our services." By regularly "killing" random instances of a software service, it was possible to test a redundant architecture to verify that a server failure did not noticeably impact customers. The concept of chaos engineering is close to the one of Phoenix Servers, first introduced by Martin Fowler in 2012. == Chaos engineering tools == === Chaos Monkey === Chaos Monkey is a tool invented in 2011 by Netflix to test the resilience of its IT infrastructure. It works by intentionally disabling computers in Netflix's production network to test how the remaining systems respond to the outage. Chaos Monkey is now part of a larger suite of tools called the Simian Army designed to simulate and test responses to various system failures and edge cases. The code behind Chaos Monkey was released by Netflix in 2012 under an Apache 2.0 license. The name "Chaos Monkey" is explained in the book Chaos Monkeys by Antonio Garcia Martinez: Imagine a monkey entering a 'data center', these 'farms' of servers that host all the critical functions of our online activities. The monkey randomly rips cables, destroys devices and returns everything that passes by the hand [i.e. flings excrement]. The challenge for IT managers is to design the information system they are responsible for so that it can work despite these monkeys, which no one ever knows when they arrive and what they will destroy. ==== Simian Army ==== The Simian Army is a suite of tools developed by Netflix to test the reliability, security, or resilience of its Amazon Web Services infrastructure and includes the following tools: At the very top of the Simian Army hierarchy, Chaos Kong drops a full AWS "Region". Though rare, loss of an entire region does happen and Chaos Kong simulates a systems response and recovery to this type of event. Chaos Gorilla drops a full Amazon "Availability Zone" (one or more entire data centers serving a geographical region). === Other === Voyages-sncf.com's 2017 "Day of Chaos" gamified simulating pre-production failures to present at the 2017 DevOps REX conference. Founded in 2019, Steadybit popularized pre-production chaos and reliability engineering. Its open-source Reliability Hub extends Steadybit. Proofdock can inject infrastructure, platform, and application failures on Microsoft Azure DevOps. Gremlin is a "failure-as-a-service" platform. Facebook's Project Storm simulates datacenter failures for natural disaster resistance. == See also == Data redundancy Error detection and correction Fail-fast system Fail fast (business), a related subject in business management Fall back and forward Fault injection Fault tolerance Fault-tolerant computer system Grease (networking) Resilience (network) Robustness (computer science) Fuzzing == Notes and references == == External links == Principle of Chaos Engineering – The Chaos Engineering manifesto Chaos Engineering – Adrian Hornsby How Chaos Engineering Practices Will Help You Design Better Software – Mariano Calandra
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https://en.wikipedia.org/wiki/Chaos_engineering
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Civil engineering is a professional engineering discipline that deals with the design, construction, and maintenance of the physical and naturally built environment, including public works such as roads, bridges, canals, dams, airports, sewage systems, pipelines, structural components of buildings, and railways. Civil engineering is traditionally broken into a number of sub-disciplines. It is considered the second-oldest engineering discipline after military engineering, and it is defined to distinguish non-military engineering from military engineering. Civil engineering can take place in the public sector from municipal public works departments through to federal government agencies, and in the private sector from locally based firms to Fortune Global 500 companies. == History == === Civil engineering as a discipline === Civil engineering is the application of physical and scientific principles for solving the problems of society, and its history is intricately linked to advances in the understanding of physics and mathematics throughout history. Because civil engineering is a broad profession, including several specialized sub-disciplines, its history is linked to knowledge of structures, materials science, geography, geology, soils, hydrology, environmental science, mechanics, project management, and other fields. Throughout ancient and medieval history most architectural design and construction was carried out by artisans, such as stonemasons and carpenters, rising to the role of master builder. Knowledge was retained in guilds and seldom supplanted by advances. Structures, roads, and infrastructure that existed were repetitive, and increases in scale were incremental. One of the earliest examples of a scientific approach to physical and mathematical problems applicable to civil engineering is the work of Archimedes in the 3rd century BC, including Archimedes' principle, which underpins our understanding of buoyancy, and practical solutions such as Archimedes' screw. Brahmagupta, an Indian mathematician, used arithmetic in the 7th century AD, based on Hindu-Arabic numerals, for excavation (volume) computations. === Civil engineering profession === Engineering has been an aspect of life since the beginnings of human existence. The earliest practice of civil engineering may have commenced between 4000 and 2000 BC in ancient Egypt, the Indus Valley civilization, and Mesopotamia (ancient Iraq) when humans started to abandon a nomadic existence, creating a need for the construction of shelter. During this time, transportation became increasingly important leading to the development of the wheel and sailing. Until modern times there was no clear distinction between civil engineering and architecture, and the term engineer and architect were mainly geographical variations referring to the same occupation, and often used interchangeably. The constructions of pyramids in Egypt (c. 2700–2500 BC) constitute some of the first instances of large structure constructions in history. Other ancient historic civil engineering constructions include the Qanat water management system in modern-day Iran (the oldest is older than 3000 years and longer than 71 kilometres (44 mi)), the Parthenon by Iktinos in Ancient Greece (447–438 BC), the Appian Way by Roman engineers (c. 312 BC), the Great Wall of China by General Meng T'ien under orders from Ch'in Emperor Shih Huang Ti (c. 220 BC) and the stupas constructed in ancient Sri Lanka like the Jetavanaramaya and the extensive irrigation works in Anuradhapura. The Romans developed civil structures throughout their empire, including especially aqueducts, insulae, harbors, bridges, dams and roads. In the 18th century, the term civil engineering was coined to incorporate all things civilian as opposed to military engineering. In 1747, the first institution for the teaching of civil engineering, the École Nationale des Ponts et Chaussées, was established in France; and more examples followed in other European countries, like Spain. The first self-proclaimed civil engineer was John Smeaton, who constructed the Eddystone Lighthouse. In 1771 Smeaton and some of his colleagues formed the Smeatonian Society of Civil Engineers, a group of leaders of the profession who met informally over dinner. Though there was evidence of some technical meetings, it was little more than a social society. In 1818 the Institution of Civil Engineers was founded in London, and in 1820 the eminent engineer Thomas Telford became its first president. The institution received a Royal charter in 1828, formally recognising civil engineering as a profession. Its charter defined civil engineering as:the art of directing the great sources of power in nature for the use and convenience of man, as the means of production and of traffic in states, both for external and internal trade, as applied in the construction of roads, bridges, aqueducts, canals, river navigation and docks for internal intercourse and exchange, and in the construction of ports, harbours, moles, breakwaters and lighthouses, and in the art of navigation by artificial power for the purposes of commerce, and in the construction and application of machinery, and in the drainage of cities and towns. === Civil engineering education === The first private college to teach civil engineering in the United States was Norwich University, founded in 1819 by Captain Alden Partridge. The first degree in civil engineering in the United States was awarded by Rensselaer Polytechnic Institute in 1835. The first such degree to be awarded to a woman was granted by Cornell University to Nora Stanton Blatch in 1905. In the UK during the early 19th century, the division between civil engineering and military engineering (served by the Royal Military Academy, Woolwich), coupled with the demands of the Industrial Revolution, spawned new engineering education initiatives: the Class of Civil Engineering and Mining was founded at King's College London in 1838, mainly as a response to the growth of the railway system and the need for more qualified engineers, the private College for Civil Engineers in Putney was established in 1839, and the UK's first Chair of Engineering was established at the University of Glasgow in 1840. == Education == Civil engineers typically possess an academic degree in civil engineering. The length of study is three to five years, and the completed degree is designated as a bachelor of technology, or a bachelor of engineering. The curriculum generally includes classes in physics, mathematics, project management, design and specific topics in civil engineering. After taking basic courses in most sub-disciplines of civil engineering, they move on to specialize in one or more sub-disciplines at advanced levels. While an undergraduate degree (BEng/BSc) normally provides successful students with industry-accredited qualifications, some academic institutions offer post-graduate degrees (MEng/MSc), which allow students to further specialize in their particular area of interest. == Practicing engineers == In most countries, a bachelor's degree in engineering represents the first step towards professional certification, and a professional body certifies the degree program. After completing a certified degree program, the engineer must satisfy a range of requirements including work experience and exam requirements before being certified. Once certified, the engineer is designated as a professional engineer (in the United States, Canada and South Africa), a chartered engineer (in most Commonwealth countries), a chartered professional engineer (in Australia and New Zealand), or a European engineer (in most countries of the European Union). There are international agreements between relevant professional bodies to allow engineers to practice across national borders. The benefits of certification vary depending upon location. For example, in the United States and Canada, "only a licensed professional engineer may prepare, sign and seal, and submit engineering plans and drawings to a public authority for approval, or seal engineering work for public and private clients." This requirement is enforced under provincial law such as the Engineers Act in Quebec. No such legislation has been enacted in other countries including the United Kingdom. In Australia, state licensing of engineers is limited to the state of Queensland. Almost all certifying bodies maintain a code of ethics which all members must abide by. Engineers must obey contract law in their contractual relationships with other parties. In cases where an engineer's work fails, they may be subject to the law of tort of negligence, and in extreme cases, criminal charges. An engineer's work must also comply with numerous other rules and regulations such as building codes and environmental law. == Sub-disciplines == There are a number of sub-disciplines within the broad field of civil engineering. General civil engineers work closely with surveyors and specialized civil engineers to design grading, drainage, pavement, water supply, sewer service, dams, electric and communications supply. General civil engineering is also referred to as site engineering, a branch of civil engineering that primarily focuses on converting a tract of land from one usage to another. Site engineers spend time visiting project sites, meeting with stakeholders, and preparing construction plans. Civil engineers apply the principles of geotechnical engineering, structural engineering, environmental engineering, transportation engineering and construction engineering to residential, commercial, industrial and public works projects of all sizes and levels of construction. === Coastal engineering === Coastal engineering is concerned with managing coastal areas. In some jurisdictions, the terms sea defense and coastal protection mean defense against flooding and erosion, respectively. Coastal defense is the more traditional term, but coastal management has become popular as well. === Construction engineering === Construction engineering involves planning and execution, transportation of materials, and site development based on hydraulic, environmental, structural, and geotechnical engineering. As construction firms tend to have higher business risk than other types of civil engineering firms, construction engineers often engage in more business-like transactions, such as drafting and reviewing contracts, evaluating logistical operations, and monitoring supply prices. === Earthquake engineering === Earthquake engineering involves designing structures to withstand hazardous earthquake exposures. Earthquake engineering is a sub-discipline of structural engineering. The main objectives of earthquake engineering are to understand interaction of structures on the shaky ground; foresee the consequences of possible earthquakes; and design, construct and maintain structures to perform at earthquake in compliance with building codes. === Environmental engineering === Environmental engineering is the contemporary term for sanitary engineering, though sanitary engineering traditionally had not included much of the hazardous waste management and environmental remediation work covered by environmental engineering. Public health engineering and environmental health engineering are other terms being used. Environmental engineering deals with treatment of chemical, biological, or thermal wastes, purification of water and air, and remediation of contaminated sites after waste disposal or accidental contamination. Among the topics covered by environmental engineering are pollutant transport, water purification, waste water treatment, air pollution, solid waste treatment, recycling, and hazardous waste management. Environmental engineers administer pollution reduction, green engineering, and industrial ecology. Environmental engineers also compile information on environmental consequences of proposed actions. === Forensic engineering === Forensic engineering is the investigation of materials, products, structures or components that fail or do not operate or function as intended, causing personal injury or damage to property. The consequences of failure are dealt with by the law of product liability. The field also deals with retracing processes and procedures leading to accidents in operation of vehicles or machinery. The subject is applied most commonly in civil law cases, although it may be of use in criminal law cases. Generally the purpose of a Forensic engineering investigation is to locate cause or causes of failure with a view to improve performance or life of a component, or to assist a court in determining the facts of an accident. It can also involve investigation of intellectual property claims, especially patents. === Geotechnical engineering === Geotechnical engineering studies rock and soil supporting civil engineering systems. Knowledge from the field of soil science, materials science, mechanics, and hydraulics is applied to safely and economically design foundations, retaining walls, and other structures. Environmental efforts to protect groundwater and safely maintain landfills have spawned a new area of research called geo-environmental engineering. Identification of soil properties presents challenges to geotechnical engineers. Boundary conditions are often well defined in other branches of civil engineering, but unlike steel or concrete, the material properties and behavior of soil are difficult to predict due to its variability and limitation on investigation. Furthermore, soil exhibits nonlinear (stress-dependent) strength, stiffness, and dilatancy (volume change associated with application of shear stress), making studying soil mechanics all the more difficult. Geotechnical engineers frequently work with professional geologists, Geological Engineering professionals and soil scientists. === Materials science and engineering === Materials science is closely related to civil engineering. It studies fundamental characteristics of materials, and deals with ceramics such as concrete and mix asphalt concrete, strong metals such as aluminum and steel, and thermosetting polymers including polymethylmethacrylate (PMMA) and carbon fibers. Materials engineering involves protection and prevention (paints and finishes). Alloying combines two types of metals to produce another metal with desired properties. It incorporates elements of applied physics and chemistry. With recent media attention on nanoscience and nanotechnology, materials engineering has been at the forefront of academic research. It is also an important part of forensic engineering and failure analysis. === Site development and planning === Site development, also known as site planning, is focused on the planning and development potential of a site as well as addressing possible impacts from permitting issues and environmental challenges. === Structural engineering === Structural engineering is concerned with the structural design and structural analysis of buildings, bridges, towers, flyovers (overpasses), tunnels, off shore structures like oil and gas fields in the sea, aerostructure and other structures. This involves identifying the loads which act upon a structure and the forces and stresses which arise within that structure due to those loads, and then designing the structure to successfully support and resist those loads. The loads can be self weight of the structures, other dead load, live loads, moving (wheel) load, wind load, earthquake load, load from temperature change etc. The structural engineer must design structures to be safe for their users and to successfully fulfill the function they are designed for (to be serviceable). Due to the nature of some loading conditions, sub-disciplines within structural engineering have emerged, including wind engineering and earthquake engineering. Design considerations will include strength, stiffness, and stability of the structure when subjected to loads which may be static, such as furniture or self-weight, or dynamic, such as wind, seismic, crowd or vehicle loads, or transitory, such as temporary construction loads or impact. Other considerations include cost, constructibility, safety, aesthetics and sustainability. === Surveying === Surveying is the process by which a surveyor measures certain dimensions that occur on or near the surface of the Earth. Surveying equipment such as levels and theodolites are used for accurate measurement of angular deviation, horizontal, vertical and slope distances. With computerization, electronic distance measurement (EDM), total stations, GPS surveying and laser scanning have to a large extent supplanted traditional instruments. Data collected by survey measurement is converted into a graphical representation of the Earth's surface in the form of a map. This information is then used by civil engineers, contractors and realtors to design from, build on, and trade, respectively. Elements of a structure must be sized and positioned in relation to each other and to site boundaries and adjacent structures. Although surveying is a distinct profession with separate qualifications and licensing arrangements, civil engineers are trained in the basics of surveying and mapping, as well as geographic information systems. Surveyors also lay out the routes of railways, tramway tracks, highways, roads, pipelines and streets as well as position other infrastructure, such as harbors, before construction. Land surveying In the United States, Canada, the United Kingdom and most Commonwealth countries land surveying is considered to be a separate and distinct profession. Land surveyors are not considered to be engineers, and have their own professional associations and licensing requirements. The services of a licensed land surveyor are generally required for boundary surveys (to establish the boundaries of a parcel using its legal description) and subdivision plans (a plot or map based on a survey of a parcel of land, with boundary lines drawn inside the larger parcel to indicate the creation of new boundary lines and roads), both of which are generally referred to as Cadastral surveying. They collect data on important geological features below and on the land. Construction surveying Construction surveying is generally performed by specialized technicians. Unlike land surveyors, the resulting plan does not have legal status. Construction surveyors perform the following tasks: Surveying existing conditions of the future work site, including topography, existing buildings and infrastructure, and underground infrastructure when possible; "lay-out" or "setting-out": placing reference points and markers that will guide the construction of new structures such as roads or buildings; Verifying the location of structures during construction; As-Built surveying: a survey conducted at the end of the construction project to verify that the work authorized was completed to the specifications set on plans. === Transportation engineering === Transportation engineering is concerned with moving people and goods efficiently, safely, and in a manner conducive to a vibrant community. This involves specifying, designing, constructing, and maintaining transportation infrastructure which includes streets, canals, highways, rail systems, airports, ports, and mass transit. It includes areas such as transportation design, transportation planning, traffic engineering, some aspects of urban engineering, queueing theory, pavement engineering, Intelligent Transportation System (ITS), and infrastructure management. === Municipal or urban engineering === Municipal engineering is concerned with municipal infrastructure. This involves specifying, designing, constructing, and maintaining streets, sidewalks, water supply networks, sewers, street lighting, municipal solid waste management and disposal, storage depots for various bulk materials used for maintenance and public works (salt, sand, etc.), public parks and cycling infrastructure. In the case of underground utility networks, it may also include the civil portion (conduits and access chambers) of the local distribution networks of electrical and telecommunications services. It can also include the optimization of waste collection and bus service networks. Some of these disciplines overlap with other civil engineering specialties, however municipal engineering focuses on the coordination of these infrastructure networks and services, as they are often built simultaneously, and managed by the same municipal authority. Municipal engineers may also design the site civil works for large buildings, industrial plants or campuses (i.e. access roads, parking lots, potable water supply, treatment or pretreatment of waste water, site drainage, etc.) === Water resources engineering === Water resources engineering is concerned with the collection and management of water (as a natural resource). As a discipline, it therefore combines elements of hydrology, environmental science, meteorology, conservation, and resource management. This area of civil engineering relates to the prediction and management of both the quality and the quantity of water in both underground (aquifers) and above ground (lakes, rivers, and streams) resources. Water resource engineers analyze and model very small to very large areas of the earth to predict the amount and content of water as it flows into, through, or out of a facility. However, the actual design of the facility may be left to other engineers. Hydraulic engineering concerns the flow and conveyance of fluids, principally water. This area of civil engineering is intimately related to the design of pipelines, water supply network, drainage facilities (including bridges, dams, channels, culverts, levees, storm sewers), and canals. Hydraulic engineers design these facilities using the concepts of fluid pressure, fluid statics, fluid dynamics, and hydraulics, among others. === Civil engineering systems === Civil engineering systems is a discipline that promotes using systems thinking to manage complexity and change in civil engineering within its broader public context. It posits that the proper development of civil engineering infrastructure requires a holistic, coherent understanding of the relationships between all of the crucial factors that contribute to successful projects while at the same time emphasizing the importance of attention to technical detail. Its purpose is to help integrate the entire civil engineering project life cycle from conception, through planning, designing, making, operating to decommissioning. == See also == === Associations === == References == == Further reading == Blockley, David (2014). Structural Engineering: a very short introduction. New York: Oxford University Press. ISBN 978-0-19-967193-9. Chen, W.F.; Liew, J.Y. Richard, eds. (2002). The Civil Engineering Handbook. CRC Press. ISBN 978-0-8493-0958-8. Muir Wood, David (2012). Civil Engineering: a very short introduction. New York: Oxford University Press. ISBN 978-0-19-957863-4. Ricketts, Jonathan T.; Loftin, M. Kent; Merritt, Frederick S., eds. (2004). Standard handbook for civil engineers (5 ed.). McGraw Hill. ISBN 978-0-07-136473-7. == External links == The Institution of Civil Engineers Civil Engineering Software Database The Institution of Civil Engineering Surveyors Civil engineering classes, from MIT OpenCourseWare
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Surface engineering is the sub-discipline of materials science which deals with the surface of solid matter. It has applications to chemistry, mechanical engineering, and electrical engineering (particularly in relation to semiconductor manufacturing). Solids are composed of a bulk material covered by a surface. The surface which bounds the bulk material is called the surface phase. It acts as an interface to the surrounding environment. The bulk material in a solid is called the bulk phase. The surface phase of a solid interacts with the surrounding environment. This interaction can degrade the surface phase over time. Environmental degradation of the surface phase over time can be caused by wear, corrosion, fatigue and creep. Surface engineering involves altering the properties of the surface phase in order to reduce the degradation over time. This is accomplished by making the surface robust to the environment in which it will be used. It provides a cost-effective material for robust design. A spectrum of topics that represent the diverse nature of the field of surface engineering includes plating technologies, nano and emerging technologies and surface engineering, characterization and testing. == Applications == Surface engineering techniques are being used in the automotive, aerospace, missile, power, electronic, biomedical, textile, petroleum, petrochemical, chemical, steel, cement, machine tools and construction industries including road surfacing. Surface engineering techniques can be used to develop a wide range of functional properties, including physical, chemical, electrical, electronic, magnetic, mechanical, wear-resistant and corrosion-resistant properties at the required substrate surfaces. Almost all types of materials, including metals, ceramics, polymers, and composites can be coated on similar or dissimilar materials. It is also possible to form coatings of newer materials (e.g., met glass. beta-C3N4), graded deposits, multi-component deposits etc. The advanced materials and deposition processes including recent developments in ultra hard materials like BAM (AlMgB compound)are fully covered in a recent book[R. Chattopadhyay:Green Tribology,Green Surface Engineering and Global Warming,ASM International,USA,2014] In 1995, surface engineering was a £10 billion market in the United Kingdom. Coatings, to make surface life robust from wear and corrosion, was approximately half the market. In recent years, there has been a paradigm shift in surface engineering from age-old electroplating to processes such as vapor phase deposition, diffusion, thermal spray & welding using heat sources, such as, laser,plasma,solar beam.microwave;friction.pulsed combustion. ion, electron pulsed arc, spark, friction and induction.[Ref:R.Chattopadhyay:Advanced Thermally Assisted Surface Engineering Processes,Springer, New York, USA,2004] It is estimated that loss due to wear and corrosion in the US is approximately $500 billion. In the US, there are around 9524 establishments (including automotive, aircraft, power and construction industries) who depend on engineered surfaces with support from 23,466 industries. There are around 65 academic institutions world-wide engaged in surface engineering research and education. == Surface cleaning techniques == Surface cleaning, synonymously referred to as dry cleaning, is a mechanical cleaning technique used to reduce superficial soil, dust, grime, insect droppings, accretions, or other surface deposits. (Dry cleaning, as the term is used in paper conservation, does not employ the use of organic solvents.) Surface cleaning may be used as an independent cleaning technique, as one step (usually the first) in a more comprehensive treatment, or as a prelude to further treatments (e.g., aqueous immersion) which may cause dirt to set irreversibly in paper fibers. == Purpose == The purpose of surface cleaning is to reduce the potential for damage to paper artifacts by removing foreign material which can be abrasive, acidic, hygroscopic, or degradative. The decision to remove surface dirt is also for aesthetic reasons when it interferes with the visibility of the imagery or information. A decision must be made balancing the probable care of each object against the possible problems related to surface cleaning. == Environmental benefits == The application of surface engineering to components leads to improved lifetime (e.g., by corrosion resistance) and improved efficiency (e.g., by reducing friction) which directly reduces the emissions corresponding to those components. Applying innovative surface engineering technologies to the energy sector has the potential of reducing annual CO2-eq emissions by up to 1.8 Gt in 2050 and 3.4 Gt in 2100. This corresponds to 7% and 8.5% annual reduction in the energy sector in 2050 and 2100, respectively. Despite those benefits, a major environmental drawback is the dissipative losses occurring throughout the life cycle of the components, and the associated environmental impacts of them. In thermal spray surface engineering applications, the majority of those dissipative losses occur at the coating stage (up to 39%), where part of the sprayed powders do not adhere to the substrate. == See also == Energetically modified cement – Class of cements, mechanically processed to transform reactivity Surface finishing – Range of processes that alter the surface of an item to achieve a certain property Surface science – Study of physical and chemical phenomena that occur at the interface of two phases Surface metrology – Measurement of small-scale features on surfaces Tribology – Science of rubbing surfaces == References == R. Chattopadhyay, ’Advanced Thermally Assisted Surface Engineering Processes’ Kluwer Academic Publishers, MA, US (now Springer, NY), 2004, ISBN 1-4020-7696-7, E-ISBN 1-4020-7764-5. R. Chattopadhyay, ’Surface Wear- Analysis, Treatment, & Prevention’, ASM-International, Materials Park, OH, US, 2001, ISBN 0-87170-702-0. Sanjay Kumar Thakur and R. Gopal Krishnan, ’Advances in Applied Surface Engineering’, Research Publishing Services, Singapore, 2011, ISBN 978-981-08-7922-8. == External links == Institute of Surface Chemistry and Catalysis Ulm University
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The study of Engineering Economics in Civil Engineering, also known generally as engineering economics, or alternatively engineering economy, is a subset of economics, more specifically, microeconomics. It is defined as a "guide for the economic selection among technically feasible alternatives for the purpose of a rational allocation of scarce resources." Its goal is to guide entities, private or public, that are confronted with the fundamental problem of economics. This fundamental problem of economics consists of two fundamental questions that must be answered, namely what objectives should be investigated or explored and how should these be achieved? Economics as a social science answers those questions and is defined as the knowledge used for selecting among "...technically feasible alternatives for the purpose of a rational allocation of scarce resources." Correspondingly, all problems involving "...profit-maximizing or cost-minimizing are engineering problems with economic objectives and are properly described by the label "engineering economy". As a subdiscipline practiced by civil engineers, engineering economics narrows the definition of the fundamental economic problem and related questions to that of problems related to the investment of capital, public or private in a broad array of infrastructure projects. Civil engineers confront more specialized forms of the fundamental problem in the form of inadequate economic evaluation of engineering projects. Civil engineers under constant pressure to deliver infrastructure effectively and efficiently confront complex problems associated with allocating scarce resources for ensuring quality, mitigating risk and controlling project delivery. Civil engineers must be educated to recognize the role played by engineering economics as part of the evaluations occurring at each phase in the project lifecycle. Thus, the application of engineering economics in the practice of civil engineering focuses on the decision-making process, its context, and environment in project execution and delivery. It is pragmatic by nature, integrating microeconomic theory with civil engineering practice but, it is also a simplified application of economic theory in that it avoids a number of microeconomic concepts such as price determination, competition and supply and demand. This poses new, underlying economic problems of resource allocation for civil engineers in delivering infrastructure projects and specifically, resources for project management, planning and control functions. Civil engineers address these fundamental economic problems using specialized engineering economics knowledge as a framework for continuously "... probing economic feasibility...using a stage-wise approach..." throughout the project lifecycle. The application of this specialized civil engineering knowledge can be in the form of engineering analyses of life-cycle cost, cost accounting, cost of capital and the economic feasibility of engineering solutions for design, construction and project management. The civil engineer must have the ability to use engineering economy methodologies for the "formulation of objectives, specification of alternatives, prediction of outcomes" and estimation of minimum acceptability for investment and optimization. They must also be capable of integrating these economic considerations into appropriate engineering solutions and management plans that predictably and reliably meet project stakeholder expectations in a sustainable manner. The civil engineering profession provides a special function in our society and economy where investing substantial sums of funding in public infrastructure requires "...some assurance that it will perform its intended function." Thus, the civil engineer exercising their professional judgment in making decisions about fundamental problems relies upon the profession's knowledge of engineering economics to provide "the practical certainty" that makes the social investment in public infrastructure feasible. == Course of Instruction == Historically, coursework and curricula in engineering economics for civil engineers has focused on capital budgeting: "...when to replace capital equipment, and which of several alternative investments to make. == Journals == The Engineering Economist - published jointly by the Engineering Economy Division of the American Society of Engineering Education (ASEE) and the Institute of Industrial and Systems Engineers (IISE). It publishes "...original research, current practice, and teaching involving problems of capital investment." == See also == American Society of Civil Engineers Cost–benefit analysis Social discount rate == Further reading == On materials specific to civil engineering: Wellington, A. M. (1877).The Economic Theory of the Location of Railways. Accessed at [3] and revised through six editions with the last published in 1914 by Wellington's wife, Agnes Wellington. Accessed at [4] Gotshall, William C. (1903) Notes on electric railway economics and preliminary engineering. McGraw Publishing Company. Accessed at [5] Hayford, John F. (1917) The relation of engineering to economics. Journal of Political Economy 25.1 : 59–63. Accessed at [6] Waddell, J. A. L. (1917). Engineering economics. Lawrence: University of Kansas. Accessed at [7] Waddell, J. A. L. (1921) Economics of Bridgework: A Sequel to Bridge Engineering. J. Wiley & Sons, Incorporated. Accessed at [8] Fish, J. C. L. (1923). Engineering economics: First-principles. New York: McGraw-Hill. Accessed at [9] Grant, Eugene L. (1930) Principles of Engineering Economy, Accessed at [10] Burnham, T. H., & Hoskins, G. O. (1958). Engineering economics, by T.H. Burnham and G.O. Hoskins. London, Pitman. Accessed at [11]. Barish, Norman N, (1962) Economic analysis for engineering and managerial decision making, Accessed at [12] Anon., (1963) Engineering economy, Engineering Dept, American Telephone and Telegraph Company. Accessed at [13]. Sepulveda, Jose A. and Souder, William E. (1984) Schaum's Outline of Engineering Economics. McGraw-Hill Companies. Accessed at [14] Newnan, Donald G., et al. (1998) Engineering economic analysis. 7th ed. Accessed at [15] For more generalized discussion: Jaffe, William J. L. P. Alford and the Evolution of Modern Industrial Management. New York: 1957 Nelson, Daniel. Frederick W. Taylor and the Rise of Scientific Management. Madison: University of Wisconsin Press, 1980. Noble, David F. America by Design: Science, Technology, and the Rise of Corporate Capitalism. New York: Alfred A. Knopf, 1977. == External links == Benefit-Cost Analysis Center at the University of Washington's Daniel J. Evans School of Public Affairs Benefit-Cost Analysis Archived 18 January 2022 at the Wayback Machine site maintained by the Transportation Economics Committee of the Transportation Research Board(TRB). == References ==
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Tsinghua University (THU) is a public university in Haidian, Beijing, China. It is affiliated with and funded by the Ministry of Education of China. The university is part of Project 211, Project 985, and the Double First-Class Construction. It is also a member in the C9 League. Tsinghua University's campus is in northwest Beijing, on the site of the former imperial gardens of the Qing dynasty. The university has 21 schools and 59 departments, with faculties in science, engineering, humanities, law, medicine, history, philosophy, economics, management, education, and art. == History == === Early 20th century (1911–1949) === Tsinghua University was established in Beijing during a tumultuous period of national upheaval and conflicts with foreign powers which culminated in the Boxer Rebellion, an uprising against foreign influence in China. After the suppression of the revolt by a foreign alliance including the United States, the ruling Qing dynasty was required to pay indemnities to alliance members. United States Secretary of State John Hay suggested that the US$30 million Boxer indemnity allotted to the United States was excessive. After much negotiation with Qing ambassador Liang Cheng, president of the United States Theodore Roosevelt obtained approval from the United States Congress in 1909 to reduce the indemnity payment by US$10.8 million, on the condition that the funds would be used as scholarships for Chinese students to study in the United States. Using this fund, the Tsinghua College (清華學堂; Qīnghuá Xuétáng) was established in Beijing, on 29 April 1911 on the site of a former royal garden to serve as a preparatory school for students the government planned to send to the United States. Faculty members for sciences were recruited by the YMCA from the United States, and its graduates transferred directly to American schools as juniors upon graduation. The motto of Tsinghua, "Self-Discipline and Social Commitment", was derived from a 1914 speech by prominent scholar and faculty member Liang Qichao, in which he quoted the I Ching to describe a notion of the ideal gentleman. In 1925, the school established its own four-year undergraduate program and started a research institute on Chinese studies. In 1928, the school changed its name to National Tsinghua University. During the Second Sino-Japanese War, many Chinese universities were forced to evacuate their campuses to avoid the Japanese invasion. In 1937, Tsinghua University, Peking University and Nankai University merged to form the Changsha Temporary University, located in Changsha, Hunan. The merged university later became the National Southwestern Associated University, located in Kunming, Yunnan. The Tsinghua University section of the merged university returned to Beijing at the end of World War II. === Later 20th century (post-1949) === After the end of the Chinese Civil War in 1949, China experienced a communist revolution leading to the creation of the People's Republic of China. Tsinghua University's then president Mei Yiqi, along with many professors, fled to Taiwan with the retreating Nationalist government. They established the National Tsing Hua Institute of Nuclear Technology in 1955, which later became the National Tsing Hua University in Taiwan, an institution independent and distinct from Tsinghua University. In 1952, the Chinese Communist Party regrouped the country's higher education institutions in an attempt to build a Soviet style system where each institution specialized in a certain field of study, such as social sciences or natural sciences. Tsinghua University was streamlined into a polytechnic institute with a focus on engineering and the natural sciences. In 1953, Tsinghua established a political counselor program, becoming the first university to do so following the Ministry of Education's 1952 directive to begin piloting such programs.: 107 As political counselors, new graduates who were also Communist Party members worked as political counselors in managing the student body and student organizations, often simultaneously serving as Communist Youth League secretaries.: 107 The program was later expanded to other universities following its endorsement by Deng Xiaoping and became further institutionalized across China in the 1990s and 2000s.: 108 During the Third Front construction, Tsinghua established a branch in Mianyang, Sichuan province. In 1966, the efforts of Tsinghua researchers were critical in China's transition from vacuum-tube computers to fully transistorized computers.: 101 From 1966 to 1976, China experienced immense sociopolitical upheaval and instability during the Cultural Revolution. Many university students walked out of classrooms at Tsinghua and other institutions, and some went on to join the Red Guards, resulting in the complete shutdown of the university as faculty were persecuted or otherwise unable to teach. It was not until 1978, after the Cultural Revolution ended, that the university began to take in students and re-emerge as a force in Chinese politics and society. During the Criticize Lin, Criticize Confucius campaign of 1973 to 1976, critique groups formed at Tsinghua and Peking University disseminated commentaries under the pseudonym of "Liang Xiao". The pseudonym sounds like a person's name but is a homophone for "two schools". In the 1980s, Tsinghua evolved beyond the polytechnic model and incorporated a multidisciplinary system emphasizing collaboration between distinct schools within the broader university environment. Under this system, several schools have been re-incorporated, including Tsinghua Law School, the School of Economics and Management, the School of Sciences, the School of Life Sciences, the School of Humanities and Social Sciences, the School of Public Policy and Management, and the Academy of Arts and Design. In 1996, the School of Economics and Management established a partnership with the Sloan School of Management at the Massachusetts Institute of Technology. One year later, Tsinghua and MIT began the MBA program known as the Tsinghua-MIT Global MBA. In 1998, Tsinghua became the first Chinese university to offer a Master of Laws (LLM) program in American law, through a cooperative venture with the Temple University Beasley School of Law. === 21st century === Tsinghua alumni include the current General Secretary of the Chinese Communist Party and paramount leader of China, Xi Jinping '79, who graduated with a degree in chemical engineering, along with the CCP General Secretary and former Paramount Leader of China Hu Jintao '64, who graduated with a degree in hydraulic engineering. In addition to its powerful alumni, Tsinghua has a reputation for hosting globally prominent guest speakers, with international leaders Bill Clinton, Tony Blair, Henry Kissinger, Carlos Ghosn, and Henry Paulson having lectured to the university community. As of 2018, Tsinghua University consists of 20 schools and 58 university departments, 41 research institutes, 35 research centers, and 167 laboratories, including 15 national key laboratories. In September 2006, the Peking Union Medical College, a renowned medical school, was renamed "Peking Union Medical College, Tsinghua University" although it and Tsinghua University are technically separate institutions. The university operates the Tsinghua University Press, which publishes academic journals, textbooks, and other scholarly works.Through its constituent colleges, graduate and professional schools, and other institutes, Tsinghua University offers more than 82 bachelor's degree programs, 80 master's degree programs and 90 PhD programs. In 2014, Tsinghua established Xinya College, a residential liberal arts college, as a pilot project to reform undergraduate education at the university. Modeled after universities in the United States and Europe, Xinya combines general and professional education in a liberal arts tradition, featuring a core curriculum of Chinese and Western literature and civilization studies and required courses in physical education and foreign languages. Furthermore, while most Tsinghua undergraduates must choose a specific major upon entrance, Xinya students declare their majors at the end of freshman year, enabling them to explore several different fields of study. In December 2014, Tsinghua University established the Advisory Committee of Undergraduate Curriculum (ACUC). It became the first student autonomous organization in mainland China for students to participate in the school's management. The Tsinghua University Academic Committee, which was formally established on 8 July 2015, has stipulated in the committee's charter that students should be consulted through the ACUC for resolutions involving undergraduate students. From then on, Tsinghua commenced a new round of academic reform lasting ever since, including establishing GPA grading system, adding the writing classes, critical thinking classes, second foreign languages classes into curriculum, requiring undergrads to be able to swim before graduation, cooperating with the Peking University on class cross-registration to supplement each other's general education curriculum, reducing fees on class withdraw, transcripts and certificates, and adjusting the graduate school co-terminal admission policies. In 2016, Schwarzman Scholars was established with almost US$400 million endowment by Steven Schwarzman, the chairman and CEO of the Blackstone Group and other multinational corporations and global leaders. Schwarzman Scholars annually selects 100–200 scholars across the world to enroll in a one-year fully-funded master's degree leadership program designed to cultivate the next generation of global leaders. 40% students are selected from the United States, 20% students are selected from China, 40% are selected from rest of the world. These scholars reside on the university campus at Schwarzman College, a residential college built specifically for the program. In 2016, Tsinghua's expenditures were RMB 13.7 billion (US$3.57 billion at purchasing power parity), the largest budget of any university in China. According to a 2018 Financial Times report, Tsinghua University has been linked to cyber-espionage. In 2024, Tsinghua announced that its office of the university president had merged into the university's Chinese Communist Party committee, which would directly administer the university henceforth. == Academics == Tsinghua University engages in extensive research and offers 51 bachelor's degree programs, 139 master's degree programs, and 107 doctoral programs through 20 colleges and 57 departments covering a broad range of subjects, including science, engineering, arts and literature, social sciences, law, medicine. Along with its membership in the C9 League, Tsinghua University affiliations include the Association of Pacific Rim Universities, a group of 50 leading Asian and American universities, Washington University in St. Louis's McDonnell International Scholars Academy, a group of 35 premier global universities, and the Association of East Asian Research Universities, a 17-member research collaboration network of top regional institutions. Tsinghua is an associate member of the Consortium Linking Universities of Science and Technology for Education and Research (CLUSTER). Tsinghua is a member of a Low Carbon Energy University Alliance (LCEUA), together with the University of Cambridge and the Massachusetts Institute of Technology (MIT). === Admissions === Admission to Tsinghua for both undergraduate and graduate schools is extremely competitive. Undergraduate admissions for domestic students is decided through the gaokao, the Chinese national college entrance exam, which allows students to list Tsinghua University among their preferred college choices. While selectivity varies by province, the sheer number of high school students applying for college each year has resulted in overall acceptance rates far lower than 0.1% of all test takers. Admission to Tsinghua's graduate schools is also very competitive. Only about 16% of MBA applicants are admitted each year. === Research === Research at Tsinghua University is mainly supported by government funding from national programs and special projects. In the areas of science and technology, funding from these sources totals over 20 billion yuan, which subsidizes more than 1,400 projects every year conducted by the university. With the prospective increase of state investment in science and technology, research at Tsinghua is projected to receive more financial support from the state. In 2007, Tsinghua was granted security clearance to conduct classified research of military interest. Each year, the university hosts the Intellectual Property Summer Institute in cooperation with Franklin Pierce Law Center of Concord, New Hampshire. The scientific research institutions in Tsinghua University are divided into three categories, including government-approved institutions, institutions independently established by the university and institutions jointly established by the university and independent legal entities outside the university. As of 31 December 2022, Tsinghua University has 428 university-level scientific research institutions in operation. === Rankings and reputation === ==== General ranking ==== Tsinghua University ranked No. 1 in China, the whole of Asia-Oceania region and emerging countries according to the Times Higher Education, with its industry income, research, and teaching performance indicator placed at 1st, 4th and 9th respectively in the world. Internationally, Tsinghua was regarded as the most reputable Chinese university by the Times Higher Education World Reputation Rankings where, it has ranked 8th globally and 1st in the Asia-Pacific. Tsinghua University ranked 10 among Global Innovative Universities according to the World's Universities with Real Impact (WURI) 2020 ranking released by United Nations Institute for Training and Research (UNITAR). Since 2013, Tsinghua also topped the newly created regional QS BRICS University Rankings. Tsinghua graduates are highly desired worldwide; in the QS Graduate Employability Rankings 2017, Tsinghua was ranked 3rd in the world and 1st in the whole of Afro-Eurasia & Oceania region. In 2020, Tsinghua was ranked 15th in the world by QS World University Rankings, and ranked 6th globally and 1st in Asia in the QS Graduate Employability Rankings. As of 2023, the Academic Ranking of World Universities, also known as the "Shanghai Ranking", placed Tsinghua University 22nd in the world and 1st in Asia & Oceania region. The U.S. News & World Report ranked Tsinghua at 1st in the Asia-Pacific and 16th globally in its 2024-2025 Best Global Universities Rankings. Tsinghua was the best-ranked university in the Asia-Pacific and the 17th worldwide in 2023 in terms of aggregate performance (THE+ARWU+QS) as reported by the Aggregate Ranking of Top Universities. ==== Research performance ==== As of 2021, it ranked 3rd among the universities around the world by SCImago Institutions Rankings. The Nature Index 2022 Annual Tables by Nature Research ranked Tsinghua 7th among the leading universities globally for the high quality of research publications in natural science. For sciences in general, the 2023 CWTS Leiden Ranking ranked Tsinghua University 3rd in the world after Harvard and Stanford based on the number of their scientific publications belonging to the top 1% in their fields. In November 2024, Clarivate Analytics ranked Tsinghua second in Afro-Eurasia & Oceania regions after Chinese Academy of Sciences (CAS) and 4th in the world after (CAS, Harvard, and Stanford) for most cited researchers. ==== Subjects rankings ==== As of 2021, it ranked 6th globally in "Education", 7th in "Clinical, pre-clinical and Health", 11th in "Business and Economics", 12th in "Computer Science", 13th in "Life Science", 17th in "Engineering and Technology", 18th in "Physical Science", 33th in "Social Science", 37th in "Law", and 40th in "Arts and Humanities" by the Times Higher Education Rankings by Subjects, which are historical strengths for Tsinghua. Since 2015, Tsinghua University has overtaken the Massachusetts Institute of Technology to top the list of Best Global Universities for Engineering published by the U.S. News & World Report and as of 2024, it also ranked number one globally in 9 subjects: "Artificial Intelligence", "Chemical Engineering", "Chemistry", "Computer Science", "Energy and Fuels", "Engineering", "Environment Engineering", "Environment/Ecology" and "Material Science". As of 2024, the U.S. News & World Report also placed "Civil Engineering", "Condensed Matter Physics", "Electrical and Electronic Engineering", "Geosciences", "Green and Sustainable Science and Technology", "Mechanical Engineering", "Meteorology and Atmospheric Sciences", "Nanoscience and Nanotechnology", "Optics", "Physical Chemistry", "Physics" and "Water Resources" at Tsinghua in the global Top 10 universities. In the ARWU's Global Ranking of Academic Subjects 2020, Tsinghua ranks in the world's top five universities in "Telecommunication Engineering", "Instruments Science & Technology", "Civil Engineering", "Chemical Engineering", "Mechanical Engineering", "Nanoscience & Nanotechnology", "Energy Science & Engineering", and "Transportation Science & Technology" and falls within the global top 10 for "Electrical & Electronic Engineering", "Computer Science & Engineering", "Materials Science & Engineering", "Environmental Science & Engineering", and "Water Resources". === List of university departments and institutions === === Department of Industrial Engineering === Department of Industrial Engineering (Tsinghua IE) has three institutes: Operations Research & Data Science System Operation and Digital Management Human Factors and Human-System Interaction The department also operates two university-level multi-disciplinary application-oriented institutes or centers: Institute of Quality and Reliability Established jointly by Tsinghua University and State Administration for Market Regulation Institute of Industrial Culture Established jointly by Tsinghua University and Ministry of Industry and Information Technology Center for Smart Logistics and Supply Chain Management Established jointly by Tsinghua University and Jiaozhou City at Qingdao City, Shandong Province. === Department of Mathematical Sciences === The Department of Mathematical Sciences (DMS) was established in 1927. In 1952, Tsinghua DMS was merged with the Peking University Department of Mathematical Sciences. Then in 1979 it was renamed "Department of Applied Mathematics", and renamed again in 1999 to its current title. Tsinghua DMS has three institutes at present, the institute of Pure Mathematics which has 27 faculty members, the Institute of Applied Mathematics and Probability and Statistics which has 27 faculty members, and the Institute of Computational Mathematics and Operations Research which has 20 faculty members. There are currently about 400 undergraduate students and 200 graduate students. === Department of Precision Instrument === The Department of Precision Instrument was called the Department of Precision Instrument and Machine Manufacturing in 1960 when it was separated out from the Department of Machine Manufacturing to be an independent department. Later, in 1971, it was renamed the Department of Precision Instrument. The mission of the Department of Precision Instrument at Tsinghua University, as its dean said, is "supporting the national development and improving the people's well-being." ==== Research ==== Research in the Department of Precision Instrument is divided to four main parts, led by its four research institutes: the Institute of Opto-electronic Engineering, the Institute of Instrument Science and Technology, the Engineering Research Center for Navigation Technology, and the Center for Photonics and Electronics. At the same time, the Department of Precision Instrument has three key laboratories: the State Key Laboratory of Tribology, the State Key Laboratory of Precision Measurement Technology and Instruments, and the Key Laboratory of High-accuracy Inertial Instrument and System. It also has two national engineering research centers, which are the National Engineering Research Center of Optical Disk and the CIMS National Engineering Research Center. The Institute of Opto-electronic Engineering The Institute of Opto-electronic Engineering (IOEE) was established in 1958. It obtained the Chinese government's authorization to offer PhD program in 1981 and the approval to build the post-doctoral research site in 1988. The research of the IOEE covers opto-electronic instruments, precision metrology and measurement, modern optical information processing, the theory and components of binary optics, and the birefringent frequency-splitting lasers. Several famous scientists work in the IOEE, including Professor Guofan Jin, an academician of the Chinese Academy of Engineering, and Professor Kegong Zhao, formerly the president of the Chinese National Institute of Metrology. The Institute of Instrument Science and Technology The Institute of Instrument Science and Technology is the most important institute in the State Key Laboratory of Precision Measuring Technology and Instrument Science at Tsinghua University. The institute is equipped with advanced instruments and facilities, and its research has included every major area in modern instrument science and technology. Up to 2012, the institute have produced over 1500 publications, more than 100 patents, and acquired many significant awards. The Engineering Research Center for Navigation Technology The Engineering Research Center for Navigation Technology is a relatively young institute in the Department of Precision Instrument which was established in 2000, with the intention to "[pursue] excellence in the research and development in the field of high-accuracy inertial instruments and navigation technology, as well as in MEMS inertial sensor fields, and to provide advanced training for future scientists and engineers in the field of inertial technology." Its research interests cover high-accuracy inertial instruments and navigation technology, MEMS inertial sensors and systems, and precise electro-mechanical control systems and their application. As of 2012, the area of the center is 2900 square meters, including approximately 550 square meters of clean rooms. Equipment and instruments in this center are worth over 50 million RMB (US$7.56 million). The Center for Photonics and Electronics The center for Photonics and Electronics works on advanced laser and photonic technology. It houses 200 square meters of clean rooms and very modern laser instruments and equipment. The research of this Center covers solid-state laser technology, fiber laser technology, active optics technology, and laser detection technology. The center has published more than published more than 100 scientific papers including 40 indexed by SCI, has 18 national patents, and also frequently exchange visits and academic conferences with foreign scholars. The SKLT has one central laboratory and four sub-laboratories. It has been awarded numerous awards, including "two National Natural Science Awards, two National Invention Awards, one National Award for Science and Technology Progress, two National Excellent Science Book Awards, 25 awards from ministries or provinces of China, Edmond E. Bisson Award in 2003 from STLE, the 2008 PE Publishing Prize by the Editor and Editorial Board of the Journal of Engineering Tribology." Moreover, China's Ministry of Education recognized the SKLT as one of the creative groups in 2005, and the National Natural Science Foundation of China recognized the SKLT as one of the creative research groups in 2007. The TRibology Science Fund of the Key Laboratory of Tribology cooperates with National Natural Science Foundation of China in founding research projects in various applied sciences and technologies. ==== Education ==== Currently, there are two disciplines in the Department of Precision Instrument: the discipline of the instrumental science and technology of precision instrument and mechanology and the discipline of optical engineering. There are six teaching laboratories or centers which serve significant roles in undergraduate and graduate education in the Department of Precision Instrument. They are: The Teaching Lab of Manufacturing Engineering The CAD Teaching Centre The Engineering Graphics Teaching Laboratory The Creative Machine Design Teaching Laboratory The Experimentation Teaching Center for Measurement and Control Technology The Teaching Laboratory of Optics and Length Measurement The department provides more than 40 courses of the undergraduate level and 25 courses of the graduate level. === School of Life Sciences === School of Life Sciences was first established in 1926 under the name Department of Biology. Botanist Qian Chongshu took up the first dean. During the nationwide reorganization of universities in the early 1950s, the Department of Biology was merged into other universities, namely Peking University etc., resulting in a vacancy in the field of biological research in Tsinghua for almost 30 years. In June 1984, decisions were made about the reestablishment of the Department of Biology, and the department officially reopened in September. During the reestablishment the Department of Biology of Peking University, the Institute of Biophysics of Chinese Academy of Sciences, and many other institutes as well as biologists provided valuable support and help. The department changed its name to the current name in September 2009. As of 2013, structural biologist and foreign associate of National Academy of Sciences of United States Dr. Wang Hongwei (王宏伟) is the current dean of School of Life Sciences. The school currently has 129 professors and employees, around 600 undergraduates (including the candidates of Tsinghua University – Peking Union Medical College joint MD program). === Peking Union Medical College === The Peking Union Medical College was established in 1917 by the Rockefeller Foundation and was modeled on the US medical education system. Tsinghua first established its medical school in 2001 and in 2006, Tsinghua's medical school merged with the Peking Union Medical College renaming it "Peking Union Medical College, Tsinghua University". The school remains the top ranked medical school and general hospital in China according to CUCAS in 2015. The Peking Union Medical College is also the only medical school to be affiliated with the Chinese Academy of Medical Sciences. It runs one of the most competitive medical programs in the country, accepting 90 students a year into its 8-year MD program. Students in the 8-year program spend 2.5 years at Tsinghua studying premedical education before moving onto Peking Union Medical College to complete the last 5.5 years in clinical medicine, basic medical education and research. === School of Economics and Management === The School of Economics and Management dates back to 1926, when Tsinghua University established its Faculty of Economics. === School of Journalism and Communication === The Tsinghua School of Journalism and Communication (TSJC) was established in April 2002. Its predecessor was Communication Studies in the Department of Chinese Language and Literature and its establishment of coincides with the development of media increasingly influencing world affairs in a time of fast-growing globalization. The school's research fields include International Communication, Film and Television Studies, New Media Studies, Media Operation and Management, and Business Journalism and are based on comprehensive academic research in journalism and communication theories. The objective of the school is to bring full advantage of Tsinghua University's comprehensive academic structure to Chinese and international media, to construct a first-rate discipline in journalism and communication studies, to cultivate talented professionals in the field and to explore advanced concepts in journalism and communication. The school also offers a two-year graduate program in international business journalism, sponsored by Bloomberg L.P. and the International Center for Journalists (ICFJ), that trains talented students and media professionals from around the globe in financial media and corporate communication. The school has five research-oriented centers to organize and conduct academic research activities. They are: Center for International Communications Studies, Center for New Media Studies, Center for Film and Television Studies, Center for Media Management Studies and Center for Cultural Industry Studies. === School of Law === The legal studies at Tsinghua University can be dated back to the "Tsinghua College" era (1911–1929), where many students were sent to universities in western countries for legal studies. Graduating from institutions such as Columbia, Yale, and Harvard, those Tsinghua alumni have played an important role in areas of law and diplomacy. Famous legal scholars Tuan-Sheng Ch'ien, Yan Shutang (燕树棠), Wang Huacheng (王化成), Kung Chuan Hsiao (萧公权), Pu Xuefeng (浦薛凤), Mei Ju'ao (梅汝璈), Xiang Zhejun (向哲浚) and diplomat Tang Yueliang (唐悦良) are all graduates from Tsinghua College or went to study abroad after passing exams in Tsinghua College. Tsinghua University School of Law was established in 1929 after Tsinghua College was renamed Tsinghua University. Legal education in Tsinghua University at the time focused on international affairs and Chinese legal studies. Courses on political science and economics could also be found on students' curriculum. Before the Japanese army invaded Beijing in 1937, the School of Law developed greatly. Many Chinese legal scholars graduated during that era, including Wang Tieya (王铁崖), Gong Xiangrui (龚祥瑞) and Lou Bangyan (楼邦彦). In 1952, in response to the government policy of turning Tsinghua University into an engineering-focused university, the law school was dismissed; the faculty were appointed to other universities, including Peking University and Peking College of Political Science and Law (the predecessor of China University of Political Science and Law). Until 1995, there was no formal "school of law" at Tsinghua University, yet courses on law were still taught in Tsinghua University from the early 1980s. On 8 September 1995, the Tsinghua University Department of Law was formally re-established; on 25 April 1999, the 88th anniversary of Tsinghua University, the university formally changed the department into the "School of Law". The "new" law school inherited the spirit of the "old" law school and has endeavored to add international factors to its students' curriculum. Due to its outstanding faculty members and students, the Tsinghua University School of Law has risen to become one of the leading law schools in China and since 2011, has been consistently ranked as the best or the second-best law school in mainland China by QS World University Rankings. === Graduate School at Shenzhen === The Graduate School at Shenzhen was jointly founded by Tsinghua University and the Shenzhen Municipal Government. The school is directly affiliated with Tsinghua University in Beijing. The campus is located in the University Town of Shenzhen since 18 October 2003. The Graduate School at Shenzhen, Tsinghua University, was jointly founded by Tsinghua University and the Shenzhen Municipal Government for cultivating top level professionals and carrying out scientific and technological innovations. The academic divisions are the following: Division of Life Science and Health Division of Energy and Environment Division of Information Science and Technology Division of Logistics and Transportation Division of Advanced Manufacturing Division of Social Sciences and Management Division of Ocean Science and Technology == Campus == The campus of Tsinghua University is located in northwest Beijing, in the Haidian district. Tsinghua University's campus was named one of the most beautiful college campuses in the world by a panel of architects and campus designers in Forbes in 2010; it was the only university in Asia on the list. Numerous architects were involved in the designing of buildings on the campus. American architect Henry Killam Murphy (1877–1954), a Yale graduate, designed early buildings such as the Grand Auditorium, the Roosevelt Memorial Gymnasium, the Science Building and the east side of the Old Library. Yang Tingbao designed the Observatory, the Life Sciences building, the Mingzhai of the student dormitory buildings and the middle and west side of the Old Library. Shen Liyuan designed the Mechanical Engineering Hall, the Chemistry Hall and the Aviation Hall. T. Chuang, a 1914 graduate of the University of Illinois at Urbana–Champaign, helped design the campus grounds of the Tsinghua University with influences of Neoclassical and Palladian architectural styles and architectures. Other notable 20th-century Chinese architects such as Li Daozeng, Zhou Weiquan, Wang Guoyu and Guan Zhaoye have all designed various buildings on the Tsinghua University campus. The university's Institute of Nuclear and New Energy Technology is on a separate campus in a northern suburb of Beijing. The Tsinghua History Museum covers a construction area of 5,060 m2. A collection of old documents, pictures, artworks, maps, graphics, videos and music tells the visitors the history of Tsinghua University. The exhibition also pays tribute to the people who contributed to the development of the institution. The university also operates its own art museum, the Tsinghua University Art Museum, which derives its collection from the university's Academy of Arts & Design since 1956. == Notable people == === Notable alumni === Tsinghua University has produced many notable graduates, especially in political sphere, academic field and industry. Forbes has referred to Tsinghua as China's "power factory", citing the amount of senior Chinese politicians the university has produced. Notable alumni who have held senior positions in Chinese politics include current general secretary and president of China, Xi Jinping, former general secretary and president of China Hu Jintao, former chairman of the National People's Congress Wu Bangguo, former premier Zhu Rongji, and the former first vice premier Huang Ju. This also includes politicians like Wu Guanzheng, former governor of the People's Bank of China Zhou Xiaochuan, former minister of finance Lou Jiwei, general Sun Li-jen, Liang Qichao, and more. Since 2016, Tsinghua graduates who have political prominence are disproportionately greater in number than graduates of other famous universities. Notable alumni in the sciences include Nobel laureate Yang Chen Ning, who was awarded the Nobel Prize in Physics for his work with Tsung-Dao Lee on parity nonconservation of weak interaction; Wolf Prize winning mathematician Shiing-Shen Chern, biologist Min Chueh Chang, theoretical physicist Zhou Peiyuan, astronomer Zhang Yuzhe, biomedical engineer Leslie Ying, mechanical engineer Qingyan Chen, anthropologist Fei Xiaotong, sociologist and ethnologist Wu Wenzao, political scientist K. C. Hsiao, and sociologist Pan Guangdan. Tsinghua is known for having educated the most billionaires of any university in China, and since 2017 counts 152 billionaires amongst its alumni. These include billionaires Sun Hongbin (real estate), chairman of Goertek Jiang Bin (components), Xu Hang (medical devices), and Zhang Zetian (e-commerce), among others. Notable alumni in the arts and poetry include author Qian Zhongshu, Wen Yiduo, painter Xinyi Cheng, historian and poet Wang Guowei, Chen Yinke, and architect Xu Tiantian. === Tsinghua clique === The term Tsinghua clique refers to a group of Chinese Communist Party politicians that have graduated from Tsinghua University. They are members of the fourth generation of Chinese leadership, and are purported to hold reformist and hesitantly pro-democratic ideas (a number have studied in the United States following graduation from Tsinghua, and some are said to be influenced by the reform ideals of Hu Yaobang). In the PRC, their ascendance to power began in 2008 at the 17th National Congress of the Chinese Communist Party. == See also == Tsinghua Shenzhen International Graduate School Tsinghua-Berkeley Shenzhen Institute Anti-Corruption and Governance Research Center Institute of Nuclear and New Energy Technology Peking Union Medical College National Tsing Hua University SMTH BBS Tsinghua clique Tsinghua Holdings Tsinghua University Press Education in the People's Republic of China Tsinghua University High School List of colleges and universities in Beijing Wudaokou == Note == == References == == External links == Media related to Tsinghua University at Wikimedia Commons Tsinghua University (in Chinese) Tsinghua University (in Chinese)
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https://en.wikipedia.org/wiki/Tsinghua_University
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A mathematical exercise is a routine application of algebra or other mathematics to a stated challenge. Mathematics teachers assign mathematical exercises to develop the skills of their students. Early exercises deal with addition, subtraction, multiplication, and division of integers. Extensive courses of exercises in school extend such arithmetic to rational numbers. Various approaches to geometry have based exercises on relations of angles, segments, and triangles. The topic of trigonometry gains many of its exercises from the trigonometric identities. In college mathematics exercises often depend on functions of a real variable or application of theorems. The standard exercises of calculus involve finding derivatives and integrals of specified functions. Usually instructors prepare students with worked examples: the exercise is stated, then a model answer is provided. Often several worked examples are demonstrated before students are prepared to attempt exercises on their own. Some texts, such as those in Schaum's Outlines, focus on worked examples rather than theoretical treatment of a mathematical topic. == Overview == In primary school students start with single digit arithmetic exercises. Later most exercises involve at least two digits. A common exercise in elementary algebra calls for factorization of polynomials. Another exercise is completing the square in a quadratic polynomial. An artificially produced word problem is a genre of exercise intended to keep mathematics relevant. Stephen Leacock described this type: The student of arithmetic who has mastered the first four rules of his art and successfully striven with sums and fractions finds himself confronted by an unbroken expanse of questions known as problems. These are short stories of adventure and industry with the end omitted and, though betraying a strong family resemblance, are not without a certain element of romance. A distinction between an exercise and a mathematical problem was made by Alan H. Schoenfeld: Students must master the relevant subject matter, and exercises are appropriate for that. But if rote exercises are the only kinds of problems that students see in their classes, we are doing the students a grave disservice. He advocated setting challenges: By "real problems" ... I mean mathematical tasks that pose an honest challenge to the student and that the student needs to work at in order to obtain a solution. A similar sentiment was expressed by Marvin Bittinger when he prepared the second edition of his textbook: In response to comments from users, the authors have added exercises that require something of the student other than an understanding of the immediate objectives of the lesson at hand, yet are not necessarily highly challenging. The zone of proximal development for each student, or cohort of students, sets exercises at a level of difficulty that challenges but does not frustrate them. Some comments in the preface of a calculus textbook show the central place of exercises in the book: The exercises comprise about one-quarter of the text – the most important part of the text in our opinion. ... Supplementary exercises at the end of each chapter expand the other exercise sets and provide cumulative exercises that require skills from earlier chapters. This text includes "Functions and Graphs in Applications" (Ch 0.6) which is fourteen pages of preparation for word problems. Authors of a book on finite fields chose their exercises freely: In order to enhance the attractiveness of this book as a textbook, we have included worked-out examples at appropriate points in the text and have included lists of exercises for Chapters 1 — 9. These exercises range from routine problems to alternative proofs of key theorems, but containing also material going beyond what is covered in the text. J. C. Maxwell explained how exercise facilitates access to the language of mathematics: As mathematicians we perform certain mental operations on the symbols of number or quantity, and, proceeding step by step from more simple to more complex operations, we are enabled to express the same thing in many different forms. The equivalence of these different forms, though a necessary consequence of self-evident axioms, is not always, to our minds, self-evident; but the mathematician, who by long practice has acquired a familiarity with many of these forms, and has become expert in the processes which lead from one to another, can often transform a perplexing expression into another which explains its meaning in more intelligible language. The individual instructors at various colleges use exercises as part of their mathematics courses. Investigating problem solving in universities, Schoenfeld noted: Upper division offerings for mathematics majors, where for the most part students worked on collections of problems that had been compiled by their individual instructors. In such courses emphasis was on learning by doing, without an attempt to teach specific heuristics: the students worked lots of problems because (according to the implicit instructional model behind such courses) that’s how one gets good at mathematics. Such exercise collections may be proprietary to the instructor and his institution. As an example of the value of exercise sets, consider the accomplishment of Toru Kumon and his Kumon method. In his program, a student does not proceed before mastery of each level of exercise. At the Russian School of Mathematics, students begin multi-step problems as early as the first grade, learning to build on previous results to progress towards the solution. In the 1960s, collections of mathematical exercises were translated from Russian and published by W. H. Freeman and Company: The USSR Olympiad Problem Book (1962), Problems in Higher Algebra (1965), and Problems in Differential Equations (1963). == History == In China, from ancient times counting rods were used to represent numbers, and arithmetic was accomplished with rod calculus and later the suanpan. The Book on Numbers and Computation and the Nine Chapters on the Mathematical Art include exercises that are exemplars of linear algebra. In about 980 Al-Sijzi wrote his Ways of Making Easy the Derivation of Geometrical Figures, which was translated and published by Jan Hogendijk in 1996. An Arabic language collection of exercises was given a Spanish translation as Compendio de Algebra de Abenbéder and reviewed in Nature. Robert Recorde first published The Ground of Arts in 1543. Firstly, it was almost all exposition with very few exercises — The later came into prominence in the eighteenth and nineteenth centuries. As a comparison we might look at another best seller, namely Walkingame’s Tutor's Assistant, first published in 1751, 70 per cent of which was devoted to exercises as opposed to about 1 per cent by Recorde. The inclusion of exercises was one of the most significant subsequent developments in arithmetical textbooks, and paralleled the development of education as teachers began to make use of textbooks as sources of exercises. Recorde was writing mainly for those who were teaching themselves, scholars who would have no one to check their answers to the exercises. In Europe before 1900, the science of graphical perspective framed geometrical exercises. For example, in 1719 Brook Taylor wrote in New Principles of Linear Perspective [The Reader] will find much more pleasure in observing how extensive these Principles are, by applying them to particular Cases which he himself shall devise, while he exercises himself in this Art,... Taylor continued ...for the true and best way of learning any Art, is not to see a great many Examples done by another Person; but to possess ones self first of the Principles of it, and then to make them familiar, by exercising ones self in the Practice. The use of writing slates in schools provided an early format for exercises. Growth of exercise programs followed introduction of written examinations and study based on pen and paper. Felix Klein described preparation for the entrance examination of École Polytechnique as ...a course of "mathematiques especiales". This is an extraordinarily strong concentration of mathematical education – up to 16 hours a week – in which elementary analytic geometry and mechanics, and recently infinitesimal calculus also, are thoroughly studied and are made into a securely mastered tool by means of many exercises. Sylvestre Lacroix was a gifted teacher and expositor. His book on descriptive geometry uses sections labelled "Probleme" to exercise the reader’s understanding. In 1816 he wrote Essays on Teaching in General, and on Mathematics Teaching in Particular which emphasized the need to exercise and test: The examiner, obliged, in the short-term, to multiply his questions enough to cover the subjects that he asks, to the greater part of the material taught, cannot be less thorough, since if, to abbreviate, he puts applications aside, he will not gain anything for the pupils’ faculties this way. Andrew Warwick has drawn attention to the historical question of exercises: The inclusion of illustrative exercises and problems at the end of chapters in textbooks of mathematical physics is now so commonplace as to seem unexceptional, but it is important to appreciate that this pedagogical device is of relatively recent origin and was introduced in a specific historical context.: 168 In reporting Mathematical tripos examinations instituted at Cambridge University, he notes Such cumulative, competitive learning was also accomplished more effectively by private tutors using individual tuition, specially prepared manuscripts, and graded examples and problems, than it was by college lecturers teaching large classes at the pace of the mediocre.: 79 Explaining the relationship of examination and exercise, he writes ...by the 1830s it was the problems on examination papers, rather than exercises in textbooks, that defined the standard to which ambitious students aspired...[Cambridge students] not only expected to find their way through the merest sketch of an example, but were taught to regard such exercises as useful preparation for tackling difficult problems in examinations.: 152 Explaining how the reform took root, Warwick wrote: It was widely believed in Cambridge that the best way of teaching mathematics, including the new analytical methods, was through practical examples and problems, and, by the mid-1830s, some of the first generation of young college fellows to have been taught higher analysis this way were beginning both to undertake their own research and to be appointed Tripos examiners.: 155 Warwick reports that in Germany, Franz Ernst Neumann about the same time "developed a common system of graded exercises that introduced student to a hierarchy of essential mathematical skills and techniques, and ...began to construct his own problem sets through which his students could learn their craft.": 174 In Russia, Stephen Timoshenko reformed instruction around exercises. In 1913 he was teaching strength of materials at the Petersburg State University of Means of Communication. As he wrote in 1968, [Practical] exercises were not given at the Institute, and on examinations the students were asked only theoretical questions from the adopted textbook. I had to put an end to this kind of teaching as soon as possible. The students clearly understood the situation, realized the need for better assimilation of the subject, and did not object to the heavy increase in their work load. The main difficulty was with the teachers – or more precisely, with the examiners, who were accustomed to basing their exams on the book. Putting practical problems on the exams complicated their job. They were persons along in years...the only hope was to bring younger people into teaching. == See also == Algorithm Worked-example effect == References == == External links == Tatyana Afanasyeva (1931) Exercises in Experimental Geometry from Pacific Institute for the Mathematical Sciences. Vladimir Arnold (2004) Exercises for students from age 5 to 15 at IMAGINARY platform James Alfred Ewing (1911) Examples in Mathematics, Mechanics, Navigation and Nautical Astronomy, Heat and Steam, Electricity, for the use of Junior Officers Afloat from Internet Archive. Jim Hefferon & others (2004) Linear Algebra at Wikibooks
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In mathematics, a knot is an embedding of the circle (S1) into three-dimensional Euclidean space, R3 (also known as E3). Often two knots are considered equivalent if they are ambient isotopic, that is, if there exists a continuous deformation of R3 which takes one knot to the other. A crucial difference between the standard mathematical and conventional notions of a knot is that mathematical knots are closed — there are no ends to tie or untie on a mathematical knot. Physical properties such as friction and thickness also do not apply, although there are mathematical definitions of a knot that take such properties into account. The term knot is also applied to embeddings of S j in Sn, especially in the case j = n − 2. The branch of mathematics that studies knots is known as knot theory and has many relations to graph theory. == Formal definition == A knot is an embedding of the circle (S1) into three-dimensional Euclidean space (R3), or the 3-sphere (S3), since the 3-sphere is compact. Two knots are defined to be equivalent if there is an ambient isotopy between them. === Projection === A knot in R3 (or alternatively in the 3-sphere, S3), can be projected onto a plane R2 (respectively a sphere S2). This projection is almost always regular, meaning that it is injective everywhere, except at a finite number of crossing points, which are the projections of only two points of the knot, and these points are not collinear. In this case, by choosing a projection side, one can completely encode the isotopy class of the knot by its regular projection by recording a simple over/under information at these crossings. In graph theory terms, a regular projection of a knot, or knot diagram is thus a quadrivalent planar graph with over/under-decorated vertices. The local modifications of this graph which allow to go from one diagram to any other diagram of the same knot (up to ambient isotopy of the plane) are called Reidemeister moves. == Types of knots == The simplest knot, called the unknot or trivial knot, is a round circle embedded in R3. In the ordinary sense of the word, the unknot is not "knotted" at all. The simplest nontrivial knots are the trefoil knot (31 in the table), the figure-eight knot (41) and the cinquefoil knot (51). Several knots, linked or tangled together, are called links. Knots are links with a single component. === Tame vs. wild knots === A polygonal knot is a knot whose image in R3 is the union of a finite set of line segments. A tame knot is any knot equivalent to a polygonal knot. Knots which are not tame are called wild, and can have pathological behavior. In knot theory and 3-manifold theory, often the adjective "tame" is omitted. Smooth knots, for example, are always tame. === Framed knot === A framed knot is the extension of a tame knot to an embedding of the solid torus D2 × S1 in S3. The framing of the knot is the linking number of the image of the ribbon I × S1 with the knot. A framed knot can be seen as the embedded ribbon and the framing is the (signed) number of twists. This definition generalizes to an analogous one for framed links. Framed links are said to be equivalent if their extensions to solid tori are ambient isotopic. Framed link diagrams are link diagrams with each component marked, to indicate framing, by an integer representing a slope with respect to the meridian and preferred longitude. A standard way to view a link diagram without markings as representing a framed link is to use the blackboard framing. This framing is obtained by converting each component to a ribbon lying flat on the plane. A type I Reidemeister move clearly changes the blackboard framing (it changes the number of twists in a ribbon), but the other two moves do not. Replacing the type I move by a modified type I move gives a result for link diagrams with blackboard framing similar to the Reidemeister theorem: Link diagrams, with blackboard framing, represent equivalent framed links if and only if they are connected by a sequence of (modified) type I, II, and III moves. Given a knot, one can define infinitely many framings on it. Suppose that we are given a knot with a fixed framing. One may obtain a new framing from the existing one by cutting a ribbon and twisting it an integer multiple of 2π around the knot and then glue back again in the place we did the cut. In this way one obtains a new framing from an old one, up to the equivalence relation for framed knots„ leaving the knot fixed. The framing in this sense is associated to the number of twists the vector field performs around the knot. Knowing how many times the vector field is twisted around the knot allows one to determine the vector field up to diffeomorphism, and the equivalence class of the framing is determined completely by this integer called the framing integer. === Knot complement === Given a knot in the 3-sphere, the knot complement is all the points of the 3-sphere not contained in the knot. A major theorem of Gordon and Luecke states that at most two knots have homeomorphic complements (the original knot and its mirror reflection). This in effect turns the study of knots into the study of their complements, and in turn into 3-manifold theory. === JSJ decomposition === The JSJ decomposition and Thurston's hyperbolization theorem reduces the study of knots in the 3-sphere to the study of various geometric manifolds via splicing or satellite operations. In the pictured knot, the JSJ-decomposition splits the complement into the union of three manifolds: two trefoil complements and the complement of the Borromean rings. The trefoil complement has the geometry of H2 × R, while the Borromean rings complement has the geometry of H3. === Harmonic knots === Parametric representations of knots are called harmonic knots. Aaron Trautwein compiled parametric representations for all knots up to and including those with a crossing number of 8 in his PhD thesis. == Applications to graph theory == === Medial graph === Another convenient representation of knot diagrams was introduced by Peter Tait in 1877. Any knot diagram defines a plane graph whose vertices are the crossings and whose edges are paths in between successive crossings. Exactly one face of this planar graph is unbounded; each of the others is homeomorphic to a 2-dimensional disk. Color these faces black or white so that the unbounded face is black and any two faces that share a boundary edge have opposite colors. The Jordan curve theorem implies that there is exactly one such coloring. We construct a new plane graph whose vertices are the white faces and whose edges correspond to crossings. We can label each edge in this graph as a left edge or a right edge, depending on which thread appears to go over the other as we view the corresponding crossing from one of the endpoints of the edge. Left and right edges are typically indicated by labeling left edges + and right edges –, or by drawing left edges with solid lines and right edges with dashed lines. The original knot diagram is the medial graph of this new plane graph, with the type of each crossing determined by the sign of the corresponding edge. Changing the sign of every edge corresponds to reflecting the knot in a mirror. === Linkless and knotless embedding === In two dimensions, only the planar graphs may be embedded into the Euclidean plane without crossings, but in three dimensions, any undirected graph may be embedded into space without crossings. However, a spatial analogue of the planar graphs is provided by the graphs with linkless embeddings and knotless embeddings. A linkless embedding is an embedding of the graph with the property that any two cycles are unlinked; a knotless embedding is an embedding of the graph with the property that any single cycle is unknotted. The graphs that have linkless embeddings have a forbidden graph characterization involving the Petersen family, a set of seven graphs that are intrinsically linked: no matter how they are embedded, some two cycles will be linked with each other. A full characterization of the graphs with knotless embeddings is not known, but the complete graph K7 is one of the minimal forbidden graphs for knotless embedding: no matter how K7 is embedded, it will contain a cycle that forms a trefoil knot. == Generalization == In contemporary mathematics the term knot is sometimes used to describe a more general phenomenon related to embeddings. Given a manifold M with a submanifold N, one sometimes says N can be knotted in M if there exists an embedding of N in M which is not isotopic to N. Traditional knots form the case where N = S1 and M = R3 or M = S3. The Schoenflies theorem states that the circle does not knot in the 2-sphere: every topological circle in the 2-sphere is isotopic to a geometric circle. Alexander's theorem states that the 2-sphere does not smoothly (or PL or tame topologically) knot in the 3-sphere. In the tame topological category, it's known that the n-sphere does not knot in the n + 1-sphere for all n. This is a theorem of Morton Brown, Barry Mazur, and Marston Morse. The Alexander horned sphere is an example of a knotted 2-sphere in the 3-sphere which is not tame. In the smooth category, the n-sphere is known not to knot in the n + 1-sphere provided n ≠ 3. The case n = 3 is a long-outstanding problem closely related to the question: does the 4-ball admit an exotic smooth structure? André Haefliger proved that there are no smooth j-dimensional knots in Sn provided 2n − 3j − 3 > 0, and gave further examples of knotted spheres for all n > j ≥ 1 such that 2n − 3j − 3 = 0. n − j is called the codimension of the knot. An interesting aspect of Haefliger's work is that the isotopy classes of embeddings of S j in Sn form a group, with group operation given by the connect sum, provided the co-dimension is greater than two. Haefliger based his work on Stephen Smale's h-cobordism theorem. One of Smale's theorems is that when one deals with knots in co-dimension greater than two, even inequivalent knots have diffeomorphic complements. This gives the subject a different flavour than co-dimension 2 knot theory. If one allows topological or PL-isotopies, Christopher Zeeman proved that spheres do not knot when the co-dimension is greater than 2. See a generalization to manifolds. == See also == Knot theory – Study of mathematical knots Knot invariant – Function of a knot that takes the same value for equivalent knots List of mathematical knots and links == Notes == == References == == Bibliography == == External links == "Main_Page", The Knot Atlas. The Manifold Atlas Project
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Indian mathematics emerged in the Indian subcontinent from 1200 BCE until the end of the 18th century. In the classical period of Indian mathematics (400 CE to 1200 CE), important contributions were made by scholars like Aryabhata, Brahmagupta, Bhaskara II, Varāhamihira, and Madhava. The decimal number system in use today was first recorded in Indian mathematics. Indian mathematicians made early contributions to the study of the concept of zero as a number, negative numbers, arithmetic, and algebra. In addition, trigonometry was further advanced in India, and, in particular, the modern definitions of sine and cosine were developed there. These mathematical concepts were transmitted to the Middle East, China, and Europe and led to further developments that now form the foundations of many areas of mathematics. Ancient and medieval Indian mathematical works, all composed in Sanskrit, usually consisted of a section of sutras in which a set of rules or problems were stated with great economy in verse in order to aid memorization by a student. This was followed by a second section consisting of a prose commentary (sometimes multiple commentaries by different scholars) that explained the problem in more detail and provided justification for the solution. In the prose section, the form (and therefore its memorization) was not considered so important as the ideas involved. All mathematical works were orally transmitted until approximately 500 BCE; thereafter, they were transmitted both orally and in manuscript form. The oldest extant mathematical document produced on the Indian subcontinent is the birch bark Bakhshali Manuscript, discovered in 1881 in the village of Bakhshali, near Peshawar (modern day Pakistan) and is likely from the 7th century CE. A later landmark in Indian mathematics was the development of the series expansions for trigonometric functions (sine, cosine, and arc tangent) by mathematicians of the Kerala school in the 15th century CE. Their work, completed two centuries before the invention of calculus in Europe, provided what is now considered the first example of a power series (apart from geometric series). However, they did not formulate a systematic theory of differentiation and integration, nor is there any evidence of their results being transmitted outside Kerala. == Prehistory == Excavations at Harappa, Mohenjo-daro and other sites of the Indus Valley civilisation have uncovered evidence of the use of "practical mathematics". The people of the Indus Valley Civilization manufactured bricks whose dimensions were in the proportion 4:2:1, considered favourable for the stability of a brick structure. They used a standardised system of weights based on the ratios: 1/20, 1/10, 1/5, 1/2, 1, 2, 5, 10, 20, 50, 100, 200, and 500, with the unit weight equaling approximately 28 grams (and approximately equal to the English ounce or Greek uncia). They mass-produced weights in regular geometrical shapes, which included hexahedra, barrels, cones, and cylinders, thereby demonstrating knowledge of basic geometry. The inhabitants of Indus civilisation also tried to standardise measurement of length to a high degree of accuracy. They designed a ruler—the Mohenjo-daro ruler—whose unit of length (approximately 1.32 inches or 3.4 centimetres) was divided into ten equal parts. Bricks manufactured in ancient Mohenjo-daro often had dimensions that were integral multiples of this unit of length. Hollow cylindrical objects made of shell and found at Lothal (2200 BCE) and Dholavira are demonstrated to have the ability to measure angles in a plane, as well as to determine the position of stars for navigation. == Vedic period == === Samhitas and Brahmanas === The texts of the Vedic Period provide evidence for the use of large numbers. By the time of the Yajurvedasaṃhitā- (1200–900 BCE), numbers as high as 1012 were being included in the texts. For example, the mantra (sacred recitation) at the end of the annahoma ("food-oblation rite") performed during the aśvamedha, and uttered just before-, during-, and just after sunrise, invokes powers of ten from a hundred to a trillion: Hail to śata ("hundred," 102), hail to sahasra ("thousand," 103), hail to ayuta ("ten thousand," 104), hail to niyuta ("hundred thousand," 105), hail to prayuta ("million," 106), hail to arbuda ("ten million," 107), hail to nyarbuda ("hundred million," 108), hail to samudra ("billion," 109, literally "ocean"), hail to madhya ("ten billion," 1010, literally "middle"), hail to anta ("hundred billion," 1011, lit., "end"), hail to parārdha ("one trillion," 1012 lit., "beyond parts"), hail to the uṣas (dawn) , hail to the vyuṣṭi (twilight), hail to udeṣyat (the one which is going to rise), hail to udyat (the one which is rising), hail udita (to the one which has just risen), hail to svarga (the heaven), hail to martya (the world), hail to all. The solution to partial fraction was known to the Rigvedic People as states in the purush Sukta (RV 10.90.4): With three-fourths Puruṣa went up: one-fourth of him again was here. The Satapatha Brahmana (c. 7th century BCE) contains rules for ritual geometric constructions that are similar to the Sulba Sutras. === Śulba Sūtras === The Śulba Sūtras (literally, "Aphorisms of the Chords" in Vedic Sanskrit) (c. 700–400 BCE) list rules for the construction of sacrificial fire altars. Most mathematical problems considered in the Śulba Sūtras spring from "a single theological requirement," that of constructing fire altars which have different shapes but occupy the same area. The altars were required to be constructed of five layers of burnt brick, with the further condition that each layer consist of 200 bricks and that no two adjacent layers have congruent arrangements of bricks. According to Hayashi, the Śulba Sūtras contain "the earliest extant verbal expression of the Pythagorean Theorem in the world, although it had already been known to the Old Babylonians." The diagonal rope (akṣṇayā-rajju) of an oblong (rectangle) produces both which the flank (pārśvamāni) and the horizontal (tiryaṇmānī) <ropes> produce separately." Since the statement is a sūtra, it is necessarily compressed and what the ropes produce is not elaborated on, but the context clearly implies the square areas constructed on their lengths, and would have been explained so by the teacher to the student. They contain lists of Pythagorean triples, which are particular cases of Diophantine equations. They also contain statements (that with hindsight we know to be approximate) about squaring the circle and "circling the square." Baudhayana (c. 8th century BCE) composed the Baudhayana Sulba Sutra, the best-known Sulba Sutra, which contains examples of simple Pythagorean triples, such as: (3, 4, 5), (5, 12, 13), (8, 15, 17), (7, 24, 25), and (12, 35, 37), as well as a statement of the Pythagorean theorem for the sides of a square: "The rope which is stretched across the diagonal of a square produces an area double the size of the original square." It also contains the general statement of the Pythagorean theorem (for the sides of a rectangle): "The rope stretched along the length of the diagonal of a rectangle makes an area which the vertical and horizontal sides make together." Baudhayana gives an expression for the square root of two: 2 ≈ 1 + 1 3 + 1 3 ⋅ 4 − 1 3 ⋅ 4 ⋅ 34 = 1.4142156 … {\displaystyle {\sqrt {2}}\approx 1+{\frac {1}{3}}+{\frac {1}{3\cdot 4}}-{\frac {1}{3\cdot 4\cdot 34}}=1.4142156\ldots } The expression is accurate up to five decimal places, the true value being 1.41421356... This expression is similar in structure to the expression found on a Mesopotamian tablet from the Old Babylonian period (1900–1600 BCE): 2 ≈ 1 + 24 60 + 51 60 2 + 10 60 3 = 1.41421297 … {\displaystyle {\sqrt {2}}\approx 1+{\frac {24}{60}}+{\frac {51}{60^{2}}}+{\frac {10}{60^{3}}}=1.41421297\ldots } which expresses √2 in the sexagesimal system, and which is also accurate up to 5 decimal places. According to mathematician S. G. Dani, the Babylonian cuneiform tablet Plimpton 322 written c. 1850 BCE "contains fifteen Pythagorean triples with quite large entries, including (13500, 12709, 18541) which is a primitive triple, indicating, in particular, that there was sophisticated understanding on the topic" in Mesopotamia in 1850 BCE. "Since these tablets predate the Sulbasutras period by several centuries, taking into account the contextual appearance of some of the triples, it is reasonable to expect that similar understanding would have been there in India." Dani goes on to say: As the main objective of the Sulvasutras was to describe the constructions of altars and the geometric principles involved in them, the subject of Pythagorean triples, even if it had been well understood may still not have featured in the Sulvasutras. The occurrence of the triples in the Sulvasutras is comparable to mathematics that one may encounter in an introductory book on architecture or another similar applied area, and would not correspond directly to the overall knowledge on the topic at that time. Since, unfortunately, no other contemporaneous sources have been found it may never be possible to settle this issue satisfactorily. In all, three Sulba Sutras were composed. The remaining two, the Manava Sulba Sutra composed by Manava (fl. 750–650 BCE) and the Apastamba Sulba Sutra, composed by Apastamba (c. 600 BCE), contained results similar to the Baudhayana Sulba Sutra. Vyakarana The Vedic period saw the work of Sanskrit grammarian Pāṇini (c. 520–460 BCE). His grammar includes a precursor of the Backus–Naur form (used in the description programming languages). == Pingala (300 BCE – 200 BCE) == Among the scholars of the post-Vedic period who contributed to mathematics, the most notable is Pingala (piṅgalá) (fl. 300–200 BCE), a music theorist who authored the Chhandas Shastra (chandaḥ-śāstra, also Chhandas Sutra chhandaḥ-sūtra), a Sanskrit treatise on prosody. Pingala's work also contains the basic ideas of Fibonacci numbers (called maatraameru). Although the Chandah sutra hasn't survived in its entirety, a 10th-century commentary on it by Halāyudha has. Halāyudha, who refers to the Pascal triangle as Meru-prastāra (literally "the staircase to Mount Meru"), has this to say: Draw a square. Beginning at half the square, draw two other similar squares below it; below these two, three other squares, and so on. The marking should be started by putting 1 in the first square. Put 1 in each of the two squares of the second line. In the third line put 1 in the two squares at the ends and, in the middle square, the sum of the digits in the two squares lying above it. In the fourth line put 1 in the two squares at the ends. In the middle ones put the sum of the digits in the two squares above each. Proceed in this way. Of these lines, the second gives the combinations with one syllable, the third the combinations with two syllables, ... The text also indicates that Pingala was aware of the combinatorial identity: ( n 0 ) + ( n 1 ) + ( n 2 ) + ⋯ + ( n n − 1 ) + ( n n ) = 2 n {\displaystyle {n \choose 0}+{n \choose 1}+{n \choose 2}+\cdots +{n \choose n-1}+{n \choose n}=2^{n}} Kātyāyana Kātyāyana (c. 3rd century BCE) is notable for being the last of the Vedic mathematicians. He wrote the Katyayana Sulba Sutra, which presented much geometry, including the general Pythagorean theorem and a computation of the square root of 2 correct to five decimal places. == Jain mathematics (400 BCE – 200 CE) == Although Jainism as a religion and philosophy predates its most famous exponent, the great Mahaviraswami (6th century BCE), most Jain texts on mathematical topics were composed after the 6th century BCE. Jain mathematicians are important historically as crucial links between the mathematics of the Vedic period and that of the "classical period." A significant historical contribution of Jain mathematicians lay in their freeing Indian mathematics from its religious and ritualistic constraints. In particular, their fascination with the enumeration of very large numbers and infinities led them to classify numbers into three classes: enumerable, innumerable and infinite. Not content with a simple notion of infinity, their texts define five different types of infinity: the infinite in one direction, the infinite in two directions, the infinite in area, the infinite everywhere, and the infinite perpetually. In addition, Jain mathematicians devised notations for simple powers (and exponents) of numbers like squares and cubes, which enabled them to define simple algebraic equations (bījagaṇita samīkaraṇa). Jain mathematicians were apparently also the first to use the word shunya (literally void in Sanskrit) to refer to zero. This word is the ultimate etymological origin of the English word "zero", as it was calqued into Arabic as ṣifr and then subsequently borrowed into Medieval Latin as zephirum, finally arriving at English after passing through one or more Romance languages (cf. French zéro, Italian zero). In addition to Surya Prajnapti, important Jain works on mathematics included the Sthānāṅga Sūtra (c. 300 BCE – 200 CE); the Anuyogadwara Sutra (c. 200 BCE – 100 CE), which includes the earliest known description of factorials in Indian mathematics; and the Ṣaṭkhaṅḍāgama (c. 2nd century CE). Important Jain mathematicians included Bhadrabahu (d. 298 BCE), the author of two astronomical works, the Bhadrabahavi-Samhita and a commentary on the Surya Prajinapti; Yativrisham Acharya (c. 176 BCE), who authored a mathematical text called Tiloyapannati; and Umasvati (c. 150 BCE), who, although better known for his influential writings on Jain philosophy and metaphysics, composed a mathematical work called the Tattvārtha Sūtra. == Oral tradition == Mathematicians of ancient and early medieval India were almost all Sanskrit pandits (paṇḍita "learned man"), who were trained in Sanskrit language and literature, and possessed "a common stock of knowledge in grammar (vyākaraṇa), exegesis (mīmāṃsā) and logic (nyāya)." Memorisation of "what is heard" (śruti in Sanskrit) through recitation played a major role in the transmission of sacred texts in ancient India. Memorisation and recitation was also used to transmit philosophical and literary works, as well as treatises on ritual and grammar. Modern scholars of ancient India have noted the "truly remarkable achievements of the Indian pandits who have preserved enormously bulky texts orally for millennia." === Styles of memorisation === Prodigious energy was expended by ancient Indian culture in ensuring that these texts were transmitted from generation to generation with inordinate fidelity. For example, memorisation of the sacred Vedas included up to eleven forms of recitation of the same text. The texts were subsequently "proof-read" by comparing the different recited versions. Forms of recitation included the jaṭā-pāṭha (literally "mesh recitation") in which every two adjacent words in the text were first recited in their original order, then repeated in the reverse order, and finally repeated in the original order. The recitation thus proceeded as: In another form of recitation, dhvaja-pāṭha (literally "flag recitation") a sequence of N words were recited (and memorised) by pairing the first two and last two words and then proceeding as: The most complex form of recitation, ghana-pāṭha (literally "dense recitation"), according to Filliozat, took the form: That these methods have been effective is testified to by the preservation of the most ancient Indian religious text, the Ṛgveda (c. 1500 BCE), as a single text, without any variant readings. Similar methods were used for memorising mathematical texts, whose transmission remained exclusively oral until the end of the Vedic period (c. 500 BCE). === The Sutra genre === Mathematical activity in ancient India began as a part of a "methodological reflexion" on the sacred Vedas, which took the form of works called Vedāṇgas, or, "Ancillaries of the Veda" (7th–4th century BCE). The need to conserve the sound of sacred text by use of śikṣā (phonetics) and chhandas (metrics); to conserve its meaning by use of vyākaraṇa (grammar) and nirukta (etymology); and to correctly perform the rites at the correct time by the use of kalpa (ritual) and jyotiṣa (astrology), gave rise to the six disciplines of the Vedāṇgas. Mathematics arose as a part of the last two disciplines, ritual and astronomy (which also included astrology). Since the Vedāṇgas immediately preceded the use of writing in ancient India, they formed the last of the exclusively oral literature. They were expressed in a highly compressed mnemonic form, the sūtra (literally, "thread"): The knowers of the sūtra know it as having few phonemes, being devoid of ambiguity, containing the essence, facing everything, being without pause and unobjectionable. Extreme brevity was achieved through multiple means, which included using ellipsis "beyond the tolerance of natural language," using technical names instead of longer descriptive names, abridging lists by only mentioning the first and last entries, and using markers and variables. The sūtras create the impression that communication through the text was "only a part of the whole instruction. The rest of the instruction must have been transmitted by the so-called Guru-shishya parampara, 'uninterrupted succession from teacher (guru) to the student (śisya),' and it was not open to the general public" and perhaps even kept secret. The brevity achieved in a sūtra is demonstrated in the following example from the Baudhāyana Śulba Sūtra (700 BCE). The domestic fire-altar in the Vedic period was required by ritual to have a square base and be constituted of five layers of bricks with 21 bricks in each layer. One method of constructing the altar was to divide one side of the square into three equal parts using a cord or rope, to next divide the transverse (or perpendicular) side into seven equal parts, and thereby sub-divide the square into 21 congruent rectangles. The bricks were then designed to be of the shape of the constituent rectangle and the layer was created. To form the next layer, the same formula was used, but the bricks were arranged transversely. The process was then repeated three more times (with alternating directions) in order to complete the construction. In the Baudhāyana Śulba Sūtra, this procedure is described in the following words: II.64. After dividing the quadri-lateral in seven, one divides the transverse [cord] in three.II.65. In another layer one places the [bricks] North-pointing. According to Filliozat, the officiant constructing the altar has only a few tools and materials at his disposal: a cord (Sanskrit, rajju, f.), two pegs (Sanskrit, śanku, m.), and clay to make the bricks (Sanskrit, iṣṭakā, f.). Concision is achieved in the sūtra, by not explicitly mentioning what the adjective "transverse" qualifies; however, from the feminine form of the (Sanskrit) adjective used, it is easily inferred to qualify "cord." Similarly, in the second stanza, "bricks" are not explicitly mentioned, but inferred again by the feminine plural form of "North-pointing." Finally, the first stanza, never explicitly says that the first layer of bricks are oriented in the east–west direction, but that too is implied by the explicit mention of "North-pointing" in the second stanza; for, if the orientation was meant to be the same in the two layers, it would either not be mentioned at all or be only mentioned in the first stanza. All these inferences are made by the officiant as he recalls the formula from his memory. == The written tradition: prose commentary == With the increasing complexity of mathematics and other exact sciences, both writing and computation were required. Consequently, many mathematical works began to be written down in manuscripts that were then copied and re-copied from generation to generation. India today is estimated to have about thirty million manuscripts, the largest body of handwritten reading material anywhere in the world. The literate culture of Indian science goes back to at least the fifth century B.C. ... as is shown by the elements of Mesopotamian omen literature and astronomy that entered India at that time and (were) definitely not ... preserved orally. The earliest mathematical prose commentary was that on the work, Āryabhaṭīya (written 499 CE), a work on astronomy and mathematics. The mathematical portion of the Āryabhaṭīya was composed of 33 sūtras (in verse form) consisting of mathematical statements or rules, but without any proofs. However, according to Hayashi, "this does not necessarily mean that their authors did not prove them. It was probably a matter of style of exposition." From the time of Bhaskara I (600 CE onwards), prose commentaries increasingly began to include some derivations (upapatti). Bhaskara I's commentary on the Āryabhaṭīya, had the following structure: Rule ('sūtra') in verse by Āryabhaṭa Commentary by Bhāskara I, consisting of: Elucidation of rule (derivations were still rare then, but became more common later) Example (uddeśaka) usually in verse. Setting (nyāsa/sthāpanā) of the numerical data. Working (karana) of the solution. Verification (pratyayakaraṇa, literally "to make conviction") of the answer. These became rare by the 13th century, derivations or proofs being favoured by then. Typically, for any mathematical topic, students in ancient India first memorised the sūtras, which, as explained earlier, were "deliberately inadequate" in explanatory details (in order to pithily convey the bare-bone mathematical rules). The students then worked through the topics of the prose commentary by writing (and drawing diagrams) on chalk- and dust-boards (i.e. boards covered with dust). The latter activity, a staple of mathematical work, was to later prompt mathematician-astronomer, Brahmagupta (fl. 7th century CE), to characterise astronomical computations as "dust work" (Sanskrit: dhulikarman). == Numerals and the decimal number system == It is well known that the decimal place-value system in use today was first recorded in India, then transmitted to the Islamic world, and eventually to Europe. The Syrian bishop Severus Sebokht wrote in the mid-7th century CE about the "nine signs" of the Indians for expressing numbers. However, how, when, and where the first decimal place value system was invented is not so clear. The earliest extant script used in India was the Kharoṣṭhī script used in the Gandhara culture of the north-west. It is thought to be of Aramaic origin and it was in use from the 4th century BCE to the 4th century CE. Almost contemporaneously, another script, the Brāhmī script, appeared on much of the sub-continent, and would later become the foundation of many scripts of South Asia and South-east Asia. Both scripts had numeral symbols and numeral systems, which were initially not based on a place-value system. The earliest surviving evidence of decimal place value numerals in India and southeast Asia is from the middle of the first millennium CE. A copper plate from Gujarat, India mentions the date 595 CE, written in a decimal place value notation, although there is some doubt as to the authenticity of the plate. Decimal numerals recording the years 683 CE have also been found in stone inscriptions in Indonesia and Cambodia, where Indian cultural influence was substantial. There are older textual sources, although the extant manuscript copies of these texts are from much later dates. Probably the earliest such source is the work of the Buddhist philosopher Vasumitra dated likely to the 1st century CE. Discussing the counting pits of merchants, Vasumitra remarks, "When [the same] clay counting-piece is in the place of units, it is denoted as one, when in hundreds, one hundred." Although such references seem to imply that his readers had knowledge of a decimal place value representation, the "brevity of their allusions and the ambiguity of their dates, however, do not solidly establish the chronology of the development of this concept." A third decimal representation was employed in a verse composition technique, later labelled Bhuta-sankhya (literally, "object numbers") used by early Sanskrit authors of technical books. Since many early technical works were composed in verse, numbers were often represented by objects in the natural or religious world that correspondence to them; this allowed a many-to-one correspondence for each number and made verse composition easier. According to Plofker, the number 4, for example, could be represented by the word "Veda" (since there were four of these religious texts), the number 32 by the word "teeth" (since a full set consists of 32), and the number 1 by "moon" (since there is only one moon). So, Veda/teeth/moon would correspond to the decimal numeral 1324, as the convention for numbers was to enumerate their digits from right to left. The earliest reference employing object numbers is a c. 269 CE Sanskrit text, Yavanajātaka (literally "Greek horoscopy") of Sphujidhvaja, a versification of an earlier (c. 150 CE) Indian prose adaptation of a lost work of Hellenistic astrology. Such use seems to make the case that by the mid-3rd century CE, the decimal place value system was familiar, at least to readers of astronomical and astrological texts in India. It has been hypothesized that the Indian decimal place value system was based on the symbols used on Chinese counting boards from as early as the middle of the first millennium BCE. According to Plofker, These counting boards, like the Indian counting pits, ..., had a decimal place value structure ... Indians may well have learned of these decimal place value "rod numerals" from Chinese Buddhist pilgrims or other travelers, or they may have developed the concept independently from their earlier non-place-value system; no documentary evidence survives to confirm either conclusion." == Bakhshali Manuscript == The oldest extant mathematical manuscript in India is the Bakhshali Manuscript, a birch bark manuscript written in "Buddhist hybrid Sanskrit" in the Śāradā script, which was used in the northwestern region of the Indian subcontinent between the 8th and 12th centuries CE. The manuscript was discovered in 1881 by a farmer while digging in a stone enclosure in the village of Bakhshali, near Peshawar (then in British India and now in Pakistan). Of unknown authorship and now preserved in the Bodleian Library in the University of Oxford, the manuscript has been dated recently as 224 AD- 383 AD. The surviving manuscript has seventy leaves, some of which are in fragments. Its mathematical content consists of rules and examples, written in verse, together with prose commentaries, which include solutions to the examples. The topics treated include arithmetic (fractions, square roots, profit and loss, simple interest, the rule of three, and regula falsi) and algebra (simultaneous linear equations and quadratic equations), and arithmetic progressions. In addition, there is a handful of geometric problems (including problems about volumes of irregular solids). The Bakhshali manuscript also "employs a decimal place value system with a dot for zero." Many of its problems are of a category known as 'equalisation problems' that lead to systems of linear equations. One example from Fragment III-5-3v is the following: One merchant has seven asava horses, a second has nine haya horses, and a third has ten camels. They are equally well off in the value of their animals if each gives two animals, one to each of the others. Find the price of each animal and the total value for the animals possessed by each merchant. The prose commentary accompanying the example solves the problem by converting it to three (under-determined) equations in four unknowns and assuming that the prices are all integers. In 2017, three samples from the manuscript were shown by radiocarbon dating to come from three different centuries: from 224 to 383 AD, 680-779 AD, and 885-993 AD. It is not known how fragments from different centuries came to be packaged together. == Classical period (400–1300) == This period is often known as the golden age of Indian Mathematics. This period saw mathematicians such as Aryabhata, Varahamihira, Brahmagupta, Bhaskara I, Mahavira, Bhaskara II, Madhava of Sangamagrama and Nilakantha Somayaji give broader and clearer shape to many branches of mathematics. Their contributions would spread to Asia, the Middle East, and eventually to Europe. Unlike Vedic mathematics, their works included both astronomical and mathematical contributions. In fact, mathematics of that period was included in the 'astral science' (jyotiḥśāstra) and consisted of three sub-disciplines: mathematical sciences (gaṇita or tantra), horoscope astrology (horā or jātaka) and divination (saṃhitā). This tripartite division is seen in Varāhamihira's 6th century compilation—Pancasiddhantika (literally panca, "five," siddhānta, "conclusion of deliberation", dated 575 CE)—of five earlier works, Surya Siddhanta, Romaka Siddhanta, Paulisa Siddhanta, Vasishtha Siddhanta and Paitamaha Siddhanta, which were adaptations of still earlier works of Mesopotamian, Greek, Egyptian, Roman and Indian astronomy. As explained earlier, the main texts were composed in Sanskrit verse, and were followed by prose commentaries. === Fourth to sixth centuries === Surya Siddhanta Though its authorship is unknown, the Surya Siddhanta (c. 400) contains the roots of modern trigonometry. Because it contains many words of foreign origin, some authors consider that it was written under the influence of Mesopotamia and Greece. This ancient text uses the following as trigonometric functions for the first time: Sine (Jya). Cosine (Kojya). Inverse sine (Otkram jya). Later Indian mathematicians such as Aryabhata made references to this text, while later Arabic and Latin translations were very influential in Europe and the Middle East. Chhedi calendar This Chhedi calendar (594) contains an early use of the modern place-value Hindu–Arabic numeral system now used universally. Aryabhata I Aryabhata (476–550) wrote the Aryabhatiya. He described the important fundamental principles of mathematics in 332 shlokas. The treatise contained: Quadratic equations Trigonometry The value of π, correct to 4 decimal places. Aryabhata also wrote the Arya Siddhanta, which is now lost. Aryabhata's contributions include: Trigonometry: (See also : Aryabhata's sine table) Introduced the trigonometric functions. Defined the sine (jya) as the modern relationship between half an angle and half a chord. Defined the cosine (kojya). Defined the versine (utkrama-jya). Defined the inverse sine (otkram jya). Gave methods of calculating their approximate numerical values. Contains the earliest tables of sine, cosine and versine values, in 3.75° intervals from 0° to 90°, to 4 decimal places of accuracy. Contains the trigonometric formula sin(n + 1)x − sin nx = sin nx − sin(n − 1)x − (1/225)sin nx. Spherical trigonometry. Arithmetic: Simple continued fractions. Algebra: Solutions of simultaneous quadratic equations. Whole number solutions of linear equations by a method equivalent to the modern method. General solution of the indeterminate linear equation . Mathematical astronomy: Accurate calculations for astronomical constants, such as the: Solar eclipse. Lunar eclipse. The formula for the sum of the cubes, which was an important step in the development of integral calculus. Varahamihira Varahamihira (505–587) produced the Pancha Siddhanta (The Five Astronomical Canons). He made important contributions to trigonometry, including sine and cosine tables to 4 decimal places of accuracy and the following formulas relating sine and cosine functions: sin 2 ( x ) + cos 2 ( x ) = 1 {\displaystyle \sin ^{2}(x)+\cos ^{2}(x)=1} sin ( x ) = cos ( π 2 − x ) {\displaystyle \sin(x)=\cos \left({\frac {\pi }{2}}-x\right)} 1 − cos ( 2 x ) 2 = sin 2 ( x ) {\displaystyle {\frac {1-\cos(2x)}{2}}=\sin ^{2}(x)} === Seventh and eighth centuries === In the 7th century, two separate fields, arithmetic (which included measurement) and algebra, began to emerge in Indian mathematics. The two fields would later be called pāṭī-gaṇita (literally "mathematics of algorithms") and bīja-gaṇita (lit. "mathematics of seeds," with "seeds"—like the seeds of plants—representing unknowns with the potential to generate, in this case, the solutions of equations). Brahmagupta, in his astronomical work Brāhma Sphuṭa Siddhānta (628 CE), included two chapters (12 and 18) devoted to these fields. Chapter 12, containing 66 Sanskrit verses, was divided into two sections: "basic operations" (including cube roots, fractions, ratio and proportion, and barter) and "practical mathematics" (including mixture, mathematical series, plane figures, stacking bricks, sawing of timber, and piling of grain). In the latter section, he stated his famous theorem on the diagonals of a cyclic quadrilateral: Brahmagupta's theorem: If a cyclic quadrilateral has diagonals that are perpendicular to each other, then the perpendicular line drawn from the point of intersection of the diagonals to any side of the quadrilateral always bisects the opposite side. Chapter 12 also included a formula for the area of a cyclic quadrilateral (a generalisation of Heron's formula), as well as a complete description of rational triangles (i.e. triangles with rational sides and rational areas). Brahmagupta's formula: The area, A, of a cyclic quadrilateral with sides of lengths a, b, c, d, respectively, is given by A = ( s − a ) ( s − b ) ( s − c ) ( s − d ) {\displaystyle A={\sqrt {(s-a)(s-b)(s-c)(s-d)}}\,} where s, the semiperimeter, given by s = a + b + c + d 2 . {\displaystyle s={\frac {a+b+c+d}{2}}.} Brahmagupta's Theorem on rational triangles: A triangle with rational sides a , b , c {\displaystyle a,b,c} and rational area is of the form: a = u 2 v + v , b = u 2 w + w , c = u 2 v + u 2 w − ( v + w ) {\displaystyle a={\frac {u^{2}}{v}}+v,\ \ b={\frac {u^{2}}{w}}+w,\ \ c={\frac {u^{2}}{v}}+{\frac {u^{2}}{w}}-(v+w)} for some rational numbers u , v , {\displaystyle u,v,} and w {\displaystyle w} . Chapter 18 contained 103 Sanskrit verses which began with rules for arithmetical operations involving zero and negative numbers and is considered the first systematic treatment of the subject. The rules (which included a + 0 = a {\displaystyle a+0=\ a} and a × 0 = 0 {\displaystyle a\times 0=0} ) were all correct, with one exception: 0 0 = 0 {\displaystyle {\frac {0}{0}}=0} . Later in the chapter, he gave the first explicit (although still not completely general) solution of the quadratic equation: a x 2 + b x = c {\displaystyle \ ax^{2}+bx=c} To the absolute number multiplied by four times the [coefficient of the] square, add the square of the [coefficient of the] middle term; the square root of the same, less the [coefficient of the] middle term, being divided by twice the [coefficient of the] square is the value. This is equivalent to: x = 4 a c + b 2 − b 2 a {\displaystyle x={\frac {{\sqrt {4ac+b^{2}}}-b}{2a}}} Also in chapter 18, Brahmagupta was able to make progress in finding (integral) solutions of Pell's equation, x 2 − N y 2 = 1 , {\displaystyle \ x^{2}-Ny^{2}=1,} where N {\displaystyle N} is a nonsquare integer. He did this by discovering the following identity: Brahmagupta's Identity: ( x 2 − N y 2 ) ( x ′ 2 − N y ′ 2 ) = ( x x ′ + N y y ′ ) 2 − N ( x y ′ + x ′ y ) 2 {\displaystyle \ (x^{2}-Ny^{2})(x'^{2}-Ny'^{2})=(xx'+Nyy')^{2}-N(xy'+x'y)^{2}} which was a generalisation of an earlier identity of Diophantus: Brahmagupta used his identity to prove the following lemma: Lemma (Brahmagupta): If x = x 1 , y = y 1 {\displaystyle x=x_{1},\ \ y=y_{1}\ \ } is a solution of x 2 − N y 2 = k 1 , {\displaystyle \ \ x^{2}-Ny^{2}=k_{1},} and, x = x 2 , y = y 2 {\displaystyle x=x_{2},\ \ y=y_{2}\ \ } is a solution of x 2 − N y 2 = k 2 , {\displaystyle \ \ x^{2}-Ny^{2}=k_{2},} , then: x = x 1 x 2 + N y 1 y 2 , y = x 1 y 2 + x 2 y 1 {\displaystyle x=x_{1}x_{2}+Ny_{1}y_{2},\ \ y=x_{1}y_{2}+x_{2}y_{1}\ \ } is a solution of x 2 − N y 2 = k 1 k 2 {\displaystyle \ x^{2}-Ny^{2}=k_{1}k_{2}} He then used this lemma to both generate infinitely many (integral) solutions of Pell's equation, given one solution, and state the following theorem: Theorem (Brahmagupta): If the equation x 2 − N y 2 = k {\displaystyle \ x^{2}-Ny^{2}=k} has an integer solution for any one of k = ± 4 , ± 2 , − 1 {\displaystyle \ k=\pm 4,\pm 2,-1} then Pell's equation: x 2 − N y 2 = 1 {\displaystyle \ x^{2}-Ny^{2}=1} also has an integer solution. Brahmagupta did not actually prove the theorem, but rather worked out examples using his method. The first example he presented was: Example (Brahmagupta): Find integers x , y {\displaystyle \ x,\ y\ } such that: x 2 − 92 y 2 = 1 {\displaystyle \ x^{2}-92y^{2}=1} In his commentary, Brahmagupta added, "a person solving this problem within a year is a mathematician." The solution he provided was: x = 1151 , y = 120 {\displaystyle \ x=1151,\ y=120} Bhaskara I Bhaskara I (c. 600–680) expanded the work of Aryabhata in his books titled Mahabhaskariya, Aryabhatiya-bhashya and Laghu-bhaskariya. He produced: Solutions of indeterminate equations. A rational approximation of the sine function. A formula for calculating the sine of an acute angle without the use of a table, correct to two decimal places. === Ninth to twelfth centuries === Virasena Virasena (8th century) was a Jain mathematician in the court of Rashtrakuta King Amoghavarsha of Manyakheta, Karnataka. He wrote the Dhavala, a commentary on Jain mathematics, which: Deals with the concept of ardhaccheda, the number of times a number could be halved, and lists various rules involving this operation. This coincides with the binary logarithm when applied to powers of two, but differs on other numbers, more closely resembling the 2-adic order. Virasena also gave: The derivation of the volume of a frustum by a sort of infinite procedure. It is thought that much of the mathematical material in the Dhavala can attributed to previous writers, especially Kundakunda, Shamakunda, Tumbulura, Samantabhadra and Bappadeva and date who wrote between 200 and 600 CE. Mahavira Mahavira Acharya (c. 800–870) from Karnataka, the last of the notable Jain mathematicians, lived in the 9th century and was patronised by the Rashtrakuta king Amoghavarsha. He wrote a book titled Ganit Saar Sangraha on numerical mathematics, and also wrote treatises about a wide range of mathematical topics. These include the mathematics of: Zero Squares Cubes square roots, cube roots, and the series extending beyond these Plane geometry Solid geometry Problems relating to the casting of shadows Formulae derived to calculate the area of an ellipse and quadrilateral inside a circle. Mahavira also: Asserted that the square root of a negative number did not exist Gave the sum of a series whose terms are squares of an arithmetical progression, and gave empirical rules for area and perimeter of an ellipse. Solved cubic equations. Solved quartic equations. Solved some quintic equations and higher-order polynomials. Gave the general solutions of the higher order polynomial equations: a x n = q {\displaystyle \ ax^{n}=q} a x n − 1 x − 1 = p {\displaystyle a{\frac {x^{n}-1}{x-1}}=p} Solved indeterminate quadratic equations. Solved indeterminate cubic equations. Solved indeterminate higher order equations. Shridhara Shridhara (c. 870–930), who lived in Bengal, wrote the books titled Nav Shatika, Tri Shatika and Pati Ganita. He gave: A good rule for finding the volume of a sphere. The formula for solving quadratic equations. The Pati Ganita is a work on arithmetic and measurement. It deals with various operations, including: Elementary operations Extracting square and cube roots. Fractions. Eight rules given for operations involving zero. Methods of summation of different arithmetic and geometric series, which were to become standard references in later works. Manjula Aryabhata's equations were elaborated in the 10th century by Manjula (also Munjala), who realised that the expression sin w ′ − sin w {\displaystyle \ \sin w'-\sin w} could be approximately expressed as ( w ′ − w ) cos w {\displaystyle \ (w'-w)\cos w} This was elaborated by his later successor Bhaskara ii thereby finding the derivative of sine. Aryabhata II Aryabhata II (c. 920–1000) wrote a commentary on Shridhara, and an astronomical treatise Maha-Siddhanta. The Maha-Siddhanta has 18 chapters, and discusses: Numerical mathematics (Ank Ganit). Algebra. Solutions of indeterminate equations (kuttaka). Shripati Shripati Mishra (1019–1066) wrote the books Siddhanta Shekhara, a major work on astronomy in 19 chapters, and Ganit Tilaka, an incomplete arithmetical treatise in 125 verses based on a work by Shridhara. He worked mainly on: Permutations and combinations. General solution of the simultaneous indeterminate linear equation. He was also the author of Dhikotidakarana, a work of twenty verses on: Solar eclipse. Lunar eclipse. The Dhruvamanasa is a work of 105 verses on: Calculating planetary longitudes eclipses. planetary transits. Nemichandra Siddhanta Chakravati Nemichandra Siddhanta Chakravati (c. 1100) authored a mathematical treatise titled Gome-mat Saar. Bhaskara II Bhāskara II (1114–1185) was a mathematician-astronomer who wrote a number of important treatises, namely the Siddhanta Shiromani, Lilavati, Bijaganita, Gola Addhaya, Griha Ganitam and Karan Kautoohal. A number of his contributions were later transmitted to the Middle East and Europe. His contributions include: Arithmetic: Interest computation Arithmetical and geometrical progressions Plane geometry Solid geometry The shadow of the gnomon Solutions of combinations Gave a proof for division by zero being infinity. Algebra: The recognition of a positive number having two square roots. Surds. Operations with products of several unknowns. The solutions of: Quadratic equations. Cubic equations. Quartic equations. Equations with more than one unknown. Quadratic equations with more than one unknown. The general form of Pell's equation using the chakravala method. The general indeterminate quadratic equation using the chakravala method. Indeterminate cubic equations. Indeterminate quartic equations. Indeterminate higher-order polynomial equations. Geometry: Gave a proof of the Pythagorean theorem. Calculus: Preliminary concept of differentiation Discovered the differential coefficient. Stated early form of Rolle's theorem, a special case of the mean value theorem (one of the most important theorems of calculus and analysis). Derived the differential of the sine function although didn't perceive the notion of derivative. Computed π, correct to five decimal places. Calculated the length of the Earth's revolution around the Sun to 9 decimal places. Trigonometry: Developments of spherical trigonometry The trigonometric formulas: sin ( a + b ) = sin ( a ) cos ( b ) + sin ( b ) cos ( a ) {\displaystyle \ \sin(a+b)=\sin(a)\cos(b)+\sin(b)\cos(a)} sin ( a − b ) = sin ( a ) cos ( b ) − sin ( b ) cos ( a ) {\displaystyle \ \sin(a-b)=\sin(a)\cos(b)-\sin(b)\cos(a)} == Medieval and early modern mathematics (1300–1800) == === Navya-Nyaya === The Navya-Nyāya or Neo-Logical darśana (school) of Indian philosophy was founded in the 13th century by the philosopher Gangesha Upadhyaya of Mithila. It was a development of the classical Nyāya darśana. Other influences on Navya-Nyāya were the work of earlier philosophers Vācaspati Miśra (900–980 CE) and Udayana (late 10th century). Gangeśa's book Tattvacintāmaṇi ("Thought-Jewel of Reality") was written partly in response to Śrīharśa's Khandanakhandakhādya, a defence of Advaita Vedānta, which had offered a set of thorough criticisms of Nyāya theories of thought and language. Navya-Nyāya developed a sophisticated language and conceptual scheme that allowed it to raise, analyze, and solve problems in logic and epistemology. It involves naming each object to be analyzed, identifying a distinguishing characteristic for the named object, and verifying the appropriateness of the defining characteristic using pramanas. === Kerala School === The Kerala school of astronomy and mathematics was founded by Madhava of Sangamagrama in Kerala, South India and included among its members: Parameshvara, Neelakanta Somayaji, Jyeshtadeva, Achyuta Pisharati, Melpathur Narayana Bhattathiri and Achyuta Panikkar. It flourished between the 14th and 16th centuries and the original discoveries of the school seems to have ended with Narayana Bhattathiri (1559–1632). In attempting to solve astronomical problems, the Kerala school astronomers independently created a number of important mathematics concepts. The most important results, series expansion for trigonometric functions, were given in Sanskrit verse in a book by Neelakanta called Tantrasangraha and a commentary on this work called Tantrasangraha-vakhya of unknown authorship. The theorems were stated without proof, but proofs for the series for sine, cosine, and inverse tangent were provided a century later in the work Yuktibhāṣā (c.1500–c.1610), written in Malayalam, by Jyesthadeva. Their discovery of these three important series expansions of calculus—several centuries before calculus was developed in Europe by Isaac Newton and Gottfried Leibniz—was an achievement. However, the Kerala School did not invent calculus, because, while they were able to develop Taylor series expansions for the important trigonometric functions, they developed neither a theory of differentiation or integration, nor the fundamental theorem of calculus. The results obtained by the Kerala school include: The (infinite) geometric series: 1 1 − x = 1 + x + x 2 + x 3 + x 4 + ⋯ for | x | < 1 {\displaystyle {\frac {1}{1-x}}=1+x+x^{2}+x^{3}+x^{4}+\cdots {\text{ for }}|x|<1} A semi-rigorous proof (see "induction" remark below) of the result: 1 p + 2 p + ⋯ + n p ≈ n p + 1 p + 1 {\displaystyle 1^{p}+2^{p}+\cdots +n^{p}\approx {\frac {n^{p+1}}{p+1}}} for large n. Intuitive use of mathematical induction, however, the inductive hypothesis was not formulated or employed in proofs. Applications of ideas from (what was to become) differential and integral calculus to obtain (Taylor–Maclaurin) infinite series for sin x, cos x, and arctan x. The Tantrasangraha-vakhya gives the series in verse, which when translated to mathematical notation, can be written as: r arctan ( y x ) = 1 1 ⋅ r y x − 1 3 ⋅ r y 3 x 3 + 1 5 ⋅ r y 5 x 5 − ⋯ , where y / x ≤ 1. {\displaystyle r\arctan \left({\frac {y}{x}}\right)={\frac {1}{1}}\cdot {\frac {ry}{x}}-{\frac {1}{3}}\cdot {\frac {ry^{3}}{x^{3}}}+{\frac {1}{5}}\cdot {\frac {ry^{5}}{x^{5}}}-\cdots ,{\text{ where }}y/x\leq 1.} r sin x = x − x x 2 ( 2 2 + 2 ) r 2 + x x 2 ( 2 2 + 2 ) r 2 ⋅ x 2 ( 4 2 + 4 ) r 2 − ⋯ {\displaystyle r\sin x=x-x{\frac {x^{2}}{(2^{2}+2)r^{2}}}+x{\frac {x^{2}}{(2^{2}+2)r^{2}}}\cdot {\frac {x^{2}}{(4^{2}+4)r^{2}}}-\cdots } r − cos x = r x 2 ( 2 2 − 2 ) r 2 − r x 2 ( 2 2 − 2 ) r 2 x 2 ( 4 2 − 4 ) r 2 + ⋯ , {\displaystyle r-\cos x=r{\frac {x^{2}}{(2^{2}-2)r^{2}}}-r{\frac {x^{2}}{(2^{2}-2)r^{2}}}{\frac {x^{2}}{(4^{2}-4)r^{2}}}+\cdots ,} where, for r = 1, the series reduces to the standard power series for these trigonometric functions, for example: sin x = x − x 3 3 ! + x 5 5 ! − x 7 7 ! + ⋯ {\displaystyle \sin x=x-{\frac {x^{3}}{3!}}+{\frac {x^{5}}{5!}}-{\frac {x^{7}}{7!}}+\cdots } and cos x = 1 − x 2 2 ! + x 4 4 ! − x 6 6 ! + ⋯ {\displaystyle \cos x=1-{\frac {x^{2}}{2!}}+{\frac {x^{4}}{4!}}-{\frac {x^{6}}{6!}}+\cdots } Use of rectification (computation of length) of the arc of a circle to give a proof of these results. (The later method of Leibniz, using quadrature, i.e. computation of area under the arc of the circle, was not used.) Use of the series expansion of arctan x {\displaystyle \arctan x} to obtain the Leibniz formula for π: π 4 = 1 − 1 3 + 1 5 − 1 7 + ⋯ {\displaystyle {\frac {\pi }{4}}=1-{\frac {1}{3}}+{\frac {1}{5}}-{\frac {1}{7}}+\cdots } A rational approximation of error for the finite sum of their series of interest. For example, the error, f i ( n + 1 ) {\displaystyle f_{i}(n+1)} , (for n odd, and i = 1, 2, 3) for the series: π 4 ≈ 1 − 1 3 + 1 5 − ⋯ + ( − 1 ) ( n − 1 ) / 2 1 n + ( − 1 ) ( n + 1 ) / 2 f i ( n + 1 ) {\displaystyle {\frac {\pi }{4}}\approx 1-{\frac {1}{3}}+{\frac {1}{5}}-\cdots +(-1)^{(n-1)/2}{\frac {1}{n}}+(-1)^{(n+1)/2}f_{i}(n+1)} where f 1 ( n ) = 1 2 n , f 2 ( n ) = n / 2 n 2 + 1 , f 3 ( n ) = ( n / 2 ) 2 + 1 ( n 2 + 5 ) n / 2 . {\displaystyle {\text{where }}f_{1}(n)={\frac {1}{2n}},\ f_{2}(n)={\frac {n/2}{n^{2}+1}},\ f_{3}(n)={\frac {(n/2)^{2}+1}{(n^{2}+5)n/2}}.} Manipulation of error term to derive a faster converging series for π {\displaystyle \pi } : π 4 = 3 4 + 1 3 3 − 3 − 1 5 3 − 5 + 1 7 3 − 7 − ⋯ {\displaystyle {\frac {\pi }{4}}={\frac {3}{4}}+{\frac {1}{3^{3}-3}}-{\frac {1}{5^{3}-5}}+{\frac {1}{7^{3}-7}}-\cdots } Using the improved series to derive a rational expression, 104348/33215 for π correct up to nine decimal places, i.e. 3.141592653. Use of an intuitive notion of limit to compute these results. A semi-rigorous (see remark on limits above) method of differentiation of some trigonometric functions. However, they did not formulate the notion of a function, or have knowledge of the exponential or logarithmic functions. The works of the Kerala school were first written up for the Western world by Englishman C.M. Whish in 1835. According to Whish, the Kerala mathematicians had "laid the foundation for a complete system of fluxions" and these works abounded "with fluxional forms and series to be found in no work of foreign countries." However, Whish's results were almost completely neglected, until over a century later, when the discoveries of the Kerala school were investigated again by C. Rajagopal and his associates. Their work includes commentaries on the proofs of the arctan series in Yuktibhāṣā given in two papers, a commentary on the Yuktibhāṣā's proof of the sine and cosine series and two papers that provide the Sanskrit verses of the Tantrasangrahavakhya for the series for arctan, sin, and cosine (with English translation and commentary). Parameshvara (c. 1370–1460) wrote commentaries on the works of Bhaskara I, Aryabhata and Bhaskara II. His Lilavati Bhasya, a commentary on Bhaskara II's Lilavati, contains one of his important discoveries: a version of the mean value theorem. Nilakantha Somayaji (1444–1544) composed the Tantra Samgraha (which 'spawned' a later anonymous commentary Tantrasangraha-vyakhya and a further commentary by the name Yuktidipaika, written in 1501). He elaborated and extended the contributions of Madhava. Citrabhanu (c. 1530) was a 16th-century mathematician from Kerala who gave integer solutions to 21 types of systems of two simultaneous algebraic equations in two unknowns. These types are all the possible pairs of equations of the following seven forms: x + y = a , x − y = b , x y = c , x 2 + y 2 = d , x 2 − y 2 = e , x 3 + y 3 = f , x 3 − y 3 = g {\displaystyle {\begin{aligned}&x+y=a,\ x-y=b,\ xy=c,x^{2}+y^{2}=d,\\[8pt]&x^{2}-y^{2}=e,\ x^{3}+y^{3}=f,\ x^{3}-y^{3}=g\end{aligned}}} For each case, Citrabhanu gave an explanation and justification of his rule as well as an example. Some of his explanations are algebraic, while others are geometric. Jyesthadeva (c. 1500–1575) was another member of the Kerala School. His key work was the Yukti-bhāṣā (written in Malayalam, a regional language of Kerala). Jyesthadeva presented proofs of most mathematical theorems and infinite series earlier discovered by Madhava and other Kerala School mathematicians. === Others === Narayana Pandit was a 14th century mathematician who composed two important mathematical works, an arithmetical treatise, Ganita Kaumudi, and an algebraic treatise, Bijganita Vatamsa. Ganita Kaumudi is one of the most revolutionary works in the field of combinatorics with developing a method for systematic generation of all permutations of a given sequence. In his Ganita Kaumudi Narayana proposed the following problem on a herd of cows and calves: A cow produces one calf every year. Beginning in its fourth year, each calf produces one calf at the beginning of each year. How many cows and calves are there altogether after 20 years? Translated into the modern mathematical language of recurrence sequences: Nn = Nn-1 + Nn-3 for n > 2, with initial values N0 = N1 = N2 = 1. The first few terms are 1, 1, 1, 2, 3, 4, 6, 9, 13, 19, 28, 41, 60, 88,... (sequence A000930 in the OEIS). The limit ratio between consecutive terms is the supergolden ratio. . Narayana is also thought to be the author of an elaborate commentary of Bhaskara II's Lilavati, titled Ganita Kaumudia(or Karma-Paddhati). == Charges of Eurocentrism == It has been suggested that Indian contributions to mathematics have not been given due acknowledgement in modern history and that many discoveries and inventions by Indian mathematicians are presently culturally attributed to their Western counterparts, as a result of Eurocentrism. According to G. G. Joseph's take on "Ethnomathematics": [Their work] takes on board some of the objections raised about the classical Eurocentric trajectory. The awareness [of Indian and Arabic mathematics] is all too likely to be tempered with dismissive rejections of their importance compared to Greek mathematics. The contributions from other civilisations – most notably China and India, are perceived either as borrowers from Greek sources or having made only minor contributions to mainstream mathematical development. An openness to more recent research findings, especially in the case of Indian and Chinese mathematics, is sadly missing" Historian of mathematics Florian Cajori wrote that he and others "suspect that Diophantus got his first glimpse of algebraic knowledge from India". He also wrote that "it is certain that portions of Hindu mathematics are of Greek origin". More recently, as discussed in the above section, the infinite series of calculus for trigonometric functions (rediscovered by Gregory, Taylor, and Maclaurin in the late 17th century) were described in India, by mathematicians of the Kerala school, some two centuries earlier. Some scholars have recently suggested that knowledge of these results might have been transmitted to Europe through the trade route from Kerala by traders and Jesuit missionaries. Kerala was in continuous contact with China and Arabia, and, from around 1500, with Europe. The fact that the communication routes existed and the chronology is suitable certainly make such transmission a possibility. However, no evidence of transmission has been found. According to David Bressoud, "there is no evidence that the Indian work of series was known beyond India, or even outside of Kerala, until the nineteenth century". Both Arab and Indian scholars made discoveries before the 17th century that are now considered a part of calculus. However, they did not (as Newton and Leibniz did) "combine many differing ideas under the two unifying themes of the derivative and the integral, show the connection between the two, and turn calculus into the great problem-solving tool we have today". The intellectual careers of both Newton and Leibniz are well-documented and there is no indication of their work not being their own; however, it is not known with certainty whether the immediate predecessors of Newton and Leibniz, "including, in particular, Fermat and Roberval, [may have] learned of some of the ideas of the Islamic and Indian mathematicians through sources we are not now aware." This is an area of current research, especially in the manuscript collections of Spain and Maghreb, and is being pursued, among other places, at the CNRS. == See also == == Notes == == References == Bourbaki, Nicolas (1998), Elements of the History of Mathematics, Berlin, Heidelberg, and New York: Springer-Verlag, 301 pages, ISBN 978-3-540-64767-6. Boyer, C. B.; Merzback (fwd. by Isaac Asimov), U. C. (1991), History of Mathematics, New York: John Wiley and Sons, 736 pages, ISBN 978-0-471-54397-8. Bressoud, David (2002), "Was Calculus Invented in India?", The College Mathematics Journal, 33 (1): 2–13, doi:10.2307/1558972, JSTOR 1558972. Bronkhorst, Johannes (2001), "Panini and Euclid: Reflections on Indian Geometry", Journal of Indian Philosophy, 29 (1–2), Springer Netherlands: 43–80, doi:10.1023/A:1017506118885, S2CID 115779583. Burnett, Charles (2006), "The Semantics of Indian Numerals in Arabic, Greek and Latin", Journal of Indian Philosophy, 34 (1–2), Springer-Netherlands: 15–30, doi:10.1007/s10781-005-8153-z, S2CID 170783929. Burton, David M. (1997), The History of Mathematics: An Introduction, The McGraw-Hill Companies, Inc., pp. 193–220. Cooke, Roger (2005), The History of Mathematics: A Brief Course, New York: Wiley-Interscience, 632 pages, ISBN 978-0-471-44459-6. Dani, S. G. (25 July 2003), "On the Pythagorean triples in the Śulvasūtras" (PDF), Current Science, 85 (2): 219–224, archived from the original (PDF) on 4 August 2003. Datta, Bibhutibhusan (December 1931), "Early Literary Evidence of the Use of the Zero in India", The American Mathematical Monthly, 38 (10): 566–572, doi:10.2307/2301384, JSTOR 2301384. Datta, Bibhutibhusan; Singh, Avadesh Narayan (1962), History of Hindu Mathematics : A source book, Bombay: Asia Publishing House{{citation}}: CS1 maint: publisher location (link). De Young, Gregg (1995), "Euclidean Geometry in the Mathematical Tradition of Islamic India", Historia Mathematica, 22 (2): 138–153, doi:10.1006/hmat.1995.1014. Kim Plofker (2007), "mathematics, South Asian", Encyclopaedia Britannica Online, pp. 1–12, retrieved 18 May 2007. Filliozat, Pierre-Sylvain (2004), "Ancient Sanskrit Mathematics: An Oral Tradition and a Written Literature", in Chemla, Karine; Cohen, Robert S.; Renn, Jürgen; et al. (eds.), History of Science, History of Text (Boston Series in the Philosophy of Science), Dordrecht: Springer Netherlands, 254 pages, pp. 137–157, pp. 360–375, doi:10.1007/1-4020-2321-9_7, ISBN 978-1-4020-2320-0. Fowler, David (1996), "Binomial Coefficient Function", The American Mathematical Monthly, 103 (1): 1–17, doi:10.2307/2975209, JSTOR 2975209. Hayashi, Takao (1995), The Bakhshali Manuscript, An ancient Indian mathematical treatise, Groningen: Egbert Forsten, 596 pages, ISBN 978-90-6980-087-5. Hayashi, Takao (1997), "Aryabhata's Rule and Table of Sine-Differences", Historia Mathematica, 24 (4): 396–406, doi:10.1006/hmat.1997.2160. Hayashi, Takao (2003), "Indian Mathematics", in Grattan-Guinness, Ivor (ed.), Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences, vol. 1, Baltimore, MD: The Johns Hopkins University Press, pp. 118–130, ISBN 978-0-8018-7396-6. Hayashi, Takao (2005), "Indian Mathematics", in Flood, Gavin (ed.), The Blackwell Companion to Hinduism, Oxford: Basil Blackwell, 616 pages, pp. 360–375, pp. 360–375, ISBN 978-1-4051-3251-0. Henderson, David W. (2000), "Square roots in the Sulba Sutras", in Gorini, Catherine A. (ed.), Geometry at Work: Papers in Applied Geometry, vol. 53, Washington DC: Mathematical Association of America Notes, pp. 39–45, ISBN 978-0-88385-164-7. Ifrah, Georges (2000). A Universal History of Numbers: From Prehistory to Computers. New York: Wiley. ISBN 0471393401. Joseph, G. G. (2000), The Crest of the Peacock: The Non-European Roots of Mathematics, Princeton, NJ: Princeton University Press, 416 pages, ISBN 978-0-691-00659-8. Katz, Victor J. (1995), "Ideas of Calculus in Islam and India", Mathematics Magazine, 68 (3): 163–174, doi:10.2307/2691411, JSTOR 2691411. Katz, Victor J., ed. (2007), The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook, Princeton, NJ: Princeton University Press, pp. 385–514, ISBN 978-0-691-11485-9. Keller, Agathe (2005), "Making diagrams speak, in Bhāskara I's commentary on the Aryabhaṭīya" (PDF), Historia Mathematica, 32 (3): 275–302, doi:10.1016/j.hm.2004.09.001. Kichenassamy, Satynad (2006), "Baudhāyana's rule for the quadrature of the circle", Historia Mathematica, 33 (2): 149–183, doi:10.1016/j.hm.2005.05.001. Neugebauer, Otto; Pingree, David, eds. (1970), The Pañcasiddhāntikā of Varāhamihira, Copenhagen{{citation}}: CS1 maint: location missing publisher (link). New edition with translation and commentary, (2 Vols.). Pingree, David (1971), "On the Greek Origin of the Indian Planetary Model Employing a Double Epicycle", Journal of Historical Astronomy, 2 (1): 80–85, Bibcode:1971JHA.....2...80P, doi:10.1177/002182867100200202, S2CID 118053453. Pingree, David (1973), "The Mesopotamian Origin of Early Indian Mathematical Astronomy", Journal of Historical Astronomy, 4 (1): 1–12, Bibcode:1973JHA.....4....1P, doi:10.1177/002182867300400102, S2CID 125228353. Pingree, David, ed. (1978), The Yavanajātaka of Sphujidhvaja, Harvard Oriental Series 48 (2 vols.), Edited, translated and commented by D. Pingree, Cambridge, MA{{citation}}: CS1 maint: location missing publisher (link). Pingree, David (1988), "Reviewed Work(s): The Fidelity of Oral Tradition and the Origins of Science by Frits Staal", Journal of the American Oriental Society, 108 (4): 637–638, doi:10.2307/603154, JSTOR 603154. Pingree, David (1992), "Hellenophilia versus the History of Science", Isis, 83 (4): 554–563, Bibcode:1992Isis...83..554P, doi:10.1086/356288, JSTOR 234257, S2CID 68570164 Pingree, David (2003), "The logic of non-Western science: mathematical discoveries in medieval India", Daedalus, 132 (4): 45–54, doi:10.1162/001152603771338779, S2CID 57559157. Plofker, Kim (1996), "An Example of the Secant Method of Iterative Approximation in a Fifteenth-Century Sanskrit Text", Historia Mathematica, 23 (3): 246–256, doi:10.1006/hmat.1996.0026. Plofker, Kim (2001), "The "Error" in the Indian "Taylor Series Approximation" to the Sine", Historia Mathematica, 28 (4): 283–295, doi:10.1006/hmat.2001.2331. Plofker, K. (2007), "Mathematics of India", in Katz, Victor J. (ed.), The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook, Princeton, NJ: Princeton University Press, pp. 385–514, ISBN 978-0-691-11485-9. Plofker, Kim (2009), Mathematics in India: 500 BCE–1800 CE, Princeton, NJ: Princeton University Press, ISBN 978-0-691-12067-6. Price, John F. (2000), "Applied geometry of the Sulba Sutras" (PDF), in Gorini, Catherine A. (ed.), Geometry at Work: Papers in Applied Geometry, vol. 53, Washington DC: Mathematical Association of America Notes, pp. 46–58, ISBN 978-0-88385-164-7, archived from the original (PDF) on 27 September 2007, retrieved 20 May 2007. Roy, Ranjan (1990), "Discovery of the Series Formula for π {\displaystyle \pi } by Leibniz, Gregory, and Nilakantha", Mathematics Magazine, 63 (5): 291–306, doi:10.2307/2690896, JSTOR 2690896. Singh, A. N. (1936), "On the Use of Series in Hindu Mathematics", Osiris, 1 (1): 606–628, doi:10.1086/368443, JSTOR 301627, S2CID 144760421 Staal, Frits (1986), "The Fidelity of Oral Tradition and the Origins of Science", Mededelingen der Koninklijke Nederlandse Akademie von Wetenschappen, Afd. Letterkunde, New Series, 49 (8), Amsterdam: North Holland Publishing Company. Staal, Frits (1995), "The Sanskrit of science", Journal of Indian Philosophy, 23 (1), Springer Netherlands: 73–127, doi:10.1007/BF01062067, S2CID 170755274. Staal, Frits (1999), "Greek and Vedic Geometry", Journal of Indian Philosophy, 27 (1–2): 105–127, doi:10.1023/A:1004364417713, S2CID 170894641. Staal, Frits (2001), "Squares and oblongs in the Veda", Journal of Indian Philosophy, 29 (1–2), Springer Netherlands: 256–272, doi:10.1023/A:1017527129520, S2CID 170403804. Staal, Frits (2006), "Artificial Languages Across Sciences and Civilisations", Journal of Indian Philosophy, 34 (1), Springer Netherlands: 89–141, doi:10.1007/s10781-005-8189-0, S2CID 170968871. Stillwell, John (2004), Mathematics and its History, Undergraduate Texts in Mathematics (2 ed.), Springer, Berlin and New York, 568 pages, doi:10.1007/978-1-4684-9281-1, ISBN 978-0-387-95336-6. Thibaut, George (1984) [1875], Mathematics in the Making in Ancient India: reprints of 'On the Sulvasutras' and 'Baudhyayana Sulva-sutra', Calcutta and Delhi: K. P. Bagchi and Company (orig. Journal of the Asiatic Society of Bengal), 133 pages. van der Waerden, B. L. (1983), Geometry and Algebra in Ancient Civilisations, Berlin and New York: Springer, 223 pages, ISBN 978-0-387-12159-8 van der Waerden, B. L. (1988), "On the Romaka-Siddhānta", Archive for History of Exact Sciences, 38 (1): 1–11, doi:10.1007/BF00329976, S2CID 189788738 van der Waerden, B. L. (1988), "Reconstruction of a Greek table of chords", Archive for History of Exact Sciences, 38 (1): 23–38, Bibcode:1988AHES...38...23V, doi:10.1007/BF00329978, S2CID 189793547 Van Nooten, B. (1993), "Binary numbers in Indian antiquity", Journal of Indian Philosophy, 21 (1), Springer Netherlands: 31–50, doi:10.1007/BF01092744, S2CID 171039636 Whish, Charles (1835), "On the Hindú Quadrature of the Circle, and the infinite Series of the proportion of the circumference to the diameter exhibited in the four S'ástras, the Tantra Sangraham, Yucti Bháshá, Carana Padhati, and Sadratnamála", Transactions of the Royal Asiatic Society of Great Britain and Ireland, 3 (3): 509–523, doi:10.1017/S0950473700001221, JSTOR 25581775 Yano, Michio (2006), "Oral and Written Transmission of the Exact Sciences in Sanskrit", Journal of Indian Philosophy, 34 (1–2), Springer Netherlands: 143–160, doi:10.1007/s10781-005-8175-6, S2CID 170679879 == Further reading == === Source books in Sanskrit === Keller, Agathe (2006), Expounding the Mathematical Seed. Vol. 1: The Translation: A Translation of Bhaskara I on the Mathematical Chapter of the Aryabhatiya, Basel, Boston, and Berlin: Birkhäuser Verlag, 172 pages, ISBN 978-3-7643-7291-0. Keller, Agathe (2006), Expounding the Mathematical Seed. Vol. 2: The Supplements: A Translation of Bhaskara I on the Mathematical Chapter of the Aryabhatiya, Basel, Boston, and Berlin: Birkhäuser Verlag, 206 pages, ISBN 978-3-7643-7292-7. Sarma, K. V., ed. (1976), Āryabhaṭīya of Āryabhaṭa with the commentary of Sūryadeva Yajvan, critically edited with Introduction and Appendices, New Delhi: Indian National Science Academy. Sen, S. N.; Bag, A. K., eds. (1983), The Śulbasūtras of Baudhāyana, Āpastamba, Kātyāyana and Mānava, with Text, English Translation and Commentary, New Delhi: Indian National Science Academy. Shukla, K. S., ed. (1976), Āryabhaṭīya of Āryabhaṭa with the commentary of Bhāskara I and Someśvara, critically edited with Introduction, English Translation, Notes, Comments and Indexes, New Delhi: Indian National Science Academy. Shukla, K. S., ed. (1988), Āryabhaṭīya of Āryabhaṭa, critically edited with Introduction, English Translation, Notes, Comments and Indexes, in collaboration with K.V. Sarma, New Delhi: Indian National Science Academy. == External links == Science and Mathematics in India An overview of Indian mathematics, MacTutor History of Mathematics Archive, St Andrews University, 2000. Indian Mathematicians Index of Ancient Indian mathematics, MacTutor History of Mathematics Archive, St Andrews University, 2004. Indian Mathematics: Redressing the balance, Student Projects in the History of Mathematics. Ian Pearce. MacTutor History of Mathematics Archive, St Andrews University, 2002. Indian Mathematics on In Our Time at the BBC InSIGHT 2009, a workshop on traditional Indian sciences for school children conducted by the Computer Science department of Anna University, Chennai, India. Mathematics in ancient India by R. Sridharan Combinatorial methods in ancient India Mathematics before S. Ramanujan
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In mathematics, a duality translates concepts, theorems or mathematical structures into other concepts, theorems or structures in a one-to-one fashion, often (but not always) by means of an involution operation: if the dual of A is B, then the dual of B is A. In other cases the dual of the dual – the double dual or bidual – is not necessarily identical to the original (also called primal). Such involutions sometimes have fixed points, so that the dual of A is A itself. For example, Desargues' theorem is self-dual in this sense under the standard duality in projective geometry. In mathematical contexts, duality has numerous meanings. It has been described as "a very pervasive and important concept in (modern) mathematics" and "an important general theme that has manifestations in almost every area of mathematics". Many mathematical dualities between objects of two types correspond to pairings, bilinear functions from an object of one type and another object of the second type to some family of scalars. For instance, linear algebra duality corresponds in this way to bilinear maps from pairs of vector spaces to scalars, the duality between distributions and the associated test functions corresponds to the pairing in which one integrates a distribution against a test function, and Poincaré duality corresponds similarly to intersection number, viewed as a pairing between submanifolds of a given manifold. From a category theory viewpoint, duality can also be seen as a functor, at least in the realm of vector spaces. This functor assigns to each space its dual space, and the pullback construction assigns to each arrow f: V → W its dual f∗: W∗ → V∗. == Introductory examples == In the words of Michael Atiyah, Duality in mathematics is not a theorem, but a "principle". The following list of examples shows the common features of many dualities, but also indicates that the precise meaning of duality may vary from case to case. === Complement of a subset === A simple duality arises from considering subsets of a fixed set S. To any subset A ⊆ S, the complement A∁ consists of all those elements in S that are not contained in A. It is again a subset of S. Taking the complement has the following properties: Applying it twice gives back the original set, i.e., (A∁)∁ = A. This is referred to by saying that the operation of taking the complement is an involution. An inclusion of sets A ⊆ B is turned into an inclusion in the opposite direction B∁ ⊆ A∁. Given two subsets A and B of S, A is contained in B∁ if and only if B is contained in A∁. This duality appears in topology as a duality between open and closed subsets of some fixed topological space X: a subset U of X is closed if and only if its complement in X is open. Because of this, many theorems about closed sets are dual to theorems about open sets. For example, any union of open sets is open, so dually, any intersection of closed sets is closed. The interior of a set is the largest open set contained in it, and the closure of the set is the smallest closed set that contains it. Because of the duality, the complement of the interior of any set U is equal to the closure of the complement of U. === Dual cone === A duality in geometry is provided by the dual cone construction. Given a set C {\displaystyle C} of points in the plane R 2 {\displaystyle \mathbb {R} ^{2}} (or more generally points in R n {\displaystyle \mathbb {R} ^{n}} ), the dual cone is defined as the set C ∗ ⊆ R 2 {\displaystyle C^{*}\subseteq \mathbb {R} ^{2}} consisting of those points ( x 1 , x 2 ) {\displaystyle (x_{1},x_{2})} satisfying x 1 c 1 + x 2 c 2 ≥ 0 {\displaystyle x_{1}c_{1}+x_{2}c_{2}\geq 0} for all points ( c 1 , c 2 ) {\displaystyle (c_{1},c_{2})} in C {\displaystyle C} , as illustrated in the diagram. Unlike for the complement of sets mentioned above, it is not in general true that applying the dual cone construction twice gives back the original set C {\displaystyle C} . Instead, C ∗ ∗ {\displaystyle C^{**}} is the smallest cone containing C {\displaystyle C} which may be bigger than C {\displaystyle C} . Therefore this duality is weaker than the one above, in that Applying the operation twice gives back a possibly bigger set: for all C {\displaystyle C} , C {\displaystyle C} is contained in C ∗ ∗ {\displaystyle C^{**}} . (For some C {\displaystyle C} , namely the cones, the two are actually equal.) The other two properties carry over without change: It is still true that an inclusion C ⊆ D {\displaystyle C\subseteq D} is turned into an inclusion in the opposite direction ( D ∗ ⊆ C ∗ {\displaystyle D^{*}\subseteq C^{*}} ). Given two subsets C {\displaystyle C} and D {\displaystyle D} of the plane, C {\displaystyle C} is contained in D ∗ {\displaystyle D^{*}} if and only if D {\displaystyle D} is contained in C ∗ {\displaystyle C^{*}} . === Dual vector space === A very important example of a duality arises in linear algebra by associating to any vector space V its dual vector space V*. Its elements are the linear functionals φ : V → K {\displaystyle \varphi :V\to K} , where K is the field over which V is defined. The three properties of the dual cone carry over to this type of duality by replacing subsets of R 2 {\displaystyle \mathbb {R} ^{2}} by vector space and inclusions of such subsets by linear maps. That is: Applying the operation of taking the dual vector space twice gives another vector space V**. There is always a map V → V**. For some V, namely precisely the finite-dimensional vector spaces, this map is an isomorphism. A linear map V → W gives rise to a map in the opposite direction (W* → V*). Given two vector spaces V and W, the maps from V to W* correspond to the maps from W to V*. A particular feature of this duality is that V and V* are isomorphic for certain objects, namely finite-dimensional vector spaces. However, this is in a sense a lucky coincidence, for giving such an isomorphism requires a certain choice, for example the choice of a basis of V. This is also true in the case if V is a Hilbert space, via the Riesz representation theorem. === Galois theory === In all the dualities discussed before, the dual of an object is of the same kind as the object itself. For example, the dual of a vector space is again a vector space. Many duality statements are not of this kind. Instead, such dualities reveal a close relation between objects of seemingly different nature. One example of such a more general duality is from Galois theory. For a fixed Galois extension K / F, one may associate the Galois group Gal(K/E) to any intermediate field E (i.e., F ⊆ E ⊆ K). This group is a subgroup of the Galois group G = Gal(K/F). Conversely, to any such subgroup H ⊆ G there is the fixed field KH consisting of elements fixed by the elements in H. Compared to the above, this duality has the following features: An extension F ⊆ F′ of intermediate fields gives rise to an inclusion of Galois groups in the opposite direction: Gal(K/F′) ⊆ Gal(K/F). Associating Gal(K/E) to E and KH to H are inverse to each other. This is the content of the fundamental theorem of Galois theory. == Order-reversing dualities == Given a poset P = (X, ≤) (short for partially ordered set; i.e., a set that has a notion of ordering but in which two elements cannot necessarily be placed in order relative to each other), the dual poset Pd = (X, ≥) comprises the same ground set but the converse relation. Familiar examples of dual partial orders include the subset and superset relations ⊂ and ⊃ on any collection of sets, such as the subsets of a fixed set S. This gives rise to the first example of a duality mentioned above. the divides and multiple-of relations on the integers. the descendant-of and ancestor-of relations on the set of humans. A duality transform is an involutive antiautomorphism f of a partially ordered set S, that is, an order-reversing involution f : S → S. In several important cases these simple properties determine the transform uniquely up to some simple symmetries. For example, if f1, f2 are two duality transforms then their composition is an order automorphism of S; thus, any two duality transforms differ only by an order automorphism. For example, all order automorphisms of a power set S = 2R are induced by permutations of R. A concept defined for a partial order P will correspond to a dual concept on the dual poset Pd. For instance, a minimal element of P will be a maximal element of Pd: minimality and maximality are dual concepts in order theory. Other pairs of dual concepts are upper and lower bounds, lower sets and upper sets, and ideals and filters. In topology, open sets and closed sets are dual concepts: the complement of an open set is closed, and vice versa. In matroid theory, the family of sets complementary to the independent sets of a given matroid themselves form another matroid, called the dual matroid. == Dimension-reversing dualities == There are many distinct but interrelated dualities in which geometric or topological objects correspond to other objects of the same type, but with a reversal of the dimensions of the features of the objects. A classical example of this is the duality of the Platonic solids, in which the cube and the octahedron form a dual pair, the dodecahedron and the icosahedron form a dual pair, and the tetrahedron is self-dual. The dual polyhedron of any of these polyhedra may be formed as the convex hull of the center points of each face of the primal polyhedron, so the vertices of the dual correspond one-for-one with the faces of the primal. Similarly, each edge of the dual corresponds to an edge of the primal, and each face of the dual corresponds to a vertex of the primal. These correspondences are incidence-preserving: if two parts of the primal polyhedron touch each other, so do the corresponding two parts of the dual polyhedron. More generally, using the concept of polar reciprocation, any convex polyhedron, or more generally any convex polytope, corresponds to a dual polyhedron or dual polytope, with an i-dimensional feature of an n-dimensional polytope corresponding to an (n − i − 1)-dimensional feature of the dual polytope. The incidence-preserving nature of the duality is reflected in the fact that the face lattices of the primal and dual polyhedra or polytopes are themselves order-theoretic duals. Duality of polytopes and order-theoretic duality are both involutions: the dual polytope of the dual polytope of any polytope is the original polytope, and reversing all order-relations twice returns to the original order. Choosing a different center of polarity leads to geometrically different dual polytopes, but all have the same combinatorial structure. From any three-dimensional polyhedron, one can form a planar graph, the graph of its vertices and edges. The dual polyhedron has a dual graph, a graph with one vertex for each face of the polyhedron and with one edge for every two adjacent faces. The same concept of planar graph duality may be generalized to graphs that are drawn in the plane but that do not come from a three-dimensional polyhedron, or more generally to graph embeddings on surfaces of higher genus: one may draw a dual graph by placing one vertex within each region bounded by a cycle of edges in the embedding, and drawing an edge connecting any two regions that share a boundary edge. An important example of this type comes from computational geometry: the duality for any finite set S of points in the plane between the Delaunay triangulation of S and the Voronoi diagram of S. As with dual polyhedra and dual polytopes, the duality of graphs on surfaces is a dimension-reversing involution: each vertex in the primal embedded graph corresponds to a region of the dual embedding, each edge in the primal is crossed by an edge in the dual, and each region of the primal corresponds to a vertex of the dual. The dual graph depends on how the primal graph is embedded: different planar embeddings of a single graph may lead to different dual graphs. Matroid duality is an algebraic extension of planar graph duality, in the sense that the dual matroid of the graphic matroid of a planar graph is isomorphic to the graphic matroid of the dual graph. A kind of geometric duality also occurs in optimization theory, but not one that reverses dimensions. A linear program may be specified by a system of real variables (the coordinates for a point in Euclidean space R n {\displaystyle \mathbb {R} ^{n}} ), a system of linear constraints (specifying that the point lie in a halfspace; the intersection of these halfspaces is a convex polytope, the feasible region of the program), and a linear function (what to optimize). Every linear program has a dual problem with the same optimal solution, but the variables in the dual problem correspond to constraints in the primal problem and vice versa. == Duality in logic and set theory == In logic, functions or relations A and B are considered dual if A(¬x) = ¬B(x), where ¬ is logical negation. The basic duality of this type is the duality of the ∃ and ∀ quantifiers in classical logic. These are dual because ∃x.¬P(x) and ¬∀x.P(x) are equivalent for all predicates P in classical logic: if there exists an x for which P fails to hold, then it is false that P holds for all x (but the converse does not hold constructively). From this fundamental logical duality follow several others: A formula is said to be satisfiable in a certain model if there are assignments to its free variables that render it true; it is valid if every assignment to its free variables makes it true. Satisfiability and validity are dual because the invalid formulas are precisely those whose negations are satisfiable, and the unsatisfiable formulas are those whose negations are valid. This can be viewed as a special case of the previous item, with the quantifiers ranging over interpretations. In classical logic, the ∧ and ∨ operators are dual in this sense, because (¬x ∧ ¬y) and ¬(x ∨ y) are equivalent. This means that for every theorem of classical logic there is an equivalent dual theorem. De Morgan's laws are examples. More generally, ∧ (¬ xi) = ¬∨ xi. The left side is true if and only if ∀i.¬xi, and the right side if and only if ¬∃i.xi. In modal logic, □p means that the proposition p is "necessarily" true, and ◊p that p is "possibly" true. Most interpretations of modal logic assign dual meanings to these two operators. For example in Kripke semantics, "p is possibly true" means "there exists some world W such that p is true in W", while "p is necessarily true" means "for all worlds W, p is true in W". The duality of □ and ◊ then follows from the analogous duality of ∀ and ∃. Other dual modal operators behave similarly. For example, temporal logic has operators denoting "will be true at some time in the future" and "will be true at all times in the future" which are similarly dual. Other analogous dualities follow from these: Set-theoretic union and intersection are dual under the set complement operator ∁. That is, A∁ ∩ B∁ = (A ∪ B)∁, and more generally, ⋂ Aα∁ = (⋃ Aα)∁. This follows from the duality of ∀ and ∃: an element x is a member of ⋂ Aα∁ if and only if ∀α.¬x ∈ Aα, and is a member of (⋂ Aα)∁ if and only if ¬∃α. x ∈ Aα. == Bidual == The dual of the dual, called the bidual or double dual, depending on context, is often identical to the original (also called primal), and duality is an involution. In this case the bidual is not usually distinguished, and instead one only refers to the primal and dual. For example, the dual poset of the dual poset is exactly the original poset, since the converse relation is defined by an involution. In other cases, the bidual is not identical with the primal, though there is often a close connection. For example, the dual cone of the dual cone of a set contains the primal set (it is the smallest cone containing the primal set), and is equal if and only if the primal set is a cone. An important case is for vector spaces, where there is a map from the primal space to the double dual, V → V**, known as the "canonical evaluation map". For finite-dimensional vector spaces this is an isomorphism, but these are not identical spaces: they are different sets. In category theory, this is generalized by § Dual objects, and a "natural transformation" from the identity functor to the double dual functor. For vector spaces (considered algebraically), this is always an injection; see Dual space § Injection into the double-dual. This can be generalized algebraically to a dual module. There is still a canonical evaluation map, but it is not always injective; if it is, this is known as a torsionless module; if it is an isomophism, the module is called reflexive. For topological vector spaces (including normed vector spaces), there is a separate notion of a topological dual, denoted V ′ {\displaystyle V'} to distinguish from the algebraic dual V*, with different possible topologies on the dual, each of which defines a different bidual space V ″ {\displaystyle V''} . In these cases the canonical evaluation map V → V ″ {\displaystyle V\to V''} is not in general an isomorphism. If it is, this is known (for certain locally convex vector spaces with the strong dual space topology) as a reflexive space. In other cases, showing a relation between the primal and bidual is a significant result, as in Pontryagin duality (a locally compact abelian group is naturally isomorphic to its bidual). == Dual objects == A group of dualities can be described by endowing, for any mathematical object X, the set of morphisms Hom (X, D) into some fixed object D, with a structure similar to that of X. This is sometimes called internal Hom. In general, this yields a true duality only for specific choices of D, in which case X* = Hom (X, D) is referred to as the dual of X. There is always a map from X to the bidual, that is to say, the dual of the dual, X → X ∗ ∗ := ( X ∗ ) ∗ = Hom ( Hom ( X , D ) , D ) . {\displaystyle X\to X^{**}:=(X^{*})^{*}=\operatorname {Hom} (\operatorname {Hom} (X,D),D).} It assigns to some x ∈ X the map that associates to any map f : X → D (i.e., an element in Hom(X, D)) the value f(x). Depending on the concrete duality considered and also depending on the object X, this map may or may not be an isomorphism. === Dual vector spaces revisited === The construction of the dual vector space V ∗ = Hom ( V , K ) {\displaystyle V^{*}=\operatorname {Hom} (V,K)} mentioned in the introduction is an example of such a duality. Indeed, the set of morphisms, i.e., linear maps, forms a vector space in its own right. The map V → V** mentioned above is always injective. It is surjective, and therefore an isomorphism, if and only if the dimension of V is finite. This fact characterizes finite-dimensional vector spaces without referring to a basis. ==== Isomorphisms of V and V∗ and inner product spaces ==== A vector space V is isomorphic to V∗ precisely if V is finite-dimensional. In this case, such an isomorphism is equivalent to a non-degenerate bilinear form φ : V × V → K {\displaystyle \varphi :V\times V\to K} In this case V is called an inner product space. For example, if K is the field of real or complex numbers, any positive definite bilinear form gives rise to such an isomorphism. In Riemannian geometry, V is taken to be the tangent space of a manifold and such positive bilinear forms are called Riemannian metrics. Their purpose is to measure angles and distances. Thus, duality is a foundational basis of this branch of geometry. Another application of inner product spaces is the Hodge star which provides a correspondence between the elements of the exterior algebra. For an n-dimensional vector space, the Hodge star operator maps k-forms to (n − k)-forms. This can be used to formulate Maxwell's equations. In this guise, the duality inherent in the inner product space exchanges the role of magnetic and electric fields. ==== Duality in projective geometry ==== In some projective planes, it is possible to find geometric transformations that map each point of the projective plane to a line, and each line of the projective plane to a point, in an incidence-preserving way. For such planes there arises a general principle of duality in projective planes: given any theorem in such a plane projective geometry, exchanging the terms "point" and "line" everywhere results in a new, equally valid theorem. A simple example is that the statement "two points determine a unique line, the line passing through these points" has the dual statement that "two lines determine a unique point, the intersection point of these two lines". For further examples, see Dual theorems. A conceptual explanation of this phenomenon in some planes (notably field planes) is offered by the dual vector space. In fact, the points in the projective plane R P 2 {\displaystyle \mathbb {RP} ^{2}} correspond to one-dimensional subvector spaces V ⊂ R 3 {\displaystyle V\subset \mathbb {R} ^{3}} while the lines in the projective plane correspond to subvector spaces W {\displaystyle W} of dimension 2. The duality in such projective geometries stems from assigning to a one-dimensional V {\displaystyle V} the subspace of ( R 3 ) ∗ {\displaystyle (\mathbb {R} ^{3})^{*}} consisting of those linear maps f : R 3 → R {\displaystyle f:\mathbb {R} ^{3}\to \mathbb {R} } which satisfy f ( V ) = 0 {\displaystyle f(V)=0} . As a consequence of the dimension formula of linear algebra, this space is two-dimensional, i.e., it corresponds to a line in the projective plane associated to ( R 3 ) ∗ {\displaystyle (\mathbb {R} ^{3})^{*}} . The (positive definite) bilinear form ⟨ ⋅ , ⋅ ⟩ : R 3 × R 3 → R , ⟨ x , y ⟩ = ∑ i = 1 3 x i y i {\displaystyle \langle \cdot ,\cdot \rangle :\mathbb {R} ^{3}\times \mathbb {R} ^{3}\to \mathbb {R} ,\langle x,y\rangle =\sum _{i=1}^{3}x_{i}y_{i}} yields an identification of this projective plane with the R P 2 {\displaystyle \mathbb {RP} ^{2}} . Concretely, the duality assigns to V ⊂ R 3 {\displaystyle V\subset \mathbb {R} ^{3}} its orthogonal { w ∈ R 3 , ⟨ v , w ⟩ = 0 for all v ∈ V } {\displaystyle \left\{w\in \mathbb {R} ^{3},\langle v,w\rangle =0{\text{ for all }}v\in V\right\}} . The explicit formulas in duality in projective geometry arise by means of this identification. === Topological vector spaces and Hilbert spaces === In the realm of topological vector spaces, a similar construction exists, replacing the dual by the topological dual vector space. There are several notions of topological dual space, and each of them gives rise to a certain concept of duality. A topological vector space X {\displaystyle X} that is canonically isomorphic to its bidual X ″ {\displaystyle X''} is called a reflexive space: X ≅ X ″ . {\displaystyle X\cong X''.} Examples: As in the finite-dimensional case, on each Hilbert space H its inner product ⟨⋅, ⋅⟩ defines a map H → H ∗ , v ↦ ( w ↦ ⟨ w , v ⟩ ) , {\displaystyle H\to H^{*},v\mapsto (w\mapsto \langle w,v\rangle ),} which is a bijection due to the Riesz representation theorem. As a corollary, every Hilbert space is a reflexive Banach space. The dual normed space of an Lp-space is Lq where 1/p + 1/q = 1 provided that 1 ≤ p < ∞, but the dual of L∞ is bigger than L1. Hence L1 is not reflexive. Distributions are linear functionals on appropriate spaces of functions. They are an important technical means in the theory of partial differential equations (PDE): instead of solving a PDE directly, it may be easier to first solve the PDE in the "weak sense", i.e., find a distribution that satisfies the PDE and, second, to show that the solution must, in fact, be a function. All the standard spaces of distributions — D ′ ( U ) {\displaystyle {\mathcal {D}}'(U)} , S ′ ( R n ) {\displaystyle {\mathcal {S}}'(\mathbb {R} ^{n})} , C ∞ ( U ) ′ {\displaystyle {\mathcal {C}}^{\infty }(U)'} — are reflexive locally convex spaces. === Further dual objects === The dual lattice of a lattice L is given by Hom ( L , Z ) , {\displaystyle \operatorname {Hom} (L,\mathbb {Z} ),} the set of linear functions on the real vector space containing the lattice that map the points of the lattice to the integers Z {\displaystyle \mathbb {Z} } . This is used in the construction of toric varieties. The Pontryagin dual of locally compact topological groups G is given by Hom ( G , S 1 ) , {\displaystyle \operatorname {Hom} (G,S^{1}),} continuous group homomorphisms with values in the circle (with multiplication of complex numbers as group operation). == Dual categories == === Opposite category and adjoint functors === In another group of dualities, the objects of one theory are translated into objects of another theory and the maps between objects in the first theory are translated into morphisms in the second theory, but with direction reversed. Using the parlance of category theory, this amounts to a contravariant functor between two categories C and D: which for any two objects X and Y of C gives a map That functor may or may not be an equivalence of categories. There are various situations, where such a functor is an equivalence between the opposite category Cop of C, and D. Using a duality of this type, every statement in the first theory can be translated into a "dual" statement in the second theory, where the direction of all arrows has to be reversed. Therefore, any duality between categories C and D is formally the same as an equivalence between C and Dop (Cop and D). However, in many circumstances the opposite categories have no inherent meaning, which makes duality an additional, separate concept. A category that is equivalent to its dual is called self-dual. An example of self-dual category is the category of Hilbert spaces. Many category-theoretic notions come in pairs in the sense that they correspond to each other while considering the opposite category. For example, Cartesian products Y1 × Y2 and disjoint unions Y1 ⊔ Y2 of sets are dual to each other in the sense that and for any set X. This is a particular case of a more general duality phenomenon, under which limits in a category C correspond to colimits in the opposite category Cop; further concrete examples of this are epimorphisms vs. monomorphism, in particular factor modules (or groups etc.) vs. submodules, direct products vs. direct sums (also called coproducts to emphasize the duality aspect). Therefore, in some cases, proofs of certain statements can be halved, using such a duality phenomenon. Further notions displaying related by such a categorical duality are projective and injective modules in homological algebra, fibrations and cofibrations in topology and more generally model categories. Two functors F: C → D and G: D → C are adjoint if for all objects c in C and d in D in a natural way. Actually, the correspondence of limits and colimits is an example of adjoints, since there is an adjunction between the colimit functor that assigns to any diagram in C indexed by some category I its colimit and the diagonal functor that maps any object c of C to the constant diagram which has c at all places. Dually, === Spaces and functions === Gelfand duality is a duality between commutative C*-algebras A and compact Hausdorff spaces X is the same: it assigns to X the space of continuous functions (which vanish at infinity) from X to C, the complex numbers. Conversely, the space X can be reconstructed from A as the spectrum of A. Both Gelfand and Pontryagin duality can be deduced in a largely formal, category-theoretic way. In a similar vein there is a duality in algebraic geometry between commutative rings and affine schemes: to every commutative ring A there is an affine spectrum, Spec A. Conversely, given an affine scheme S, one gets back a ring by taking global sections of the structure sheaf OS. In addition, ring homomorphisms are in one-to-one correspondence with morphisms of affine schemes, thereby there is an equivalence (Commutative rings)op ≅ (affine schemes) Affine schemes are the local building blocks of schemes. The previous result therefore tells that the local theory of schemes is the same as commutative algebra, the study of commutative rings. Noncommutative geometry draws inspiration from Gelfand duality and studies noncommutative C*-algebras as if they were functions on some imagined space. Tannaka–Krein duality is a non-commutative analogue of Pontryagin duality. === Galois connections === In a number of situations, the two categories which are dual to each other are actually arising from partially ordered sets, i.e., there is some notion of an object "being smaller" than another one. A duality that respects the orderings in question is known as a Galois connection. An example is the standard duality in Galois theory mentioned in the introduction: a bigger field extension corresponds—under the mapping that assigns to any extension L ⊃ K (inside some fixed bigger field Ω) the Galois group Gal (Ω / L) —to a smaller group. The collection of all open subsets of a topological space X forms a complete Heyting algebra. There is a duality, known as Stone duality, connecting sober spaces and spatial locales. Birkhoff's representation theorem relating distributive lattices and partial orders === Pontryagin duality === Pontryagin duality gives a duality on the category of locally compact abelian groups: given any such group G, the character group χ(G) = Hom (G, S1) given by continuous group homomorphisms from G to the circle group S1 can be endowed with the compact-open topology. Pontryagin duality states that the character group is again locally compact abelian and that G ≅ χ(χ(G)). Moreover, discrete groups correspond to compact abelian groups; finite groups correspond to finite groups. On the one hand, Pontryagin is a special case of Gelfand duality. On the other hand, it is the conceptual reason of Fourier analysis, see below. == Analytic dualities == In analysis, problems are frequently solved by passing to the dual description of functions and operators. Fourier transform switches between functions on a vector space and its dual: f ^ ( ξ ) := ∫ − ∞ ∞ f ( x ) e − 2 π i x ξ d x , {\displaystyle {\widehat {f}}(\xi ):=\int _{-\infty }^{\infty }f(x)\ e^{-2\pi ix\xi }\,dx,} and conversely f ( x ) = ∫ − ∞ ∞ f ^ ( ξ ) e 2 π i x ξ d ξ . {\displaystyle f(x)=\int _{-\infty }^{\infty }{\widehat {f}}(\xi )\ e^{2\pi ix\xi }\,d\xi .} If f is an L2-function on R or RN, say, then so is f ^ {\displaystyle {\widehat {f}}} and f ( − x ) = f ^ ^ ( x ) {\displaystyle f(-x)={\widehat {\widehat {f}}}(x)} . Moreover, the transform interchanges operations of multiplication and convolution on the corresponding function spaces. A conceptual explanation of the Fourier transform is obtained by the aforementioned Pontryagin duality, applied to the locally compact groups R (or RN etc.): any character of R is given by ξ ↦ e−2πixξ. The dualizing character of Fourier transform has many other manifestations, for example, in alternative descriptions of quantum mechanical systems in terms of coordinate and momentum representations. Laplace transform is similar to Fourier transform and interchanges operators of multiplication by polynomials with constant coefficient linear differential operators. Legendre transformation is an important analytic duality which switches between velocities in Lagrangian mechanics and momenta in Hamiltonian mechanics. == Homology and cohomology == Theorems showing that certain objects of interest are the dual spaces (in the sense of linear algebra) of other objects of interest are often called dualities. Many of these dualities are given by a bilinear pairing of two K-vector spaces A ⊗ B → K. For perfect pairings, there is, therefore, an isomorphism of A to the dual of B. === Poincaré duality === Poincaré duality of a smooth compact complex manifold X is given by a pairing of singular cohomology with C-coefficients (equivalently, sheaf cohomology of the constant sheaf C) Hi(X) ⊗ H2n−i(X) → C, where n is the (complex) dimension of X. Poincaré duality can also be expressed as a relation of singular homology and de Rham cohomology, by asserting that the map ( γ , ω ) ↦ ∫ γ ω {\displaystyle (\gamma ,\omega )\mapsto \int _{\gamma }\omega } (integrating a differential k-form over a (2n − k)-(real-)dimensional cycle) is a perfect pairing. Poincaré duality also reverses dimensions; it corresponds to the fact that, if a topological manifold is represented as a cell complex, then the dual of the complex (a higher-dimensional generalization of the planar graph dual) represents the same manifold. In Poincaré duality, this homeomorphism is reflected in an isomorphism of the kth homology group and the (n − k)th cohomology group. === Duality in algebraic and arithmetic geometry === The same duality pattern holds for a smooth projective variety over a separably closed field, using l-adic cohomology with Qℓ-coefficients instead. This is further generalized to possibly singular varieties, using intersection cohomology instead, a duality called Verdier duality. Serre duality or coherent duality are similar to the statements above, but applies to cohomology of coherent sheaves instead. With increasing level of generality, it turns out, an increasing amount of technical background is helpful or necessary to understand these theorems: the modern formulation of these dualities can be done using derived categories and certain direct and inverse image functors of sheaves (with respect to the classical analytical topology on manifolds for Poincaré duality, l-adic sheaves and the étale topology in the second case, and with respect to coherent sheaves for coherent duality). Yet another group of similar duality statements is encountered in arithmetics: étale cohomology of finite, local and global fields (also known as Galois cohomology, since étale cohomology over a field is equivalent to group cohomology of the (absolute) Galois group of the field) admit similar pairings. The absolute Galois group G(Fq) of a finite field, for example, is isomorphic to Z ^ {\displaystyle {\widehat {\mathbf {Z} }}} , the profinite completion of Z, the integers. Therefore, the perfect pairing (for any G-module M) Hn(G, M) × H1−n (G, Hom (M, Q/Z)) → Q/Z is a direct consequence of Pontryagin duality of finite groups. For local and global fields, similar statements exist (local duality and global or Poitou–Tate duality). == See also == == Notes == == References == === Duality in general === Atiyah, Michael (2007). "Duality in Mathematics and Physics lecture notes from the Institut de Matematica de la Universitat de Barcelona (IMUB)" (PDF). Kostrikin, A. I. (2001) [1994], "Duality", Encyclopedia of Mathematics, EMS Press. Gowers, Timothy (2008), "III.19 Duality", The Princeton Companion to Mathematics, Princeton University Press, pp. 187–190. Cartier, Pierre (2001), "A mad day's work: from Grothendieck to Connes and Kontsevich. The evolution of concepts of space and symmetry", Bulletin of the American Mathematical Society, New Series, 38 (4): 389–408, doi:10.1090/S0273-0979-01-00913-2, ISSN 0002-9904, MR 1848254 (a non-technical overview about several aspects of geometry, including dualities) === Duality in algebraic topology === James C. Becker and Daniel Henry Gottlieb, A History of Duality in Algebraic Topology === Specific dualities === Artstein-Avidan, Shiri; Milman, Vitali (2008), "The concept of duality for measure projections of convex bodies", Journal of Functional Analysis, 254 (10): 2648–66, CiteSeerX 10.1.1.417.3470, doi:10.1016/j.jfa.2007.11.008. Also author's site. Artstein-Avidan, Shiri; Milman, Vitali (2007), "A characterization of the concept of duality", Electronic Research Announcements in Mathematical Sciences, 14: 42–59, archived from the original on 2011-07-24, retrieved 2009-05-30. Also author's site. Dwyer, William G.; Spaliński, Jan (1995), "Homotopy theories and model categories", Handbook of algebraic topology, Amsterdam: North-Holland, pp. 73–126, MR 1361887, archived from the original on 2021-02-09, retrieved 2009-03-11 Fulton, William (1993), Introduction to toric varieties, Princeton University Press, ISBN 978-0-691-00049-7 Griffiths, Phillip; Harris, Joseph (1994), Principles of algebraic geometry, Wiley Classics Library, New York: John Wiley & Sons, ISBN 978-0-471-05059-9, MR 1288523 Hartshorne, Robin (1966), Residues and Duality, Lecture Notes in Mathematics, vol. 20, Springer-Verlag, pp. 20–48, ISBN 978-3-540-34794-1 Hartshorne, Robin (1977), Algebraic Geometry, Springer-Verlag, ISBN 978-0-387-90244-9, MR 0463157, OCLC 13348052 Iversen, Birger (1986), Cohomology of sheaves, Universitext, Springer-Verlag, ISBN 978-3-540-16389-3, MR 0842190 Joyal, André; Street, Ross (1991), "An introduction to Tannaka duality and quantum groups" (PDF), Category theory, Lecture Notes in Mathematics, vol. 1488, Springer-Verlag, pp. 413–492, doi:10.1007/BFb0084235, ISBN 978-3-540-46435-8, MR 1173027 Lam, Tsit-Yuen (1999), Lectures on modules and rings, Graduate Texts in Mathematics, vol. 189, Springer-Verlag, ISBN 978-0-387-98428-5, MR 1653294 Lang, Serge (2002), Algebra, Graduate Texts in Mathematics, vol. 211, Springer-Verlag, ISBN 978-0-387-95385-4, MR 1878556 Loomis, Lynn H. (1953), An introduction to abstract harmonic analysis, D. Van Nostrand, pp. x+190, hdl:2027/uc1.b4250788 Mac Lane, Saunders (1998), Categories for the Working Mathematician (2nd ed.), Springer-Verlag, ISBN 978-0-387-98403-2 Mazur, Barry (1973), "Notes on étale cohomology of number fields", Annales Scientifiques de l'École Normale Supérieure, Série 4, 6 (4): 521–552, doi:10.24033/asens.1257, ISSN 0012-9593, MR 0344254 Milne, James S. (1980), Étale cohomology, Princeton University Press, ISBN 978-0-691-08238-7 Milne, James S. (2006), Arithmetic duality theorems (2nd ed.), Charleston, South Carolina: BookSurge, LLC, ISBN 978-1-4196-4274-6, MR 2261462 Negrepontis, Joan W. (1971), "Duality in analysis from the point of view of triples", Journal of Algebra, 19 (2): 228–253, doi:10.1016/0021-8693(71)90105-0, ISSN 0021-8693, MR 0280571 Rudin, Walter (1976), Principles Of Mathematical Analysis (3rd ed.), New York: McGraw-Hill, ISBN 0-07-054235-X Veblen, Oswald; Young, John Wesley (1965), Projective geometry. Vols. 1, 2, Blaisdell Publishing Co. Ginn and Co., MR 0179666 Weibel, Charles A. (1994), An introduction to homological algebra, Cambridge University Press, ISBN 978-0-521-55987-4, MR 1269324 Edwards, R. E. (1965). Functional analysis. Theory and applications. New York: Holt, Rinehart and Winston. ISBN 0030505356.
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In mathematics, a real interval is the set of all real numbers lying between two fixed endpoints with no "gaps". Each endpoint is either a real number or positive or negative infinity, indicating the interval extends without a bound. A real interval can contain neither endpoint, either endpoint, or both endpoints, excluding any endpoint which is infinite. For example, the set of real numbers consisting of 0, 1, and all numbers in between is an interval, denoted [0, 1] and called the unit interval; the set of all positive real numbers is an interval, denoted (0, ∞); the set of all real numbers is an interval, denoted (−∞, ∞); and any single real number a is an interval, denoted [a, a]. Intervals are ubiquitous in mathematical analysis. For example, they occur implicitly in the epsilon-delta definition of continuity; the intermediate value theorem asserts that the image of an interval by a continuous function is an interval; integrals of real functions are defined over an interval; etc. Interval arithmetic consists of computing with intervals instead of real numbers for providing a guaranteed enclosure of the result of a numerical computation, even in the presence of uncertainties of input data and rounding errors. Intervals are likewise defined on an arbitrary totally ordered set, such as integers or rational numbers. The notation of integer intervals is considered in the special section below. == Definitions and terminology == An interval is a subset of the real numbers that contains all real numbers lying between any two numbers of the subset. In particular, the empty set ∅ {\displaystyle \varnothing } and the entire set of real numbers R {\displaystyle \mathbb {R} } are both intervals. The endpoints of an interval are its supremum, and its infimum, if they exist as real numbers. If the infimum does not exist, one says often that the corresponding endpoint is − ∞ . {\displaystyle -\infty .} Similarly, if the supremum does not exist, one says that the corresponding endpoint is + ∞ . {\displaystyle +\infty .} Intervals are completely determined by their endpoints and whether each endpoint belong to the interval. This is a consequence of the least-upper-bound property of the real numbers. This characterization is used to specify intervals by mean of interval notation, which is described below. An open interval does not include any endpoint, and is indicated with parentheses. For example, ( 0 , 1 ) = { x ∣ 0 < x < 1 } {\displaystyle (0,1)=\{x\mid 0<x<1\}} is the interval of all real numbers greater than 0 and less than 1. (This interval can also be denoted by ]0, 1[, see below). The open interval (0, +∞) consists of real numbers greater than 0, i.e., positive real numbers. The open intervals have thus one of the forms ( a , b ) = { x ∈ R ∣ a < x < b } , ( − ∞ , b ) = { x ∈ R ∣ x < b } , ( a , + ∞ ) = { x ∈ R ∣ a < x } , ( − ∞ , + ∞ ) = R , ( a , a ) = ∅ , {\displaystyle {\begin{aligned}(a,b)&=\{x\in \mathbb {R} \mid a<x<b\},\\(-\infty ,b)&=\{x\in \mathbb {R} \mid x<b\},\\(a,+\infty )&=\{x\in \mathbb {R} \mid a<x\},\\(-\infty ,+\infty )&=\mathbb {R} ,\\(a,a)&=\emptyset ,\end{aligned}}} where a {\displaystyle a} and b {\displaystyle b} are real numbers such that a < b . {\displaystyle a<b.} In the last case, the resulting interval is the empty set and does not depend on a {\displaystyle a} . The open intervals are those intervals that are open sets for the usual topology on the real numbers. A closed interval is an interval that includes all its endpoints and is denoted with square brackets. For example, [0, 1] means greater than or equal to 0 and less than or equal to 1. Closed intervals have one of the following forms in which a and b are real numbers such that a < b : {\displaystyle a<b\colon } [ a , b ] = { x ∈ R ∣ a ≤ x ≤ b } , ( − ∞ , b ] = { x ∈ R ∣ x ≤ b } , [ a , + ∞ ) = { x ∈ R ∣ a ≤ x } , ( − ∞ , + ∞ ) = R , [ a , a ] = { a } . {\displaystyle {\begin{aligned}\;[a,b]&=\{x\in \mathbb {R} \mid a\leq x\leq b\},\\\left(-\infty ,b\right]&=\{x\in \mathbb {R} \mid x\leq b\},\\\left[a,+\infty \right)&=\{x\in \mathbb {R} \mid a\leq x\},\\(-\infty ,+\infty )&=\mathbb {R} ,\\\left[a,a\right]&=\{a\}.\end{aligned}}} The closed intervals are those intervals that are closed sets for the usual topology on the real numbers. A half-open interval has two endpoints and includes only one of them. It is said left-open or right-open depending on whether the excluded endpoint is on the left or on the right. These intervals are denoted by mixing notations for open and closed intervals. For example, (0, 1] means greater than 0 and less than or equal to 1, while [0, 1) means greater than or equal to 0 and less than 1. The half-open intervals have the form ( a , b ] = { x ∈ R ∣ a < x ≤ b } , [ a , b ) = { x ∈ R ∣ a ≤ x < b } . {\displaystyle {\begin{aligned}\left(a,b\right]&=\{x\in \mathbb {R} \mid a<x\leq b\},\\\left[a,b\right)&=\{x\in \mathbb {R} \mid a\leq x<b\}.\\\end{aligned}}} In summary, a set of the real numbers is an interval, if and only if it is an open interval, a closed interval, or a half-open interval. The only intervals that appear twice in the above classification are ∅ {\displaystyle \emptyset } and R {\displaystyle \mathbb {R} } that are both open and closed. A degenerate interval is any set consisting of a single real number (i.e., an interval of the form [a, a]). Some authors include the empty set in this definition. A real interval that is neither empty nor degenerate is said to be proper, and has infinitely many elements. An interval is said to be left-bounded or right-bounded, if there is some real number that is, respectively, smaller than or larger than all its elements. An interval is said to be bounded, if it is both left- and right-bounded; and is said to be unbounded otherwise. Intervals that are bounded at only one end are said to be half-bounded. The empty set is bounded, and the set of all reals is the only interval that is unbounded at both ends. Bounded intervals are also commonly known as finite intervals. Bounded intervals are bounded sets, in the sense that their diameter (which is equal to the absolute difference between the endpoints) is finite. The diameter may be called the length, width, measure, range, or size of the interval. The size of unbounded intervals is usually defined as +∞, and the size of the empty interval may be defined as 0 (or left undefined). The centre (midpoint) of a bounded interval with endpoints a and b is (a + b)/2, and its radius is the half-length |a − b|/2. These concepts are undefined for empty or unbounded intervals. An interval is said to be left-open if and only if it contains no minimum (an element that is smaller than all other elements); right-open if it contains no maximum; and open if it contains neither. The interval [0, 1) = {x | 0 ≤ x < 1}, for example, is left-closed and right-open. The empty set and the set of all reals are both open and closed intervals, while the set of non-negative reals, is a closed interval that is right-open but not left-open. The open intervals are open sets of the real line in its standard topology, and form a base of the open sets. An interval is said to be left-closed if it has a minimum element or is left-unbounded, right-closed if it has a maximum or is right unbounded; it is simply closed if it is both left-closed and right closed. So, the closed intervals coincide with the closed sets in that topology. The interior of an interval I is the largest open interval that is contained in I; it is also the set of points in I which are not endpoints of I. The closure of I is the smallest closed interval that contains I; which is also the set I augmented with its finite endpoints. For any set X of real numbers, the interval enclosure or interval span of X is the unique interval that contains X, and does not properly contain any other interval that also contains X. An interval I is a subinterval of interval J if I is a subset of J. An interval I is a proper subinterval of J if I is a proper subset of J. However, there is conflicting terminology for the terms segment and interval, which have been employed in the literature in two essentially opposite ways, resulting in ambiguity when these terms are used. The Encyclopedia of Mathematics defines interval (without a qualifier) to exclude both endpoints (i.e., open interval) and segment to include both endpoints (i.e., closed interval), while Rudin's Principles of Mathematical Analysis calls sets of the form [a, b] intervals and sets of the form (a, b) segments throughout. These terms tend to appear in older works; modern texts increasingly favor the term interval (qualified by open, closed, or half-open), regardless of whether endpoints are included. == Notations for intervals == The interval of numbers between a and b, including a and b, is often denoted [a, b]. The two numbers are called the endpoints of the interval. In countries where numbers are written with a decimal comma, a semicolon may be used as a separator to avoid ambiguity. === Including or excluding endpoints === To indicate that one of the endpoints is to be excluded from the set, the corresponding square bracket can be either replaced with a parenthesis, or reversed. Both notations are described in International standard ISO 31-11. Thus, in set builder notation, ( a , b ) = ] a , b [ = { x ∈ R ∣ a < x < b } , [ a , b ) = [ a , b [ = { x ∈ R ∣ a ≤ x < b } , ( a , b ] = ] a , b ] = { x ∈ R ∣ a < x ≤ b } , [ a , b ] = [ a , b ] = { x ∈ R ∣ a ≤ x ≤ b } . {\displaystyle {\begin{aligned}(a,b)={\mathopen {]}}a,b{\mathclose {[}}&=\{x\in \mathbb {R} \mid a<x<b\},\\[5mu][a,b)={\mathopen {[}}a,b{\mathclose {[}}&=\{x\in \mathbb {R} \mid a\leq x<b\},\\[5mu](a,b]={\mathopen {]}}a,b{\mathclose {]}}&=\{x\in \mathbb {R} \mid a<x\leq b\},\\[5mu][a,b]={\mathopen {[}}a,b{\mathclose {]}}&=\{x\in \mathbb {R} \mid a\leq x\leq b\}.\end{aligned}}} Each interval (a, a), [a, a), and (a, a] represents the empty set, whereas [a, a] denotes the singleton set {a}. When a > b, all four notations are usually taken to represent the empty set. Both notations may overlap with other uses of parentheses and brackets in mathematics. For instance, the notation (a, b) is often used to denote an ordered pair in set theory, the coordinates of a point or vector in analytic geometry and linear algebra, or (sometimes) a complex number in algebra. That is why Bourbaki introduced the notation ]a, b[ to denote the open interval. The notation [a, b] too is occasionally used for ordered pairs, especially in computer science. Some authors such as Yves Tillé use ]a, b[ to denote the complement of the interval (a, b); namely, the set of all real numbers that are either less than or equal to a, or greater than or equal to b. === Infinite endpoints === In some contexts, an interval may be defined as a subset of the extended real numbers, the set of all real numbers augmented with −∞ and +∞. In this interpretation, the notations [−∞, b] , (−∞, b] , [a, +∞] , and [a, +∞) are all meaningful and distinct. In particular, (−∞, +∞) denotes the set of all ordinary real numbers, while [−∞, +∞] denotes the extended reals. Even in the context of the ordinary reals, one may use an infinite endpoint to indicate that there is no bound in that direction. For example, (0, +∞) is the set of positive real numbers, also written as R + . {\displaystyle \mathbb {R} _{+}.} The context affects some of the above definitions and terminology. For instance, the interval (−∞, +∞) = R {\displaystyle \mathbb {R} } is closed in the realm of ordinary reals, but not in the realm of the extended reals. === Integer intervals === When a and b are integers, the notation ⟦a, b⟧, or [a .. b] or {a .. b} or just a .. b, is sometimes used to indicate the interval of all integers between a and b included. The notation [a .. b] is used in some programming languages; in Pascal, for example, it is used to formally define a subrange type, most frequently used to specify lower and upper bounds of valid indices of an array. Another way to interpret integer intervals are as sets defined by enumeration, using ellipsis notation. An integer interval that has a finite lower or upper endpoint always includes that endpoint. Therefore, the exclusion of endpoints can be explicitly denoted by writing a .. b − 1 , a + 1 .. b , or a + 1 .. b − 1. Alternate-bracket notations like [a .. b) or [a .. b[ are rarely used for integer intervals. == Properties == The intervals are precisely the connected subsets of R . {\displaystyle \mathbb {R} .} It follows that the image of an interval by any continuous function from R {\displaystyle \mathbb {R} } to R {\displaystyle \mathbb {R} } is also an interval. This is one formulation of the intermediate value theorem. The intervals are also the convex subsets of R . {\displaystyle \mathbb {R} .} The interval enclosure of a subset X ⊆ R {\displaystyle X\subseteq \mathbb {R} } is also the convex hull of X . {\displaystyle X.} The closure of an interval is the union of the interval and the set of its finite endpoints, and hence is also an interval. (The latter also follows from the fact that the closure of every connected subset of a topological space is a connected subset.) In other words, we have cl ( a , b ) = cl ( a , b ] = cl [ a , b ) = cl [ a , b ] = [ a , b ] , {\displaystyle \operatorname {cl} (a,b)=\operatorname {cl} (a,b]=\operatorname {cl} [a,b)=\operatorname {cl} [a,b]=[a,b],} cl ( a , + ∞ ) = cl [ a , + ∞ ) = [ a , + ∞ ) , {\displaystyle \operatorname {cl} (a,+\infty )=\operatorname {cl} [a,+\infty )=[a,+\infty ),} cl ( − ∞ , a ) = cl ( − ∞ , a ] = ( − ∞ , a ] , {\displaystyle \operatorname {cl} (-\infty ,a)=\operatorname {cl} (-\infty ,a]=(-\infty ,a],} cl ( − ∞ , + ∞ ) = ( − ∞ , ∞ ) . {\displaystyle \operatorname {cl} (-\infty ,+\infty )=(-\infty ,\infty ).} The intersection of any collection of intervals is always an interval. The union of two intervals is an interval if and only if they have a non-empty intersection or an open end-point of one interval is a closed end-point of the other, for example ( a , b ) ∪ [ b , c ] = ( a , c ] . {\displaystyle (a,b)\cup [b,c]=(a,c].} If R {\displaystyle \mathbb {R} } is viewed as a metric space, its open balls are the open bounded intervals (c + r, c − r), and its closed balls are the closed bounded intervals [c + r, c − r]. In particular, the metric and order topologies in the real line coincide, which is the standard topology of the real line. Any element x of an interval I defines a partition of I into three disjoint intervals I1, I2, I3: respectively, the elements of I that are less than x, the singleton [ x , x ] = { x } , {\displaystyle [x,x]=\{x\},} and the elements that are greater than x. The parts I1 and I3 are both non-empty (and have non-empty interiors), if and only if x is in the interior of I. This is an interval version of the trichotomy principle. == Dyadic intervals == A dyadic interval is a bounded real interval whose endpoints are j 2 n {\displaystyle {\tfrac {j}{2^{n}}}} and j + 1 2 n , {\displaystyle {\tfrac {j+1}{2^{n}}},} where j {\displaystyle j} and n {\displaystyle n} are integers. Depending on the context, either endpoint may or may not be included in the interval. Dyadic intervals have the following properties: The length of a dyadic interval is always an integer power of two. Each dyadic interval is contained in exactly one dyadic interval of twice the length. Each dyadic interval is spanned by two dyadic intervals of half the length. If two open dyadic intervals overlap, then one of them is a subset of the other. The dyadic intervals consequently have a structure that reflects that of an infinite binary tree. Dyadic intervals are relevant to several areas of numerical analysis, including adaptive mesh refinement, multigrid methods and wavelet analysis. Another way to represent such a structure is p-adic analysis (for p = 2). == Generalizations == === Balls === An open finite interval ( a , b ) {\displaystyle (a,b)} is a 1-dimensional open ball with a center at 1 2 ( a + b ) {\displaystyle {\tfrac {1}{2}}(a+b)} and a radius of 1 2 ( b − a ) . {\displaystyle {\tfrac {1}{2}}(b-a).} The closed finite interval [ a , b ] {\displaystyle [a,b]} is the corresponding closed ball, and the interval's two endpoints { a , b } {\displaystyle \{a,b\}} form a 0-dimensional sphere. Generalized to n {\displaystyle n} -dimensional Euclidean space, a ball is the set of points whose distance from the center is less than the radius. In the 2-dimensional case, a ball is called a disk. If a half-space is taken as a kind of degenerate ball (without a well-defined center or radius), a half-space can be taken as analogous to a half-bounded interval, with its boundary plane as the (degenerate) sphere corresponding to the finite endpoint. === Multi-dimensional intervals === A finite interval is (the interior of) a 1-dimensional hyperrectangle. Generalized to real coordinate space R n , {\displaystyle \mathbb {R} ^{n},} an axis-aligned hyperrectangle (or box) is the Cartesian product of n {\displaystyle n} finite intervals. For n = 2 {\displaystyle n=2} this is a rectangle; for n = 3 {\displaystyle n=3} this is a rectangular cuboid (also called a "box"). Allowing for a mix of open, closed, and infinite endpoints, the Cartesian product of any n {\displaystyle n} intervals, I = I 1 × I 2 × ⋯ × I n {\displaystyle I=I_{1}\times I_{2}\times \cdots \times I_{n}} is sometimes called an n {\displaystyle n} -dimensional interval. A facet of such an interval I {\displaystyle I} is the result of replacing any non-degenerate interval factor I k {\displaystyle I_{k}} by a degenerate interval consisting of a finite endpoint of I k . {\displaystyle I_{k}.} The faces of I {\displaystyle I} comprise I {\displaystyle I} itself and all faces of its facets. The corners of I {\displaystyle I} are the faces that consist of a single point of R n . {\displaystyle \mathbb {R} ^{n}.} === Convex polytopes === Any finite interval can be constructed as the intersection of half-bounded intervals (with an empty intersection taken to mean the whole real line), and the intersection of any number of half-bounded intervals is a (possibly empty) interval. Generalized to n {\displaystyle n} -dimensional affine space, an intersection of half-spaces (of arbitrary orientation) is (the interior of) a convex polytope, or in the 2-dimensional case a convex polygon. === Domains === An open interval is a connected open set of real numbers. Generalized to topological spaces in general, a non-empty connected open set is called a domain. === Complex intervals === Intervals of complex numbers can be defined as regions of the complex plane, either rectangular or circular. === Intervals in posets and preordered sets === ==== Definitions ==== The concept of intervals can be defined in arbitrary partially ordered sets or more generally, in arbitrary preordered sets. For a preordered set ( X , ≲ ) {\displaystyle (X,\lesssim )} and two elements a , b ∈ X , {\displaystyle a,b\in X,} one similarly defines the intervals: 11, Definition 11 ( a , b ) = { x ∈ X ∣ a < x < b } , {\displaystyle (a,b)=\{x\in X\mid a<x<b\},} [ a , b ] = { x ∈ X ∣ a ≲ x ≲ b } , {\displaystyle [a,b]=\{x\in X\mid a\lesssim x\lesssim b\},} ( a , b ] = { x ∈ X ∣ a < x ≲ b } , {\displaystyle (a,b]=\{x\in X\mid a<x\lesssim b\},} [ a , b ) = { x ∈ X ∣ a ≲ x < b } , {\displaystyle [a,b)=\{x\in X\mid a\lesssim x<b\},} ( a , ∞ ) = { x ∈ X ∣ a < x } , {\displaystyle (a,\infty )=\{x\in X\mid a<x\},} [ a , ∞ ) = { x ∈ X ∣ a ≲ x } , {\displaystyle [a,\infty )=\{x\in X\mid a\lesssim x\},} ( − ∞ , b ) = { x ∈ X ∣ x < b } , {\displaystyle (-\infty ,b)=\{x\in X\mid x<b\},} ( − ∞ , b ] = { x ∈ X ∣ x ≲ b } , {\displaystyle (-\infty ,b]=\{x\in X\mid x\lesssim b\},} ( − ∞ , ∞ ) = X , {\displaystyle (-\infty ,\infty )=X,} where x < y {\displaystyle x<y} means x ≲ y ≴ x . {\displaystyle x\lesssim y\not \lesssim x.} Actually, the intervals with single or no endpoints are the same as the intervals with two endpoints in the larger preordered set X ¯ = X ⊔ { − ∞ , ∞ } {\displaystyle {\bar {X}}=X\sqcup \{-\infty ,\infty \}} − ∞ < x < ∞ ( ∀ x ∈ X ) {\displaystyle -\infty <x<\infty \qquad (\forall x\in X)} defined by adding new smallest and greatest elements (even if there were ones), which are subsets of X . {\displaystyle X.} In the case of X = R {\displaystyle X=\mathbb {R} } one may take R ¯ {\displaystyle {\bar {\mathbb {R} }}} to be the extended real line. ==== Convex sets and convex components in order theory ==== A subset A ⊆ X {\displaystyle A\subseteq X} of the preordered set ( X , ≲ ) {\displaystyle (X,\lesssim )} is (order-)convex if for every x , y ∈ A {\displaystyle x,y\in A} and every x ≲ z ≲ y {\displaystyle x\lesssim z\lesssim y} we have z ∈ A . {\displaystyle z\in A.} Unlike in the case of the real line, a convex set of a preordered set need not be an interval. For example, in the totally ordered set ( Q , ≤ ) {\displaystyle (\mathbb {Q} ,\leq )} of rational numbers, the set Q = { x ∈ Q ∣ x 2 < 2 } {\displaystyle \mathbb {Q} =\{x\in \mathbb {Q} \mid x^{2}<2\}} is convex, but not an interval of Q , {\displaystyle \mathbb {Q} ,} since there is no square root of two in Q . {\displaystyle \mathbb {Q} .} Let ( X , ≲ ) {\displaystyle (X,\lesssim )} be a preordered set and let Y ⊆ X . {\displaystyle Y\subseteq X.} The convex sets of X {\displaystyle X} contained in Y {\displaystyle Y} form a poset under inclusion. A maximal element of this poset is called a convex component of Y . {\displaystyle Y.} : Definition 5.1 : 727 By the Zorn lemma, any convex set of X {\displaystyle X} contained in Y {\displaystyle Y} is contained in some convex component of Y , {\displaystyle Y,} but such components need not be unique. In a totally ordered set, such a component is always unique. That is, the convex components of a subset of a totally ordered set form a partition. ==== Properties ==== A generalization of the characterizations of the real intervals follows. For a non-empty subset I {\displaystyle I} of a linear continuum ( L , ≤ ) , {\displaystyle (L,\leq ),} the following conditions are equivalent.: 153, Theorem 24.1 The set I {\displaystyle I} is an interval. The set I {\displaystyle I} is order-convex. The set I {\displaystyle I} is a connected subset when L {\displaystyle L} is endowed with the order topology. For a subset S {\displaystyle S} of a lattice L , {\displaystyle L,} the following conditions are equivalent. The set S {\displaystyle S} is a sublattice and an (order-)convex set. There is an ideal I ⊆ L {\displaystyle I\subseteq L} and a filter F ⊆ L {\displaystyle F\subseteq L} such that S = I ∩ F . {\displaystyle S=I\cap F.} == Applications == === In general topology === Every Tychonoff space is embeddable into a product space of the closed unit intervals [ 0 , 1 ] . {\displaystyle [0,1].} Actually, every Tychonoff space that has a base of cardinality κ {\displaystyle \kappa } is embeddable into the product [ 0 , 1 ] κ {\displaystyle [0,1]^{\kappa }} of κ {\displaystyle \kappa } copies of the intervals.: p. 83, Theorem 2.3.23 The concepts of convex sets and convex components are used in a proof that every totally ordered set endowed with the order topology is completely normal or moreover, monotonically normal. == Topological algebra == Intervals can be associated with points of the plane, and hence regions of intervals can be associated with regions of the plane. Generally, an interval in mathematics corresponds to an ordered pair (x, y) taken from the direct product R × R {\displaystyle \mathbb {R} \times \mathbb {R} } of real numbers with itself, where it is often assumed that y > x. For purposes of mathematical structure, this restriction is discarded, and "reversed intervals" where y − x < 0 are allowed. Then, the collection of all intervals [x, y] can be identified with the topological ring formed by the direct sum of R {\displaystyle \mathbb {R} } with itself, where addition and multiplication are defined component-wise. The direct sum algebra ( R ⊕ R , + , × ) {\displaystyle (\mathbb {R} \oplus \mathbb {R} ,+,\times )} has two ideals, { [x,0] : x ∈ R } and { [0,y] : y ∈ R }. The identity element of this algebra is the condensed interval [1, 1]. If interval [x, y] is not in one of the ideals, then it has multiplicative inverse [1/x, 1/y]. Endowed with the usual topology, the algebra of intervals forms a topological ring. The group of units of this ring consists of four quadrants determined by the axes, or ideals in this case. The identity component of this group is quadrant I. Every interval can be considered a symmetric interval around its midpoint. In a reconfiguration published in 1956 by M Warmus, the axis of "balanced intervals" [x, −x] is used along with the axis of intervals [x, x] that reduce to a point. Instead of the direct sum R ⊕ R , {\displaystyle R\oplus R,} the ring of intervals has been identified with the hyperbolic numbers by M. Warmus and D. H. Lehmer through the identification z = 1 2 ( x + y ) + 1 2 ( x − y ) j , {\displaystyle z={\tfrac {1}{2}}(x+y)+{\tfrac {1}{2}}(x-y)j,} where j 2 = 1. {\displaystyle j^{2}=1.} This linear mapping of the plane, which amounts of a ring isomorphism, provides the plane with a multiplicative structure having some analogies to ordinary complex arithmetic, such as polar decomposition. == See also == Arc (geometry) Inequality Interval graph Interval finite element Interval (statistics) Line segment Partition of an interval Unit interval == References == == Bibliography == T. Sunaga, "Theory of interval algebra and its application to numerical analysis" Archived 2012-03-09 at the Wayback Machine, In: Research Association of Applied Geometry (RAAG) Memoirs, Ggujutsu Bunken Fukuy-kai. Tokyo, Japan, 1958, Vol. 2, pp. 29–46 (547-564); reprinted in Japan Journal on Industrial and Applied Mathematics, 2009, Vol. 26, No. 2-3, pp. 126–143. == External links == A Lucid Interval by Brian Hayes: An American Scientist article provides an introduction. Interval computations website Archived 2006-03-02 at the Wayback Machine Interval computations research centers Archived 2007-02-03 at the Wayback Machine Interval Notation by George Beck, Wolfram Demonstrations Project. Weisstein, Eric W. "Interval". MathWorld.
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In mathematics, the term socle has several related meanings. == Socle of a group == In the context of group theory, the socle of a group G, denoted soc(G), is the subgroup generated by the minimal normal subgroups of G. It can happen that a group has no minimal non-trivial normal subgroup (that is, every non-trivial normal subgroup properly contains another such subgroup) and in that case the socle is defined to be the subgroup generated by the identity. The socle is a direct product of minimal normal subgroups. As an example, consider the cyclic group Z12 with generator u, which has two minimal normal subgroups, one generated by u4 (which gives a normal subgroup with 3 elements) and the other by u6 (which gives a normal subgroup with 2 elements). Thus the socle of Z12 is the group generated by u4 and u6, which is just the group generated by u2. The socle is a characteristic subgroup, and hence a normal subgroup. It is not necessarily transitively normal, however. If a group G is a finite solvable group, then the socle can be expressed as a product of elementary abelian p-groups. Thus, in this case, it is just a product of copies of Z/pZ for various p, where the same p may occur multiple times in the product. == Socle of a module == In the context of module theory and ring theory the socle of a module M over a ring R is defined to be the sum of the minimal nonzero submodules of M. It can be considered as a dual notion to that of the radical of a module. In set notation, s o c ( M ) = ∑ N is a simple submodule of M N . {\displaystyle \mathrm {soc} (M)=\sum _{N{\text{ is a simple submodule of }}M}N.} Equivalently, s o c ( M ) = ⋂ E is an essential submodule of M E . {\displaystyle \mathrm {soc} (M)=\bigcap _{E{\text{ is an essential submodule of }}M}E.} The socle of a ring R can refer to one of two sets in the ring. Considering R as a right R-module, soc(RR) is defined, and considering R as a left R-module, soc(RR) is defined. Both of these socles are ring ideals, and it is known they are not necessarily equal. If M is an Artinian module, soc(M) is itself an essential submodule of M. In fact, if M is a semiartinian module, then soc(M) is itself an essential submodule of M. Additionally, if M is a non-zero module over a left semi-Artinian ring, then soc(M) is itself an essential submodule of M. This is because any non-zero module over a left semi-Artinian ring is a semiartinian module. A module is semisimple if and only if soc(M) = M. Rings for which soc(M) = M for all M are precisely semisimple rings. soc(soc(M)) = soc(M). M is a finitely cogenerated module if and only if soc(M) is finitely generated and soc(M) is an essential submodule of M. Since the sum of semisimple modules is semisimple, the socle of a module could also be defined as the unique maximal semisimple submodule. From the definition of rad(R), it is easy to see that rad(R) annihilates soc(R). If R is a finite-dimensional unital algebra and M a finitely generated R-module then the socle consists precisely of the elements annihilated by the Jacobson radical of R. == Socle of a Lie algebra == In the context of Lie algebras, a socle of a symmetric Lie algebra is the eigenspace of its structural automorphism that corresponds to the eigenvalue −1. (A symmetric Lie algebra decomposes into the direct sum of its socle and cosocle.) == See also == Injective hull Radical of a module Cosocle == References == Alperin, J.L.; Bell, Rowen B. (1995). Groups and Representations. Springer-Verlag. p. 136. ISBN 0-387-94526-1. Anderson, Frank Wylie; Fuller, Kent R. (1992). Rings and Categories of Modules. Springer-Verlag. ISBN 978-0-387-97845-1. Robinson, Derek J. S. (1996), A course in the theory of groups, Graduate Texts in Mathematics, vol. 80 (2 ed.), New York: Springer-Verlag, pp. xviii+499, doi:10.1007/978-1-4419-8594-1, ISBN 0-387-94461-3, MR 1357169
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In mathematics, a character is (most commonly) a special kind of function from a group to a field (such as the complex numbers). There are at least two distinct, but overlapping meanings. Other uses of the word "character" are almost always qualified. == Multiplicative character == A multiplicative character (or linear character, or simply character) on a group G is a group homomorphism from G to the multiplicative group of a field (Artin 1966), usually the field of complex numbers. If G is any group, then the set Ch(G) of these morphisms forms an abelian group under pointwise multiplication. This group is referred to as the character group of G. Sometimes only unitary characters are considered (thus the image is in the unit circle); other such homomorphisms are then called quasi-characters. Dirichlet characters can be seen as a special case of this definition. Multiplicative characters are linearly independent, i.e. if χ 1 , χ 2 , … , χ n {\displaystyle \chi _{1},\chi _{2},\ldots ,\chi _{n}} are different characters on a group G then from a 1 χ 1 + a 2 χ 2 + ⋯ + a n χ n = 0 {\displaystyle a_{1}\chi _{1}+a_{2}\chi _{2}+\dots +a_{n}\chi _{n}=0} it follows that a 1 = a 2 = ⋯ = a n = 0 {\displaystyle a_{1}=a_{2}=\cdots =a_{n}=0} . == Character of a representation == The character χ : G → F {\displaystyle \chi :G\to F} of a representation ϕ : G → G L ( V ) {\displaystyle \phi \colon G\to \mathrm {GL} (V)} of a group G on a finite-dimensional vector space V over a field F is the trace of the representation ϕ {\displaystyle \phi } (Serre 1977), i.e. χ ϕ ( g ) = Tr ( ϕ ( g ) ) {\displaystyle \chi _{\phi }(g)=\operatorname {Tr} (\phi (g))} for g ∈ G {\displaystyle g\in G} In general, the trace is not a group homomorphism, nor does the set of traces form a group. The characters of one-dimensional representations are identical to one-dimensional representations, so the above notion of multiplicative character can be seen as a special case of higher-dimensional characters. The study of representations using characters is called "character theory" and one-dimensional characters are also called "linear characters" within this context. === Alternative definition === If restricted to finite abelian group with 1 × 1 {\displaystyle 1\times 1} representation in C {\displaystyle \mathbb {C} } (i.e. G L ( V ) = G L ( 1 , C ) {\displaystyle \mathrm {GL} (V)=\mathrm {GL} (1,\mathbb {C} )} ), the following alternative definition would be equivalent to the above (For abelian groups, every matrix representation decomposes into a direct sum of 1 × 1 {\displaystyle 1\times 1} representations. For non-abelian groups, the original definition would be more general than this one): A character χ {\displaystyle \chi } of group ( G , ⋅ ) {\displaystyle (G,\cdot )} is a group homomorphism χ : G → C ∗ {\displaystyle \chi :G\rightarrow \mathbb {C} ^{*}} i.e. χ ( x ⋅ y ) = χ ( x ) χ ( y ) {\displaystyle \chi (x\cdot y)=\chi (x)\chi (y)} for all x , y ∈ G . {\displaystyle x,y\in G.} If G {\displaystyle G} is a finite abelian group, the characters play the role of harmonics. For infinite abelian groups, the above would be replaced by χ : G → T {\displaystyle \chi :G\to \mathbb {T} } where T {\displaystyle \mathbb {T} } is the circle group. == See also == Character group Dirichlet character Harish-Chandra character Hecke character Infinitesimal character Alternating character Characterization (mathematics) Pontryagin duality Base (topology) § Weight and character == References == Artin, Emil (1966), Galois Theory, Notre Dame Mathematical Lectures, number 2, Arthur Norton Milgram (Reprinted Dover Publications, 1997), ISBN 978-0-486-62342-9 Lectures Delivered at the University of Notre Dame Serre, Jean-Pierre (1977), Linear Representations of Finite Groups, Graduate Texts in Mathematics, vol. 42, Translated from the second French edition by Leonard L. Scott, New York-Heidelberg: Springer-Verlag, doi:10.1007/978-1-4684-9458-7, ISBN 0-387-90190-6, MR 0450380 == External links == "Character of a group", Encyclopedia of Mathematics, EMS Press, 2001 [1994]
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https://en.wikipedia.org/wiki/Character_(mathematics)
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Vedic Mathematics is a book written by Indian Shankaracharya Bharati Krishna Tirtha and first published in 1965. It contains a list of mathematical techniques which were falsely claimed to contain advanced mathematical knowledge. The book was posthumously published under its deceptive title by editor V. S. Agrawala, who noted in the foreword that the claim of Vedic origin, made by the original author and implied by the title, was unsupported. Neither Krishna Tirtha nor Agrawala were able to produce sources, and scholars unanimously note it to be a compendium of methods for increasing the speed of elementary mathematical calculations sharing no overlap with historical mathematical developments during the Vedic period. Nonetheless, there has been a proliferation of publications in this area and multiple attempts to integrate the subject into mainstream education at the state level by right-wing Hindu nationalist governments. S. G. Dani of the Indian Institute of Technology Bombay wrote that despite the dubious historigraphy, some of the calculation methods it describes are themselves interesting, a product of the author's academic training in mathematics and long recorded habit of experimentation with numbers. == Contents == The book contains metaphorical aphorisms in the form of sixteen sutras and thirteen sub-sutras, which Krishna Tirtha states allude to significant mathematical tools. The range of their asserted applications spans from topic as diverse as statics and pneumatics to astronomy and financial domains. Tirtha stated that no part of advanced mathematics lay beyond the realms of his book and propounded that studying it for a couple of hours every day for a year equated to spending about two decades in any standardized education system to become professionally trained in the discipline of mathematics. STS scholar S. G. Dani in 'Vedic Mathematics': Myth and Reality states that the book is primarily a compendium of "tricks" that can be applied in elementary, middle and high school arithmetic and algebra, to gain faster results. The sutras and sub-sutras are abstract literary expressions (for example, "as much less" or "one less than previous one") prone to creative interpretations; Krishna Tirtha exploited this to the extent of manipulating the same shloka to generate widely different mathematical equivalencies across a multitude of contexts. === Relationship with the Vedas === According to Krishna Tirtha, the sutras and other accessory content were found after years of solitary study of the Vedas—a set of sacred ancient Hindu scriptures—in a forest. They were supposedly contained in the pariśiṣṭa—a supplementary text/appendix—of the Atharvaveda. He does not provide any more bibliographic clarification on the sourcing. The book's editor, V. S. Agrawala, argues that since the Vedas are defined as the traditional repositories of all knowledge, any knowledge can be assumed to be somewhere in the Vedas, by definition; he even went to the extent of deeming Krishna Tirtha's work as a pariśiṣṭa in itself. However, numerous mathematicians and STS scholars (Dani, Kim Plofker, K.S. Shukla, Jan Hogendijk et al.) note that the Vedas do not contain any of those sutras and sub-sutras. When Shukla, a mathematician and historiographer of ancient Indian mathematics, challenged Krishna Tirtha to locate the sutras in the Parishishta of a standard edition of the Atharvaveda, Krishna Tirtha stated that they were not included in the standard editions but only in a hitherto-undiscovered version, chanced upon by him; the foreword and introduction of the book also takes a similar stand. Sanskrit scholars have observed that the book's linguistic style is not that of the Vedic period but rather reflects modern Sanskrit. Dani points out that the contents of the book have "practically nothing in common" with the mathematics of the Vedic period or even with subsequent developments in Indian mathematics. Shukla reiterates the observations, on a per-chapter basis. For example, multiple techniques in the book involve the use of decimals. These were unknown during the Vedic times and were introduced in India only in the sixteenth century; works of numerous ancient mathematicians such as Aryabhata, Brahmagupta and Bhaskara were based entirely on fractions. From a historiographic perspective, Vedic India had no knowledge of differentiation or integration. The book also claims that analytic geometry of conics occupied an important tier in Vedic mathematics, which runs contrary to all available evidence. == Publication history and reprints == First published in 1965, five years after Krishna Tirtha's death, the work consisted of forty chapters, originally on 367 pages, and covered techniques he had promulgated through his lectures. A foreword by Tirtha's disciple Manjula Trivedi stated that he had originally written 16 volumes—one on each sutra—but the manuscripts were lost before publication, and that this work was penned in 1957.: 10 Reprints were published in 1975 and 1978 to accommodate typographical corrections. Several reprints have been published since the 1990s.: 6 == Reception == S. G. Dani of the Indian Institute of Technology Bombay (IIT Bombay) notes the book to be of dubious quality. He believes it did a disservice both to the pedagogy of mathematical education by presenting the subject as a collection of methods without any conceptual rigor, and to science and technology studies in India (STS) by adhering to dubious standards of historiography. He also points out that while Tirtha's system could be used as a teaching aid, there was a need to prevent the use of "public money and energy on its propagation" except in a limited way and that authentic Vedic studies were being neglected in India even as Tirtha's system received support from several government and private agencies. Jayant Narlikar has voiced similar concerns. Hartosh Singh Bal notes that whilst Krishna Tirtha's attempts might be somewhat acceptable in light of his nationalistic inclinations during colonial rule—he had left his spiritual endeavors to be appointed as the principal of a college to counter Macaulayism—it provided a fertile ground for further ethnonationalist abuse of historiography by Hindu nationalist parties; Thomas Trautmann views the development of Vedic Mathematics in a similar manner. Meera Nanda has noted hagiographic descriptions of Indian knowledge systems by various right-wing cultural movements (including the BJP), which have deemed Krishna Tirtha to be in the same league as Srinivasa Ramanujan. Some have, however, praised the methods and commented on its potential to attract school-children to mathematics and increase popular engagement with the subject. Others have viewed the works as an attempt at harmonizing religion with science. === Originality of methods === Dani speculated that Krishna Tirtha's methods were a product of his academic training in mathematics and long-recorded habit of experimentation with numbers. Similar systems include the Trachtenberg system or the techniques mentioned in Lester Meyers's 1947 book High-speed Mathematics. Alex Bellos points out that several of the calculation methods can also be found in certain European treatises on calculation from the early Modern period. === Computation algorithms === Some of the algorithms have been tested for efficiency, with positive results. However, most of the algorithms have higher time complexity than conventional ones, which explains the lack of adoption of Vedic mathematics in real life. == Integration into mainstream education == The book has been included in the school syllabus of the Indian states of Madhya Pradesh and Uttar Pradesh, soon after the Bharatiya Janata Party (BJP), a right-wing nationalist political party, came to power and remade the education system to emphasize historically dubious notions like that that Vedic Mathematics represented a genuinely ancient and inherently superior Indian and Hindu system of mathematics, knowledge, and thinking.: 6 Dinanath Batra had conducted a lengthy campaign for the inclusion of Vedic Maths into the National Council of Educational Research and Training (NCERT) curricula. Subsequently, there was a proposal from NCERT to induct Vedic Maths, along with a number of fringe pseudo-scientific subjects (Vedic Astrology et al.), into the standard academic curricula. This was only shelved after a number of academics and mathematicians, led by Dani and sometimes backed by political parties, opposed these attempts based on previously discussed rationales and criticized the move as a politically guided attempt at saffronisation. After the BJP's return to power in 2014, three universities began offering courses on the subject of Vedic Mathematics while a television channel catering to the topic was also launched; generous education and research grants have also been allotted to the subject despite a lack of genuine scientific, mathematical, historical, or religious basis for doing so. The topic was introduced into the elementary curriculum of Himachal Pradesh in 2022. The same year, the government of Karnataka allocated funds for teaching the subject. This move by the BJP provoked criticism from academics and from Dalit groups. == Editions == Swami Sri Bharati Krsna Tirthaji Maharaja (1965). V. S. Agrawala (ed.). Vedic Mathematics: Sixteen Simple Mathematical Formulae from the Vedas (First ed.). Varanasi: Motilal Banarsidass. == Notes == == References == === Works cited === Dani, S. G. (2006) [1993]. "Myths and reality: On 'Vedic Mathematics'" (PDF). In Kandasamy, W. B. Vasantha; Smarandache, Florentin (eds.). Vedic Mathematics, 'Vedic' or 'Mathematics': A Fuzzy & Neutrosophic Analysis (PDF). Gallup, New Mexico: Multimedia Larga. ISBN 978-1-59973-004-2. Archived from the original (PDF) on 6 January 2022. Retrieved 23 May 2013. Shukla, K. S. (2019). "Vedic Mathematics: The deceptive title of Swamiji's book". In Kolachana, Aditya; Mahesh, K.; Ramasubramanian, K. (eds.). Studies in Indian Mathematics and Astronomy: Selected Articles of Kripa Shankar Shukla. Sources and Studies in the History of Mathematics and Physical Sciences. Singapore: Springer Publishing. pp. 697–704. doi:10.1007/978-981-13-7326-8. ISBN 978-981-13-7325-1.
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https://en.wikipedia.org/wiki/Vedic_Mathematics
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Computational mathematics is the study of the interaction between mathematics and calculations done by a computer. A large part of computational mathematics consists roughly of using mathematics for allowing and improving computer computation in areas of science and engineering where mathematics are useful. This involves in particular algorithm design, computational complexity, numerical methods and computer algebra. Computational mathematics refers also to the use of computers for mathematics itself. This includes mathematical experimentation for establishing conjectures (particularly in number theory), the use of computers for proving theorems (for example the four color theorem), and the design and use of proof assistants. == Areas of computational mathematics == Computational mathematics emerged as a distinct part of applied mathematics by the early 1950s. Currently, computational mathematics can refer to or include: Computational sciences, also known as scientific computation or computational engineering Systems sciences, for which directly requires the mathematical models from Systems engineering Solving mathematical problems by computer simulation as opposed to traditional engineering methods. Numerical methods used in scientific computation, for example numerical linear algebra and numerical solution of partial differential equations Stochastic methods, such as Monte Carlo methods and other representations of uncertainty in scientific computation The mathematics of scientific computation, in particular numerical analysis, the theory of numerical methods Computational complexity Computer algebra and computer algebra systems Computer-assisted research in various areas of mathematics, such as logic (automated theorem proving), discrete mathematics, combinatorics, number theory, and computational algebraic topology Cryptography and computer security, which involve, in particular, research on primality testing, factorization, elliptic curves, and mathematics of blockchain Computational linguistics, the use of mathematical and computer techniques in natural languages Computational algebraic geometry Computational group theory Computational geometry Computational number theory Computational topology Computational statistics Algorithmic information theory Algorithmic game theory Mathematical economics, the use of mathematics in economics, finance and, to certain extents, of accounting. Experimental mathematics == Journals == Journals that publish contributions from computational mathematics include ACM Transactions on Mathematical Software Mathematics of Computation SIAM Journal on Scientific Computing SIAM Journal on Numerical Analysis == See also == Mathematics portal Computer-based mathematics education == References == == Further reading == Cucker, F. (2003). Foundations of Computational Mathematics: Special Volume. Handbook of Numerical Analysis. North-Holland Publishing. ISBN 978-0-444-51247-5. Harris, J. W.; Stocker, H. (1998). Handbook of Mathematics and Computational Science. Springer-Verlag. ISBN 978-0-387-94746-4. Hartmann, A.K. (2009). Practical Guide to Computer Simulations. World Scientific. ISBN 978-981-283-415-7. Archived from the original on February 11, 2009. Retrieved May 3, 2012. Nonweiler, T. R. (1986). Computational Mathematics: An Introduction to Numerical Approximation. John Wiley and Sons. ISBN 978-0-470-20260-9. Gentle, J. E. (2007). Foundations of Computational Science. Springer-Verlag. ISBN 978-0-387-00450-1. White, R. E. (2003). Computational Mathematics: Models, Methods, and Analysis with MATLAB. Chapman and Hall. ISBN 978-1584883647. Yang, X. S. (2008). Introduction to Computational Mathematics. World Scientific. ISBN 978-9812818171. Strang, G. (2007). Computational Science and Engineering. Wiley. ISBN 978-0961408817. == External links == Foundations of Computational Mathematics, a non-profit organization International Journal of Computer Discovered Mathematics
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https://en.wikipedia.org/wiki/Computational_mathematics
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In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a function of time. Historically, the concept was elaborated with the infinitesimal calculus at the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable (that is, they had a high degree of regularity). The concept of a function was formalized at the end of the 19th century in terms of set theory, and this greatly increased the possible applications of the concept. A function is often denoted by a letter such as f, g or h. The value of a function f at an element x of its domain (that is, the element of the codomain that is associated with x) is denoted by f(x); for example, the value of f at x = 4 is denoted by f(4). Commonly, a specific function is defined by means of an expression depending on x, such as f ( x ) = x 2 + 1 ; {\displaystyle f(x)=x^{2}+1;} in this case, some computation, called function evaluation, may be needed for deducing the value of the function at a particular value; for example, if f ( x ) = x 2 + 1 , {\displaystyle f(x)=x^{2}+1,} then f ( 4 ) = 4 2 + 1 = 17. {\displaystyle f(4)=4^{2}+1=17.} Given its domain and its codomain, a function is uniquely represented by the set of all pairs (x, f (x)), called the graph of the function, a popular means of illustrating the function. When the domain and the codomain are sets of real numbers, each such pair may be thought of as the Cartesian coordinates of a point in the plane. Functions are widely used in science, engineering, and in most fields of mathematics. It has been said that functions are "the central objects of investigation" in most fields of mathematics. The concept of a function has evolved significantly over centuries, from its informal origins in ancient mathematics to its formalization in the 19th century. See History of the function concept for details. == Definition == A function f from a set X to a set Y is an assignment of one element of Y to each element of X. The set X is called the domain of the function and the set Y is called the codomain of the function. If the element y in Y is assigned to x in X by the function f, one says that f maps x to y, and this is commonly written y = f ( x ) . {\displaystyle y=f(x).} In this notation, x is the argument or variable of the function. A specific element x of X is a value of the variable, and the corresponding element of Y is the value of the function at x, or the image of x under the function. The image of a function, sometimes called its range, is the set of the images of all elements in the domain. A function f, its domain X, and its codomain Y are often specified by the notation f : X → Y . {\displaystyle f:X\to Y.} One may write x ↦ y {\displaystyle x\mapsto y} instead of y = f ( x ) {\displaystyle y=f(x)} , where the symbol ↦ {\displaystyle \mapsto } (read 'maps to') is used to specify where a particular element x in the domain is mapped to by f. This allows the definition of a function without naming. For example, the square function is the function x ↦ x 2 . {\displaystyle x\mapsto x^{2}.} The domain and codomain are not always explicitly given when a function is defined. In particular, it is common that one might only know, without some (possibly difficult) computation, that the domain of a specific function is contained in a larger set. For example, if f : R → R {\displaystyle f:\mathbb {R} \to \mathbb {R} } is a real function, the determination of the domain of the function x ↦ 1 / f ( x ) {\displaystyle x\mapsto 1/f(x)} requires knowing the zeros of f. This is one of the reasons for which, in mathematical analysis, "a function from X to Y " may refer to a function having a proper subset of X as a domain. For example, a "function from the reals to the reals" may refer to a real-valued function of a real variable whose domain is a proper subset of the real numbers, typically a subset that contains a non-empty open interval. Such a function is then called a partial function. A function f on a set S means a function from the domain S, without specifying a codomain. However, some authors use it as shorthand for saying that the function is f : S → S. === Formal definition === The above definition of a function is essentially that of the founders of calculus, Leibniz, Newton and Euler. However, it cannot be formalized, since there is no mathematical definition of an "assignment". It is only at the end of the 19th century that the first formal definition of a function could be provided, in terms of set theory. This set-theoretic definition is based on the fact that a function establishes a relation between the elements of the domain and some (possibly all) elements of the codomain. Mathematically, a binary relation between two sets X and Y is a subset of the set of all ordered pairs ( x , y ) {\displaystyle (x,y)} such that x ∈ X {\displaystyle x\in X} and y ∈ Y . {\displaystyle y\in Y.} The set of all these pairs is called the Cartesian product of X and Y and denoted X × Y . {\displaystyle X\times Y.} Thus, the above definition may be formalized as follows. A function with domain X and codomain Y is a binary relation R between X and Y that satisfies the two following conditions: For every x {\displaystyle x} in X {\displaystyle X} there exists y {\displaystyle y} in Y {\displaystyle Y} such that ( x , y ) ∈ R . {\displaystyle (x,y)\in R.} If ( x , y ) ∈ R {\displaystyle (x,y)\in R} and ( x , z ) ∈ R , {\displaystyle (x,z)\in R,} then y = z . {\displaystyle y=z.} This definition may be rewritten more formally, without referring explicitly to the concept of a relation, but using more notation (including set-builder notation): A function is formed by three sets, the domain X , {\displaystyle X,} the codomain Y , {\displaystyle Y,} and the graph R {\displaystyle R} that satisfy the three following conditions. R ⊆ { ( x , y ) ∣ x ∈ X , y ∈ Y } {\displaystyle R\subseteq \{(x,y)\mid x\in X,y\in Y\}} ∀ x ∈ X , ∃ y ∈ Y , ( x , y ) ∈ R {\displaystyle \forall x\in X,\exists y\in Y,\left(x,y\right)\in R\qquad } ( x , y ) ∈ R ∧ ( x , z ) ∈ R ⟹ y = z {\displaystyle (x,y)\in R\land (x,z)\in R\implies y=z\qquad } === Partial functions === Partial functions are defined similarly to ordinary functions, with the "total" condition removed. That is, a partial function from X to Y is a binary relation R between X and Y such that, for every x ∈ X , {\displaystyle x\in X,} there is at most one y in Y such that ( x , y ) ∈ R . {\displaystyle (x,y)\in R.} Using functional notation, this means that, given x ∈ X , {\displaystyle x\in X,} either f ( x ) {\displaystyle f(x)} is in Y, or it is undefined. The set of the elements of X such that f ( x ) {\displaystyle f(x)} is defined and belongs to Y is called the domain of definition of the function. A partial function from X to Y is thus an ordinary function that has as its domain a subset of X called the domain of definition of the function. If the domain of definition equals X, one often says that the partial function is a total function. In several areas of mathematics, the term "function" refers to partial functions rather than to ordinary (total) functions. This is typically the case when functions may be specified in a way that makes difficult or even impossible to determine their domain. In calculus, a real-valued function of a real variable or real function is a partial function from the set R {\displaystyle \mathbb {R} } of the real numbers to itself. Given a real function f : x ↦ f ( x ) {\displaystyle f:x\mapsto f(x)} its multiplicative inverse x ↦ 1 / f ( x ) {\displaystyle x\mapsto 1/f(x)} is also a real function. The determination of the domain of definition of a multiplicative inverse of a (partial) function amounts to compute the zeros of the function, the values where the function is defined but not its multiplicative inverse. Similarly, a function of a complex variable is generally a partial function whose domain of definition is a subset of the complex numbers C {\displaystyle \mathbb {C} } . The difficulty of determining the domain of definition of a complex function is illustrated by the multiplicative inverse of the Riemann zeta function: the determination of the domain of definition of the function z ↦ 1 / ζ ( z ) {\displaystyle z\mapsto 1/\zeta (z)} is more or less equivalent to the proof or disproof of one of the major open problems in mathematics, the Riemann hypothesis. In computability theory, a general recursive function is a partial function from the integers to the integers whose values can be computed by an algorithm (roughly speaking). The domain of definition of such a function is the set of inputs for which the algorithm does not run forever. A fundamental theorem of computability theory is that there cannot exist an algorithm that takes an arbitrary general recursive function as input and tests whether 0 belongs to its domain of definition (see Halting problem). === Multivariate functions === A multivariate function, multivariable function, or function of several variables is a function that depends on several arguments. Such functions are commonly encountered. For example, the position of a car on a road is a function of the time travelled and its average speed. Formally, a function of n variables is a function whose domain is a set of n-tuples. For example, multiplication of integers is a function of two variables, or bivariate function, whose domain is the set of all ordered pairs (2-tuples) of integers, and whose codomain is the set of integers. The same is true for every binary operation. The graph of a bivariate surface over a two-dimensional real domain may be interpreted as defining a parametric surface, as used in, e.g., bivariate interpolation. Commonly, an n-tuple is denoted enclosed between parentheses, such as in ( 1 , 2 , … , n ) . {\displaystyle (1,2,\ldots ,n).} When using functional notation, one usually omits the parentheses surrounding tuples, writing f ( x 1 , … , x n ) {\displaystyle f(x_{1},\ldots ,x_{n})} instead of f ( ( x 1 , … , x n ) ) . {\displaystyle f((x_{1},\ldots ,x_{n})).} Given n sets X 1 , … , X n , {\displaystyle X_{1},\ldots ,X_{n},} the set of all n-tuples ( x 1 , … , x n ) {\displaystyle (x_{1},\ldots ,x_{n})} such that x 1 ∈ X 1 , … , x n ∈ X n {\displaystyle x_{1}\in X_{1},\ldots ,x_{n}\in X_{n}} is called the Cartesian product of X 1 , … , X n , {\displaystyle X_{1},\ldots ,X_{n},} and denoted X 1 × ⋯ × X n . {\displaystyle X_{1}\times \cdots \times X_{n}.} Therefore, a multivariate function is a function that has a Cartesian product or a proper subset of a Cartesian product as a domain. f : U → Y , {\displaystyle f:U\to Y,} where the domain U has the form U ⊆ X 1 × ⋯ × X n . {\displaystyle U\subseteq X_{1}\times \cdots \times X_{n}.} If all the X i {\displaystyle X_{i}} are equal to the set R {\displaystyle \mathbb {R} } of the real numbers or to the set C {\displaystyle \mathbb {C} } of the complex numbers, one talks respectively of a function of several real variables or of a function of several complex variables. == Notation == There are various standard ways for denoting functions. The most commonly used notation is functional notation, which is the first notation described below. === Functional notation === The functional notation requires that a name is given to the function, which, in the case of a unspecified function is often the letter f. Then, the application of the function to an argument is denoted by its name followed by its argument (or, in the case of a multivariate functions, its arguments) enclosed between parentheses, such as in f ( x ) , sin ( 3 ) , or f ( x 2 + 1 ) . {\displaystyle f(x),\quad \sin(3),\quad {\text{or}}\quad f(x^{2}+1).} The argument between the parentheses may be a variable, often x, that represents an arbitrary element of the domain of the function, a specific element of the domain (3 in the above example), or an expression that can be evaluated to an element of the domain ( x 2 + 1 {\displaystyle x^{2}+1} in the above example). The use of a unspecified variable between parentheses is useful for defining a function explicitly such as in "let f ( x ) = sin ( x 2 + 1 ) {\displaystyle f(x)=\sin(x^{2}+1)} ". When the symbol denoting the function consists of several characters and no ambiguity may arise, the parentheses of functional notation might be omitted. For example, it is common to write sin x instead of sin(x). Functional notation was first used by Leonhard Euler in 1734. Some widely used functions are represented by a symbol consisting of several letters (usually two or three, generally an abbreviation of their name). In this case, a roman type is customarily used instead, such as "sin" for the sine function, in contrast to italic font for single-letter symbols. The functional notation is often used colloquially for referring to a function and simultaneously naming its argument, such as in "let f ( x ) {\displaystyle f(x)} be a function". This is an abuse of notation that is useful for a simpler formulation. === Arrow notation === Arrow notation defines the rule of a function inline, without requiring a name to be given to the function. It uses the ↦ arrow symbol, pronounced "maps to". For example, x ↦ x + 1 {\displaystyle x\mapsto x+1} is the function which takes a real number as input and outputs that number plus 1. Again, a domain and codomain of R {\displaystyle \mathbb {R} } is implied. The domain and codomain can also be explicitly stated, for example: sqr : Z → Z x ↦ x 2 . {\displaystyle {\begin{aligned}\operatorname {sqr} \colon \mathbb {Z} &\to \mathbb {Z} \\x&\mapsto x^{2}.\end{aligned}}} This defines a function sqr from the integers to the integers that returns the square of its input. As a common application of the arrow notation, suppose f : X × X → Y ; ( x , t ) ↦ f ( x , t ) {\displaystyle f:X\times X\to Y;\;(x,t)\mapsto f(x,t)} is a function in two variables, and we want to refer to a partially applied function X → Y {\displaystyle X\to Y} produced by fixing the second argument to the value t0 without introducing a new function name. The map in question could be denoted x ↦ f ( x , t 0 ) {\displaystyle x\mapsto f(x,t_{0})} using the arrow notation. The expression x ↦ f ( x , t 0 ) {\displaystyle x\mapsto f(x,t_{0})} (read: "the map taking x to f of x comma t nought") represents this new function with just one argument, whereas the expression f(x0, t0) refers to the value of the function f at the point (x0, t0). === Index notation === Index notation may be used instead of functional notation. That is, instead of writing f (x), one writes f x . {\displaystyle f_{x}.} This is typically the case for functions whose domain is the set of the natural numbers. Such a function is called a sequence, and, in this case the element f n {\displaystyle f_{n}} is called the nth element of the sequence. The index notation can also be used for distinguishing some variables called parameters from the "true variables". In fact, parameters are specific variables that are considered as being fixed during the study of a problem. For example, the map x ↦ f ( x , t ) {\displaystyle x\mapsto f(x,t)} (see above) would be denoted f t {\displaystyle f_{t}} using index notation, if we define the collection of maps f t {\displaystyle f_{t}} by the formula f t ( x ) = f ( x , t ) {\displaystyle f_{t}(x)=f(x,t)} for all x , t ∈ X {\displaystyle x,t\in X} . === Dot notation === In the notation x ↦ f ( x ) , {\displaystyle x\mapsto f(x),} the symbol x does not represent any value; it is simply a placeholder, meaning that, if x is replaced by any value on the left of the arrow, it should be replaced by the same value on the right of the arrow. Therefore, x may be replaced by any symbol, often an interpunct " ⋅ ". This may be useful for distinguishing the function f (⋅) from its value f (x) at x. For example, a ( ⋅ ) 2 {\displaystyle a(\cdot )^{2}} may stand for the function x ↦ a x 2 {\displaystyle x\mapsto ax^{2}} , and ∫ a ( ⋅ ) f ( u ) d u {\textstyle \int _{a}^{\,(\cdot )}f(u)\,du} may stand for a function defined by an integral with variable upper bound: x ↦ ∫ a x f ( u ) d u {\textstyle x\mapsto \int _{a}^{x}f(u)\,du} . === Specialized notations === There are other, specialized notations for functions in sub-disciplines of mathematics. For example, in linear algebra and functional analysis, linear forms and the vectors they act upon are denoted using a dual pair to show the underlying duality. This is similar to the use of bra–ket notation in quantum mechanics. In logic and the theory of computation, the function notation of lambda calculus is used to explicitly express the basic notions of function abstraction and application. In category theory and homological algebra, networks of functions are described in terms of how they and their compositions commute with each other using commutative diagrams that extend and generalize the arrow notation for functions described above. === Functions of more than one variable === In some cases the argument of a function may be an ordered pair of elements taken from some set or sets. For example, a function f can be defined as mapping any pair of real numbers ( x , y ) {\displaystyle (x,y)} to the sum of their squares, x 2 + y 2 {\displaystyle x^{2}+y^{2}} . Such a function is commonly written as f ( x , y ) = x 2 + y 2 {\displaystyle f(x,y)=x^{2}+y^{2}} and referred to as "a function of two variables". Likewise one can have a function of three or more variables, with notations such as f ( w , x , y ) {\displaystyle f(w,x,y)} , f ( w , x , y , z ) {\displaystyle f(w,x,y,z)} . == Other terms == A function may also be called a map or a mapping, but some authors make a distinction between the term "map" and "function". For example, the term "map" is often reserved for a "function" with some sort of special structure (e.g. maps of manifolds). In particular map may be used in place of homomorphism for the sake of succinctness (e.g., linear map or map from G to H instead of group homomorphism from G to H). Some authors reserve the word mapping for the case where the structure of the codomain belongs explicitly to the definition of the function. Some authors, such as Serge Lang, use "function" only to refer to maps for which the codomain is a subset of the real or complex numbers, and use the term mapping for more general functions. In the theory of dynamical systems, a map denotes an evolution function used to create discrete dynamical systems. See also Poincaré map. Whichever definition of map is used, related terms like domain, codomain, injective, continuous have the same meaning as for a function. == Specifying a function == Given a function f {\displaystyle f} , by definition, to each element x {\displaystyle x} of the domain of the function f {\displaystyle f} , there is a unique element associated to it, the value f ( x ) {\displaystyle f(x)} of f {\displaystyle f} at x {\displaystyle x} . There are several ways to specify or describe how x {\displaystyle x} is related to f ( x ) {\displaystyle f(x)} , both explicitly and implicitly. Sometimes, a theorem or an axiom asserts the existence of a function having some properties, without describing it more precisely. Often, the specification or description is referred to as the definition of the function f {\displaystyle f} . === By listing function values === On a finite set a function may be defined by listing the elements of the codomain that are associated to the elements of the domain. For example, if A = { 1 , 2 , 3 } {\displaystyle A=\{1,2,3\}} , then one can define a function f : A → R {\displaystyle f:A\to \mathbb {R} } by f ( 1 ) = 2 , f ( 2 ) = 3 , f ( 3 ) = 4. {\displaystyle f(1)=2,f(2)=3,f(3)=4.} === By a formula === Functions are often defined by an expression that describes a combination of arithmetic operations and previously defined functions; such a formula allows computing the value of the function from the value of any element of the domain. For example, in the above example, f {\displaystyle f} can be defined by the formula f ( n ) = n + 1 {\displaystyle f(n)=n+1} , for n ∈ { 1 , 2 , 3 } {\displaystyle n\in \{1,2,3\}} . When a function is defined this way, the determination of its domain is sometimes difficult. If the formula that defines the function contains divisions, the values of the variable for which a denominator is zero must be excluded from the domain; thus, for a complicated function, the determination of the domain passes through the computation of the zeros of auxiliary functions. Similarly, if square roots occur in the definition of a function from R {\displaystyle \mathbb {R} } to R , {\displaystyle \mathbb {R} ,} the domain is included in the set of the values of the variable for which the arguments of the square roots are nonnegative. For example, f ( x ) = 1 + x 2 {\displaystyle f(x)={\sqrt {1+x^{2}}}} defines a function f : R → R {\displaystyle f:\mathbb {R} \to \mathbb {R} } whose domain is R , {\displaystyle \mathbb {R} ,} because 1 + x 2 {\displaystyle 1+x^{2}} is always positive if x is a real number. On the other hand, f ( x ) = 1 − x 2 {\displaystyle f(x)={\sqrt {1-x^{2}}}} defines a function from the reals to the reals whose domain is reduced to the interval [−1, 1]. (In old texts, such a domain was called the domain of definition of the function.) Functions can be classified by the nature of formulas that define them: A quadratic function is a function that may be written f ( x ) = a x 2 + b x + c , {\displaystyle f(x)=ax^{2}+bx+c,} where a, b, c are constants. More generally, a polynomial function is a function that can be defined by a formula involving only additions, subtractions, multiplications, and exponentiation to nonnegative integer powers. For example, f ( x ) = x 3 − 3 x − 1 {\displaystyle f(x)=x^{3}-3x-1} and f ( x ) = ( x − 1 ) ( x 3 + 1 ) + 2 x 2 − 1 {\displaystyle f(x)=(x-1)(x^{3}+1)+2x^{2}-1} are polynomial functions of x {\displaystyle x} . A rational function is the same, with divisions also allowed, such as f ( x ) = x − 1 x + 1 , {\displaystyle f(x)={\frac {x-1}{x+1}},} and f ( x ) = 1 x + 1 + 3 x − 2 x − 1 . {\displaystyle f(x)={\frac {1}{x+1}}+{\frac {3}{x}}-{\frac {2}{x-1}}.} An algebraic function is the same, with nth roots and roots of polynomials also allowed. An elementary function is the same, with logarithms and exponential functions allowed. === Inverse and implicit functions === A function f : X → Y , {\displaystyle f:X\to Y,} with domain X and codomain Y, is bijective, if for every y in Y, there is one and only one element x in X such that y = f(x). In this case, the inverse function of f is the function f − 1 : Y → X {\displaystyle f^{-1}:Y\to X} that maps y ∈ Y {\displaystyle y\in Y} to the element x ∈ X {\displaystyle x\in X} such that y = f(x). For example, the natural logarithm is a bijective function from the positive real numbers to the real numbers. It thus has an inverse, called the exponential function, that maps the real numbers onto the positive numbers. If a function f : X → Y {\displaystyle f:X\to Y} is not bijective, it may occur that one can select subsets E ⊆ X {\displaystyle E\subseteq X} and F ⊆ Y {\displaystyle F\subseteq Y} such that the restriction of f to E is a bijection from E to F, and has thus an inverse. The inverse trigonometric functions are defined this way. For example, the cosine function induces, by restriction, a bijection from the interval [0, π] onto the interval [−1, 1], and its inverse function, called arccosine, maps [−1, 1] onto [0, π]. The other inverse trigonometric functions are defined similarly. More generally, given a binary relation R between two sets X and Y, let E be a subset of X such that, for every x ∈ E , {\displaystyle x\in E,} there is some y ∈ Y {\displaystyle y\in Y} such that x R y. If one has a criterion allowing selecting such a y for every x ∈ E , {\displaystyle x\in E,} this defines a function f : E → Y , {\displaystyle f:E\to Y,} called an implicit function, because it is implicitly defined by the relation R. For example, the equation of the unit circle x 2 + y 2 = 1 {\displaystyle x^{2}+y^{2}=1} defines a relation on real numbers. If −1 < x < 1 there are two possible values of y, one positive and one negative. For x = ± 1, these two values become both equal to 0. Otherwise, there is no possible value of y. This means that the equation defines two implicit functions with domain [−1, 1] and respective codomains [0, +∞) and (−∞, 0]. In this example, the equation can be solved in y, giving y = ± 1 − x 2 , {\displaystyle y=\pm {\sqrt {1-x^{2}}},} but, in more complicated examples, this is impossible. For example, the relation y 5 + y + x = 0 {\displaystyle y^{5}+y+x=0} defines y as an implicit function of x, called the Bring radical, which has R {\displaystyle \mathbb {R} } as domain and range. The Bring radical cannot be expressed in terms of the four arithmetic operations and nth roots. The implicit function theorem provides mild differentiability conditions for existence and uniqueness of an implicit function in the neighborhood of a point. === Using differential calculus === Many functions can be defined as the antiderivative of another function. This is the case of the natural logarithm, which is the antiderivative of 1/x that is 0 for x = 1. Another common example is the error function. More generally, many functions, including most special functions, can be defined as solutions of differential equations. The simplest example is probably the exponential function, which can be defined as the unique function that is equal to its derivative and takes the value 1 for x = 0. Power series can be used to define functions on the domain in which they converge. For example, the exponential function is given by e x = ∑ n = 0 ∞ x n n ! {\textstyle e^{x}=\sum _{n=0}^{\infty }{x^{n} \over n!}} . However, as the coefficients of a series are quite arbitrary, a function that is the sum of a convergent series is generally defined otherwise, and the sequence of the coefficients is the result of some computation based on another definition. Then, the power series can be used to enlarge the domain of the function. Typically, if a function for a real variable is the sum of its Taylor series in some interval, this power series allows immediately enlarging the domain to a subset of the complex numbers, the disc of convergence of the series. Then analytic continuation allows enlarging further the domain for including almost the whole complex plane. This process is the method that is generally used for defining the logarithm, the exponential and the trigonometric functions of a complex number. === By recurrence === Functions whose domain are the nonnegative integers, known as sequences, are sometimes defined by recurrence relations. The factorial function on the nonnegative integers ( n ↦ n ! {\displaystyle n\mapsto n!} ) is a basic example, as it can be defined by the recurrence relation n ! = n ( n − 1 ) ! for n > 0 , {\displaystyle n!=n(n-1)!\quad {\text{for}}\quad n>0,} and the initial condition 0 ! = 1. {\displaystyle 0!=1.} == Representing a function == A graph is commonly used to give an intuitive picture of a function. As an example of how a graph helps to understand a function, it is easy to see from its graph whether a function is increasing or decreasing. Some functions may also be represented by bar charts. === Graphs and plots === Given a function f : X → Y , {\displaystyle f:X\to Y,} its graph is, formally, the set G = { ( x , f ( x ) ) ∣ x ∈ X } . {\displaystyle G=\{(x,f(x))\mid x\in X\}.} In the frequent case where X and Y are subsets of the real numbers (or may be identified with such subsets, e.g. intervals), an element ( x , y ) ∈ G {\displaystyle (x,y)\in G} may be identified with a point having coordinates x, y in a 2-dimensional coordinate system, e.g. the Cartesian plane. Parts of this may create a plot that represents (parts of) the function. The use of plots is so ubiquitous that they too are called the graph of the function. Graphic representations of functions are also possible in other coordinate systems. For example, the graph of the square function x ↦ x 2 , {\displaystyle x\mapsto x^{2},} consisting of all points with coordinates ( x , x 2 ) {\displaystyle (x,x^{2})} for x ∈ R , {\displaystyle x\in \mathbb {R} ,} yields, when depicted in Cartesian coordinates, the well known parabola. If the same quadratic function x ↦ x 2 , {\displaystyle x\mapsto x^{2},} with the same formal graph, consisting of pairs of numbers, is plotted instead in polar coordinates ( r , θ ) = ( x , x 2 ) , {\displaystyle (r,\theta )=(x,x^{2}),} the plot obtained is Fermat's spiral. === Tables === A function can be represented as a table of values. If the domain of a function is finite, then the function can be completely specified in this way. For example, the multiplication function f : { 1 , … , 5 } 2 → R {\displaystyle f:\{1,\ldots ,5\}^{2}\to \mathbb {R} } defined as f ( x , y ) = x y {\displaystyle f(x,y)=xy} can be represented by the familiar multiplication table On the other hand, if a function's domain is continuous, a table can give the values of the function at specific values of the domain. If an intermediate value is needed, interpolation can be used to estimate the value of the function. For example, a portion of a table for the sine function might be given as follows, with values rounded to 6 decimal places: Before the advent of handheld calculators and personal computers, such tables were often compiled and published for functions such as logarithms and trigonometric functions. === Bar chart === A bar chart can represent a function whose domain is a finite set, the natural numbers, or the integers. In this case, an element x of the domain is represented by an interval of the x-axis, and the corresponding value of the function, f(x), is represented by a rectangle whose base is the interval corresponding to x and whose height is f(x) (possibly negative, in which case the bar extends below the x-axis). == General properties == This section describes general properties of functions, that are independent of specific properties of the domain and the codomain. === Standard functions === There are a number of standard functions that occur frequently: For every set X, there is a unique function, called the empty function, or empty map, from the empty set to X. The graph of an empty function is the empty set. The existence of empty functions is needed both for the coherency of the theory and for avoiding exceptions concerning the empty set in many statements. Under the usual set-theoretic definition of a function as an ordered triplet (or equivalent ones), there is exactly one empty function for each set, thus the empty function ∅ → X {\displaystyle \varnothing \to X} is not equal to ∅ → Y {\displaystyle \varnothing \to Y} if and only if X ≠ Y {\displaystyle X\neq Y} , although their graphs are both the empty set. For every set X and every singleton set {s}, there is a unique function from X to {s}, which maps every element of X to s. This is a surjection (see below) unless X is the empty set. Given a function f : X → Y , {\displaystyle f:X\to Y,} the canonical surjection of f onto its image f ( X ) = { f ( x ) ∣ x ∈ X } {\displaystyle f(X)=\{f(x)\mid x\in X\}} is the function from X to f(X) that maps x to f(x). For every subset A of a set X, the inclusion map of A into X is the injective (see below) function that maps every element of A to itself. The identity function on a set X, often denoted by idX, is the inclusion of X into itself. === Function composition === Given two functions f : X → Y {\displaystyle f:X\to Y} and g : Y → Z {\displaystyle g:Y\to Z} such that the domain of g is the codomain of f, their composition is the function g ∘ f : X → Z {\displaystyle g\circ f:X\rightarrow Z} defined by ( g ∘ f ) ( x ) = g ( f ( x ) ) . {\displaystyle (g\circ f)(x)=g(f(x)).} That is, the value of g ∘ f {\displaystyle g\circ f} is obtained by first applying f to x to obtain y = f(x) and then applying g to the result y to obtain g(y) = g(f(x)). In this notation, the function that is applied first is always written on the right. The composition g ∘ f {\displaystyle g\circ f} is an operation on functions that is defined only if the codomain of the first function is the domain of the second one. Even when both g ∘ f {\displaystyle g\circ f} and f ∘ g {\displaystyle f\circ g} satisfy these conditions, the composition is not necessarily commutative, that is, the functions g ∘ f {\displaystyle g\circ f} and f ∘ g {\displaystyle f\circ g} need not be equal, but may deliver different values for the same argument. For example, let f(x) = x2 and g(x) = x + 1, then g ( f ( x ) ) = x 2 + 1 {\displaystyle g(f(x))=x^{2}+1} and f ( g ( x ) ) = ( x + 1 ) 2 {\displaystyle f(g(x))=(x+1)^{2}} agree just for x = 0. {\displaystyle x=0.} The function composition is associative in the sense that, if one of ( h ∘ g ) ∘ f {\displaystyle (h\circ g)\circ f} and h ∘ ( g ∘ f ) {\displaystyle h\circ (g\circ f)} is defined, then the other is also defined, and they are equal, that is, ( h ∘ g ) ∘ f = h ∘ ( g ∘ f ) . {\displaystyle (h\circ g)\circ f=h\circ (g\circ f).} Therefore, it is usual to just write h ∘ g ∘ f . {\displaystyle h\circ g\circ f.} The identity functions id X {\displaystyle \operatorname {id} _{X}} and id Y {\displaystyle \operatorname {id} _{Y}} are respectively a right identity and a left identity for functions from X to Y. That is, if f is a function with domain X, and codomain Y, one has f ∘ id X = id Y ∘ f = f . {\displaystyle f\circ \operatorname {id} _{X}=\operatorname {id} _{Y}\circ f=f.} === Image and preimage === Let f : X → Y . {\displaystyle f:X\to Y.} The image under f of an element x of the domain X is f(x). If A is any subset of X, then the image of A under f, denoted f(A), is the subset of the codomain Y consisting of all images of elements of A, that is, f ( A ) = { f ( x ) ∣ x ∈ A } . {\displaystyle f(A)=\{f(x)\mid x\in A\}.} The image of f is the image of the whole domain, that is, f(X). It is also called the range of f, although the term range may also refer to the codomain. On the other hand, the inverse image or preimage under f of an element y of the codomain Y is the set of all elements of the domain X whose images under f equal y. In symbols, the preimage of y is denoted by f − 1 ( y ) {\displaystyle f^{-1}(y)} and is given by the equation f − 1 ( y ) = { x ∈ X ∣ f ( x ) = y } . {\displaystyle f^{-1}(y)=\{x\in X\mid f(x)=y\}.} Likewise, the preimage of a subset B of the codomain Y is the set of the preimages of the elements of B, that is, it is the subset of the domain X consisting of all elements of X whose images belong to B. It is denoted by f − 1 ( B ) {\displaystyle f^{-1}(B)} and is given by the equation f − 1 ( B ) = { x ∈ X ∣ f ( x ) ∈ B } . {\displaystyle f^{-1}(B)=\{x\in X\mid f(x)\in B\}.} For example, the preimage of { 4 , 9 } {\displaystyle \{4,9\}} under the square function is the set { − 3 , − 2 , 2 , 3 } {\displaystyle \{-3,-2,2,3\}} . By definition of a function, the image of an element x of the domain is always a single element of the codomain. However, the preimage f − 1 ( y ) {\displaystyle f^{-1}(y)} of an element y of the codomain may be empty or contain any number of elements. For example, if f is the function from the integers to themselves that maps every integer to 0, then f − 1 ( 0 ) = Z {\displaystyle f^{-1}(0)=\mathbb {Z} } . If f : X → Y {\displaystyle f:X\to Y} is a function, A and B are subsets of X, and C and D are subsets of Y, then one has the following properties: A ⊆ B ⟹ f ( A ) ⊆ f ( B ) {\displaystyle A\subseteq B\Longrightarrow f(A)\subseteq f(B)} C ⊆ D ⟹ f − 1 ( C ) ⊆ f − 1 ( D ) {\displaystyle C\subseteq D\Longrightarrow f^{-1}(C)\subseteq f^{-1}(D)} A ⊆ f − 1 ( f ( A ) ) {\displaystyle A\subseteq f^{-1}(f(A))} C ⊇ f ( f − 1 ( C ) ) {\displaystyle C\supseteq f(f^{-1}(C))} f ( f − 1 ( f ( A ) ) ) = f ( A ) {\displaystyle f(f^{-1}(f(A)))=f(A)} f − 1 ( f ( f − 1 ( C ) ) ) = f − 1 ( C ) {\displaystyle f^{-1}(f(f^{-1}(C)))=f^{-1}(C)} The preimage by f of an element y of the codomain is sometimes called, in some contexts, the fiber of y under f. If a function f has an inverse (see below), this inverse is denoted f − 1 . {\displaystyle f^{-1}.} In this case f − 1 ( C ) {\displaystyle f^{-1}(C)} may denote either the image by f − 1 {\displaystyle f^{-1}} or the preimage by f of C. This is not a problem, as these sets are equal. The notation f ( A ) {\displaystyle f(A)} and f − 1 ( C ) {\displaystyle f^{-1}(C)} may be ambiguous in the case of sets that contain some subsets as elements, such as { x , { x } } . {\displaystyle \{x,\{x\}\}.} In this case, some care may be needed, for example, by using square brackets f [ A ] , f − 1 [ C ] {\displaystyle f[A],f^{-1}[C]} for images and preimages of subsets and ordinary parentheses for images and preimages of elements. === Injective, surjective and bijective functions === Let f : X → Y {\displaystyle f:X\to Y} be a function. The function f is injective (or one-to-one, or is an injection) if f(a) ≠ f(b) for every two different elements a and b of X. Equivalently, f is injective if and only if, for every y ∈ Y , {\displaystyle y\in Y,} the preimage f − 1 ( y ) {\displaystyle f^{-1}(y)} contains at most one element. An empty function is always injective. If X is not the empty set, then f is injective if and only if there exists a function g : Y → X {\displaystyle g:Y\to X} such that g ∘ f = id X , {\displaystyle g\circ f=\operatorname {id} _{X},} that is, if f has a left inverse. Proof: If f is injective, for defining g, one chooses an element x 0 {\displaystyle x_{0}} in X (which exists as X is supposed to be nonempty), and one defines g by g ( y ) = x {\displaystyle g(y)=x} if y = f ( x ) {\displaystyle y=f(x)} and g ( y ) = x 0 {\displaystyle g(y)=x_{0}} if y ∉ f ( X ) . {\displaystyle y\not \in f(X).} Conversely, if g ∘ f = id X , {\displaystyle g\circ f=\operatorname {id} _{X},} and y = f ( x ) , {\displaystyle y=f(x),} then x = g ( y ) , {\displaystyle x=g(y),} and thus f − 1 ( y ) = { x } . {\displaystyle f^{-1}(y)=\{x\}.} The function f is surjective (or onto, or is a surjection) if its range f ( X ) {\displaystyle f(X)} equals its codomain Y {\displaystyle Y} , that is, if, for each element y {\displaystyle y} of the codomain, there exists some element x {\displaystyle x} of the domain such that f ( x ) = y {\displaystyle f(x)=y} (in other words, the preimage f − 1 ( y ) {\displaystyle f^{-1}(y)} of every y ∈ Y {\displaystyle y\in Y} is nonempty). If, as usual in modern mathematics, the axiom of choice is assumed, then f is surjective if and only if there exists a function g : Y → X {\displaystyle g:Y\to X} such that f ∘ g = id Y , {\displaystyle f\circ g=\operatorname {id} _{Y},} that is, if f has a right inverse. The axiom of choice is needed, because, if f is surjective, one defines g by g ( y ) = x , {\displaystyle g(y)=x,} where x {\displaystyle x} is an arbitrarily chosen element of f − 1 ( y ) . {\displaystyle f^{-1}(y).} The function f is bijective (or is a bijection or a one-to-one correspondence) if it is both injective and surjective. That is, f is bijective if, for every y ∈ Y , {\displaystyle y\in Y,} the preimage f − 1 ( y ) {\displaystyle f^{-1}(y)} contains exactly one element. The function f is bijective if and only if it admits an inverse function, that is, a function g : Y → X {\displaystyle g:Y\to X} such that g ∘ f = id X {\displaystyle g\circ f=\operatorname {id} _{X}} and f ∘ g = id Y . {\displaystyle f\circ g=\operatorname {id} _{Y}.} (Contrarily to the case of surjections, this does not require the axiom of choice; the proof is straightforward). Every function f : X → Y {\displaystyle f:X\to Y} may be factorized as the composition i ∘ s {\displaystyle i\circ s} of a surjection followed by an injection, where s is the canonical surjection of X onto f(X) and i is the canonical injection of f(X) into Y. This is the canonical factorization of f. "One-to-one" and "onto" are terms that were more common in the older English language literature; "injective", "surjective", and "bijective" were originally coined as French words in the second quarter of the 20th century by the Bourbaki group and imported into English. As a word of caution, "a one-to-one function" is one that is injective, while a "one-to-one correspondence" refers to a bijective function. Also, the statement "f maps X onto Y" differs from "f maps X into B", in that the former implies that f is surjective, while the latter makes no assertion about the nature of f. In a complicated reasoning, the one letter difference can easily be missed. Due to the confusing nature of this older terminology, these terms have declined in popularity relative to the Bourbakian terms, which have also the advantage of being more symmetrical. === Restriction and extension === If f : X → Y {\displaystyle f:X\to Y} is a function and S is a subset of X, then the restriction of f {\displaystyle f} to S, denoted f | S {\displaystyle f|_{S}} , is the function from S to Y defined by f | S ( x ) = f ( x ) {\displaystyle f|_{S}(x)=f(x)} for all x in S. Restrictions can be used to define partial inverse functions: if there is a subset S of the domain of a function f {\displaystyle f} such that f | S {\displaystyle f|_{S}} is injective, then the canonical surjection of f | S {\displaystyle f|_{S}} onto its image f | S ( S ) = f ( S ) {\displaystyle f|_{S}(S)=f(S)} is a bijection, and thus has an inverse function from f ( S ) {\displaystyle f(S)} to S. One application is the definition of inverse trigonometric functions. For example, the cosine function is injective when restricted to the interval [0, π]. The image of this restriction is the interval [−1, 1], and thus the restriction has an inverse function from [−1, 1] to [0, π], which is called arccosine and is denoted arccos. Function restriction may also be used for "gluing" functions together. Let X = ⋃ i ∈ I U i {\textstyle X=\bigcup _{i\in I}U_{i}} be the decomposition of X as a union of subsets, and suppose that a function f i : U i → Y {\displaystyle f_{i}:U_{i}\to Y} is defined on each U i {\displaystyle U_{i}} such that for each pair i , j {\displaystyle i,j} of indices, the restrictions of f i {\displaystyle f_{i}} and f j {\displaystyle f_{j}} to U i ∩ U j {\displaystyle U_{i}\cap U_{j}} are equal. Then this defines a unique function f : X → Y {\displaystyle f:X\to Y} such that f | U i = f i {\displaystyle f|_{U_{i}}=f_{i}} for all i. This is the way that functions on manifolds are defined. An extension of a function f is a function g such that f is a restriction of g. A typical use of this concept is the process of analytic continuation, that allows extending functions whose domain is a small part of the complex plane to functions whose domain is almost the whole complex plane. Here is another classical example of a function extension that is encountered when studying homographies of the real line. A homography is a function h ( x ) = a x + b c x + d {\displaystyle h(x)={\frac {ax+b}{cx+d}}} such that ad − bc ≠ 0. Its domain is the set of all real numbers different from − d / c , {\displaystyle -d/c,} and its image is the set of all real numbers different from a / c . {\displaystyle a/c.} If one extends the real line to the projectively extended real line by including ∞, one may extend h to a bijection from the extended real line to itself by setting h ( ∞ ) = a / c {\displaystyle h(\infty )=a/c} and h ( − d / c ) = ∞ {\displaystyle h(-d/c)=\infty } . == In calculus == The idea of function, starting in the 17th century, was fundamental to the new infinitesimal calculus. At that time, only real-valued functions of a real variable were considered, and all functions were assumed to be smooth. But the definition was soon extended to functions of several variables and to functions of a complex variable. In the second half of the 19th century, the mathematically rigorous definition of a function was introduced, and functions with arbitrary domains and codomains were defined. Functions are now used throughout all areas of mathematics. In introductory calculus, when the word function is used without qualification, it means a real-valued function of a single real variable. The more general definition of a function is usually introduced to second or third year college students with STEM majors, and in their senior year they are introduced to calculus in a larger, more rigorous setting in courses such as real analysis and complex analysis. === Real function === A real function is a real-valued function of a real variable, that is, a function whose codomain is the field of real numbers and whose domain is a set of real numbers that contains an interval. In this section, these functions are simply called functions. The functions that are most commonly considered in mathematics and its applications have some regularity, that is they are continuous, differentiable, and even analytic. This regularity insures that these functions can be visualized by their graphs. In this section, all functions are differentiable in some interval. Functions enjoy pointwise operations, that is, if f and g are functions, their sum, difference and product are functions defined by ( f + g ) ( x ) = f ( x ) + g ( x ) ( f − g ) ( x ) = f ( x ) − g ( x ) ( f ⋅ g ) ( x ) = f ( x ) ⋅ g ( x ) . {\displaystyle {\begin{aligned}(f+g)(x)&=f(x)+g(x)\\(f-g)(x)&=f(x)-g(x)\\(f\cdot g)(x)&=f(x)\cdot g(x)\\\end{aligned}}.} The domains of the resulting functions are the intersection of the domains of f and g. The quotient of two functions is defined similarly by f g ( x ) = f ( x ) g ( x ) , {\displaystyle {\frac {f}{g}}(x)={\frac {f(x)}{g(x)}},} but the domain of the resulting function is obtained by removing the zeros of g from the intersection of the domains of f and g. The polynomial functions are defined by polynomials, and their domain is the whole set of real numbers. They include constant functions, linear functions and quadratic functions. Rational functions are quotients of two polynomial functions, and their domain is the real numbers with a finite number of them removed to avoid division by zero. The simplest rational function is the function x ↦ 1 x , {\displaystyle x\mapsto {\frac {1}{x}},} whose graph is a hyperbola, and whose domain is the whole real line except for 0. The derivative of a real differentiable function is a real function. An antiderivative of a continuous real function is a real function that has the original function as a derivative. For example, the function x ↦ 1 x {\textstyle x\mapsto {\frac {1}{x}}} is continuous, and even differentiable, on the positive real numbers. Thus one antiderivative, which takes the value zero for x = 1, is a differentiable function called the natural logarithm. A real function f is monotonic in an interval if the sign of f ( x ) − f ( y ) x − y {\displaystyle {\frac {f(x)-f(y)}{x-y}}} does not depend of the choice of x and y in the interval. If the function is differentiable in the interval, it is monotonic if the sign of the derivative is constant in the interval. If a real function f is monotonic in an interval I, it has an inverse function, which is a real function with domain f(I) and image I. This is how inverse trigonometric functions are defined in terms of trigonometric functions, where the trigonometric functions are monotonic. Another example: the natural logarithm is monotonic on the positive real numbers, and its image is the whole real line; therefore it has an inverse function that is a bijection between the real numbers and the positive real numbers. This inverse is the exponential function. Many other real functions are defined either by the implicit function theorem (the inverse function is a particular instance) or as solutions of differential equations. For example, the sine and the cosine functions are the solutions of the linear differential equation y ″ + y = 0 {\displaystyle y''+y=0} such that sin 0 = 0 , cos 0 = 1 , ∂ sin x ∂ x ( 0 ) = 1 , ∂ cos x ∂ x ( 0 ) = 0. {\displaystyle \sin 0=0,\quad \cos 0=1,\quad {\frac {\partial \sin x}{\partial x}}(0)=1,\quad {\frac {\partial \cos x}{\partial x}}(0)=0.} === Vector-valued function === When the elements of the codomain of a function are vectors, the function is said to be a vector-valued function. These functions are particularly useful in applications, for example modeling physical properties. For example, the function that associates to each point of a fluid its velocity vector is a vector-valued function. Some vector-valued functions are defined on a subset of R n {\displaystyle \mathbb {R} ^{n}} or other spaces that share geometric or topological properties of R n {\displaystyle \mathbb {R} ^{n}} , such as manifolds. These vector-valued functions are given the name vector fields. == Function space == In mathematical analysis, and more specifically in functional analysis, a function space is a set of scalar-valued or vector-valued functions, which share a specific property and form a topological vector space. For example, the real smooth functions with a compact support (that is, they are zero outside some compact set) form a function space that is at the basis of the theory of distributions. Function spaces play a fundamental role in advanced mathematical analysis, by allowing the use of their algebraic and topological properties for studying properties of functions. For example, all theorems of existence and uniqueness of solutions of ordinary or partial differential equations result of the study of function spaces. == Multi-valued functions == Several methods for specifying functions of real or complex variables start from a local definition of the function at a point or on a neighbourhood of a point, and then extend by continuity the function to a much larger domain. Frequently, for a starting point x 0 , {\displaystyle x_{0},} there are several possible starting values for the function. For example, in defining the square root as the inverse function of the square function, for any positive real number x 0 , {\displaystyle x_{0},} there are two choices for the value of the square root, one of which is positive and denoted x 0 , {\displaystyle {\sqrt {x_{0}}},} and another which is negative and denoted − x 0 . {\displaystyle -{\sqrt {x_{0}}}.} These choices define two continuous functions, both having the nonnegative real numbers as a domain, and having either the nonnegative or the nonpositive real numbers as images. When looking at the graphs of these functions, one can see that, together, they form a single smooth curve. It is therefore often useful to consider these two square root functions as a single function that has two values for positive x, one value for 0 and no value for negative x. In the preceding example, one choice, the positive square root, is more natural than the other. This is not the case in general. For example, let consider the implicit function that maps y to a root x of x 3 − 3 x − y = 0 {\displaystyle x^{3}-3x-y=0} (see the figure on the right). For y = 0 one may choose either 0 , 3 , or − 3 {\displaystyle 0,{\sqrt {3}},{\text{ or }}-{\sqrt {3}}} for x. By the implicit function theorem, each choice defines a function; for the first one, the (maximal) domain is the interval [−2, 2] and the image is [−1, 1]; for the second one, the domain is [−2, ∞) and the image is [1, ∞); for the last one, the domain is (−∞, 2] and the image is (−∞, −1]. As the three graphs together form a smooth curve, and there is no reason for preferring one choice, these three functions are often considered as a single multi-valued function of y that has three values for −2 < y < 2, and only one value for y ≤ −2 and y ≥ −2. Usefulness of the concept of multi-valued functions is clearer when considering complex functions, typically analytic functions. The domain to which a complex function may be extended by analytic continuation generally consists of almost the whole complex plane. However, when extending the domain through two different paths, one often gets different values. For example, when extending the domain of the square root function, along a path of complex numbers with positive imaginary parts, one gets i for the square root of −1; while, when extending through complex numbers with negative imaginary parts, one gets −i. There are generally two ways of solving the problem. One may define a function that is not continuous along some curve, called a branch cut. Such a function is called the principal value of the function. The other way is to consider that one has a multi-valued function, which is analytic everywhere except for isolated singularities, but whose value may "jump" if one follows a closed loop around a singularity. This jump is called the monodromy. == In the foundations of mathematics == The definition of a function that is given in this article requires the concept of set, since the domain and the codomain of a function must be a set. This is not a problem in usual mathematics, as it is generally not difficult to consider only functions whose domain and codomain are sets, which are well defined, even if the domain is not explicitly defined. However, it is sometimes useful to consider more general functions. For example, the singleton set may be considered as a function x ↦ { x } . {\displaystyle x\mapsto \{x\}.} Its domain would include all sets, and therefore would not be a set. In usual mathematics, one avoids this kind of problem by specifying a domain, which means that one has many singleton functions. However, when establishing foundations of mathematics, one may have to use functions whose domain, codomain or both are not specified, and some authors, often logicians, give precise definitions for these weakly specified functions. These generalized functions may be critical in the development of a formalization of the foundations of mathematics. For example, Von Neumann–Bernays–Gödel set theory, is an extension of the set theory in which the collection of all sets is a class. This theory includes the replacement axiom, which may be stated as: If X is a set and F is a function, then F[X] is a set. In alternative formulations of the foundations of mathematics using type theory rather than set theory, functions are taken as primitive notions rather than defined from other kinds of object. They are the inhabitants of function types, and may be constructed using expressions in the lambda calculus. == In computer science == In computer programming, a function is, in general, a subroutine which implements the abstract concept of function. That is, it is a program unit that produces an output for each input. Functional programming is the programming paradigm consisting of building programs by using only subroutines that behave like mathematical functions, meaning that they have no side effects and depend only on their arguments: they are referentially transparent. For example, if_then_else is a function that takes three (nullary) functions as arguments, and, depending on the value of the first argument (true or false), returns the value of either the second or the third argument. An important advantage of functional programming is that it makes easier program proofs, as being based on a well founded theory, the lambda calculus (see below). However, side effects are generally necessary for practical programs, ones that perform input/output. There is a class of purely functional languages, such as Haskell, which encapsulate the possibility of side effects in the type of a function. Others, such as the ML family, simply allow side effects. In many programming languages, every subroutine is called a function, even when there is no output but only side effects, and when the functionality consists simply of modifying some data in the computer memory. Outside the context of programming languages, "function" has the usual mathematical meaning in computer science. In this area, a property of major interest is the computability of a function. For giving a precise meaning to this concept, and to the related concept of algorithm, several models of computation have been introduced, the old ones being general recursive functions, lambda calculus, and Turing machine. The fundamental theorem of computability theory is that these three models of computation define the same set of computable functions, and that all the other models of computation that have ever been proposed define the same set of computable functions or a smaller one. The Church–Turing thesis is the claim that every philosophically acceptable definition of a computable function defines also the same functions. General recursive functions are partial functions from integers to integers that can be defined from constant functions, successor, and projection functions via the operators composition, primitive recursion, and minimization. Although defined only for functions from integers to integers, they can model any computable function as a consequence of the following properties: a computation is the manipulation of finite sequences of symbols (digits of numbers, formulas, etc.), every sequence of symbols may be coded as a sequence of bits, a bit sequence can be interpreted as the binary representation of an integer. Lambda calculus is a theory that defines computable functions without using set theory, and is the theoretical background of functional programming. It consists of terms that are either variables, function definitions (𝜆-terms), or applications of functions to terms. Terms are manipulated by interpreting its axioms (the α-equivalence, the β-reduction, and the η-conversion) as rewriting rules, which can be used for computation. In its original form, lambda calculus does not include the concepts of domain and codomain of a function. Roughly speaking, they have been introduced in the theory under the name of type in typed lambda calculus. Most kinds of typed lambda calculi can define fewer functions than untyped lambda calculus. == See also == === Subpages === === Generalizations === === Related topics === == Notes == == References == == Sources == == Further reading == == External links == The Wolfram Functions – website giving formulae and visualizations of many mathematical functions NIST Digital Library of Mathematical Functions
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Mathematical puzzles make up an integral part of recreational mathematics. They have specific rules, but they do not usually involve competition between two or more players. Instead, to solve such a puzzle, the solver must find a solution that satisfies the given conditions. Mathematical puzzles require mathematics to solve them. Logic puzzles are a common type of mathematical puzzle. Conway's Game of Life and fractals, as two examples, may also be considered mathematical puzzles even though the solver interacts with them only at the beginning by providing a set of initial conditions. After these conditions are set, the rules of the puzzle determine all subsequent changes and moves. Many of the puzzles are well known because they were discussed by Martin Gardner in his "Mathematical Games" column in Scientific American. Mathematical puzzles are sometimes used to motivate students in teaching elementary school math problem solving techniques. Creative thinking – or "thinking outside the box" – often helps to find the solution. == List of mathematical puzzles == === Numbers, arithmetic, and algebra === Cross-figures or cross number puzzles Dyson numbers Four fours KenKen Water pouring puzzle The monkey and the coconuts Pirate loot problem Verbal arithmetics 24 Game === Combinatorial === Cryptograms Fifteen Puzzle Kakuro Rubik's Cube and other sequential movement puzzles Str8ts a number puzzle based on sequences Sudoku Sujiko Think-a-Dot Tower of Hanoi Bridges Game === Analytical or differential === Ant on a rubber rope See also: Zeno's paradoxes === Probability === Monty Hall problem === Tiling, packing, and dissection === Bedlam cube Conway puzzle Mutilated chessboard problem Packing problem Pentominoes tiling Slothouber–Graatsma puzzle Soma cube T puzzle Tangram === Involves a board === Conway's Game of Life Mutilated chessboard problem Peg solitaire Sudoku Nine dots problem ==== Chessboard tasks ==== Eight queens puzzle Knight's Tour No-three-in-line problem === Topology, knots, graph theory === The fields of knot theory and topology, especially their non-intuitive conclusions, are often seen as a part of recreational mathematics. Disentanglement puzzles Seven Bridges of Königsberg Water, gas, and electricity Slitherlink === Mechanical === Rubik's Cube Think-a-Dot Matchstick puzzle === 0-player puzzles === Conway's Game of Life Flexagon Polyominoes == References == == External links == Historical Math Problems/Puzzles at Mathematical Association of America Convergence
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https://en.wikipedia.org/wiki/Mathematical_puzzle
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In mathematics, a category (sometimes called an abstract category to distinguish it from a concrete category) is a collection of "objects" that are linked by "arrows". A category has two basic properties: the ability to compose the arrows associatively and the existence of an identity arrow for each object. A simple example is the category of sets, whose objects are sets and whose arrows are functions. Category theory is a branch of mathematics that seeks to generalize all of mathematics in terms of categories, independent of what their objects and arrows represent. Virtually every branch of modern mathematics can be described in terms of categories, and doing so often reveals deep insights and similarities between seemingly different areas of mathematics. As such, category theory provides an alternative foundation for mathematics to set theory and other proposed axiomatic foundations. In general, the objects and arrows may be abstract entities of any kind, and the notion of category provides a fundamental and abstract way to describe mathematical entities and their relationships. In addition to formalizing mathematics, category theory is also used to formalize many other systems in computer science, such as the semantics of programming languages. Two categories are the same if they have the same collection of objects, the same collection of arrows, and the same associative method of composing any pair of arrows. Two different categories may also be considered "equivalent" for purposes of category theory, even if they do not have precisely the same structure. Well-known categories are denoted by a short capitalized word or abbreviation in bold or italics: examples include Set, the category of sets and set functions; Ring, the category of rings and ring homomorphisms; and Top, the category of topological spaces and continuous maps. All of the preceding categories have the identity map as identity arrows and composition as the associative operation on arrows. The classic and still much used text on category theory is Categories for the Working Mathematician by Saunders Mac Lane. Other references are given in the References below. The basic definitions in this article are contained within the first few chapters of any of these books. Any monoid can be understood as a special sort of category (with a single object whose self-morphisms are represented by the elements of the monoid), and so can any preorder. == Definition == There are many equivalent definitions of a category. One commonly used definition is as follows. A category C consists of a class ob(C) of objects, a class mor(C) of morphisms or arrows, a domain or source class function dom: mor(C) → ob(C), a codomain or target class function cod: mor(C) → ob(C), for every three objects a, b and c, a binary operation hom(a, b) × hom(b, c) → hom(a, c) called composition of morphisms. Here hom(a, b) denotes the subclass of morphisms f in mor(C) such that dom(f) = a and cod(f) = b. Morphisms in this subclass are written f : a → b, and the composite of f : a → b and g : b → c is often written as g ∘ f or gf. such that the following axioms hold: the associative law: if f : a → b, g : b → c and h : c → d then h ∘ (g ∘ f) = (h ∘ g) ∘ f, and the (left and right unit laws): for every object x, there exists a morphism 1x : x → x (some authors write idx) called the identity morphism for x, such that every morphism f : a → x satisfies 1x ∘ f = f, and every morphism g : x → b satisfies g ∘ 1x = g. We write f: a → b, and we say "f is a morphism from a to b". We write hom(a, b) (or homC(a, b) when there may be confusion about to which category hom(a, b) refers) to denote the hom-class of all morphisms from a to b. Some authors write the composite of morphisms in "diagrammatic order", writing f;g or fg instead of g ∘ f. From these axioms, one can prove that there is exactly one identity morphism for every object. Often the map assigning each object its identity morphism is treated as an extra part of the structure of a category, namely a class function i: ob(C) → mor(C). Some authors use a slight variant of the definition in which each object is identified with the corresponding identity morphism. This stems from the idea that the fundamental data of categories are morphisms and not objects. In fact, categories can be defined without reference to objects at all using a partial binary operation with additional properties. == Small and large categories == A category C is called small if both ob(C) and mor(C) are actually sets and not proper classes, and large otherwise. A locally small category is a category such that for all objects a and b, the hom-class hom(a, b) is a set, called a homset. Many important categories in mathematics (such as the category of sets), although not small, are at least locally small. Since, in small categories, the objects form a set, a small category can be viewed as an algebraic structure similar to a monoid but without requiring closure properties. Large categories on the other hand can be used to create "structures" of algebraic structures. == Examples == The class of all sets (as objects) together with all functions between them (as morphisms), where the composition of morphisms is the usual function composition, forms a large category, Set. It is the most basic and the most commonly used category in mathematics. The category Rel consists of all sets (as objects) with binary relations between them (as morphisms). Abstracting from relations instead of functions yields allegories, a special class of categories. Any class can be viewed as a category whose only morphisms are the identity morphisms. Such categories are called discrete. For any given set I, the discrete category on I is the small category that has the elements of I as objects and only the identity morphisms as morphisms. Discrete categories are the simplest kind of category. Any preordered set (P, ≤) forms a small category, where the objects are the members of P, the morphisms are arrows pointing from x to y when x ≤ y. Furthermore, if ≤ is antisymmetric, there can be at most one morphism between any two objects. The existence of identity morphisms and the composability of the morphisms are guaranteed by the reflexivity and the transitivity of the preorder. By the same argument, any partially ordered set and any equivalence relation can be seen as a small category. Any ordinal number can be seen as a category when viewed as an ordered set. Any monoid (any algebraic structure with a single associative binary operation and an identity element) forms a small category with a single object x. (Here, x is any fixed set.) The morphisms from x to x are precisely the elements of the monoid, the identity morphism of x is the identity of the monoid, and the categorical composition of morphisms is given by the monoid operation. Several definitions and theorems about monoids may be generalized for categories. Similarly any group can be seen as a category with a single object in which every morphism is invertible, that is, for every morphism f there is a morphism g that is both left and right inverse to f under composition. A morphism that is invertible in this sense is called an isomorphism. A groupoid is a category in which every morphism is an isomorphism. Groupoids are generalizations of groups, group actions and equivalence relations. Actually, in the view of category the only difference between groupoid and group is that a groupoid may have more than one object but the group must have only one. Consider a topological space X and fix a base point x 0 {\displaystyle x_{0}} of X, then π 1 ( X , x 0 ) {\displaystyle \pi _{1}(X,x_{0})} is the fundamental group of the topological space X and the base point x 0 {\displaystyle x_{0}} , and as a set it has the structure of group; if then let the base point x 0 {\displaystyle x_{0}} runs over all points of X, and take the union of all π 1 ( X , x 0 ) {\displaystyle \pi _{1}(X,x_{0})} , then the set we get has only the structure of groupoid (which is called as the fundamental groupoid of X): two loops (under equivalence relation of homotopy) may not have the same base point so they cannot multiply with each other. In the language of category, this means here two morphisms may not have the same source object (or target object, because in this case for any morphism the source object and the target object are same: the base point) so they can not compose with each other. Any directed graph generates a small category: the objects are the vertices of the graph, and the morphisms are the paths in the graph (augmented with loops as needed) where composition of morphisms is concatenation of paths. Such a category is called the free category generated by the graph. The class of all preordered sets with order-preserving functions (i.e., monotone-increasing functions) as morphisms forms a category, Ord. It is a concrete category, i.e. a category obtained by adding some type of structure onto Set, and requiring that morphisms are functions that respect this added structure. The class of all groups with group homomorphisms as morphisms and function composition as the composition operation forms a large category, Grp. Like Ord, Grp is a concrete category. The category Ab, consisting of all abelian groups and their group homomorphisms, is a full subcategory of Grp, and the prototype of an abelian category. The class of all graphs forms another concrete category, where morphisms are graph homomorphisms (i.e., mappings between graphs which send vertices to vertices and edges to edges in a way that preserves all adjacency and incidence relations). Other examples of concrete categories are given by the following table. Fiber bundles with bundle maps between them form a concrete category. The category Cat consists of all small categories, with functors between them as morphisms. == Construction of new categories == === Dual category === Any category C can itself be considered as a new category in a different way: the objects are the same as those in the original category but the arrows are those of the original category reversed. This is called the dual or opposite category and is denoted Cop. === Product categories === If C and D are categories, one can form the product category C × D: the objects are pairs consisting of one object from C and one from D, and the morphisms are also pairs, consisting of one morphism in C and one in D. Such pairs can be composed componentwise. == Types of morphisms == A morphism f : a → b is called a monomorphism (or monic) if it is left-cancellable, i.e. fg1 = fg2 implies g1 = g2 for all morphisms g1, g2 : x → a. an epimorphism (or epic) if it is right-cancellable, i.e. g1f = g2f implies g1 = g2 for all morphisms g1, g2 : b → x. a bimorphism if it is both a monomorphism and an epimorphism. a retraction if it has a right inverse, i.e. if there exists a morphism g : b → a with fg = 1b. a section if it has a left inverse, i.e. if there exists a morphism g : b → a with gf = 1a. an isomorphism if it has an inverse, i.e. if there exists a morphism g : b → a with fg = 1b and gf = 1a. an endomorphism if a = b. The class of endomorphisms of a is denoted end(a). For locally small categories, end(a) is a set and forms a monoid under morphism composition. an automorphism if f is both an endomorphism and an isomorphism. The class of automorphisms of a is denoted aut(a). For locally small categories, it forms a group under morphism composition called the automorphism group of a. Every retraction is an epimorphism. Every section is a monomorphism. The following three statements are equivalent: f is a monomorphism and a retraction; f is an epimorphism and a section; f is an isomorphism. Relations among morphisms (such as fg = h) can most conveniently be represented with commutative diagrams, where the objects are represented as points and the morphisms as arrows. == Types of categories == In many categories, e.g. Ab or VectK, the hom-sets hom(a, b) are not just sets but actually abelian groups, and the composition of morphisms is compatible with these group structures; i.e. is bilinear. Such a category is called preadditive. If, furthermore, the category has all finite products and coproducts, it is called an additive category. If all morphisms have a kernel and a cokernel, and all epimorphisms are cokernels and all monomorphisms are kernels, then we speak of an abelian category. A typical example of an abelian category is the category of abelian groups. A category is called complete if all small limits exist in it. The categories of sets, abelian groups and topological spaces are complete. A category is called cartesian closed if it has finite direct products and a morphism defined on a finite product can always be represented by a morphism defined on just one of the factors. Examples include Set and CPO, the category of complete partial orders with Scott-continuous functions. A topos is a certain type of cartesian closed category in which all of mathematics can be formulated (just like classically all of mathematics is formulated in the category of sets). A topos can also be used to represent a logical theory. == See also == Enriched category Higher category theory Quantaloid Table of mathematical symbols Space (mathematics) Structure (mathematics) == Notes == == References ==
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In mathematics, when a mathematical phenomenon runs counter to some intuition, then the phenomenon is sometimes called pathological. On the other hand, if a phenomenon does not run counter to intuition, it is sometimes called well-behaved or nice. These terms are sometimes useful in mathematical research and teaching, but there is no strict mathematical definition of pathological or well-behaved. == In analysis == A classic example of a pathology is the Weierstrass function, a function that is continuous everywhere but differentiable nowhere. The sum of a differentiable function and the Weierstrass function is again continuous but nowhere differentiable; so there are at least as many such functions as differentiable functions. In fact, using the Baire category theorem, one can show that continuous functions are generically nowhere differentiable. Such examples were deemed pathological when they were first discovered. To quote Henri Poincaré: Logic sometimes breeds monsters. For half a century there has been springing up a host of weird functions, which seem to strive to have as little resemblance as possible to honest functions that are of some use. No more continuity, or else continuity but no derivatives, etc. More than this, from the point of view of logic, it is these strange functions that are the most general; those that are met without being looked for no longer appear as more than a particular case, and they have only quite a little corner left them. Formerly, when a new function was invented, it was in view of some practical end. To-day they are invented on purpose to show our ancestors' reasonings at fault, and we shall never get anything more than that out of them. If logic were the teacher's only guide, he would have to begin with the most general, that is to say, with the most weird, functions. He would have to set the beginner to wrestle with this collection of monstrosities. If you don't do so, the logicians might say, you will only reach exactness by stages. Since Poincaré, nowhere differentiable functions have been shown to appear in basic physical and biological processes such as Brownian motion and in applications such as the Black-Scholes model in finance. Counterexamples in Analysis is a whole book of such counterexamples. Another example of pathological function is Du-Bois Reymond continuous function, that can't be represented as a Fourier series. == In topology == One famous counterexample in topology is the Alexander horned sphere, showing that topologically embedding the sphere S2 in R3 may fail to separate the space cleanly. As a counterexample, it motivated mathematicians to define the tameness property, which suppresses the kind of wild behavior exhibited by the horned sphere, wild knot, and other similar examples. Like many other pathologies, the horned sphere in a sense plays on infinitely fine, recursively generated structure, which in the limit violates ordinary intuition. In this case, the topology of an ever-descending chain of interlocking loops of continuous pieces of the sphere in the limit fully reflects that of the common sphere, and one would expect the outside of it, after an embedding, to work the same. Yet it does not: it fails to be simply connected. For the underlying theory, see Jordan–Schönflies theorem. Counterexamples in Topology is a whole book of such counterexamples. == Well-behaved == Mathematicians (and those in related sciences) very frequently speak of whether a mathematical object—a function, a set, a space of one sort or another—is "well-behaved". While the term has no fixed formal definition, it generally refers to the quality of satisfying a list of prevailing conditions, which might be dependent on context, mathematical interests, fashion, and taste. To ensure that an object is "well-behaved", mathematicians introduce further axioms to narrow down the domain of study. This has the benefit of making analysis easier, but produces a loss of generality of any conclusions reached. In both pure and applied mathematics (e.g., optimization, numerical integration, mathematical physics), well-behaved also means not violating any assumptions needed to successfully apply whatever analysis is being discussed. The opposite case is usually labeled "pathological". It is not unusual to have situations in which most cases (in terms of cardinality or measure) are pathological, but the pathological cases will not arise in practice—unless constructed deliberately. The term "well-behaved" is generally applied in an absolute sense—either something is well-behaved or it is not. For example: In algorithmic inference, a well-behaved statistic is monotonic, well-defined, and sufficient. In Bézout's theorem, two polynomials are well-behaved, and thus the formula given by the theorem for the number of their intersections is valid, if their polynomial greatest common divisor is a constant. A meromorphic function is a ratio of two well-behaved functions, in the sense of those two functions being holomorphic. The Karush–Kuhn–Tucker conditions are first-order necessary conditions for a solution in a well-behaved nonlinear programming problem to be optimal; a problem is referred to as well-behaved if some regularity conditions are satisfied. In probability, events contained in the probability space's corresponding sigma-algebra are well-behaved, as are measurable functions. Unusually, the term could also be applied in a comparative sense: In calculus: Analytic functions are better-behaved than general smooth functions. Smooth functions are better-behaved than general differentiable functions. Continuous differentiable functions are better-behaved than general continuous functions. The larger the number of times the function can be differentiated, the more well-behaved it is. Continuous functions are better-behaved than Riemann-integrable functions on compact sets. Riemann-integrable functions are better-behaved than Lebesgue-integrable functions. Lebesgue-integrable functions are better-behaved than general functions. In topology: Continuous functions are better-behaved than discontinuous ones. Euclidean space is better-behaved than non-Euclidean geometry. Attractive fixed points are better-behaved than repulsive fixed points. Hausdorff topologies are better-behaved than those in arbitrary general topology. Borel sets are better-behaved than arbitrary sets of real numbers. Spaces with integer dimension are better-behaved than spaces with fractal dimension. In abstract algebra: Groups are better-behaved than magmas and semigroups. Abelian groups are better-behaved than non-Abelian groups. Finitely-generated Abelian groups are better-behaved than non-finitely-generated Abelian groups. Finite-dimensional vector spaces are better-behaved than infinite-dimensional ones. Fields are better-behaved than skew fields or general rings. Separable field extensions are better-behaved than non-separable ones. Normed division algebras are better-behaved than general composition algebras. == Pathological examples == Pathological examples often have some undesirable or unusual properties that make it difficult to contain or explain within a theory. Such pathological behaviors often prompt new investigation and research, which leads to new theory and more general results. Some important historical examples of this are: Ranked-choice voting is commonly described as a pathological social choice function, because of its tendency to eliminate candidates for winning too many votes. The discovery of irrational numbers by the school of Pythagoras in ancient Greece; for example, the length of the diagonal of a unit square, that is 2 {\displaystyle {\sqrt {2}}} . The discovery of complex numbers in the 16th century in order to find the roots of cubic and quartic polynomial functions. Some number fields have rings of integers that do not form a unique factorization domain, for example the extended field Q ( − 5 ) {\displaystyle \mathbb {Q} ({\sqrt {-5}})} . The discovery of fractals and other "rough" geometric objects (see Hausdorff dimension). Weierstrass function, a real-valued function on the real line, that is continuous everywhere but differentiable nowhere. Test functions in real analysis and distribution theory, which are infinitely differentiable functions on the real line that are 0 everywhere outside of a given limited interval. An example of such a function is the test function, φ ( t ) = { e − 1 / ( 1 − t 2 ) , − 1 < t < 1 , 0 , otherwise . {\displaystyle \varphi (t)={\begin{cases}e^{-1/(1-t^{2})},&-1<t<1,\\0,&{\text{otherwise}}.\end{cases}}} The Cantor set is a subset of the interval [ 0 , 1 ] {\displaystyle [0,1]} that has measure zero but is uncountable. The fat Cantor set is nowhere dense but has positive measure. The Fabius function is everywhere smooth but nowhere analytic. Volterra's function is differentiable with bounded derivative everywhere, but the derivative is not Riemann-integrable. The Peano space-filling curve is a continuous surjective function that maps the unit interval [ 0 , 1 ] {\displaystyle [0,1]} onto [ 0 , 1 ] × [ 0 , 1 ] {\displaystyle [0,1]\times [0,1]} . The Dirichlet function, which is the indicator function for rationals, is a bounded function that is not Riemann integrable. The Cantor function is a monotonic continuous surjective function that maps [ 0 , 1 ] {\displaystyle [0,1]} onto [ 0 , 1 ] {\displaystyle [0,1]} , but has zero derivative almost everywhere. The Minkowski question-mark function is continuous and strictly increasing but has zero derivative almost everywhere. Satisfaction classes containing "intuitively false" arithmetical statements can be constructed for countable, recursively saturated models of Peano arithmetic. The Osgood curve is a Jordan curve (unlike most space-filling curves) of positive area. An exotic sphere is homeomorphic but not diffeomorphic to the standard Euclidean n-sphere. At the time of their discovery, each of these was considered highly pathological; today, each has been assimilated into modern mathematical theory. These examples prompt their observers to correct their beliefs or intuitions, and in some cases necessitate a reassessment of foundational definitions and concepts. Over the course of history, they have led to more correct, more precise, and more powerful mathematics. For example, the Dirichlet function is Lebesgue integrable, and convolution with test functions is used to approximate any locally integrable function by smooth functions. Whether a behavior is pathological is by definition subject to personal intuition. Pathologies depend on context, training, and experience, and what is pathological to one researcher may very well be standard behavior to another. Pathological examples can show the importance of the assumptions in a theorem. For example, in statistics, the Cauchy distribution does not satisfy the central limit theorem, even though its symmetric bell-shape appears similar to many distributions which do; it fails the requirement to have a mean and standard deviation which exist and that are finite. Some of the best-known paradoxes, such as Banach–Tarski paradox and Hausdorff paradox, are based on the existence of non-measurable sets. Mathematicians, unless they take the minority position of denying the axiom of choice, are in general resigned to living with such sets. == Computer science == In computer science, pathological has a slightly different sense with regard to the study of algorithms. Here, an input (or set of inputs) is said to be pathological if it causes atypical behavior from the algorithm, such as a violation of its average case complexity, or even its correctness. For example, hash tables generally have pathological inputs: sets of keys that collide on hash values. Quicksort normally has O ( n log n ) {\displaystyle O(n\log {n})} time complexity, but deteriorates to O ( n 2 ) {\displaystyle O(n^{2})} when it is given input that triggers suboptimal behavior. The term is often used pejoratively, as a way of dismissing such inputs as being specially designed to break a routine that is otherwise sound in practice (compare with Byzantine). On the other hand, awareness of pathological inputs is important, as they can be exploited to mount a denial-of-service attack on a computer system. Also, the term in this sense is a matter of subjective judgment as with its other senses. Given enough run time, a sufficiently large and diverse user community (or other factors), an input which may be dismissed as pathological could in fact occur (as seen in the first test flight of the Ariane 5). == Exceptions == A similar but distinct phenomenon is that of exceptional objects (and exceptional isomorphisms), which occurs when there are a "small" number of exceptions to a general pattern (such as a finite set of exceptions to an otherwise infinite rule). By contrast, in cases of pathology, often most or almost all instances of a phenomenon are pathological (e.g., almost all real numbers are irrational). Subjectively, exceptional objects (such as the icosahedron or sporadic simple groups) are generally considered "beautiful", unexpected examples of a theory, while pathological phenomena are often considered "ugly", as the name implies. Accordingly, theories are usually expanded to include exceptional objects. For example, the exceptional Lie algebras are included in the theory of semisimple Lie algebras: the axioms are seen as good, the exceptional objects as unexpected but valid. By contrast, pathological examples are instead taken to point out a shortcoming in the axioms, requiring stronger axioms to rule them out. For example, requiring tameness of an embedding of a sphere in the Schönflies problem. In general, one may study the more general theory, including the pathologies, which may provide its own simplifications (the real numbers have properties very different from the rationals, and likewise continuous maps have very different properties from smooth ones), but also the narrower theory, from which the original examples were drawn. == See also == Fractal curve List of mathematical jargon Runge's phenomenon Gibbs phenomenon Paradoxical set == References == == Notes == == External links == Pathological Structures & Fractals – Extract of an article by Freeman Dyson, "Characterising Irregularity", Science, May 1978 This article incorporates material from pathological on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.
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https://en.wikipedia.org/wiki/Pathological_(mathematics)
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In mathematics, a matrix (pl.: matrices) is a rectangular array or table of numbers, symbols, or expressions, with elements or entries arranged in rows and columns, which is used to represent a mathematical object or property of such an object. For example, [ 1 9 − 13 20 5 − 6 ] {\displaystyle {\begin{bmatrix}1&9&-13\\20&5&-6\end{bmatrix}}} is a matrix with two rows and three columns. This is often referred to as a "two-by-three matrix", a " 2 × 3 {\displaystyle 2\times 3} matrix", or a matrix of dimension 2 × 3 {\displaystyle 2\times 3} . Matrices are commonly used in linear algebra, where they represent linear maps. In geometry, matrices are widely used for specifying and representing geometric transformations (for example rotations) and coordinate changes. In numerical analysis, many computational problems are solved by reducing them to a matrix computation, and this often involves computing with matrices of huge dimensions. Matrices are used in most areas of mathematics and scientific fields, either directly, or through their use in geometry and numerical analysis. Square matrices, matrices with the same number of rows and columns, play a major role in matrix theory. Square matrices of a given dimension form a noncommutative ring, which is one of the most common examples of a noncommutative ring. The determinant of a square matrix is a number associated with the matrix, which is fundamental for the study of a square matrix; for example, a square matrix is invertible if and only if it has a nonzero determinant and the eigenvalues of a square matrix are the roots of a polynomial determinant. Matrix theory is the branch of mathematics that focuses on the study of matrices. It was initially a sub-branch of linear algebra, but soon grew to include subjects related to graph theory, algebra, combinatorics and statistics. == Definition == A matrix is a rectangular array of numbers (or other mathematical objects), called the "entries" of the matrix. Matrices are subject to standard operations such as addition and multiplication. Most commonly, a matrix over a field F {\displaystyle F} is a rectangular array of elements of F {\displaystyle F} . A real matrix and a complex matrix are matrices whose entries are respectively real numbers or complex numbers. More general types of entries are discussed below. For instance, this is a real matrix: A = [ − 1.3 0.6 20.4 5.5 9.7 − 6.2 ] . {\displaystyle \mathbf {A} ={\begin{bmatrix}-1.3&0.6\\20.4&5.5\\9.7&-6.2\end{bmatrix}}.} The numbers, symbols, or expressions in the matrix are called its entries or its elements. The horizontal and vertical lines of entries in a matrix are respectively called rows and columns. === Size === The size of a matrix is defined by the number of rows and columns it contains. There is no limit to the number of rows and columns that a matrix (in the usual sense) can have as long as they are positive integers. A matrix with m {\displaystyle m} rows and n {\displaystyle n} columns is called an m × n {\displaystyle m\times n} matrix, or m {\displaystyle {m}} -by- n {\displaystyle {n}} matrix, where m {\displaystyle {m}} and n {\displaystyle {n}} are called its dimensions. For example, the matrix A {\displaystyle {\mathbf {A} }} above is a 3 × 2 {\displaystyle {3\times 2}} matrix. Matrices with a single row are called row matrices or row vectors, and those with a single column are called column matrices or column vectors. A matrix with the same number of rows and columns is called a square matrix. A matrix with an infinite number of rows or columns (or both) is called an infinite matrix. In some contexts, such as computer algebra programs, it is useful to consider a matrix with no rows or no columns, called an empty matrix. == Notation == The specifics of symbolic matrix notation vary widely, with some prevailing trends. Matrices are commonly written in square brackets or parentheses, so that an m × n {\displaystyle m\times n} matrix A {\displaystyle \mathbf {A} } is represented as A = [ a 11 a 12 ⋯ a 1 n a 21 a 22 ⋯ a 2 n ⋮ ⋮ ⋱ ⋮ a m 1 a m 2 ⋯ a m n ] = ( a 11 a 12 ⋯ a 1 n a 21 a 22 ⋯ a 2 n ⋮ ⋮ ⋱ ⋮ a m 1 a m 2 ⋯ a m n ) . {\displaystyle \mathbf {A} ={\begin{bmatrix}a_{11}&a_{12}&\cdots &a_{1n}\\a_{21}&a_{22}&\cdots &a_{2n}\\\vdots &\vdots &\ddots &\vdots \\a_{m1}&a_{m2}&\cdots &a_{mn}\end{bmatrix}}={\begin{pmatrix}a_{11}&a_{12}&\cdots &a_{1n}\\a_{21}&a_{22}&\cdots &a_{2n}\\\vdots &\vdots &\ddots &\vdots \\a_{m1}&a_{m2}&\cdots &a_{mn}\end{pmatrix}}.} This may be abbreviated by writing only a single generic term, possibly along with indices, as in A = ( a i j ) , [ a i j ] , or ( a i j ) 1 ≤ i ≤ m , 1 ≤ j ≤ n {\displaystyle \mathbf {A} =\left(a_{ij}\right),\quad \left[a_{ij}\right],\quad {\text{or}}\quad \left(a_{ij}\right)_{1\leq i\leq m,\;1\leq j\leq n}} or A = ( a i , j ) 1 ≤ i , j ≤ n {\displaystyle \mathbf {A} =(a_{i,j})_{1\leq i,j\leq n}} in the case that n = m {\displaystyle n=m} . Matrices are usually symbolized using upper-case letters (such as A {\displaystyle {\mathbf {A} }} in the examples above), while the corresponding lower-case letters, with two subscript indices (e.g., a 11 {\displaystyle a_{11}} , or a 1 , 1 {\displaystyle a_{1,1}} ), represent the entries. In addition to using upper-case letters to symbolize matrices, many authors use a special typographical style, commonly boldface Roman (non-italic), to further distinguish matrices from other mathematical objects. An alternative notation involves the use of a double-underline with the variable name, with or without boldface style, as in A _ _ {\displaystyle {\underline {\underline {A}}}} . The entry in the ith row and jth column of a matrix A is sometimes referred to as the i , j {\displaystyle {i,j}} or ( i , j ) {\displaystyle (i,j)} entry of the matrix, and commonly denoted by a i , j {\displaystyle a_{i,j}} or a i j {\displaystyle a_{ij}} . Alternative notations for that entry are A [ i , j ] {\displaystyle {\mathbf {A} [i,j]}} and A i , j {\displaystyle \mathbf {A} _{i,j}} . For example, the ( 1 , 3 ) {\displaystyle (1,3)} entry of the following matrix A {\displaystyle \mathbf {A} } is 5 (also denoted a 13 {\displaystyle a_{13}} , a 1 , 3 {\displaystyle a_{1,3}} , A [ 1 , 3 ] {\displaystyle \mathbf {A} [1,3]} or A 1 , 3 {\displaystyle {\mathbf {A} }_{1,3}} ): A = [ 4 − 7 5 0 − 2 0 11 8 19 1 − 3 12 ] {\displaystyle \mathbf {A} ={\begin{bmatrix}4&-7&\color {red}{5}&0\\-2&0&11&8\\19&1&-3&12\end{bmatrix}}} Sometimes, the entries of a matrix can be defined by a formula such as a i , j = f ( i , j ) {\displaystyle a_{i,j}=f(i,j)} . For example, each of the entries of the following matrix A {\displaystyle \mathbf {A} } is determined by the formula a i j = i − j {\displaystyle a_{ij}=i-j} . A = [ 0 − 1 − 2 − 3 1 0 − 1 − 2 2 1 0 − 1 ] {\displaystyle \mathbf {A} ={\begin{bmatrix}0&-1&-2&-3\\1&0&-1&-2\\2&1&0&-1\end{bmatrix}}} In this case, the matrix itself is sometimes defined by that formula, within square brackets or double parentheses. For example, the matrix above is defined as A = [ i − j ] {\displaystyle {\mathbf {A} }=[i-j]} or A = ( ( i − j ) ) {\displaystyle \mathbf {A} =((i-j))} . If matrix size is m × n {\displaystyle m\times n} , the above-mentioned formula f ( i , j ) {\displaystyle f(i,j)} is valid for any i = 1 , … , m {\displaystyle i=1,\dots ,m} and any j = 1 , … , n {\displaystyle j=1,\dots ,n} . This can be specified separately or indicated using m × n {\displaystyle m\times n} as a subscript. For instance, the matrix A {\displaystyle \mathbf {A} } above is 3 × 4 {\displaystyle 3\times 4} , and can be defined as A = [ i − j ] ( i = 1 , 2 , 3 ; j = 1 , … , 4 ) {\displaystyle {\mathbf {A} }=[i-j](i=1,2,3;j=1,\dots ,4)} or A = [ i − j ] 3 × 4 {\displaystyle \mathbf {A} =[i-j]_{3\times 4}} . Some programming languages utilize doubly subscripted arrays (or arrays of arrays) to represent an m-by-n matrix. Some programming languages start the numbering of array indexes at zero, in which case the entries of an m-by-n matrix are indexed by 0 ≤ i ≤ m − 1 {\displaystyle 0\leq i\leq m-1} and 0 ≤ j ≤ n − 1 {\displaystyle 0\leq j\leq n-1} . This article follows the more common convention in mathematical writing where enumeration starts from 1. The set of all m-by-n real matrices is often denoted M ( m , n ) {\displaystyle {\mathcal {M}}(m,n)} , or M m × n ( R ) {\displaystyle {\mathcal {M}}_{m\times n}(\mathbb {R} )} . The set of all m-by-n matrices over another field, or over a ring R, is similarly denoted M ( m , n , R ) {\displaystyle {\mathcal {M}}(m,n,R)} , or M m × n ( R ) {\displaystyle {\mathcal {M}}_{m\times n}(R)} . If m = n, such as in the case of square matrices, one does not repeat the dimension: M ( n , R ) {\displaystyle {\mathcal {M}}(n,R)} , or M n ( R ) {\displaystyle {\mathcal {M}}_{n}(R)} . Often, M {\displaystyle M} , or Mat {\displaystyle \operatorname {Mat} } , is used in place of M {\displaystyle {\mathcal {M}}} . == Basic operations == Several basic operations can be applied to matrices. Some, such as transposition and submatrix do not depend on the nature of the entries. Others, such as matrix addition, scalar multiplication, matrix multiplication, and row operations involve operations on matrix entries and therefore require that matrix entries are numbers or belong to a field or a ring. In this section, it is supposed that matrix entries belong to a fixed ring, which is typically a field of numbers. === Addition, scalar multiplication, subtraction and transposition === Addition The sum A + B of two m×n matrices A and B is calculated entrywise: ( A + B ) i , j = A i , j + B i , j , 1 ≤ i ≤ m , 1 ≤ j ≤ n . {\displaystyle ({\mathbf {A}}+{\mathbf {B}})_{i,j}={\mathbf {A}}_{i,j}+{\mathbf {B}}_{i,j},\quad 1\leq i\leq m,\quad 1\leq j\leq n.} For example, [ 1 3 1 1 0 0 ] + [ 0 0 5 7 5 0 ] = [ 1 + 0 3 + 0 1 + 5 1 + 7 0 + 5 0 + 0 ] = [ 1 3 6 8 5 0 ] {\displaystyle {\begin{bmatrix}1&3&1\\1&0&0\end{bmatrix}}+{\begin{bmatrix}0&0&5\\7&5&0\end{bmatrix}}={\begin{bmatrix}1+0&3+0&1+5\\1+7&0+5&0+0\end{bmatrix}}={\begin{bmatrix}1&3&6\\8&5&0\end{bmatrix}}} Scalar multiplication The product cA of a number c (also called a scalar in this context) and a matrix A is computed by multiplying every entry of A by c: ( c A ) i , j = c ⋅ A i , j {\displaystyle (c{\mathbf {A}})_{i,j}=c\cdot {\mathbf {A}}_{i,j}} This operation is called scalar multiplication, but its result is not named "scalar product" to avoid confusion, since "scalar product" is often used as a synonym for "inner product". For example: 2 ⋅ [ 1 8 − 3 4 − 2 5 ] = [ 2 ⋅ 1 2 ⋅ 8 2 ⋅ − 3 2 ⋅ 4 2 ⋅ − 2 2 ⋅ 5 ] = [ 2 16 − 6 8 − 4 10 ] {\displaystyle 2\cdot {\begin{bmatrix}1&8&-3\\4&-2&5\end{bmatrix}}={\begin{bmatrix}2\cdot 1&2\cdot 8&2\cdot -3\\2\cdot 4&2\cdot -2&2\cdot 5\end{bmatrix}}={\begin{bmatrix}2&16&-6\\8&-4&10\end{bmatrix}}} Subtraction The subtraction of two m×n matrices is defined by composing matrix addition with scalar multiplication by –1: A − B = A + ( − 1 ) ⋅ B {\displaystyle \mathbf {A} -\mathbf {B} =\mathbf {A} +(-1)\cdot \mathbf {B} } Transposition The transpose of an m×n matrix A is the n×m matrix AT (also denoted Atr or tA) formed by turning rows into columns and vice versa: ( A T ) i , j = A j , i . {\displaystyle \left({\mathbf {A}}^{\rm {T}}\right)_{i,j}={\mathbf {A}}_{j,i}.} For example: [ 1 2 3 0 − 6 7 ] T = [ 1 0 2 − 6 3 7 ] {\displaystyle {\begin{bmatrix}1&2&3\\0&-6&7\end{bmatrix}}^{\mathrm {T} }={\begin{bmatrix}1&0\\2&-6\\3&7\end{bmatrix}}} Familiar properties of numbers extend to these operations on matrices: for example, addition is commutative, that is, the matrix sum does not depend on the order of the summands: A + B = B + A. The transpose is compatible with addition and scalar multiplication, as expressed by (cA)T = c(AT) and (A + B)T = AT + BT. Finally, (AT)T = A. === Matrix multiplication === Multiplication of two matrices is defined if and only if the number of columns of the left matrix is the same as the number of rows of the right matrix. If A is an m×n matrix and B is an n×p matrix, then their matrix product AB is the m×p matrix whose entries are given by the dot product of the corresponding row of A and the corresponding column of B: [ A B ] i , j = a i , 1 b 1 , j + a i , 2 b 2 , j + ⋯ + a i , n b n , j = ∑ r = 1 n a i , r b r , j , {\displaystyle [\mathbf {AB} ]_{i,j}=a_{i,1}b_{1,j}+a_{i,2}b_{2,j}+\cdots +a_{i,n}b_{n,j}=\sum _{r=1}^{n}a_{i,r}b_{r,j},} where 1 ≤ i ≤ m and 1 ≤ j ≤ p. For example, the underlined entry 2340 in the product is calculated as (2 × 1000) + (3 × 100) + (4 × 10) = 2340: [ 2 _ 3 _ 4 _ 1 0 0 ] [ 0 1000 _ 1 100 _ 0 10 _ ] = [ 3 2340 _ 0 1000 ] . {\displaystyle {\begin{aligned}{\begin{bmatrix}{\underline {2}}&{\underline {3}}&{\underline {4}}\\1&0&0\\\end{bmatrix}}{\begin{bmatrix}0&{\underline {1000}}\\1&{\underline {100}}\\0&{\underline {10}}\\\end{bmatrix}}&={\begin{bmatrix}3&{\underline {2340}}\\0&1000\\\end{bmatrix}}.\end{aligned}}} Matrix multiplication satisfies the rules (AB)C = A(BC) (associativity), and (A + B)C = AC + BC as well as C(A + B) = CA + CB (left and right distributivity), whenever the size of the matrices is such that the various products are defined. The product AB may be defined without BA being defined, namely if A and B are m×n and n×k matrices, respectively, and m ≠ k. Even if both products are defined, they generally need not be equal, that is: A B ≠ B A . {\displaystyle {\mathbf {AB}}\neq {\mathbf {BA}}.} In other words, matrix multiplication is not commutative, in marked contrast to (rational, real, or complex) numbers, whose product is independent of the order of the factors. An example of two matrices not commuting with each other is: [ 1 2 3 4 ] [ 0 1 0 0 ] = [ 0 1 0 3 ] , {\displaystyle {\begin{bmatrix}1&2\\3&4\\\end{bmatrix}}{\begin{bmatrix}0&1\\0&0\\\end{bmatrix}}={\begin{bmatrix}0&1\\0&3\\\end{bmatrix}},} whereas [ 0 1 0 0 ] [ 1 2 3 4 ] = [ 3 4 0 0 ] . {\displaystyle {\begin{bmatrix}0&1\\0&0\\\end{bmatrix}}{\begin{bmatrix}1&2\\3&4\\\end{bmatrix}}={\begin{bmatrix}3&4\\0&0\\\end{bmatrix}}.} Besides the ordinary matrix multiplication just described, other less frequently used operations on matrices that can be considered forms of multiplication also exist, such as the Hadamard product and the Kronecker product. They arise in solving matrix equations such as the Sylvester equation. === Row operations === There are three types of row operations: row addition, that is, adding a row to another. row multiplication, that is, multiplying all entries of a row by a non-zero constant; row switching, that is, interchanging two rows of a matrix; These operations are used in several ways, including solving linear equations and finding matrix inverses with Gauss elimination and Gauss–Jordan elimination, respectively. === Submatrix === A submatrix of a matrix is a matrix obtained by deleting any collection of rows and/or columns. For example, from the following 3-by-4 matrix, we can construct a 2-by-3 submatrix by removing row 3 and column 2: A = [ 1 2 3 4 5 6 7 8 9 10 11 12 ] → [ 1 3 4 5 7 8 ] . {\displaystyle \mathbf {A} ={\begin{bmatrix}1&\color {red}{2}&3&4\\5&\color {red}{6}&7&8\\\color {red}{9}&\color {red}{10}&\color {red}{11}&\color {red}{12}\end{bmatrix}}\rightarrow {\begin{bmatrix}1&3&4\\5&7&8\end{bmatrix}}.} The minors and cofactors of a matrix are found by computing the determinant of certain submatrices. A principal submatrix is a square submatrix obtained by removing certain rows and columns. The definition varies from author to author. According to some authors, a principal submatrix is a submatrix in which the set of row indices that remain is the same as the set of column indices that remain. Other authors define a principal submatrix as one in which the first k rows and columns, for some number k, are the ones that remain; this type of submatrix has also been called a leading principal submatrix. == Linear equations == Matrices can be used to compactly write and work with multiple linear equations, that is, systems of linear equations. For example, if A is an m×n matrix, x designates a column vector (that is, n×1-matrix) of n variables x1, x2, ..., xn, and b is an m×1-column vector, then the matrix equation A x = b {\displaystyle \mathbf {Ax} =\mathbf {b} } is equivalent to the system of linear equations a 1 , 1 x 1 + a 1 , 2 x 2 + ⋯ + a 1 , n x n = b 1 ⋮ a m , 1 x 1 + a m , 2 x 2 + ⋯ + a m , n x n = b m {\displaystyle {\begin{aligned}a_{1,1}x_{1}+a_{1,2}x_{2}+&\cdots +a_{1,n}x_{n}=b_{1}\\&\ \ \vdots \\a_{m,1}x_{1}+a_{m,2}x_{2}+&\cdots +a_{m,n}x_{n}=b_{m}\end{aligned}}} Using matrices, this can be solved more compactly than would be possible by writing out all the equations separately. If n = m and the equations are independent, then this can be done by writing x = A − 1 b {\displaystyle \mathbf {x} =\mathbf {A} ^{-1}\mathbf {b} } where A−1 is the inverse matrix of A. If A has no inverse, solutions—if any—can be found using its generalized inverse. == Linear transformations == Matrices and matrix multiplication reveal their essential features when related to linear transformations, also known as linear maps. A real m-by-n matrix A gives rise to a linear transformation R n → R m {\displaystyle \mathbb {R} ^{n}\to \mathbb {R} ^{m}} mapping each vector x in R n {\displaystyle \mathbb {R} ^{n}} to the (matrix) product Ax, which is a vector in R m . {\displaystyle \mathbb {R} ^{m}.} Conversely, each linear transformation f : R n → R m {\displaystyle f:\mathbb {R} ^{n}\to \mathbb {R} ^{m}} arises from a unique m-by-n matrix A: explicitly, the (i, j)-entry of A is the ith coordinate of f (ej), where ej = (0, ..., 0, 1, 0, ..., 0) is the unit vector with 1 in the jth position and 0 elsewhere. The matrix A is said to represent the linear map f, and A is called the transformation matrix of f. For example, the 2×2 matrix A = [ a c b d ] {\displaystyle \mathbf {A} ={\begin{bmatrix}a&c\\b&d\end{bmatrix}}} can be viewed as the transform of the unit square into a parallelogram with vertices at (0, 0), (a, b), (a + c, b + d), and (c, d). The parallelogram pictured at the right is obtained by multiplying A with each of the column vectors [ 0 0 ] {\displaystyle \left[{\begin{smallmatrix}0\\0\end{smallmatrix}}\right]} , [ 1 0 ] {\displaystyle \left[{\begin{smallmatrix}1\\0\end{smallmatrix}}\right]} , [ 1 1 ] {\displaystyle \left[{\begin{smallmatrix}1\\1\end{smallmatrix}}\right]} , and [ 0 1 ] {\displaystyle \left[{\begin{smallmatrix}0\\1\end{smallmatrix}}\right]} in turn. These vectors define the vertices of the unit square. The following table shows several 2×2 real matrices with the associated linear maps of R 2 {\displaystyle \mathbb {R} ^{2}} . The blue original is mapped to the green grid and shapes. The origin (0, 0) is marked with a black point. Under the 1-to-1 correspondence between matrices and linear maps, matrix multiplication corresponds to composition of maps: if a k-by-m matrix B represents another linear map g : R m → R k {\displaystyle g:\mathbb {R} ^{m}\to \mathbb {R} ^{k}} , then the composition g ∘ f is represented by BA since ( g ∘ f ) ( x ) = g ( f ( x ) ) = g ( A x ) = B ( A x ) = ( B A ) x . {\displaystyle (g\circ f)({\mathbf {x}})=g(f({\mathbf {x}}))=g({\mathbf {Ax}})={\mathbf {B}}({\mathbf {Ax}})=({\mathbf {BA}}){\mathbf {x}}.} The last equality follows from the above-mentioned associativity of matrix multiplication. The rank of a matrix A is the maximum number of linearly independent row vectors of the matrix, which is the same as the maximum number of linearly independent column vectors. Equivalently it is the dimension of the image of the linear map represented by A. The rank–nullity theorem states that the dimension of the kernel of a matrix plus the rank equals the number of columns of the matrix. == Square matrix == A square matrix is a matrix with the same number of rows and columns. An n-by-n matrix is known as a square matrix of order n. Any two square matrices of the same order can be added and multiplied. The entries aii form the main diagonal of a square matrix. They lie on the imaginary line running from the top left corner to the bottom right corner of the matrix. === Main types === ==== Diagonal and triangular matrix ==== If all entries of A below the main diagonal are zero, A is called an upper triangular matrix. Similarly, if all entries of A above the main diagonal are zero, A is called a lower triangular matrix. If all entries outside the main diagonal are zero, A is called a diagonal matrix. ==== Identity matrix ==== The identity matrix In of size n is the n-by-n matrix in which all the elements on the main diagonal are equal to 1 and all other elements are equal to 0, for example, I 1 = [ 1 ] , I 2 = [ 1 0 0 1 ] , ⋮ I n = [ 1 0 ⋯ 0 0 1 ⋯ 0 ⋮ ⋮ ⋱ ⋮ 0 0 ⋯ 1 ] {\displaystyle {\begin{aligned}\mathbf {I} _{1}&={\begin{bmatrix}1\end{bmatrix}},\\[4pt]\mathbf {I} _{2}&={\begin{bmatrix}1&0\\0&1\end{bmatrix}},\\[4pt]\vdots &\\[4pt]\mathbf {I} _{n}&={\begin{bmatrix}1&0&\cdots &0\\0&1&\cdots &0\\\vdots &\vdots &\ddots &\vdots \\0&0&\cdots &1\end{bmatrix}}\end{aligned}}} It is a square matrix of order n, and also a special kind of diagonal matrix. It is called an identity matrix because multiplication with it leaves a matrix unchanged: A I n = I m A = A {\displaystyle {\mathbf {AI}}_{n}={\mathbf {I}}_{m}{\mathbf {A}}={\mathbf {A}}} for any m-by-n matrix A. A scalar multiple of an identity matrix is called a scalar matrix. ==== Symmetric or skew-symmetric matrix ==== A square matrix A that is equal to its transpose, that is, A = AT, is a symmetric matrix. If instead, A is equal to the negative of its transpose, that is, A = −AT, then A is a skew-symmetric matrix. In complex matrices, symmetry is often replaced by the concept of Hermitian matrices, which satisfies A∗ = A, where the star or asterisk denotes the conjugate transpose of the matrix, that is, the transpose of the complex conjugate of A. By the spectral theorem, real symmetric matrices and complex Hermitian matrices have an eigenbasis; that is, every vector is expressible as a linear combination of eigenvectors. In both cases, all eigenvalues are real. This theorem can be generalized to infinite-dimensional situations related to matrices with infinitely many rows and columns. ==== Invertible matrix and its inverse ==== A square matrix A is called invertible or non-singular if there exists a matrix B such that A B = B A = I n , {\displaystyle {\mathbf {AB}}={\mathbf {BA}}={\mathbf {I}}_{n},} where In is the n×n identity matrix with 1 for each entry on the main diagonal and 0 elsewhere. If B exists, it is unique and is called the inverse matrix of A, denoted A−1. There are many algorithms for testing whether a square matrix is invertible, and, if it is, computing its inverse. One of the oldest, which is still in common use is Gaussian elimination. ==== Definite matrix ==== A symmetric real matrix A is called positive-definite if the associated quadratic form f ( x ) = x T A x {\displaystyle f({\mathbf {x}})={\mathbf {x}}^{\rm {T}}{\mathbf {Ax}}} has a positive value for every nonzero vector x in R n {\displaystyle \mathbb {R} ^{n}} . If f(x) yields only negative values then A is negative-definite; if f does produce both negative and positive values then A is indefinite. If the quadratic form f yields only non-negative values (positive or zero), the symmetric matrix is called positive-semidefinite (or if only non-positive values, then negative-semidefinite); hence the matrix is indefinite precisely when it is neither positive-semidefinite nor negative-semidefinite. A symmetric matrix is positive-definite if and only if all its eigenvalues are positive, that is, the matrix is positive-semidefinite and it is invertible. The table at the right shows two possibilities for 2-by-2 matrices. The eigenvalues of a diagonal matrix are simply the entries along the diagonal, and so in these examples, the eigenvalues can be read directly from the matrices themselves. The first matrix has two eigenvalues that are both positive, while the second has one that is positive and another that is negative. Allowing as input two different vectors instead yields the bilinear form associated to A: B A ( x , y ) = x T A y . {\displaystyle B_{\mathbf {A}}({\mathbf {x}},{\mathbf {y}})={\mathbf {x}}^{\rm {T}}{\mathbf {Ay}}.} In the case of complex matrices, the same terminology and results apply, with symmetric matrix, quadratic form, bilinear form, and transpose xT replaced respectively by Hermitian matrix, Hermitian form, sesquilinear form, and conjugate transpose xH. ==== Orthogonal matrix ==== An orthogonal matrix is a square matrix with real entries whose columns and rows are orthogonal unit vectors (that is, orthonormal vectors). Equivalently, a matrix A is orthogonal if its transpose is equal to its inverse: A T = A − 1 , {\displaystyle \mathbf {A} ^{\mathrm {T} }=\mathbf {A} ^{-1},\,} which entails A T A = A A T = I n , {\displaystyle \mathbf {A} ^{\mathrm {T} }\mathbf {A} =\mathbf {A} \mathbf {A} ^{\mathrm {T} }=\mathbf {I} _{n},} where In is the identity matrix of size n. An orthogonal matrix A is necessarily invertible (with inverse A−1 = AT), unitary (A−1 = A*), and normal (A*A = AA*). The determinant of any orthogonal matrix is either +1 or −1. A special orthogonal matrix is an orthogonal matrix with determinant +1. As a linear transformation, every orthogonal matrix with determinant +1 is a pure rotation without reflection, i.e., the transformation preserves the orientation of the transformed structure, while every orthogonal matrix with determinant −1 reverses the orientation, i.e., is a composition of a pure reflection and a (possibly null) rotation. The identity matrices have determinant 1 and are pure rotations by an angle zero. The complex analog of an orthogonal matrix is a unitary matrix. === Main operations === ==== Trace ==== The trace, tr(A) of a square matrix A is the sum of its diagonal entries. While matrix multiplication is not commutative as mentioned above, the trace of the product of two matrices is independent of the order of the factors: tr ( A B ) = tr ( B A ) . {\displaystyle \operatorname {tr} (\mathbf {AB} )=\operatorname {tr} (\mathbf {BA} ).} This is immediate from the definition of matrix multiplication: tr ( A B ) = ∑ i = 1 m ∑ j = 1 n a i j b j i = tr ( B A ) . {\displaystyle \operatorname {tr} (\mathbf {AB} )=\sum _{i=1}^{m}\sum _{j=1}^{n}a_{ij}b_{ji}=\operatorname {tr} (\mathbf {BA} ).} It follows that the trace of the product of more than two matrices is independent of cyclic permutations of the matrices; however, this does not in general apply for arbitrary permutations. For example, tr(ABC) ≠ tr(BAC), in general. Also, the trace of a matrix is equal to that of its transpose, that is, tr ( A ) = tr ( A T ) . {\displaystyle \operatorname {tr} ({\mathbf {A}})=\operatorname {tr} ({\mathbf {A}}^{\rm {T}}).} ==== Determinant ==== The determinant of a square matrix A (denoted det(A) or |A|) is a number encoding certain properties of the matrix. A matrix is invertible if and only if its determinant is nonzero. Its absolute value equals the area (in R 2 {\displaystyle \mathbb {R} ^{2}} ) or volume (in R 3 {\displaystyle \mathbb {R} ^{3}} ) of the image of the unit square (or cube), while its sign corresponds to the orientation of the corresponding linear map: the determinant is positive if and only if the orientation is preserved. The determinant of 2-by-2 matrices is given by det [ a b c d ] = a d − b c . {\displaystyle \det {\begin{bmatrix}a&b\\c&d\end{bmatrix}}=ad-bc.} The determinant of 3-by-3 matrices involves 6 terms (rule of Sarrus). The more lengthy Leibniz formula generalizes these two formulae to all dimensions. The determinant of a product of square matrices equals the product of their determinants: det ( A B ) = det ( A ) ⋅ det ( B ) , {\displaystyle \det({\mathbf {AB}})=\det({\mathbf {A}})\cdot \det({\mathbf {B}}),} or using alternate notation: | A B | = | A | ⋅ | B | . {\displaystyle |{\mathbf {AB}}|=|{\mathbf {A}}|\cdot |{\mathbf {B}}|.} Adding a multiple of any row to another row, or a multiple of any column to another column, does not change the determinant. Interchanging two rows or two columns affects the determinant by multiplying it by −1. Using these operations, any matrix can be transformed to a lower (or upper) triangular matrix, and for such matrices, the determinant equals the product of the entries on the main diagonal; this provides a method to calculate the determinant of any matrix. Finally, the Laplace expansion expresses the determinant in terms of minors, that is, determinants of smaller matrices. This expansion can be used for a recursive definition of determinants (taking as starting case the determinant of a 1-by-1 matrix, which is its unique entry, or even the determinant of a 0-by-0 matrix, which is 1), that can be seen to be equivalent to the Leibniz formula. Determinants can be used to solve linear systems using Cramer's rule, where the division of the determinants of two related square matrices equates to the value of each of the system's variables. ==== Eigenvalues and eigenvectors ==== A number λ {\textstyle \lambda } and a nonzero vector v satisfying A v = λ v {\displaystyle \mathbf {A} \mathbf {v} =\lambda \mathbf {v} } are called an eigenvalue and an eigenvector of A, respectively. The number λ is an eigenvalue of an n×n-matrix A if and only if (A − λIn) is not invertible, which is equivalent to det ( A − λ I ) = 0. {\displaystyle \det(\mathbf {A} -\lambda \mathbf {I} )=0.} The polynomial pA in an indeterminate X given by evaluation of the determinant det(XIn − A) is called the characteristic polynomial of A. It is a monic polynomial of degree n. Therefore the polynomial equation pA(λ) = 0 has at most n different solutions, that is, eigenvalues of the matrix. They may be complex even if the entries of A are real. According to the Cayley–Hamilton theorem, pA(A) = 0, that is, the result of substituting the matrix itself into its characteristic polynomial yields the zero matrix. == Computational aspects == Matrix calculations can be often performed with different techniques. Many problems can be solved by both direct algorithms and iterative approaches. For example, the eigenvectors of a square matrix can be obtained by finding a sequence of vectors xn converging to an eigenvector when n tends to infinity. To choose the most appropriate algorithm for each specific problem, it is important to determine both the effectiveness and precision of all the available algorithms. The domain studying these matters is called numerical linear algebra. As with other numerical situations, two main aspects are the complexity of algorithms and their numerical stability. Determining the complexity of an algorithm means finding upper bounds or estimates of how many elementary operations such as additions and multiplications of scalars are necessary to perform some algorithm, for example, multiplication of matrices. Calculating the matrix product of two n-by-n matrices using the definition given above needs n3 multiplications, since for any of the n2 entries of the product, n multiplications are necessary. The Strassen algorithm outperforms this "naive" algorithm; it needs only n2.807 multiplications. Theoretically faster but impractical matrix multiplication algorithms have been developed, as have speedups to this problem using parallel algorithms or distributed computation systems such as MapReduce. In many practical situations, additional information about the matrices involved is known. An important case is sparse matrices, that is, matrices whose entries are mostly zero. There are specifically adapted algorithms for, say, solving linear systems Ax = b for sparse matrices A, such as the conjugate gradient method. An algorithm is, roughly speaking, numerically stable if little deviations in the input values do not lead to big deviations in the result. For example, one can calculate the inverse of a matrix by computing its adjugate matrix: A − 1 = adj ( A ) / det ( A ) . {\displaystyle {\mathbf {A}}^{-1}=\operatorname {adj} ({\mathbf {A}})/\det({\mathbf {A}}).} However, this may lead to significant rounding errors if the determinant of the matrix is very small. The norm of a matrix can be used to capture the conditioning of linear algebraic problems, such as computing a matrix's inverse. == Decomposition == There are several methods to render matrices into a more easily accessible form. They are generally referred to as matrix decomposition or matrix factorization techniques. These techniques are of interest because they can make computations easier. The LU decomposition factors matrices as a product of lower (L) and an upper triangular matrices (U). Once this decomposition is calculated, linear systems can be solved more efficiently by a simple technique called forward and back substitution. Likewise, inverses of triangular matrices are algorithmically easier to calculate. The Gaussian elimination is a similar algorithm; it transforms any matrix to row echelon form. Both methods proceed by multiplying the matrix by suitable elementary matrices, which correspond to permuting rows or columns and adding multiples of one row to another row. Singular value decomposition expresses any matrix A as a product UDV∗, where U and V are unitary matrices and D is a diagonal matrix. The eigendecomposition or diagonalization expresses A as a product VDV−1, where D is a diagonal matrix and V is a suitable invertible matrix. If A can be written in this form, it is called diagonalizable. More generally, and applicable to all matrices, the Jordan decomposition transforms a matrix into Jordan normal form, that is to say matrices whose only nonzero entries are the eigenvalues λ1 to λn of A, placed on the main diagonal and possibly entries equal to one directly above the main diagonal, as shown at the right. Given the eigendecomposition, the nth power of A (that is, n-fold iterated matrix multiplication) can be calculated via A n = ( V D V − 1 ) n = V D V − 1 V D V − 1 … V D V − 1 = V D n V − 1 {\displaystyle {\mathbf {A}}^{n}=({\mathbf {VDV}}^{-1})^{n}={\mathbf {VDV}}^{-1}{\mathbf {VDV}}^{-1}\ldots {\mathbf {VDV}}^{-1}={\mathbf {VD}}^{n}{\mathbf {V}}^{-1}} and the power of a diagonal matrix can be calculated by taking the corresponding powers of the diagonal entries, which is much easier than doing the exponentiation for A instead. This can be used to compute the matrix exponential eA, a need frequently arising in solving linear differential equations, matrix logarithms and square roots of matrices. To avoid numerically ill-conditioned situations, further algorithms such as the Schur decomposition can be employed. == Abstract algebraic aspects and generalizations == Matrices can be generalized in different ways. Abstract algebra uses matrices with entries in more general fields or even rings, while linear algebra codifies properties of matrices in the notion of linear maps. It is possible to consider matrices with infinitely many columns and rows. Another extension is tensors, which can be seen as higher-dimensional arrays of numbers, as opposed to vectors, which can often be realized as sequences of numbers, while matrices are rectangular or two-dimensional arrays of numbers. Matrices, subject to certain requirements tend to form groups known as matrix groups. Similarly under certain conditions matrices form rings known as matrix rings. Though the product of matrices is not in general commutative certain matrices form fields known as matrix fields. In general, matrices and their multiplication also form a category, the category of matrices. === Matrices with more general entries === This article focuses on matrices whose entries are real or complex numbers. However, matrices can be considered with much more general types of entries than real or complex numbers. As a first step of generalization, any field, that is, a set where addition, subtraction, multiplication, and division operations are defined and well-behaved, may be used instead of R {\displaystyle \mathbb {R} } or C {\displaystyle \mathbb {C} } , for example rational numbers or finite fields. For example, coding theory makes use of matrices over finite fields. Wherever eigenvalues are considered, as these are roots of a polynomial they may exist only in a larger field than that of the entries of the matrix; for instance, they may be complex in the case of a matrix with real entries. The possibility to reinterpret the entries of a matrix as elements of a larger field (for example, to view a real matrix as a complex matrix whose entries happen to be all real) then allows considering each square matrix to possess a full set of eigenvalues. Alternatively one can consider only matrices with entries in an algebraically closed field, such as C , {\displaystyle \mathbb {C} ,} from the outset. More generally, matrices with entries in a ring R are widely used in mathematics. Rings are a more general notion than fields in that a division operation need not exist. The very same addition and multiplication operations of matrices extend to this setting, too. The set M(n, R) (also denoted Mn(R)) of all square n-by-n matrices over R is a ring called matrix ring, isomorphic to the endomorphism ring of the left R-module Rn. If the ring R is commutative, that is, its multiplication is commutative, then the ring M(n, R) is also an associative algebra over R. The determinant of square matrices over a commutative ring R can still be defined using the Leibniz formula; such a matrix is invertible if and only if its determinant is invertible in R, generalizing the situation over a field F, where every nonzero element is invertible. Matrices over superrings are called supermatrices. Matrices do not always have all their entries in the same ring – or even in any ring at all. One special but common case is block matrices, which may be considered as matrices whose entries themselves are matrices. The entries need not be square matrices, and thus need not be members of any ring; but their sizes must fulfill certain compatibility conditions. === Relationship to linear maps === Linear maps R n → R m {\displaystyle \mathbb {R} ^{n}\to \mathbb {R} ^{m}} are equivalent to m-by-n matrices, as described above. More generally, any linear map f : V → W between finite-dimensional vector spaces can be described by a matrix A = (aij), after choosing bases v1, ..., vn of V, and w1, ..., wm of W (so n is the dimension of V and m is the dimension of W), which is such that f ( v j ) = ∑ i = 1 m a i , j w i for j = 1 , … , n . {\displaystyle f(\mathbf {v} _{j})=\sum _{i=1}^{m}a_{i,j}\mathbf {w} _{i}\qquad {\mbox{for}}\ j=1,\ldots ,n.} In other words, column j of A expresses the image of vj in terms of the basis vectors wi of W; thus this relation uniquely determines the entries of the matrix A. The matrix depends on the choice of the bases: different choices of bases give rise to different, but equivalent matrices. Many of the above concrete notions can be reinterpreted in this light, for example, the transpose matrix AT describes the transpose of the linear map given by A, concerning the dual bases. These properties can be restated more naturally: the category of matrices with entries in a field k {\displaystyle k} with multiplication as composition is equivalent to the category of finite-dimensional vector spaces and linear maps over this field. More generally, the set of m×n matrices can be used to represent the R-linear maps between the free modules Rm and Rn for an arbitrary ring R with unity. When n = m composition of these maps is possible, and this gives rise to the matrix ring of n×n matrices representing the endomorphism ring of Rn. === Matrix groups === A group is a mathematical structure consisting of a set of objects together with a binary operation, that is, an operation combining any two objects to a third, subject to certain requirements. A group in which the objects are matrices and the group operation is matrix multiplication is called a matrix group. Since a group of every element must be invertible, the most general matrix groups are the groups of all invertible matrices of a given size, called the general linear groups. Any property of matrices that is preserved under matrix products and inverses can be used to define further matrix groups. For example, matrices with a given size and with a determinant of 1 form a subgroup of (that is, a smaller group contained in) their general linear group, called a special linear group. Orthogonal matrices, determined by the condition M T M = I , {\displaystyle {\mathbf {M}}^{\rm {T}}{\mathbf {M}}={\mathbf {I}},} form the orthogonal group. Every orthogonal matrix has determinant 1 or −1. Orthogonal matrices with determinant 1 form a subgroup called the special orthogonal group. Every finite group is isomorphic to a matrix group, as one can see by considering the regular representation of the symmetric group. General groups can be studied using matrix groups, which are comparatively well understood, using representation theory. === Infinite matrices === It is also possible to consider matrices with infinitely many rows and/or columns. The basic operations introduced above are defined the same way in this case. Matrix multiplication, however, and all operations stemming therefrom are only meaningful when restricted to certain matrices, since the sum featuring in the above definition of the matrix product will contain an infinity of summands. An easy way to circumvent this issue is to restrict to matrices all of whose rows (or columns) contain only finitely many nonzero terms. As in the finite case (see above), where matrices describe linear maps, infinite matrices can be used to describe operators on Hilbert spaces, where convergence and continuity questions arise. However, the explicit point of view of matrices tends to obfuscate the matter, and the abstract and more powerful tools of functional analysis are used instead, by relating matrices to linear maps (as in the finite case above), but imposing additional convergence and continuity constraints. === Empty matrix === An empty matrix is a matrix in which the number of rows or columns (or both) is zero. Empty matrices help to deal with maps involving the zero vector space. For example, if A is a 3-by-0 matrix and B is a 0-by-3 matrix, then AB is the 3-by-3 zero matrix corresponding to the null map from a 3-dimensional space V to itself, while BA is a 0-by-0 matrix. There is no common notation for empty matrices, but most computer algebra systems allow creating and computing with them. The determinant of the 0-by-0 matrix is 1 as follows regarding the empty product occurring in the Leibniz formula for the determinant as 1. This value is also consistent with the fact that the identity map from any finite-dimensional space to itself has determinant 1, a fact that is often used as a part of the characterization of determinants. == Applications == There are numerous applications of matrices, both in mathematics and other sciences. Some of them merely take advantage of the compact representation of a set of numbers in a matrix. For example, in game theory and economics, the payoff matrix encodes the payoff for two players, depending on which out of a given (finite) set of strategies the players choose. Text mining and automated thesaurus compilation makes use of document-term matrices such as tf-idf to track frequencies of certain words in several documents. Complex numbers can be represented by particular real 2-by-2 matrices via a + i b ↔ [ a − b b a ] , {\displaystyle a+ib\leftrightarrow {\begin{bmatrix}a&-b\\b&a\end{bmatrix}},} under which addition and multiplication of complex numbers and matrices correspond to each other. For example, 2-by-2 rotation matrices represent the multiplication with some complex number of absolute value 1, as above. A similar interpretation is possible for quaternions and Clifford algebras in general. Early encryption techniques such as the Hill cipher also used matrices. However, due to the linear nature of matrices, these codes are comparatively easy to break. Computer graphics uses matrices to represent objects; to calculate transformations of objects using affine rotation matrices to accomplish tasks such as projecting a three-dimensional object onto a two-dimensional screen, corresponding to a theoretical camera observation; and to apply image convolutions such as sharpening, blurring, edge detection, and more. Matrices over a polynomial ring are important in the study of control theory. Chemistry makes use of matrices in various ways, particularly since the use of quantum theory to discuss molecular bonding and spectroscopy. Examples are the overlap matrix and the Fock matrix used in solving the Roothaan equations to obtain the molecular orbitals of the Hartree–Fock method. === Graph theory === The adjacency matrix of a finite graph is a basic notion of graph theory. It records which vertices of the graph are connected by an edge. Matrices containing just two different values (1 and 0 meaning for example "yes" and "no", respectively) are called logical matrices. The distance (or cost) matrix contains information about the distances of the edges. These concepts can be applied to websites connected by hyperlinks, or cities connected by roads etc., in which case (unless the connection network is extremely dense) the matrices tend to be sparse, that is, contain few nonzero entries. Therefore, specifically tailored matrix algorithms can be used in network theory. === Analysis and geometry === The Hessian matrix of a differentiable function f : R n → R {\displaystyle f:\mathbb {R} ^{n}\to \mathbb {R} } consists of the second derivatives of ƒ concerning the several coordinate directions, that is, H ( f ) = [ ∂ 2 f ∂ x i ∂ x j ] . {\displaystyle H(f)=\left[{\frac {\partial ^{2}f}{\partial x_{i}\,\partial x_{j}}}\right].} It encodes information about the local growth behavior of the function: given a critical point x = (x1, ..., xn), that is, a point where the first partial derivatives ∂ f / ∂ x i {\displaystyle \partial f/\partial x_{i}} of f vanish, the function has a local minimum if the Hessian matrix is positive definite. Quadratic programming can be used to find global minima or maxima of quadratic functions closely related to the ones attached to matrices (see above). Another matrix frequently used in geometrical situations is the Jacobi matrix of a differentiable map f : R n → R m {\displaystyle f:\mathbb {R} ^{n}\to \mathbb {R} ^{m}} . If f1, ..., fm denote the components of f, then the Jacobi matrix is defined as J ( f ) = [ ∂ f i ∂ x j ] 1 ≤ i ≤ m , 1 ≤ j ≤ n . {\displaystyle J(f)=\left[{\frac {\partial f_{i}}{\partial x_{j}}}\right]_{1\leq i\leq m,1\leq j\leq n}.} If n > m, and if the rank of the Jacobi matrix attains its maximal value m, f is locally invertible at that point, by the implicit function theorem. Partial differential equations can be classified by considering the matrix of coefficients of the highest-order differential operators of the equation. For elliptic partial differential equations this matrix is positive definite, which has a decisive influence on the set of possible solutions of the equation in question. The finite element method is an important numerical method to solve partial differential equations, widely applied in simulating complex physical systems. It attempts to approximate the solution to some equation by piecewise linear functions, where the pieces are chosen concerning a sufficiently fine grid, which in turn can be recast as a matrix equation. === Probability theory and statistics === Stochastic matrices are square matrices whose rows are probability vectors, that is, whose entries are non-negative and sum up to one. Stochastic matrices are used to define Markov chains with finitely many states. A row of the stochastic matrix gives the probability distribution for the next position of some particle currently in the state that corresponds to the row. Properties of the Markov chain—like absorbing states, that is, states that any particle attains eventually—can be read off the eigenvectors of the transition matrices. Statistics also makes use of matrices in many different forms. Descriptive statistics is concerned with describing data sets, which can often be represented as data matrices, which may then be subjected to dimensionality reduction techniques. The covariance matrix encodes the mutual variance of several random variables. Another technique using matrices are linear least squares, a method that approximates a finite set of pairs (x1, y1), (x2, y2), ..., (xN, yN), by a linear function y i ≈ a x i + b , i = 1 , … , N {\displaystyle y_{i}\approx ax_{i}+b,\quad i=1,\ldots ,N} which can be formulated in terms of matrices, related to the singular value decomposition of matrices. Random matrices are matrices whose entries are random numbers, subject to suitable probability distributions, such as matrix normal distribution. Beyond probability theory, they are applied in domains ranging from number theory to physics. === Quantum mechanics and particle physics === The first model of quantum mechanics (Heisenberg, 1925) used infinite-dimensional matrices to define the operators that took over the role of variables like position, momentum and energy from classical physics. (This is sometimes referred to as matrix mechanics.) Matrices, both finite and infinite-dimensional, have since been employed for many purposes in quantum mechanics. One particular example is the density matrix, a tool used in calculating the probabilities of the outcomes of measurements performed on physical systems. Linear transformations and the associated symmetries play a key role in modern physics. For example, elementary particles in quantum field theory are classified as representations of the Lorentz group of special relativity and, more specifically, by their behavior under the spin group. Concrete representations involving the Pauli matrices and more general gamma matrices are an integral part of the physical description of fermions, which behave as spinors. For the three lightest quarks, there is a group-theoretical representation involving the special unitary group SU(3); for their calculations, physicists use a convenient matrix representation known as the Gell-Mann matrices, which are also used for the SU(3) gauge group that forms the basis of the modern description of strong nuclear interactions, quantum chromodynamics. The Cabibbo–Kobayashi–Maskawa matrix, in turn, expresses the fact that the basic quark states that are important for weak interactions are not the same as, but linearly related to the basic quark states that define particles with specific and distinct masses. Another matrix serves as a key tool for describing the scattering experiments that form the cornerstone of experimental particle physics: Collision reactions such as occur in particle accelerators, where non-interacting particles head towards each other and collide in a small interaction zone, with a new set of non-interacting particles as the result, can be described as the scalar product of outgoing particle states and a linear combination of ingoing particle states. The linear combination is given by a matrix known as the S-matrix, which encodes all information about the possible interactions between particles. === Normal modes === A general application of matrices in physics is the description of linearly coupled harmonic systems. The equations of motion of such systems can be described in matrix form, with a mass matrix multiplying a generalized velocity to give the kinetic term, and a force matrix multiplying a displacement vector to characterize the interactions. The best way to obtain solutions is to determine the system's eigenvectors, its normal modes, by diagonalizing the matrix equation. Techniques like this are crucial when it comes to the internal dynamics of molecules: the internal vibrations of systems consisting of mutually bound component atoms. They are also needed for describing mechanical vibrations, and oscillations in electrical circuits. === Geometrical optics === Geometrical optics provides further matrix applications. In this approximative theory, the wave nature of light is neglected. The result is a model in which light rays are indeed geometrical rays. If the deflection of light rays by optical elements is small, the action of a lens or reflective element on a given light ray can be expressed as multiplication of a two-component vector with a two-by-two matrix called ray transfer matrix analysis: the vector's components are the light ray's slope and its distance from the optical axis, while the matrix encodes the properties of the optical element. There are two kinds of matrices, viz. a refraction matrix describing the refraction at a lens surface, and a translation matrix, describing the translation of the plane of reference to the next refracting surface, where another refraction matrix applies. The optical system, consisting of a combination of lenses and/or reflective elements, is simply described by the matrix resulting from the product of the components' matrices. === Electronics === Electronic circuits that are composed of linear components (such as resistors, inductors and capacitors) obey Kirchhoff's circuit laws, which leads to a system of linear equations, which can be described with a matrix equation that relates the source currents and voltages to the resultant currents and voltages at each point in the circuit, and where the matrix entries are determined by the circuit. == History == Matrices have a long history of application in solving linear equations but they were known as arrays until the 1800s. The Chinese text The Nine Chapters on the Mathematical Art written in the 10th–2nd century BCE is the first example of the use of array methods to solve simultaneous equations, including the concept of determinants. In 1545 Italian mathematician Gerolamo Cardano introduced the method to Europe when he published Ars Magna. The Japanese mathematician Seki used the same array methods to solve simultaneous equations in 1683. The Dutch mathematician Jan de Witt represented transformations using arrays in his 1659 book Elements of Curves (1659). Between 1700 and 1710 Gottfried Wilhelm Leibniz publicized the use of arrays for recording information or solutions and experimented with over 50 different systems of arrays. Cramer presented his rule in 1750. The term "matrix" (Latin for "womb", "dam" (non-human female animal kept for breeding), "source", "origin", "list", and "register", are derived from mater—mother) was coined by James Joseph Sylvester in 1850, who understood a matrix as an object giving rise to several determinants today called minors, that is to say, determinants of smaller matrices that derive from the original one by removing columns and rows. In an 1851 paper, Sylvester explains: I have in previous papers defined a "Matrix" as a rectangular array of terms, out of which different systems of determinants may be engendered from the womb of a common parent. Arthur Cayley published a treatise on geometric transformations using matrices that were not rotated versions of the coefficients being investigated as had previously been done. Instead, he defined operations such as addition, subtraction, multiplication, and division as transformations of those matrices and showed the associative and distributive properties held. Cayley investigated and demonstrated the non-commutative property of matrix multiplication as well as the commutative property of matrix addition. Early matrix theory had limited the use of arrays almost exclusively to determinants and Arthur Cayley's abstract matrix operations were revolutionary. He was instrumental in proposing a matrix concept independent of equation systems. In 1858 Cayley published his A memoir on the theory of matrices in which he proposed and demonstrated the Cayley–Hamilton theorem. The English mathematician Cuthbert Edmund Cullis was the first to use modern bracket notation for matrices in 1913 and he simultaneously demonstrated the first significant use of the notation A = [ai,j] to represent a matrix where ai,j refers to the ith row and the jth column. The modern study of determinants sprang from several sources. Number-theoretical problems led Gauss to relate coefficients of quadratic forms, that is, expressions such as x2 + xy − 2y2, and linear maps in three dimensions to matrices. Eisenstein further developed these notions, including the remark that, in modern parlance, matrix products are non-commutative. Cauchy was the first to prove general statements about determinants, using as the definition of the determinant of a matrix A = [ai,j] the following: replace the powers ajk by aj,k in the polynomial a 1 a 2 ⋯ a n ∏ i < j ( a j − a i ) , {\displaystyle a_{1}a_{2}\cdots a_{n}\prod _{i<j}(a_{j}-a_{i}),} where ∏ {\displaystyle \textstyle \prod } denotes the product of the indicated terms. He also showed, in 1829, that the eigenvalues of symmetric matrices are real. Jacobi studied "functional determinants"—later called Jacobi determinants by Sylvester—which can be used to describe geometric transformations at a local (or infinitesimal) level, see above. Kronecker's Vorlesungen über die Theorie der Determinanten and Weierstrass's Zur Determinantentheorie, both published in 1903, first treated determinants axiomatically, as opposed to previous more concrete approaches such as the mentioned formula of Cauchy. At that point, determinants were firmly established. Many theorems were first established for small matrices only, for example, the Cayley–Hamilton theorem was proved for 2×2 matrices by Cayley in the aforementioned memoir, and by Hamilton for 4×4 matrices. Frobenius, working on bilinear forms, generalized the theorem to all dimensions (1898). Also at the end of the 19th century, the Gauss–Jordan elimination (generalizing a special case now known as Gauss elimination) was established by Wilhelm Jordan. In the early 20th century, matrices attained a central role in linear algebra, partially due to their use in the classification of the hypercomplex number systems of the previous century. The inception of matrix mechanics by Heisenberg, Born and Jordan led to studying matrices with infinitely many rows and columns. Later, von Neumann carried out the mathematical formulation of quantum mechanics, by further developing functional analytic notions such as linear operators on Hilbert spaces, which, very roughly speaking, correspond to Euclidean space, but with an infinity of independent directions. === Other historical usages of the word "matrix" in mathematics === The word has been used in unusual ways by at least two authors of historical importance. Bertrand Russell and Alfred North Whitehead in their Principia Mathematica (1910–1913) use the word "matrix" in the context of their axiom of reducibility. They proposed this axiom as a means to reduce any function to one of lower type, successively, so that at the "bottom" (0 order) the function is identical to its extension: Let us give the name of matrix to any function, of however many variables, that does not involve any apparent variables. Then, any possible function other than a matrix derives from a matrix using generalization, that is, by considering the proposition that the function in question is true with all possible values or with some value of one of the arguments, the other argument or arguments remaining undetermined. For example, a function Φ(x, y) of two variables x and y can be reduced to a collection of functions of a single variable, such as y, by "considering" the function for all possible values of "individuals" ai substituted in place of a variable x. And then the resulting collection of functions of the single variable y, that is, ∀ai: Φ(ai, y), can be reduced to a "matrix" of values by "considering" the function for all possible values of "individuals" bi substituted in place of variable y: ∀ b j ∀ a i : ϕ ( a i , b j ) . {\displaystyle \forall b_{j}\forall a_{i}\colon \phi (a_{i},b_{j}).} Alfred Tarski in his 1941 Introduction to Logic used the word "matrix" synonymously with the notion of truth table as used in mathematical logic. == See also == List of named matrices Gram–Schmidt process – Orthonormalization of a set of vectors Irregular matrix Matrix calculus – Specialized notation for multivariable calculus Matrix function – Function that maps matrices to matricesPages displaying short descriptions of redirect targets == Notes == == References == === Mathematical references === === Physics references === === Historical references === == Further reading == "Matrix", Encyclopedia of Mathematics, EMS Press, 2001 [1994] The Matrix Cookbook (PDF), retrieved 24 March 2014 Brookes, Mike (2005), The Matrix Reference Manual, London: Imperial College, archived from the original on 16 December 2008, retrieved 10 Dec 2008 == External links == MacTutor: Matrices and determinants Matrices and Linear Algebra on the Earliest Uses Pages Earliest Uses of Symbols for Matrices and Vectors
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Mathematics has no generally accepted definition. Different schools of thought, particularly in philosophy, have put forth radically different definitions. All are controversial. == Early definitions == Aristotle defined mathematics as: The science of quantity. In Aristotle's classification of the sciences, discrete quantities were studied by arithmetic, continuous quantities by geometry. Aristotle also thought that quantity alone does not distinguish mathematics from sciences like physics; in his view, abstraction and studying quantity as a property "separable in thought" from real instances set mathematics apart. Auguste Comte's definition tried to explain the role of mathematics in coordinating phenomena in all other fields: The science of indirect measurement. Auguste Comte 1851 The "indirectness" in Comte's definition refers to determining quantities that cannot be measured directly, such as the distance to planets or the size of atoms, by means of their relations to quantities that can be measured directly. == Greater abstraction and competing philosophical schools == The preceding kinds of definitions, which had prevailed since Aristotle's time, were abandoned in the 19th century as new branches of mathematics were developed, which bore no obvious relation to measurement or the physical world, such as group theory, projective geometry, and non-Euclidean geometry. Three leading types of definition of mathematics today are called logicist, intuitionist, and formalist, each reflecting a different philosophy of mathematics. Each has its own flaws, none has achieved mainstream consensus, and all three appear irreconcilable. === Logicism === With mathematicians pursuing greater rigor and more abstract foundations, some proposed defining mathematics purely in terms of deduction and logic: Mathematics is the science that draws necessary conclusions. Benjamin Peirce 1870 All Mathematics is Symbolic Logic. Bertrand Russell 1903 Peirce did not think that mathematics is the same as logic, since he thought mathematics makes only hypothetical assertions, not categorical ones. Russell's definition, on the other hand, expresses the logicist view without reservation. === Intuitionism === Rather than characterize mathematics by deductive logic, intuitionism views mathematics as primarily about the construction of ideas in the mind: The only possible foundation of mathematics must be sought in this construction under the obligation carefully to watch which constructions intuition allows and which not. L. E. J. Brouwer 1907 ... intuitionist mathematics is nothing more nor less than an investigation of the utmost limits which the intellect can attain in its self-unfolding. Arend Heyting 1968 Intuitionism sprang from the philosophy of mathematician L. E. J. Brouwer and also led to the development of a modified intuitionistic logic. As a result, intuitionism has generated some genuinely different results that, while coherent and valid, differ from some theorems grounded in classical logic. === Formalism === Formalism denies logical or intuitive meanings altogether, making the symbols and rules themselves the objects of study. A formalist definition: Mathematics is the science of formal systems. Haskell Curry 1951 === Other views === Still other definitions emphasize pattern, order, or structure. For example: Mathematics is the classification and study of all possible patterns. Walter Warwick Sawyer, 1955 Yet another approach makes abstraction the defining criterion: Mathematics is a broad-ranging field of study in which the properties and interactions of idealized objects are examined. == Contemporary general reference works == Most contemporary reference works define mathematics by summarizing its main topics and methods: The abstract science which investigates deductively the conclusions implicit in the elementary conceptions of spatial and numerical relations, and which includes as its main divisions geometry, arithmetic, and algebra. Oxford English Dictionary, 1933 The study of the measurement, properties, and relationships of quantities and sets, using numbers and symbols. American Heritage Dictionary, 2000 The science of structure, order, and relation that has evolved from elemental practices of counting, measuring, and describing the shapes of objects. Encyclopædia Britannica, 2006 == Playful, metaphorical, and poetic definitions == Bertrand Russell wrote this famous tongue-in-cheek definition, describing the way all terms in mathematics are ultimately defined by reference to undefined terms: The subject in which we never know what we are talking about, nor whether what we are saying is true. Bertrand Russell 1901 Many other attempts to characterize mathematics have led to humor or poetic prose: A mathematician is a blind man in a dark room looking for a black cat which isn't there. Charles Darwin A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas. G. H. Hardy, 1940 Mathematics is the art of giving the same name to different things. Henri Poincaré Mathematics is the science of skillful operations with concepts and rules invented just for this purpose. [this purpose being the skillful operation ....] Eugene Wigner Mathematics is not a book confined within a cover and bound between brazen clasps, whose contents it needs only patience to ransack; it is not a mine, whose treasures may take long to reduce into possession, but which fill only a limited number of veins and lodes; it is not a soil, whose fertility can be exhausted by the yield of successive harvests; it is not a continent or an ocean, whose area can be mapped out and its contour defined: it is limitless as that space which it finds too narrow for its aspirations; its possibilities are as infinite as the worlds which are forever crowding in and multiplying upon the astronomer's gaze; it is as incapable of being restricted within assigned boundaries or being reduced to definitions of permanent validity, as the consciousness of life, which seems to slumber in each monad, in every atom of matter, in each leaf and bud cell, and is forever ready to burst forth into new forms of vegetable and animal existence. James Joseph Sylvester What is mathematics? What is it for? What are mathematicians doing nowadays? Wasn't it all finished long ago? How many new numbers can you invent anyway? Is today's mathematics just a matter of huge calculations, with the mathematician as a kind of zookeeper, making sure the precious computers are fed and watered? If it's not, what is it other than the incomprehensible outpourings of superpowered brainboxes with their heads in the clouds and their feet dangling from the lofty balconies of their ivory towers? Mathematics is all of these, and none. Mostly, it's just different. It's not what you expect it to be, you turn your back for a moment and it's changed. It's certainly not just a fixed body of knowledge, its growth is not confined to inventing new numbers, and its hidden tendrils pervade every aspect of modern life. Ian Stewart == See also == Philosophy of mathematics Foundations of mathematics == References == == Further reading == Courant, Richard; Robbins, Herbert (1996), What Is Mathematics? (2nd ed.), Oxford University Press, ISBN 978-0-19-510519-3 Gowers, Timothy; Barrow-Green, June; Leader, Imre, eds. (2008), The Princeton Companion to Mathematics, Princeton University Press, ISBN 978-0-691-11880-2 Hersh, Reuben (1999), What is Mathematics, Really?, Oxford University Press, ISBN 978-0-19-513087-4 Paulos, John Allen (1991), "Beyond Numeracy", Nature, 359 (6394), Viking: 463–464, Bibcode:1992Natur.359..463B, doi:10.1038/359463b0, ISBN 978-0-670-83654-3, S2CID 30811417 Stewart, Ian (1996), From Here to Infinity, Oxford University Press, ISBN 978-0-19-283202-3
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In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational and real numbers. A field is thus a fundamental algebraic structure which is widely used in algebra, number theory, and many other areas of mathematics. The best known fields are the field of rational numbers, the field of real numbers and the field of complex numbers. Many other fields, such as fields of rational functions, algebraic function fields, algebraic number fields, and p-adic fields are commonly used and studied in mathematics, particularly in number theory and algebraic geometry. Most cryptographic protocols rely on finite fields, i.e., fields with finitely many elements. The theory of fields proves that angle trisection and squaring the circle cannot be done with a compass and straightedge. Galois theory, devoted to understanding the symmetries of field extensions, provides an elegant proof of the Abel–Ruffini theorem that general quintic equations cannot be solved in radicals. Fields serve as foundational notions in several mathematical domains. This includes different branches of mathematical analysis, which are based on fields with additional structure. Basic theorems in analysis hinge on the structural properties of the field of real numbers. Most importantly for algebraic purposes, any field may be used as the scalars for a vector space, which is the standard general context for linear algebra. Number fields, the siblings of the field of rational numbers, are studied in depth in number theory. Function fields can help describe properties of geometric objects. == Definition == Informally, a field is a set, along with two operations defined on that set: an addition operation a + b and a multiplication operation a ⋅ b, both of which behave similarly as they do for rational numbers and real numbers. This includes the existence of an additive inverse −a for all elements a and of a multiplicative inverse b−1 for every nonzero element b. This allows the definition of the so-called inverse operations, subtraction a − b and division a / b, as a − b = a + (−b) and a / b = a ⋅ b−1. Often the product a ⋅ b is represented by juxtaposition, as ab. === Classic definition === Formally, a field is a set F together with two binary operations on F called addition and multiplication. A binary operation on F is a mapping F × F → F, that is, a correspondence that associates with each ordered pair of elements of F a uniquely determined element of F. The result of the addition of a and b is called the sum of a and b, and is denoted a + b. Similarly, the result of the multiplication of a and b is called the product of a and b, and is denoted a ⋅ b. These operations are required to satisfy the following properties, referred to as field axioms. These axioms are required to hold for all elements a, b, c of the field F: Associativity of addition and multiplication: a + (b + c) = (a + b) + c, and a ⋅ (b ⋅ c) = (a ⋅ b) ⋅ c. Commutativity of addition and multiplication: a + b = b + a, and a ⋅ b = b ⋅ a. Additive and multiplicative identity: there exist two distinct elements 0 and 1 in F such that a + 0 = a and a ⋅ 1 = a. Additive inverses: for every a in F, there exists an element in F, denoted −a, called the additive inverse of a, such that a + (−a) = 0. Multiplicative inverses: for every a ≠ 0 in F, there exists an element in F, denoted by a−1 or 1/a, called the multiplicative inverse of a, such that a ⋅ a−1 = 1. Distributivity of multiplication over addition: a ⋅ (b + c) = (a ⋅ b) + (a ⋅ c). An equivalent, and more succinct, definition is: a field has two commutative operations, called addition and multiplication; it is a group under addition with 0 as the additive identity; the nonzero elements form a group under multiplication with 1 as the multiplicative identity; and multiplication distributes over addition. Even more succinctly: a field is a commutative ring where 0 ≠ 1 and all nonzero elements are invertible under multiplication. === Alternative definition === Fields can also be defined in different, but equivalent ways. One can alternatively define a field by four binary operations (addition, subtraction, multiplication, and division) and their required properties. Division by zero is, by definition, excluded. In order to avoid existential quantifiers, fields can be defined by two binary operations (addition and multiplication), two unary operations (yielding the additive and multiplicative inverses respectively), and two nullary operations (the constants 0 and 1). These operations are then subject to the conditions above. Avoiding existential quantifiers is important in constructive mathematics and computing. One may equivalently define a field by the same two binary operations, one unary operation (the multiplicative inverse), and two (not necessarily distinct) constants 1 and −1, since 0 = 1 + (−1) and −a = (−1)a. == Examples == === Rational numbers === Rational numbers have been widely used a long time before the elaboration of the concept of field. They are numbers that can be written as fractions a/b, where a and b are integers, and b ≠ 0. The additive inverse of such a fraction is −a/b, and the multiplicative inverse (provided that a ≠ 0) is b/a, which can be seen as follows: b a ⋅ a b = b a a b = 1. {\displaystyle {\frac {b}{a}}\cdot {\frac {a}{b}}={\frac {ba}{ab}}=1.} The abstractly required field axioms reduce to standard properties of rational numbers. For example, the law of distributivity can be proven as follows: a b ⋅ ( c d + e f ) = a b ⋅ ( c d ⋅ f f + e f ⋅ d d ) = a b ⋅ ( c f d f + e d f d ) = a b ⋅ c f + e d d f = a ( c f + e d ) b d f = a c f b d f + a e d b d f = a c b d + a e b f = a b ⋅ c d + a b ⋅ e f . {\displaystyle {\begin{aligned}&{\frac {a}{b}}\cdot \left({\frac {c}{d}}+{\frac {e}{f}}\right)\\[6pt]={}&{\frac {a}{b}}\cdot \left({\frac {c}{d}}\cdot {\frac {f}{f}}+{\frac {e}{f}}\cdot {\frac {d}{d}}\right)\\[6pt]={}&{\frac {a}{b}}\cdot \left({\frac {cf}{df}}+{\frac {ed}{fd}}\right)={\frac {a}{b}}\cdot {\frac {cf+ed}{df}}\\[6pt]={}&{\frac {a(cf+ed)}{bdf}}={\frac {acf}{bdf}}+{\frac {aed}{bdf}}={\frac {ac}{bd}}+{\frac {ae}{bf}}\\[6pt]={}&{\frac {a}{b}}\cdot {\frac {c}{d}}+{\frac {a}{b}}\cdot {\frac {e}{f}}.\end{aligned}}} === Real and complex numbers === The real numbers R, with the usual operations of addition and multiplication, also form a field. The complex numbers C consist of expressions a + bi, with a, b real, where i is the imaginary unit, i.e., a (non-real) number satisfying i2 = −1. Addition and multiplication of real numbers are defined in such a way that expressions of this type satisfy all field axioms and thus hold for C. For example, the distributive law enforces (a + bi)(c + di) = ac + bci + adi + bdi2 = (ac − bd) + (bc + ad)i. It is immediate that this is again an expression of the above type, and so the complex numbers form a field. Complex numbers can be geometrically represented as points in the plane, with Cartesian coordinates given by the real numbers of their describing expression, or as the arrows from the origin to these points, specified by their length and an angle enclosed with some distinct direction. Addition then corresponds to combining the arrows to the intuitive parallelogram (adding the Cartesian coordinates), and the multiplication is – less intuitively – combining rotating and scaling of the arrows (adding the angles and multiplying the lengths). The fields of real and complex numbers are used throughout mathematics, physics, engineering, statistics, and many other scientific disciplines. === Constructible numbers === In antiquity, several geometric problems concerned the (in)feasibility of constructing certain numbers with compass and straightedge. For example, it was unknown to the Greeks that it is, in general, impossible to trisect a given angle in this way. These problems can be settled using the field of constructible numbers. Real constructible numbers are, by definition, lengths of line segments that can be constructed from the points 0 and 1 in finitely many steps using only compass and straightedge. These numbers, endowed with the field operations of real numbers, restricted to the constructible numbers, form a field, which properly includes the field Q of rational numbers. The illustration shows the construction of square roots of constructible numbers, not necessarily contained within Q. Using the labeling in the illustration, construct the segments AB, BD, and a semicircle over AD (center at the midpoint C), which intersects the perpendicular line through B in a point F, at a distance of exactly h = p {\displaystyle h={\sqrt {p}}} from B when BD has length one. Not all real numbers are constructible. It can be shown that 2 3 {\displaystyle {\sqrt[{3}]{2}}} is not a constructible number, which implies that it is impossible to construct with compass and straightedge the length of the side of a cube with volume 2, another problem posed by the ancient Greeks. === A field with four elements === In addition to familiar number systems such as the rationals, there are other, less immediate examples of fields. The following example is a field consisting of four elements called O, I, A, and B. The notation is chosen such that O plays the role of the additive identity element (denoted 0 in the axioms above), and I is the multiplicative identity (denoted 1 in the axioms above). The field axioms can be verified by using some more field theory, or by direct computation. For example, A ⋅ (B + A) = A ⋅ I = A, which equals A ⋅ B + A ⋅ A = I + B = A, as required by the distributivity. This field is called a finite field or Galois field with four elements, and is denoted F4 or GF(4). The subset consisting of O and I (highlighted in red in the tables at the right) is also a field, known as the binary field F2 or GF(2). == Elementary notions == In this section, F denotes an arbitrary field and a and b are arbitrary elements of F. === Consequences of the definition === One has a ⋅ 0 = 0 and −a = (−1) ⋅ a. In particular, one may deduce the additive inverse of every element as soon as one knows −1. If ab = 0 then a or b must be 0, since, if a ≠ 0, then b = (a−1a)b = a−1(ab) = a−1 ⋅ 0 = 0. This means that every field is an integral domain. In addition, the following properties are true for any elements a and b: −0 = 0 1−1 = 1 (−(−a)) = a (−a) ⋅ b = a ⋅ (−b) = −(a ⋅ b) (a−1)−1 = a if a ≠ 0 === Additive and multiplicative groups of a field === The axioms of a field F imply that it is an abelian group under addition. This group is called the additive group of the field, and is sometimes denoted by (F, +) when denoting it simply as F could be confusing. Similarly, the nonzero elements of F form an abelian group under multiplication, called the multiplicative group, and denoted by ( F ∖ { 0 } , ⋅ ) {\displaystyle (F\smallsetminus \{0\},\cdot )} or just F ∖ { 0 } {\displaystyle F\smallsetminus \{0\}} , or F×. A field may thus be defined as set F equipped with two operations denoted as an addition and a multiplication such that F is an abelian group under addition, F ∖ { 0 } {\displaystyle F\smallsetminus \{0\}} is an abelian group under multiplication (where 0 is the identity element of the addition), and multiplication is distributive over addition. Some elementary statements about fields can therefore be obtained by applying general facts of groups. For example, the additive and multiplicative inverses −a and a−1 are uniquely determined by a. The requirement 1 ≠ 0 is imposed by convention to exclude the trivial ring, which consists of a single element; this guides any choice of the axioms that define fields. Every finite subgroup of the multiplicative group of a field is cyclic (see Root of unity § Cyclic groups). === Characteristic === In addition to the multiplication of two elements of F, it is possible to define the product n ⋅ a of an arbitrary element a of F by a positive integer n to be the n-fold sum a + a + ... + a (which is an element of F.) If there is no positive integer such that n ⋅ 1 = 0, then F is said to have characteristic 0. For example, the field of rational numbers Q has characteristic 0 since no positive integer n is zero. Otherwise, if there is a positive integer n satisfying this equation, the smallest such positive integer can be shown to be a prime number. It is usually denoted by p and the field is said to have characteristic p then. For example, the field F4 has characteristic 2 since (in the notation of the above addition table) I + I = O. If F has characteristic p, then p ⋅ a = 0 for all a in F. This implies that (a + b)p = ap + bp, since all other binomial coefficients appearing in the binomial formula are divisible by p. Here, ap := a ⋅ a ⋅ ⋯ ⋅ a (p factors) is the pth power, i.e., the p-fold product of the element a. Therefore, the Frobenius map F → F : x ↦ xp is compatible with the addition in F (and also with the multiplication), and is therefore a field homomorphism. The existence of this homomorphism makes fields in characteristic p quite different from fields of characteristic 0. === Subfields and prime fields === A subfield E of a field F is a subset of F that is a field with respect to the field operations of F. Equivalently E is a subset of F that contains 1, and is closed under addition, multiplication, additive inverse and multiplicative inverse of a nonzero element. This means that 1 ∊ E, that for all a, b ∊ E both a + b and a ⋅ b are in E, and that for all a ≠ 0 in E, both −a and 1/a are in E. Field homomorphisms are maps φ: E → F between two fields such that φ(e1 + e2) = φ(e1) + φ(e2), φ(e1e2) = φ(e1) φ(e2), and φ(1E) = 1F, where e1 and e2 are arbitrary elements of E. All field homomorphisms are injective. If φ is also surjective, it is called an isomorphism (or the fields E and F are called isomorphic). A field is called a prime field if it has no proper (i.e., strictly smaller) subfields. Any field F contains a prime field. If the characteristic of F is p (a prime number), the prime field is isomorphic to the finite field Fp introduced below. Otherwise the prime field is isomorphic to Q. == Finite fields == Finite fields (also called Galois fields) are fields with finitely many elements, whose number is also referred to as the order of the field. The above introductory example F4 is a field with four elements. Its subfield F2 is the smallest field, because by definition a field has at least two distinct elements, 0 and 1. The simplest finite fields, with prime order, are most directly accessible using modular arithmetic. For a fixed positive integer n, arithmetic "modulo n" means to work with the numbers Z/nZ = {0, 1, ..., n − 1}. The addition and multiplication on this set are done by performing the operation in question in the set Z of integers, dividing by n and taking the remainder as result. This construction yields a field precisely if n is a prime number. For example, taking the prime n = 2 results in the above-mentioned field F2. For n = 4 and more generally, for any composite number (i.e., any number n which can be expressed as a product n = r ⋅ s of two strictly smaller natural numbers), Z/nZ is not a field: the product of two non-zero elements is zero since r ⋅ s = 0 in Z/nZ, which, as was explained above, prevents Z/nZ from being a field. The field Z/pZ with p elements (p being prime) constructed in this way is usually denoted by Fp. Every finite field F has q = pn elements, where p is prime and n ≥ 1. This statement holds since F may be viewed as a vector space over its prime field. The dimension of this vector space is necessarily finite, say n, which implies the asserted statement. A field with q = pn elements can be constructed as the splitting field of the polynomial f(x) = xq − x. Such a splitting field is an extension of Fp in which the polynomial f has q zeros. This means f has as many zeros as possible since the degree of f is q. For q = 22 = 4, it can be checked case by case using the above multiplication table that all four elements of F4 satisfy the equation x4 = x, so they are zeros of f. By contrast, in F2, f has only two zeros (namely 0 and 1), so f does not split into linear factors in this smaller field. Elaborating further on basic field-theoretic notions, it can be shown that two finite fields with the same order are isomorphic. It is thus customary to speak of the finite field with q elements, denoted by Fq or GF(q). == History == Historically, three algebraic disciplines led to the concept of a field: the question of solving polynomial equations, algebraic number theory, and algebraic geometry. A first step towards the notion of a field was made in 1770 by Joseph-Louis Lagrange, who observed that permuting the zeros x1, x2, x3 of a cubic polynomial in the expression (x1 + ωx2 + ω2x3)3 (with ω being a third root of unity) only yields two values. This way, Lagrange conceptually explained the classical solution method of Scipione del Ferro and François Viète, which proceeds by reducing a cubic equation for an unknown x to a quadratic equation for x3. Together with a similar observation for equations of degree 4, Lagrange thus linked what eventually became the concept of fields and the concept of groups. Vandermonde, also in 1770, and to a fuller extent, Carl Friedrich Gauss, in his Disquisitiones Arithmeticae (1801), studied the equation x p = 1 for a prime p and, again using modern language, the resulting cyclic Galois group. Gauss deduced that a regular p-gon can be constructed if p = 22k + 1. Building on Lagrange's work, Paolo Ruffini claimed (1799) that quintic equations (polynomial equations of degree 5) cannot be solved algebraically; however, his arguments were flawed. These gaps were filled by Niels Henrik Abel in 1824. Évariste Galois, in 1832, devised necessary and sufficient criteria for a polynomial equation to be algebraically solvable, thus establishing in effect what is known as Galois theory today. Both Abel and Galois worked with what is today called an algebraic number field, but conceived neither an explicit notion of a field, nor of a group. In 1871 Richard Dedekind introduced, for a set of real or complex numbers that is closed under the four arithmetic operations, the German word Körper, which means "body" or "corpus" (to suggest an organically closed entity). The English term "field" was introduced by Moore (1893). By a field we will mean every infinite system of real or complex numbers so closed in itself and perfect that addition, subtraction, multiplication, and division of any two of these numbers again yields a number of the system. In 1881 Leopold Kronecker defined what he called a domain of rationality, which is a field of rational fractions in modern terms. Kronecker's notion did not cover the field of all algebraic numbers (which is a field in Dedekind's sense), but on the other hand was more abstract than Dedekind's in that it made no specific assumption on the nature of the elements of a field. Kronecker interpreted a field such as Q(π) abstractly as the rational function field Q(X). Prior to this, examples of transcendental numbers were known since Joseph Liouville's work in 1844, until Charles Hermite (1873) and Ferdinand von Lindemann (1882) proved the transcendence of e and π, respectively. The first clear definition of an abstract field is due to Weber (1893). In particular, Heinrich Martin Weber's notion included the field Fp. Giuseppe Veronese (1891) studied the field of formal power series, which led Hensel (1904) to introduce the field of p-adic numbers. Steinitz (1910) synthesized the knowledge of abstract field theory accumulated so far. He axiomatically studied the properties of fields and defined many important field-theoretic concepts. The majority of the theorems mentioned in the sections Galois theory, Constructing fields and Elementary notions can be found in Steinitz's work. Artin & Schreier (1927) linked the notion of orderings in a field, and thus the area of analysis, to purely algebraic properties. Emil Artin redeveloped Galois theory from 1928 through 1942, eliminating the dependency on the primitive element theorem. == Constructing fields == === Constructing fields from rings === A commutative ring is a set that is equipped with an addition and multiplication operation and satisfies all the axioms of a field, except for the existence of multiplicative inverses a−1. For example, the integers Z form a commutative ring, but not a field: the reciprocal of an integer n is not itself an integer, unless n = ±1. In the hierarchy of algebraic structures fields can be characterized as the commutative rings R in which every nonzero element is a unit (which means every element is invertible). Similarly, fields are the commutative rings with precisely two distinct ideals, (0) and R. Fields are also precisely the commutative rings in which (0) is the only prime ideal. Given a commutative ring R, there are two ways to construct a field related to R, i.e., two ways of modifying R such that all nonzero elements become invertible: forming the field of fractions, and forming residue fields. The field of fractions of Z is Q, the rationals, while the residue fields of Z are the finite fields Fp. ==== Field of fractions ==== Given an integral domain R, its field of fractions Q(R) is built with the fractions of two elements of R exactly as Q is constructed from the integers. More precisely, the elements of Q(R) are the fractions a/b where a and b are in R, and b ≠ 0. Two fractions a/b and c/d are equal if and only if ad = bc. The operation on the fractions work exactly as for rational numbers. For example, a b + c d = a d + b c b d . {\displaystyle {\frac {a}{b}}+{\frac {c}{d}}={\frac {ad+bc}{bd}}.} It is straightforward to show that, if the ring is an integral domain, the set of the fractions form a field. The field F(x) of the rational fractions over a field (or an integral domain) F is the field of fractions of the polynomial ring F[x]. The field F((x)) of Laurent series ∑ i = k ∞ a i x i ( k ∈ Z , a i ∈ F ) {\displaystyle \sum _{i=k}^{\infty }a_{i}x^{i}\ (k\in \mathbb {Z} ,a_{i}\in F)} over a field F is the field of fractions of the ring F[[x]] of formal power series (in which k ≥ 0). Since any Laurent series is a fraction of a power series divided by a power of x (as opposed to an arbitrary power series), the representation of fractions is less important in this situation, though. ==== Residue fields ==== In addition to the field of fractions, which embeds R injectively into a field, a field can be obtained from a commutative ring R by means of a surjective map onto a field F. Any field obtained in this way is a quotient R / m, where m is a maximal ideal of R. If R has only one maximal ideal m, this field is called the residue field of R. The ideal generated by a single polynomial f in the polynomial ring R = E[X] (over a field E) is maximal if and only if f is irreducible in E, i.e., if f cannot be expressed as the product of two polynomials in E[X] of smaller degree. This yields a field F = E[X] / (f(X)). This field F contains an element x (namely the residue class of X) which satisfies the equation f(x) = 0. For example, C is obtained from R by adjoining the imaginary unit symbol i, which satisfies f(i) = 0, where f(X) = X2 + 1. Moreover, f is irreducible over R, which implies that the map that sends a polynomial f(X) ∊ R[X] to f(i) yields an isomorphism R [ X ] / ( X 2 + 1 ) ⟶ ≅ C . {\displaystyle \mathbf {R} [X]/\left(X^{2}+1\right)\ {\stackrel {\cong }{\longrightarrow }}\ \mathbf {C} .} === Constructing fields within a bigger field === Fields can be constructed inside a given bigger container field. Suppose given a field E, and a field F containing E as a subfield. For any element x of F, there is a smallest subfield of F containing E and x, called the subfield of F generated by x and denoted E(x). The passage from E to E(x) is referred to by adjoining an element to E. More generally, for a subset S ⊂ F, there is a minimal subfield of F containing E and S, denoted by E(S). The compositum of two subfields E and E′ of some field F is the smallest subfield of F containing both E and E′. The compositum can be used to construct the biggest subfield of F satisfying a certain property, for example the biggest subfield of F, which is, in the language introduced below, algebraic over E. === Field extensions === The notion of a subfield E ⊂ F can also be regarded from the opposite point of view, by referring to F being a field extension (or just extension) of E, denoted by F / E, and read "F over E". A basic datum of a field extension is its degree [F : E], i.e., the dimension of F as an E-vector space. It satisfies the formula [G : E] = [G : F] [F : E]. Extensions whose degree is finite are referred to as finite extensions. The extensions C / R and F4 / F2 are of degree 2, whereas R / Q is an infinite extension. ==== Algebraic extensions ==== A pivotal notion in the study of field extensions F / E are algebraic elements. An element x ∈ F is algebraic over E if it is a root of a polynomial with coefficients in E, that is, if it satisfies a polynomial equation en xn + en−1xn−1 + ⋯ + e1x + e0 = 0, with en, ..., e0 in E, and en ≠ 0. For example, the imaginary unit i in C is algebraic over R, and even over Q, since it satisfies the equation i2 + 1 = 0. A field extension in which every element of F is algebraic over E is called an algebraic extension. Any finite extension is necessarily algebraic, as can be deduced from the above multiplicativity formula. The subfield E(x) generated by an element x, as above, is an algebraic extension of E if and only if x is an algebraic element. That is to say, if x is algebraic, all other elements of E(x) are necessarily algebraic as well. Moreover, the degree of the extension E(x) / E, i.e., the dimension of E(x) as an E-vector space, equals the minimal degree n such that there is a polynomial equation involving x, as above. If this degree is n, then the elements of E(x) have the form ∑ k = 0 n − 1 a k x k , a k ∈ E . {\displaystyle \sum _{k=0}^{n-1}a_{k}x^{k},\ \ a_{k}\in E.} For example, the field Q(i) of Gaussian rationals is the subfield of C consisting of all numbers of the form a + bi where both a and b are rational numbers: summands of the form i2 (and similarly for higher exponents) do not have to be considered here, since a + bi + ci2 can be simplified to a − c + bi. ==== Transcendence bases ==== The above-mentioned field of rational fractions E(X), where X is an indeterminate, is not an algebraic extension of E since there is no polynomial equation with coefficients in E whose zero is X. Elements, such as X, which are not algebraic are called transcendental. Informally speaking, the indeterminate X and its powers do not interact with elements of E. A similar construction can be carried out with a set of indeterminates, instead of just one. Once again, the field extension E(x) / E discussed above is a key example: if x is not algebraic (i.e., x is not a root of a polynomial with coefficients in E), then E(x) is isomorphic to E(X). This isomorphism is obtained by substituting x to X in rational fractions. A subset S of a field F is a transcendence basis if it is algebraically independent (do not satisfy any polynomial relations) over E and if F is an algebraic extension of E(S). Any field extension F / E has a transcendence basis. Thus, field extensions can be split into ones of the form E(S) / E (purely transcendental extensions) and algebraic extensions. === Closure operations === A field is algebraically closed if it does not have any strictly bigger algebraic extensions or, equivalently, if any polynomial equation fn xn + fn−1xn−1 + ⋯ + f1x + f0 = 0, with coefficients fn, ..., f0 ∈ F, n > 0, has a solution x ∊ F. By the fundamental theorem of algebra, C is algebraically closed, i.e., any polynomial equation with complex coefficients has a complex solution. The rational and the real numbers are not algebraically closed since the equation x2 + 1 = 0 does not have any rational or real solution. A field containing F is called an algebraic closure of F if it is algebraic over F (roughly speaking, not too big compared to F) and is algebraically closed (big enough to contain solutions of all polynomial equations). By the above, C is an algebraic closure of R. The situation that the algebraic closure is a finite extension of the field F is quite special: by the Artin–Schreier theorem, the degree of this extension is necessarily 2, and F is elementarily equivalent to R. Such fields are also known as real closed fields. Any field F has an algebraic closure, which is moreover unique up to (non-unique) isomorphism. It is commonly referred to as the algebraic closure and denoted F. For example, the algebraic closure Q of Q is called the field of algebraic numbers. The field F is usually rather implicit since its construction requires the ultrafilter lemma, a set-theoretic axiom that is weaker than the axiom of choice. In this regard, the algebraic closure of Fq, is exceptionally simple. It is the union of the finite fields containing Fq (the ones of order qn). For any algebraically closed field F of characteristic 0, the algebraic closure of the field F((t)) of Laurent series is the field of Puiseux series, obtained by adjoining roots of t. == Fields with additional structure == Since fields are ubiquitous in mathematics and beyond, several refinements of the concept have been adapted to the needs of particular mathematical areas. === Ordered fields === A field F is called an ordered field if any two elements can be compared, so that x + y ≥ 0 and xy ≥ 0 whenever x ≥ 0 and y ≥ 0. For example, the real numbers form an ordered field, with the usual ordering ≥. The Artin–Schreier theorem states that a field can be ordered if and only if it is a formally real field, which means that any quadratic equation x 1 2 + x 2 2 + ⋯ + x n 2 = 0 {\displaystyle x_{1}^{2}+x_{2}^{2}+\dots +x_{n}^{2}=0} only has the solution x1 = x2 = ⋯ = xn = 0. The set of all possible orders on a fixed field F is isomorphic to the set of ring homomorphisms from the Witt ring W(F) of quadratic forms over F, to Z. An Archimedean field is an ordered field such that for each element there exists a finite expression 1 + 1 + ⋯ + 1 whose value is greater than that element, that is, there are no infinite elements. Equivalently, the field contains no infinitesimals (elements smaller than all rational numbers); or, yet equivalent, the field is isomorphic to a subfield of R. An ordered field is Dedekind-complete if all upper bounds, lower bounds (see Dedekind cut) and limits, which should exist, do exist. More formally, each bounded subset of F is required to have a least upper bound. Any complete field is necessarily Archimedean, since in any non-Archimedean field there is neither a greatest infinitesimal nor a least positive rational, whence the sequence 1/2, 1/3, 1/4, ..., every element of which is greater than every infinitesimal, has no limit. Since every proper subfield of the reals also contains such gaps, R is the unique complete ordered field, up to isomorphism. Several foundational results in calculus follow directly from this characterization of the reals. The hyperreals R* form an ordered field that is not Archimedean. It is an extension of the reals obtained by including infinite and infinitesimal numbers. These are larger, respectively smaller than any real number. The hyperreals form the foundational basis of non-standard analysis. === Topological fields === Another refinement of the notion of a field is a topological field, in which the set F is a topological space, such that all operations of the field (addition, multiplication, the maps a ↦ −a and a ↦ a−1) are continuous maps with respect to the topology of the space. The topology of all the fields discussed below is induced from a metric, i.e., a function d : F × F → R, that measures a distance between any two elements of F. The completion of F is another field in which, informally speaking, the "gaps" in the original field F are filled, if there are any. For example, any irrational number x, such as x = √2, is a "gap" in the rationals Q in the sense that it is a real number that can be approximated arbitrarily closely by rational numbers p/q, in the sense that distance of x and p/q given by the absolute value |x − p/q| is as small as desired. The following table lists some examples of this construction. The fourth column shows an example of a zero sequence, i.e., a sequence whose limit (for n → ∞) is zero. The field Qp is used in number theory and p-adic analysis. The algebraic closure Qp carries a unique norm extending the one on Qp, but is not complete. The completion of this algebraic closure, however, is algebraically closed. Because of its rough analogy to the complex numbers, it is sometimes called the field of complex p-adic numbers and is denoted by Cp. ==== Local fields ==== The following topological fields are called local fields: finite extensions of Qp (local fields of characteristic zero) finite extensions of Fp((t)), the field of Laurent series over Fp (local fields of characteristic p). These two types of local fields share some fundamental similarities. In this relation, the elements p ∈ Qp and t ∈ Fp((t)) (referred to as uniformizer) correspond to each other. The first manifestation of this is at an elementary level: the elements of both fields can be expressed as power series in the uniformizer, with coefficients in Fp. (However, since the addition in Qp is done using carrying, which is not the case in Fp((t)), these fields are not isomorphic.) The following facts show that this superficial similarity goes much deeper: Any first-order statement that is true for almost all Qp is also true for almost all Fp((t)). An application of this is the Ax–Kochen theorem describing zeros of homogeneous polynomials in Qp. Tamely ramified extensions of both fields are in bijection to one another. Adjoining arbitrary p-power roots of p (in Qp), respectively of t (in Fp((t))), yields (infinite) extensions of these fields known as perfectoid fields. Strikingly, the Galois groups of these two fields are isomorphic, which is the first glimpse of a remarkable parallel between these two fields: Gal ( Q p ( p 1 / p ∞ ) ) ≅ Gal ( F p ( ( t ) ) ( t 1 / p ∞ ) ) . {\displaystyle \operatorname {Gal} \left(\mathbf {Q} _{p}\left(p^{1/p^{\infty }}\right)\right)\cong \operatorname {Gal} \left(\mathbf {F} _{p}((t))\left(t^{1/p^{\infty }}\right)\right).} === Differential fields === Differential fields are fields equipped with a derivation, i.e., allow to take derivatives of elements in the field. For example, the field R(X), together with the standard derivative of polynomials forms a differential field. These fields are central to differential Galois theory, a variant of Galois theory dealing with linear differential equations. == Galois theory == Galois theory studies algebraic extensions of a field by studying the symmetry in the arithmetic operations of addition and multiplication. An important notion in this area is that of finite Galois extensions F / E, which are, by definition, those that are separable and normal. The primitive element theorem shows that finite separable extensions are necessarily simple, i.e., of the form F = E[X] / f(X), where f is an irreducible polynomial (as above). For such an extension, being normal and separable means that all zeros of f are contained in F and that f has only simple zeros. The latter condition is always satisfied if E has characteristic 0. For a finite Galois extension, the Galois group Gal(F/E) is the group of field automorphisms of F that are trivial on E (i.e., the bijections σ : F → F that preserve addition and multiplication and that send elements of E to themselves). The importance of this group stems from the fundamental theorem of Galois theory, which constructs an explicit one-to-one correspondence between the set of subgroups of Gal(F/E) and the set of intermediate extensions of the extension F/E. By means of this correspondence, group-theoretic properties translate into facts about fields. For example, if the Galois group of a Galois extension as above is not solvable (cannot be built from abelian groups), then the zeros of f cannot be expressed in terms of addition, multiplication, and radicals, i.e., expressions involving n {\displaystyle {\sqrt[{n}]{~}}} . For example, the symmetric groups Sn is not solvable for n ≥ 5. Consequently, as can be shown, the zeros of the following polynomials are not expressible by sums, products, and radicals. For the latter polynomial, this fact is known as the Abel–Ruffini theorem: f(X) = X5 − 4X + 2 (and E = Q), f(X) = Xn + an−1Xn−1 + ⋯ + a0 (where f is regarded as a polynomial in E(a0, ..., an−1), for some indeterminates ai, E is any field, and n ≥ 5). The tensor product of fields is not usually a field. For example, a finite extension F / E of degree n is a Galois extension if and only if there is an isomorphism of F-algebras F ⊗E F ≅ Fn. This fact is the beginning of Grothendieck's Galois theory, a far-reaching extension of Galois theory applicable to algebro-geometric objects. == Invariants of fields == Basic invariants of a field F include the characteristic and the transcendence degree of F over its prime field. The latter is defined as the maximal number of elements in F that are algebraically independent over the prime field. Two algebraically closed fields E and F are isomorphic precisely if these two data agree. This implies that any two uncountable algebraically closed fields of the same cardinality and the same characteristic are isomorphic. For example, Qp, Cp and C are isomorphic (but not isomorphic as topological fields). === Model theory of fields === In model theory, a branch of mathematical logic, two fields E and F are called elementarily equivalent if every mathematical statement that is true for E is also true for F and conversely. The mathematical statements in question are required to be first-order sentences (involving 0, 1, the addition and multiplication). A typical example, for n > 0, n an integer, is φ(E) = "any polynomial of degree n in E has a zero in E" The set of such formulas for all n expresses that E is algebraically closed. The Lefschetz principle states that C is elementarily equivalent to any algebraically closed field F of characteristic zero. Moreover, any fixed statement φ holds in C if and only if it holds in any algebraically closed field of sufficiently high characteristic. If U is an ultrafilter on a set I, and Fi is a field for every i in I, the ultraproduct of the Fi with respect to U is a field. It is denoted by ulimi→∞ Fi, since it behaves in several ways as a limit of the fields Fi: Łoś's theorem states that any first order statement that holds for all but finitely many Fi, also holds for the ultraproduct. Applied to the above sentence φ, this shows that there is an isomorphism ulim p → ∞ F ¯ p ≅ C . {\displaystyle \operatorname {ulim} _{p\to \infty }{\overline {\mathbf {F} }}_{p}\cong \mathbf {C} .} The Ax–Kochen theorem mentioned above also follows from this and an isomorphism of the ultraproducts (in both cases over all primes p) ulimp Qp ≅ ulimp Fp((t)). In addition, model theory also studies the logical properties of various other types of fields, such as real closed fields or exponential fields (which are equipped with an exponential function exp : F → F×). === Absolute Galois group === For fields that are not algebraically closed (or not separably closed), the absolute Galois group Gal(F) is fundamentally important: extending the case of finite Galois extensions outlined above, this group governs all finite separable extensions of F. By elementary means, the group Gal(Fq) can be shown to be the Prüfer group, the profinite completion of Z. This statement subsumes the fact that the only algebraic extensions of Gal(Fq) are the fields Gal(Fqn) for n > 0, and that the Galois groups of these finite extensions are given by Gal(Fqn / Fq) = Z/nZ. A description in terms of generators and relations is also known for the Galois groups of p-adic number fields (finite extensions of Qp). Representations of Galois groups and of related groups such as the Weil group are fundamental in many branches of arithmetic, such as the Langlands program. The cohomological study of such representations is done using Galois cohomology. For example, the Brauer group, which is classically defined as the group of central simple F-algebras, can be reinterpreted as a Galois cohomology group, namely Br(F) = H2(F, Gm). === K-theory === Milnor K-theory is defined as K n M ( F ) = F × ⊗ ⋯ ⊗ F × / ⟨ x ⊗ ( 1 − x ) ∣ x ∈ F ∖ { 0 , 1 } ⟩ . {\displaystyle K_{n}^{M}(F)=F^{\times }\otimes \cdots \otimes F^{\times }/\left\langle x\otimes (1-x)\mid x\in F\smallsetminus \{0,1\}\right\rangle .} The norm residue isomorphism theorem, proved around 2000 by Vladimir Voevodsky, relates this to Galois cohomology by means of an isomorphism K n M ( F ) / p = H n ( F , μ l ⊗ n ) . {\displaystyle K_{n}^{M}(F)/p=H^{n}(F,\mu _{l}^{\otimes n}).} Algebraic K-theory is related to the group of invertible matrices with coefficients the given field. For example, the process of taking the determinant of an invertible matrix leads to an isomorphism K1(F) = F×. Matsumoto's theorem shows that K2(F) agrees with K2M(F). In higher degrees, K-theory diverges from Milnor K-theory and remains hard to compute in general. == Applications == === Linear algebra and commutative algebra === If a ≠ 0, then the equation ax = b has a unique solution x in a field F, namely x = a − 1 b . {\displaystyle x=a^{-1}b.} This immediate consequence of the definition of a field is fundamental in linear algebra. For example, it is an essential ingredient of Gaussian elimination and of the proof that any vector space has a basis. The theory of modules (the analogue of vector spaces over rings instead of fields) is much more complicated, because the above equation may have several or no solutions. In particular systems of linear equations over a ring are much more difficult to solve than in the case of fields, even in the specially simple case of the ring Z of the integers. === Finite fields: cryptography and coding theory === A widely applied cryptographic routine uses the fact that discrete exponentiation, i.e., computing an = a ⋅ a ⋅ ⋯ ⋅ a (n factors, for an integer n ≥ 1) in a (large) finite field Fq can be performed much more efficiently than the discrete logarithm, which is the inverse operation, i.e., determining the solution n to an equation an = b. In elliptic curve cryptography, the multiplication in a finite field is replaced by the operation of adding points on an elliptic curve, i.e., the solutions of an equation of the form y2 = x3 + ax + b. Finite fields are also used in coding theory and combinatorics. === Geometry: field of functions === Functions on a suitable topological space X into a field F can be added and multiplied pointwise, e.g., the product of two functions is defined by the product of their values within the domain: (f ⋅ g)(x) = f(x) ⋅ g(x). This makes these functions a F-commutative algebra. For having a field of functions, one must consider algebras of functions that are integral domains. In this case the ratios of two functions, i.e., expressions of the form f ( x ) g ( x ) , {\displaystyle {\frac {f(x)}{g(x)}},} form a field, called field of functions. This occurs in two main cases. When X is a complex manifold X. In this case, one considers the algebra of holomorphic functions, i.e., complex differentiable functions. Their ratios form the field of meromorphic functions on X. The function field of an algebraic variety X (a geometric object defined as the common zeros of polynomial equations) consists of ratios of regular functions, i.e., ratios of polynomial functions on the variety. The function field of the n-dimensional space over a field F is F(x1, ..., xn), i.e., the field consisting of ratios of polynomials in n indeterminates. The function field of X is the same as the one of any open dense subvariety. In other words, the function field is insensitive to replacing X by a (slightly) smaller subvariety. The function field is invariant under isomorphism and birational equivalence of varieties. It is therefore an important tool for the study of abstract algebraic varieties and for the classification of algebraic varieties. For example, the dimension, which equals the transcendence degree of F(X), is invariant under birational equivalence. For curves (i.e., the dimension is one), the function field F(X) is very close to X: if X is smooth and proper (the analogue of being compact), X can be reconstructed, up to isomorphism, from its field of functions. In higher dimension the function field remembers less, but still decisive information about X. The study of function fields and their geometric meaning in higher dimensions is referred to as birational geometry. The minimal model program attempts to identify the simplest (in a certain precise sense) algebraic varieties with a prescribed function field. === Number theory: global fields === Global fields are in the limelight in algebraic number theory and arithmetic geometry. They are, by definition, number fields (finite extensions of Q) or function fields over Fq (finite extensions of Fq(t)). As for local fields, these two types of fields share several similar features, even though they are of characteristic 0 and positive characteristic, respectively. This function field analogy can help to shape mathematical expectations, often first by understanding questions about function fields, and later treating the number field case. The latter is often more difficult. For example, the Riemann hypothesis concerning the zeros of the Riemann zeta function (open as of 2017) can be regarded as being parallel to the Weil conjectures (proven in 1974 by Pierre Deligne). Cyclotomic fields are among the most intensely studied number fields. They are of the form Q(ζn), where ζn is a primitive nth root of unity, i.e., a complex number ζ that satisfies ζn = 1 and ζm ≠ 1 for all 0 < m < n. For n being a regular prime, Kummer used cyclotomic fields to prove Fermat's Last Theorem, which asserts the non-existence of rational nonzero solutions to the equation xn + yn = zn. Local fields are completions of global fields. Ostrowski's theorem asserts that the only completions of Q, a global field, are the local fields Qp and R. Studying arithmetic questions in global fields may sometimes be done by looking at the corresponding questions locally. This technique is called the local–global principle. For example, the Hasse–Minkowski theorem reduces the problem of finding rational solutions of quadratic equations to solving these equations in R and Qp, whose solutions can easily be described. Unlike for local fields, the Galois groups of global fields are not known. Inverse Galois theory studies the (unsolved) problem whether any finite group is the Galois group Gal(F/Q) for some number field F. Class field theory describes the abelian extensions, i.e., ones with abelian Galois group, or equivalently the abelianized Galois groups of global fields. A classical statement, the Kronecker–Weber theorem, describes the maximal abelian Qab extension of Q: it is the field Q(ζn, n ≥ 2) obtained by adjoining all primitive nth roots of unity. Kronecker's Jugendtraum asks for a similarly explicit description of Fab of general number fields F. For imaginary quadratic fields, F = Q ( − d ) {\displaystyle F=\mathbf {Q} ({\sqrt {-d}})} , d > 0, the theory of complex multiplication describes Fab using elliptic curves. For general number fields, no such explicit description is known. == Related notions == In addition to the additional structure that fields may enjoy, fields admit various other related notions. Since in any field 0 ≠ 1, any field has at least two elements. Nonetheless, there is a concept of field with one element, which is suggested to be a limit of the finite fields Fp, as p tends to 1. In addition to division rings, there are various other weaker algebraic structures related to fields such as quasifields, near-fields and semifields. There are also proper classes with field structure, which are sometimes called Fields, with a capital 'F'. The surreal numbers form a Field containing the reals, and would be a field except for the fact that they are a proper class, not a set. The nimbers, a concept from game theory, form such a Field as well. === Division rings === Dropping one or several axioms in the definition of a field leads to other algebraic structures. As was mentioned above, commutative rings satisfy all field axioms except for the existence of multiplicative inverses. Dropping instead commutativity of multiplication leads to the concept of a division ring or skew field; sometimes associativity is weakened as well. The only division rings that are finite-dimensional R-vector spaces are R itself, C (which is a field), and the quaternions H (in which multiplication is non-commutative). This result is known as the Frobenius theorem. The octonions O, for which multiplication is neither commutative nor associative, is a normed alternative division algebra, but is not a division ring. This fact was proved using methods of algebraic topology in 1958 by Michel Kervaire, Raoul Bott, and John Milnor. Wedderburn's little theorem states that all finite division rings are fields. == Notes == == Citations == == References == == External links ==
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https://en.wikipedia.org/wiki/Field_(mathematics)
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Abstraction in mathematics is the process of extracting the underlying structures, patterns or properties of a mathematical concept, removing any dependence on real world objects with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena. In other words, to be abstract is to remove context and application. Two of the most highly abstract areas of modern mathematics are category theory and model theory. == Description == Many areas of mathematics began with the study of real world problems, before the underlying rules and concepts were identified and defined as abstract structures. For example, geometry has its origins in the calculation of distances and areas in the real world, and algebra started with methods of solving problems in arithmetic. Abstraction is an ongoing process in mathematics and the historical development of many mathematical topics exhibits a progression from the concrete to the abstract. For example, the first steps in the abstraction of geometry were historically made by the ancient Greeks, with Euclid's Elements being the earliest extant documentation of the axioms of plane geometry—though Proclus tells of an earlier axiomatisation by Hippocrates of Chios. In the 17th century, Descartes introduced Cartesian co-ordinates which allowed the development of analytic geometry. Further steps in abstraction were taken by Lobachevsky, Bolyai, Riemann and Gauss, who generalised the concepts of geometry to develop non-Euclidean geometries. Later in the 19th century, mathematicians generalised geometry even further, developing such areas as geometry in n dimensions, projective geometry, affine geometry and finite geometry. Finally Felix Klein's "Erlangen program" identified the underlying theme of all of these geometries, defining each of them as the study of properties invariant under a given group of symmetries. This level of abstraction revealed connections between geometry and abstract algebra. In mathematics, abstraction can be advantageous in the following ways: It reveals deep connections between different areas of mathematics. Known results in one area can suggest conjectures in another related area. Techniques and methods from one area can be applied to prove results in other related areas. Patterns from one mathematical object can be generalized to other similar objects in the same class. On the other hand, abstraction can also be disadvantageous in that highly abstract concepts can be difficult to learn. A degree of mathematical maturity and experience may be needed for conceptual assimilation of abstractions. Bertrand Russell, in The Scientific Outlook (1931), writes that "Ordinary language is totally unsuited for expressing what physics really asserts, since the words of everyday life are not sufficiently abstract. Only mathematics and mathematical logic can say as little as the physicist means to say." == See also == Abstract detail Generalization Abstract thinking Abstract logic Abstract algebraic logic Abstract model theory Abstract nonsense Concept Mathematical maturity == References == == Further reading == Bajnok, Béla (2013). An Invitation to Abstract Mathematics. Springer. ISBN 978-1-4614-6635-2.
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https://en.wikipedia.org/wiki/Abstraction_(mathematics)
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In mathematics, equality is a relationship between two quantities or expressions, stating that they have the same value, or represent the same mathematical object. Equality between A and B is written A = B, and pronounced "A equals B". In this equality, A and B are distinguished by calling them left-hand side (LHS), and right-hand side (RHS). Two objects that are not equal are said to be distinct. Equality is often considered a kind of primitive notion, meaning, it is not formally defined, but rather informally said to be "a relation each thing bears to itself and nothing else". This characterization is notably circular ("nothing else"). This makes equality a somewhat slippery idea to pin down. Basic properties about equality like reflexivity, symmetry, and transitivity have been understood intuitively since at least the ancient Greeks, but were not symbolically stated as general properties of relations until the late 19th century by Giuseppe Peano. Other properties like substitution and function application weren't formally stated until the development of symbolic logic. There are generally two ways that equality is formalized in mathematics: through logic or through set theory. In logic, equality is a primitive predicate (a statement that may have free variables) with the reflexive property (called the law of identity), and the substitution property. From those, one can derive the rest of the properties usually needed for equality. After the foundational crisis in mathematics at the turn of the 20th century, set theory (specifically Zermelo–Fraenkel set theory) became the most common foundation of mathematics. In set theory, any two sets are defined to be equal if they have all the same members. This is called the axiom of extensionality. == Etymology == In English, the word equal is derived from the Latin aequālis ('like', 'comparable', 'similar'), which itself stems from aequus ('level', 'just'). The word entered Middle English around the 14th century, borrowed from Old French equalité (modern égalité). More generally, the interlingual synonyms of equal have been used more broadly throughout history (see § Geometry). Before the 16th century, there was no common symbol for equality, and equality was usually expressed with a word, such as aequales, aequantur, esgale, faciunt, ghelijck, or gleich, and sometimes by the abbreviated form aeq, or simply ⟨æ⟩ and ⟨œ⟩. Diophantus's use of ⟨ἴσ⟩, short for ἴσος (ísos 'equals'), in Arithmetica (c. 250 AD) is considered one of the first uses of an equals sign. The sign =, now universally accepted in mathematics for equality, was first recorded by Welsh mathematician Robert Recorde in The Whetstone of Witte (1557). The original form of the symbol was much wider than the present form. In his book, Recorde explains his symbol as "Gemowe lines", from the Latin gemellus ('twin'), using two parallel lines to represent equality because he believed that "no two things could be more equal." Recorde's symbol was not immediately popular. After its introduction, it wasn't used again in print until 1618 (61 years later), in an anonymous Appendix in Edward Wright's English translation of Descriptio, by John Napier. It wasn't until 1631 that it received more than general recognition in England, being adopted as the symbol for equality in a few influential works. Later used by several influential mathematicians, most notably, both Isaac Newton and Gottfried Leibniz, and due to the prevalence of calculus at the time, it quickly spread throughout the rest of Europe. == Basic properties == Reflexivity For every a, one has a = a. Symmetry For every a and b, if a = b, then b = a. Transitivity For every a, b, and c, if a = b and b = c, then a = c. Substitution Informally, this just means that if a = b, then a can replace b in any mathematical expression or formula without changing its meaning. (For a formal explanation, see § Axioms) For example: Operation application For every a and b, with some operation f ( x ) , {\displaystyle f(x),} if a = b, then f ( a ) = f ( b ) . {\displaystyle f(a)=f(b).} For example: The first three properties are generally attributed to Giuseppe Peano for being the first to explicitly state these as fundamental properties of equality in his Arithmetices principia (1889). However, the basic notions have always existed; for example, in Euclid's Elements (c. 300 BC), he includes 'common notions': "Things that are equal to the same thing are also equal to one another" (transitivity), "Things that coincide with one another are equal to one another" (reflexivity), along with some operation-application properties for addition and subtraction. The operation-application property was also stated in Peano's Arithmetices principia, however, it had been common practice in algebra since at least Diophantus (c. 250 AD). The substitution property is generally attributed to Gottfried Leibniz (c. 1686), and often called Leibniz's Law. == Equations == An equation is a symbolic equality of two mathematical expressions connected with an equals sign (=). Algebra is the branch of mathematics concerned with equation solving: the problem of finding values of some variable, called unknown, for which the specified equality is true. Each value of the unknown for which the equation holds is called a solution of the given equation; also stated as satisfying the equation. For example, the equation x 2 − 6 x + 5 = 0 {\displaystyle x^{2}-6x+5=0} has the values x = 1 {\displaystyle x=1} and x = 5 {\displaystyle x=5} as its only solutions. The terminology is used similarly for equations with several unknowns. The set of solutions to an equation or system of equations is called its solution set. In mathematics education, students are taught to rely on concrete models and visualizations of equations, including geometric analogies, manipulatives including sticks or cups, and "function machines" representing equations as flow diagrams. One method uses balance scales as a pictorial approach to help students grasp basic problems of algebra. The mass of some objects on the scale is unknown and represents variables. Solving an equation corresponds to adding and removing objects on both sides in such a way that the sides stay in balance until the only object remaining on one side is the object of unknown mass. Often, equations are considered to be a statement, or relation, which can be true or false. For example, 1 + 1 = 2 {\displaystyle 1+1=2} is true, and 1 + 1 = 3 {\displaystyle 1+1=3} is false. Equations with unknowns are considered conditionally true; for example, x 2 − 6 x + 5 = 0 {\displaystyle x^{2}-6x+5=0} is true when x = 1 {\displaystyle x=1} or x = 5 , {\displaystyle x=5,} and false otherwise. There are several different terminologies for this. In mathematical logic, an equation is a binary predicate (i.e. a logical statement, that can have free variables) which satisfies certain properties. In computer science, an equation is defined as a boolean-valued expression, or relational operator, which returns 1 and 0 for true and false respectively. === Identities === An identity is an equality that is true for all values of its variables in a given domain. An "equation" may sometimes mean an identity, but more often than not, it specifies a subset of the variable space to be the subset where the equation is true. An example is ( x + 1 ) ( x + 1 ) = x 2 + 2 x + 1 , {\displaystyle \left(x+1\right)\left(x+1\right)=x^{2}+2x+1,} which is true for each real number x . {\displaystyle x.} There is no standard notation that distinguishes an equation from an identity, or other use of the equality relation: one has to guess an appropriate interpretation from the semantics of expressions and the context. Sometimes, but not always, an identity is written with a triple bar: ( x + 1 ) ( x + 1 ) ≡ x 2 + 2 x + 1. {\displaystyle \left(x+1\right)\left(x+1\right)\equiv x^{2}+2x+1.} This notation was introduced by Bernhard Riemann in his 1857 Elliptische Funktionen lectures (published in 1899). Alternatively, identities may be viewed as an equality of functions, where instead of writing f ( a ) = g ( a ) for all a , {\displaystyle f(a)=g(a){\text{ for all }}a,} one may simply write f = g . {\displaystyle f=g.} This is called the extensionality of functions. In this sense, the operation-application property refers to operators, operations on a function space (functions mapping between functions) like composition or the derivative, commonly used in operational calculus. An identity can contain an functions as "unknowns", which can be solved for similarly to a regular equation, called a functional equation. A functional equation involving derivatives is called a differential equation. === Definitions === Equations are often used to introduce new terms or symbols for constants, assert equalities, and introduce shorthand for complex expressions, which is called "equal by definition", and often denoted with ( := {\displaystyle :=} ). It is similar to the concept of assignment of a variable in computer science. For example, e := ∑ n = 0 ∞ 1 n ! {\textstyle \mathbb {e} :=\sum _{n=0}^{\infty }{\frac {1}{n!}}} defines Euler's number, and i 2 = − 1 {\displaystyle i^{2}=-1} is the defining property of the imaginary number i . {\displaystyle i.} In mathematical logic, this is called an extension by definition (by equality) which is a conservative extension to a formal system. This is done by taking the equation defining the new constant symbol as a new axiom of the theory. The first recorded symbolic use of "Equal by definition" appeared in Logica Matematica (1894) by Cesare Burali-Forti, an Italian mathematician. Burali-Forti, in his book, used the notation ( = Def {\displaystyle =_{\text{Def}}} ). == In logic == === History === Equality is often considered a primitive notion, informally said to be "a relation each thing bears to itself and to no other thing". This tradition can be traced back to at least 350 BC by Aristotle: in his Categories, he defines the notion of quantity in terms of a more primitive equality (distinct from identity or similarity), stating: The most distinctive mark of quantity is that equality and inequality are predicated of it. Each of the aforesaid quantities is said to be equal or unequal. For instance, one solid is said to be equal or unequal to another; number, too, and time can have these terms applied to them, indeed can all those kinds of quantity that have been mentioned.That which is not a quantity can by no means, it would seem, be termed equal or unequal to anything else. One particular disposition or one particular quality, such as whiteness, is by no means compared with another in terms of equality and inequality but rather in terms of similarity. Thus it is the distinctive mark of quantity that it can be called equal and unequal. ― (translated by E. M. Edghill) Aristotle had separate categories for quantities (number, length, volume) and qualities (temperature, density, pressure), now called intensive and extensive properties. The Scholastics, particularly Richard Swineshead and other Oxford Calculators in the 14th century, began seriously thinking about kinematics and quantitative treatment of qualities. For example, two flames have the same heat-intensity if they produce the same effect on water (e.g, warming vs boiling). Since two intensities could be shown to be equal, and equality was considered the defining feature of quantities, it meant those intensities were quantifiable. Around the 19th century, with the growth of modern logic, it became necessary to have a more concrete description of equality. With the rise of predicate logic due to the work of Gottlob Frege, logic shifted from being focused on classes of objects to being property-based. This was followed by a movement for describing mathematics in logical foundations, called logicism. This trend lead to the axiomatization of equality through the law of identity and the substitution property especially in mathematical logic and analytic philosophy. The precursor to the substitution property of equality was first formulated by Gottfried Leibniz in his Discourse on Metaphysics (1686), stating, roughly, that "No two distinct things can have all properties in common." This has since broken into two principles, the substitution property (if x = y , {\displaystyle x=y,} then any property of x {\displaystyle x} is a property of y {\displaystyle y} ), and its converse, the identity of indiscernibles (if x {\displaystyle x} and y {\displaystyle y} have all properties in common, then x = y {\displaystyle x=y} ). Its introduction to logic, and first symbolic formulation is due to Bertrand Russell and Alfred Whitehead in their Principia Mathematica (1910), who claim it follows from their axiom of reducibility, but credit Leibniz for the idea. === Axioms === Law of identity: Stating that each thing is identical with itself, without restriction. That is, for every a , {\displaystyle a,} a = a . {\displaystyle a=a.} It is the first of the traditional three laws of thought. Stated symbolically as: ∀ a ( a = a ) {\displaystyle \forall a(a=a)} Substitution property: Sometimes referred to as Leibniz's law, generally states that if two things are equal, then any property of one must be a property of the other. It can be stated formally as: for every a and b, and any formula ϕ ( x ) , {\displaystyle \phi (x),} (with a free variable x), if a = b , {\displaystyle a=b,} then ϕ ( a ) {\displaystyle \phi (a)} implies ϕ ( b ) . {\displaystyle \phi (b).} Stated symbolically as: ( a = b ) ⟹ [ ϕ ( a ) ⇒ ϕ ( b ) ] {\displaystyle (a=b)\implies {\bigl [}\phi (a)\Rightarrow \phi (b){\bigr ]}} Function application is also sometimes included in the axioms of equality, but isn't necessary as it can be deduced from the other two axioms, and similarly for symmetry and transitivity. (See § Derivations of basic properties) In first-order logic, these are axiom schemas (usually, see below), each of which specify an infinite set of axioms. If a theory has a predicate that satisfies the Law of Identity and Substitution property, it is common to say that it "has equality", or is "a theory with equality". The use of "equality" here somewhat of a misnomer in that any system with equality can be modeled by a theory without standard identity, and with indiscernibles. Those two axioms are strong enough, however, to be isomorphic to a model with idenitity; that is, if a system has a predicate staisfying those axioms without standard equality, there is a model of that system with standard equality. This can be done by defining a new domain whose objects are the equivalence classes of the original "equality". If the relation is interpreted as equality, then those properties are enough, since if x {\displaystyle x} has all the same properties as y , {\displaystyle y,} and x {\displaystyle x} has the property of being equal to x , {\displaystyle x,} then y {\displaystyle y} has the property of being equal to x . {\displaystyle x.} As axioms, one can deduce from the first using universal instantiation, and the from second, given a = b {\displaystyle a=b} and ϕ ( a ) , {\displaystyle \phi (a),} by using modus ponens twice. Alternatively, each of these may be included in logic as rules of inference. The first called "equality introduction", and the second "equality elimination" (also called paramodulation), used by some theoretical computer scientists like John Alan Robinson in their work on resolution and automated theorem proving. === Derivations of basic properties === Reflexivity: Given any expression a , {\displaystyle a,} by the Law of Identity, a = a . {\displaystyle a=a.} Symmetry: Given a = b , {\displaystyle a=b,} take the formula ϕ ( x ) : x = a . {\displaystyle \phi (x):x=a.} So we have ( a = b ) ⟹ ( ( a = a ) ⇒ ( b = a ) ) . {\displaystyle (a=b)\implies ((a=a)\Rightarrow (b=a)).} Since a = b {\displaystyle a=b} by assumption, and a = a {\displaystyle a=a} by Reflexivity, we have that b = a . {\displaystyle b=a.} Transitivity: Given a = b {\displaystyle a=b} and b = c , {\displaystyle b=c,} take the formula ϕ ( x ) : x = c . {\displaystyle \phi (x):x=c.} So we have ( b = a ) ⟹ ( ( b = c ) ⇒ ( a = c ) ) . {\displaystyle (b=a)\implies ((b=c)\Rightarrow (a=c)).} Since b = a {\displaystyle b=a} by symmetry, and b = c {\displaystyle b=c} by assumption, we have that a = c . {\displaystyle a=c.} Function application: Given some function f ( x ) {\displaystyle f(x)} and expressions a and b, such that a = b, then take the formula ϕ ( x ) : f ( a ) = f ( x ) . {\displaystyle \phi (x):f(a)=f(x).} So we have: ( a = b ) ⟹ [ ( f ( a ) = f ( a ) ) ⇒ ( f ( a ) = f ( b ) ) ] {\displaystyle (a=b)\implies [(f(a)=f(a))\Rightarrow (f(a)=f(b))]} Since a = b {\displaystyle a=b} by assumption, and f ( a ) = f ( a ) {\displaystyle f(a)=f(a)} by reflexivity, we have that f ( a ) = f ( b ) . {\displaystyle f(a)=f(b).} == In set theory == Set theory is the branch of mathematics that studies sets, which can be informally described as "collections of objects". Although objects of any kind can be collected into a set, set theory – as a branch of mathematics – is mostly concerned with those that are relevant to mathematics as a whole. Sets are uniquely characterized by their elements; this means that two sets that have precisely the same elements are equal (they are the same set). In a formalized set theory, this is usually defined by an axiom called the Axiom of extensionality. For example, using set builder notation, the following states that "The set of all integers ( Z ) {\displaystyle (\mathbb {Z} )} greater than 0 but not more than 3 is equal to the set containing only 1, 2, and 3", despite the differences in notation. { x ∈ Z ∣ 0 < x ≤ 3 } = { 1 , 2 , 3 } , {\displaystyle \{x\in \mathbb {Z} \mid 0<x\leq 3\}=\{1,2,3\},} The term extensionality, as used in 'Axiom of Extensionality' has its roots in logic and grammar (cf. Extension (semantics)). In grammar, intensional definition describes the necessary and sufficient conditions for a term to apply to an object. For example: "A Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space." An extensional definition instead lists all objects where the term applies. For example: "A Platonic solid is one of the following: Tetrahedron, Cube, Octahedron, Dodecahedron, or Icosahedron." In logic, the extension of a predicate is the set of all objects for which the predicate is true. Further, the logical principle of extensionality judges two objects to objects to be equal if they satisfy the same external properties. Since, by the axiom, two sets are defined to be equal if they satisfy membership, sets are extentional. José Ferreirós credits Richard Dedekind for being the first to explicitly state the principle, although he does not assert it as a definition: It very frequently happens that different things a, b, c... considered for any reason under a common point of view, are collected together in the mind, and one then says that they form a system S; one calls the things a, b, c... the elements of the system S, they are contained in S; conversely, S consists of these elements. Such a system S (or a collection, a manifold, a totality), as an object of our thought, is likewise a thing; it is completely determined when, for every thing, it is determined whether it is an element of S or not. === Background === Around the turn of the 20th century, mathematics faced several paradoxes and counter-intuitive results. For example, Russell's paradox showed a contradiction of naive set theory, it was shown that the parallel postulate cannot be proved, the existence of mathematical objects that cannot be computed or explicitly described, and the existence of theorems of arithmetic that cannot be proved with Peano arithmetic. The result was a foundational crisis of mathematics. The resolution of this crisis involved the rise of a new mathematical discipline called mathematical logic, which studies formal logic within mathematics. Subsequent discoveries in the 20th century then stabilized the foundations of mathematics into a coherent framework valid for all mathematics. This framework is based on a systematic use of axiomatic method and on set theory, specifically Zermelo–Fraenkel set theory, developed by Ernst Zermelo and Abraham Fraenkel. This set theory (and set theory in general) is now considered the most common foundation of mathematics. === Set equality based on first-order logic with equality === In first-order logic with equality (See § Axioms), the axiom of extensionality states that two sets that contain the same elements are the same set. Logic axiom: x = y ⟹ ∀ z , ( z ∈ x ⟺ z ∈ y ) {\displaystyle x=y\implies \forall z,(z\in x\iff z\in y)} Logic axiom: x = y ⟹ ∀ z , ( x ∈ z ⟺ y ∈ z ) {\displaystyle x=y\implies \forall z,(x\in z\iff y\in z)} Set theory axiom: ( ∀ z , ( z ∈ x ⟺ z ∈ y ) ) ⟹ x = y {\displaystyle (\forall z,(z\in x\iff z\in y))\implies x=y} The first two are given by the substitution property of equality from first-order logic; the last is a new axiom of the theory. Incorporating half of the work into the first-order logic may be regarded as a mere matter of convenience, as noted by Azriel Lévy. "The reason why we take up first-order predicate calculus with equality is a matter of convenience; by this, we save the labor of defining equality and proving all its properties; this burden is now assumed by the logic." === Set equality based on first-order logic without equality === In first-order logic without equality, two sets are defined to be equal if they contain the same elements. Then the axiom of extensionality states that two equal sets are contained in the same sets. Set theory definition: ( x = y ) := ∀ z , ( z ∈ x ⟺ z ∈ y ) {\displaystyle (x=y)\ :=\ \forall z,(z\in x\iff z\in y)} Set theory axiom: x = y ⟹ ∀ z , ( x ∈ z ⟺ y ∈ z ) {\displaystyle x=y\implies \forall z,(x\in z\iff y\in z)} Or, equivalently, one may choose to define equality in a way that mimics, the substitution property explicitly, as the conjunction of all atomic formuals: Set theory definition: ( x = y ) := {\displaystyle (x=y):=} ∀ z ( z ∈ x ⟹ z ∈ y ) ∧ {\displaystyle \;\forall z(z\in x\implies z\in y)\,\land \,} ∀ w ( x ∈ w ⟹ y ∈ w ) {\displaystyle \forall w(x\in w\implies y\in w)} Set theory axiom: ( ∀ z , ( z ∈ x ⟺ z ∈ y ) ) ⟹ x = y {\displaystyle (\forall z,(z\in x\iff z\in y))\implies x=y} In either case, the Axiom of Extensionality based on first-order logic without equality states: ∀ z ( z ∈ x ⇒ z ∈ y ) ⟹ ∀ w ( x ∈ w ⇒ y ∈ w ) {\displaystyle \forall z(z\in x\Rightarrow z\in y)\implies \forall w(x\in w\Rightarrow y\in w)} === Proof of basic properties === Reflexivity: Given a set X , {\displaystyle X,} assume z ∈ X , {\displaystyle z\in X,} it follows trivially that z ∈ X , {\displaystyle z\in X,} and the same follows in reverse, therefore ∀ z , ( z ∈ X ⟺ z ∈ X ) {\displaystyle \forall z,(z\in X\iff z\in X)} , thus X = X . {\displaystyle X=X.} Symmetry: Given sets X , Y , {\displaystyle X,Y,} such that X = Y , {\displaystyle X=Y,} then ∀ z , ( z ∈ X ⟺ z ∈ Y ) , {\displaystyle \forall z,(z\in X\iff z\in Y),} which implies ∀ z , ( z ∈ Y ⟺ z ∈ X ) , {\displaystyle \forall z,(z\in Y\iff z\in X),} thus Y = X . {\displaystyle Y=X.} Transitivity: Given sets X , Y , Z , {\displaystyle X,Y,Z,} such that (1) X = Y {\displaystyle X=Y} and (2) Y = Z , {\displaystyle Y=Z,} assume z ∈ X , {\displaystyle z\in X,} then z ∈ Y {\displaystyle z\in Y} by (1), which implies z ∈ Z {\displaystyle z\in Z} by (2), and similarly for the reverse, therefore ∀ z , ( z ∈ X ⟺ z ∈ Z ) , {\displaystyle \forall z,(z\in X\iff z\in Z),} thus X = Z . {\displaystyle X=Z.} Substitution: See Substitution (logic) § Proof of substitution in ZFC. Function application: Given a = b {\displaystyle a=b} and f ( a ) = c , {\displaystyle f(a)=c,} then ( a , c ) ∈ f . {\displaystyle (a,c)\in f.} Since a = b {\displaystyle a=b} and c = c , {\displaystyle c=c,} then ( a , c ) = ( b , c ) . {\displaystyle (a,c)=(b,c).} This is the defining property of an ordered pair. Since ( a , c ) = ( b , c ) , {\displaystyle (a,c)=(b,c),} by the Axiom of Extensionality, they must belong to the same sets, so, since ( a , c ) ∈ f , {\displaystyle (a,c)\in f,} we have ( b , c ) ∈ f , {\displaystyle (b,c)\in f,} or f ( b ) = c . {\displaystyle f(b)=c.} Thus f ( a ) = f ( b ) . {\displaystyle f(a)=f(b).} == Similar relations == === Approximate equality === Numerical analysis is the study of constructive methods and algorithms to find numerical approximations (as opposed to symbolic manipulations) of solutions to problems in mathematical analysis. Especially those which cannot be solved analytically. Calculations are likely to involve rounding errors and other approximation errors. Log tables, slide rules, and calculators produce approximate answers to all but the simplest calculations. The results of computer calculations are normally an approximation, expressed in a limited number of significant digits, although they can be programmed to produce more precise results. If viewed as a binary relation, (denoted by the symbol ≈ {\displaystyle \approx } ) between real numbers or other things, if precisely defined, is not an equivalence relation since it's not transitive, even if modeled as a fuzzy relation. In computer science, equality is given by some relational operator. Real numbers are often approximated by floating-point numbers (A sequence of some fixed number of digits of a given base, scaled by an integer exponent of that base), thus it is common to store an expression that denotes the real number as to not lose precision. However, the equality of two real numbers given by an expression is known to be undecidable (specifically, real numbers defined by expressions involving the integers, the basic arithmetic operations, the logarithm and the exponential function). In other words, there cannot exist any algorithm for deciding such an equality (see Richardson's theorem). === Equivalence relation === An equivalence relation is a mathematical relation that generalizes the idea of similarity or sameness. It is defined on a set X {\displaystyle X} as a binary relation ∼ {\displaystyle \sim } that satisfies the three properties: reflexivity, symmetry, and transitivity. Reflexivity means that every element in X {\displaystyle X} is equivalent to itself ( a ∼ a {\displaystyle a\sim a} for all a ∈ X {\displaystyle a\in X} ). Symmetry requires that if one element is equivalent to another, the reverse also holds ( a ∼ b ⟹ b ∼ a {\displaystyle a\sim b\implies b\sim a} ). Transitivity ensures that if one element is equivalent to a second, and the second to a third, then the first is equivalent to the third ( a ∼ b {\displaystyle a\sim b} and b ∼ c ⟹ a ∼ c {\displaystyle b\sim c\implies a\sim c} ). These properties are enough to partition a set into disjoint equivalence classes. Conversely, every partition defines an equivalence class. The equivalence relation of equality is a special case, as, if restricted to a given set S , {\displaystyle S,} it is the strictest possible equivalence relation on S {\displaystyle S} ; specifically, equality partitions a set into equivalence classes consisting of all singleton sets. Other equivalence relations, since they're less restrictive, generalize equality by identifying elements based on shared properties or transformations, such as congruence in modular arithmetic or similarity in geometry. ==== Congruence relation ==== In abstract algebra, a congruence relation extends the idea of an equivalence relation to include the operation-application property. That is, given a set X , {\displaystyle X,} and a set of operations on X , {\displaystyle X,} then a congruence relation ∼ {\displaystyle \sim } has the property that a ∼ b ⟹ f ( a ) ∼ f ( b ) {\displaystyle a\sim b\implies f(a)\sim f(b)} for all operations f {\displaystyle f} (here, written as unary to avoid cumbersome notation, but f {\displaystyle f} may be of any arity). A congruence relation on an algebraic structure such as a group, ring, or module is an equivalence relation that respects the operations defined on that structure. === Isomorphism === In mathematics, especially in abstract algebra and category theory, it is common to deal with objects that already have some internal structure. An isomorphism describes a kind of structure-preserving correspondence between two objects, establishing them as essentially identical in their structure or properties. More formally, an isomorphism is a bijective mapping (or morphism) f {\displaystyle f} between two sets or structures A {\displaystyle A} and B {\displaystyle B} such that f {\displaystyle f} and its inverse f − 1 {\displaystyle f^{-1}} preserve the operations, relations, or functions defined on those structures. This means that any operation or relation valid in A {\displaystyle A} corresponds precisely to the operation or relation in B {\displaystyle B} under the mapping. For example, in group theory, a group isomorphism f : G ↦ H {\displaystyle f:G\mapsto H} satisfies f ( a ∗ b ) = f ( a ) ∗ f ( b ) {\displaystyle f(a*b)=f(a)*f(b)} for all elements a , b , {\displaystyle a,b,} where ∗ {\displaystyle *} denotes the group operation. When two objects or systems are isomorphic, they are considered indistinguishable in terms of their internal structure, even though their elements or representations may differ. For instance, all cyclic groups of order ∞ {\displaystyle \infty } are isomorphic to the integers, Z , {\displaystyle \mathbb {Z} ,} with addition. Similarly, in linear algebra, two vector spaces are isomorphic if they have the same dimension, as there exists a linear bijection between their elements. The concept of isomorphism extends to numerous branches of mathematics, including graph theory (graph isomorphism), topology (homeomorphism), and algebra (group and ring isomorpisms), among others. Isomorphisms facilitate the classification of mathematical entities and enable the transfer of results and techniques between similar systems. Bridging the gap between isomorphism and equality was one motivation for the development of category theory, as well as for homotopy type theory and univalent foundations. === Geometry === In geometry, formally, two figures are equal if they contain exactly the same points. However, historically, geometric-equality has always been taken to be much broader. Euclid and Archimedes used "equal" (ἴσος isos) often referring to figures with the same area or those that could be cut and rearranged to form one another. For example, Euclid stated the Pythagorean theorem as "the square on the hypotenuse is equal to the squares on the sides, taken together"; and Archimedes said that "a circle is equal to the rectangle whose sides are the radius and half the circumference." This notion persisted until Adrien-Marie Legendre, who introduced the term "equivalent" to describe figures of equal area and restricted "equal" to what we now call "congruent"—the same shape and size, or if one has the same shape and size as the mirror image of the other. Euclid's terminology continued in the work of David Hilbert in his Grundlagen der Geometrie, who further refined Euclid's ideas by introducing the notions of polygons being "divisibly equal" (zerlegungsgleich) if they can be cut into finitely many triangles which are congruent, and "equal in content" (inhaltsgleichheit) if one can add finitely many divisibly equal polygons to each such that the resulting polygons are divisibly equal. After the rise of set theory, around the 1960s, there was a push for a reform in mathematics education called New Math, following Andrey Kolmogorov, who, in an effort to restructure Russian geometry courses, proposed presenting geometry through the lens of transformations and set theory. Since a figure was seen as a set of points, it could only be equal to itself, as a result of Kolmogorov, the term "congruent" became standard in schools for figures that were previously called "equal", which popularized the term. While Euclid addressed proportionality and figures of the same shape, it was not until the 17th century that the concept of similarity was formalized in the modern sense. Similar figures are those that have the same shape but can differ in size; they can be transformed into one another by scaling and congruence. Later a concept of equality of directed line segments, equipollence, was advanced by Giusto Bellavitis in 1835. == See also == Essentially unique Glossary of mathematical symbols § Equality, equivalence and similarity Identity type Identity (object-oriented programming) Inequality Logical equality Logical equivalence Relational operator § Equality Setoid Theory of pure equality Uniqueness quantification == Notes == == References == === Citations === === Bibliography ===
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https://en.wikipedia.org/wiki/Equality_(mathematics)
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Elementary mathematics, also known as primary or secondary school mathematics, is the study of mathematics topics that are commonly taught at the primary or secondary school levels around the world. It includes a wide range of mathematical concepts and skills, including number sense, algebra, geometry, measurement, and data analysis. These concepts and skills form the foundation for more advanced mathematical study and are essential for success in many fields and everyday life. The study of elementary mathematics is a crucial part of a student's education and lays the foundation for future academic and career success. == Strands of elementary mathematics == === Number sense and numeration === Number sense is an understanding of numbers and operations. In the 'Number Sense and Numeration' strand students develop an understanding of numbers by being taught various ways of representing numbers, as well as the relationships among numbers. Properties of the natural numbers such as divisibility and the distribution of prime numbers, are studied in basic number theory, another part of elementary mathematics. Elementary Focus: === Spatial sense === 'Measurement skills and concepts' or 'Spatial Sense' are directly related to the world in which students live. Many of the concepts that students are taught in this strand are also used in other subjects such as science, social studies, and physical education In the measurement strand students learn about the measurable attributes of objects,in addition to the basic metric system. Elementary Focus: The measurement strand consists of multiple forms of measurement, as Marian Small states: "Measurement is the process of assigning a qualitative or quantitative description of size to an object based on a particular attribute." === Equations and formulas === A formula is an entity constructed using the symbols and formation rules of a given logical language. For example, determining the volume of a sphere requires a significant amount of integral calculus or its geometrical analogue, the method of exhaustion; but, having done this once in terms of some parameter (the radius for example), mathematicians have produced a formula to describe the volume. An equation is a formula of the form A = B, where A and B are expressions that may contain one or several variables called unknowns, and "=" denotes the equality binary relation. Although written in the form of proposition, an equation is not a statement that is either true or false, but a problem consisting of finding the values, called solutions, that, when substituted for the unknowns, yield equal values of the expressions A and B. For example, 2 is the unique solution of the equation x + 2 = 4, in which the unknown is x. === Data === Data is a set of values of qualitative or quantitative variables; restated, pieces of data are individual pieces of information. Data in computing (or data processing) is represented in a structure that is often tabular (represented by rows and columns), a tree (a set of nodes with parent-children relationship), or a graph (a set of connected nodes). Data is typically the result of measurements and can be visualized using graphs or images. Data as an abstract concept can be viewed as the lowest level of abstraction, from which information and then knowledge are derived. === Basic two-dimensional geometry === Two-dimensional geometry is a branch of mathematics concerned with questions of shape, size, and relative position of two-dimensional figures. Basic topics in elementary mathematics include polygons, circles, perimeter and areas. A polygon is a shape that is bounded by a finite chain of straight line segments closing in a loop to form a closed chain or circuit. These segments are called its edges or sides, and the points where two edges meet are the polygon's vertices (singular: vertex) or corners. The interior of the polygon is sometimes called its body. An n-gon is a polygon with n sides. A polygon is a 2-dimensional example of the more general polytope in any number of dimensions. A circle is a simple shape of two-dimensional geometry that is the set of all points in a plane that are at a given distance from a given point, the center.The distance between any of the points and the center is called the radius. It can also be defined as the locus of a point equidistant from a fixed point. A perimeter is a path that surrounds a two-dimensional shape. The term may be used either for the path or its length - it can be thought of as the length of the outline of a shape. The perimeter of a circle or ellipse is called its circumference. Area is the quantity that expresses the extent of a two-dimensional figure or shape. There are several well-known formulas for the areas of simple shapes such as triangles, rectangles, and circles. === Proportions === Two quantities are proportional if a change in one is always accompanied by a change in the other, and if the changes are always related by use of a constant multiplier. The constant is called the coefficient of proportionality or proportionality constant. If one quantity is always the product of the other and a constant, the two are said to be directly proportional. x and y are directly proportional if the ratio y x {\displaystyle {\tfrac {y}{x}}} is constant. If the product of the two quantities is always equal to a constant, the two are said to be inversely proportional. x and y are inversely proportional if the product x y {\displaystyle xy} is constant. === Analytic geometry === Analytic geometry is the study of geometry using a coordinate system. This contrasts with synthetic geometry. Usually the Cartesian coordinate system is applied to manipulate equations for planes, straight lines, and squares, often in two and sometimes in three dimensions. Geometrically, one studies the Euclidean plane (2 dimensions) and Euclidean space (3 dimensions). As taught in school books, analytic geometry can be explained more simply: it is concerned with defining and representing geometrical shapes in a numerical way and extracting numerical information from shapes' numerical definitions and representations. Transformations are ways of shifting and scaling functions using different algebraic formulas. === Negative numbers === A negative number is a real number that is less than zero. Such numbers are often used to represent the amount of a loss or absence. For example, a debt that is owed may be thought of as a negative asset, or a decrease in some quantity may be thought of as a negative increase. Negative numbers are used to describe values on a scale that goes below zero, such as the Celsius and Fahrenheit scales for temperature. === Exponents and radicals === Exponentiation is a mathematical operation, written as bn, involving two numbers, the base b and the exponent (or power) n. When n is a natural number (i.e., a positive integer), exponentiation corresponds to repeated multiplication of the base: that is, bn is the product of multiplying n bases: b n = b × ⋯ × b ⏟ n {\displaystyle b^{n}=\underbrace {b\times \cdots \times b} _{n}} Roots are the opposite of exponents. The nth root of a number x (written x n {\displaystyle {\sqrt[{n}]{x}}} ) is a number r which when raised to the power n yields x. That is, x n = r ⟺ r n = x , {\displaystyle {\sqrt[{n}]{x}}=r\iff r^{n}=x,} where n is the degree of the root. A root of degree 2 is called a square root and a root of degree 3, a cube root. Roots of higher degree are referred to by using ordinal numbers, as in fourth root, twentieth root, etc. For example: 2 is a square root of 4, since 22 = 4. −2 is also a square root of 4, since (−2)2 = 4. === Compass-and-straightedge === Compass-and-straightedge, also known as ruler-and-compass construction, is the construction of lengths, angles, and other geometric figures using only an idealized ruler and compass. The idealized ruler, known as a straightedge, is assumed to be infinite in length, and has no markings on it and only one edge. The compass is assumed to collapse when lifted from the page, so may not be directly used to transfer distances. (This is an unimportant restriction since, using a multi-step procedure, a distance can be transferred even with a collapsing compass, see compass equivalence theorem.) More formally, the only permissible constructions are those granted by the first three postulates of Euclid. === Congruence and similarity === Two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other. More formally, two sets of points are called congruent if, and only if, one can be transformed into the other by an isometry, i.e., a combination of rigid motions, namely a translation, a rotation, and a reflection. This means that either object can be repositioned and reflected (but not resized) so as to coincide precisely with the other object. So two distinct plane figures on a piece of paper are congruent if we can cut them out and then match them up completely. Turning the paper over is permitted. Two geometrical objects are called similar if they both have the same shape, or one has the same shape as the mirror image of the other. More precisely, one can be obtained from the other by uniformly scaling (enlarging or shrinking), possibly with additional translation, rotation and reflection. This means that either object can be rescaled, repositioned, and reflected, so as to coincide precisely with the other object. If two objects are similar, each is congruent to the result of a uniform scaling of the other. === Three-dimensional geometry === Solid geometry was the traditional name for the geometry of three-dimensional Euclidean space. Stereometry deals with the measurements of volumes of various solid figures (three-dimensional figures) including pyramids, cylinders, cones, truncated cones, spheres, and prisms. === Rational numbers === Rational number is any number that can be expressed as the quotient or fraction p/q of two integers, with the denominator q not equal to zero. Since q may be equal to 1, every integer is a rational number. The set of all rational numbers is usually denoted by a boldface Q (or blackboard bold Q {\displaystyle \mathbb {Q} } ). === Patterns, relations and functions === A pattern is a discernible regularity in the world or in a manmade design. As such, the elements of a pattern repeat in a predictable manner. A geometric pattern is a kind of pattern formed of geometric shapes and typically repeating like aa allpaper. A relation on a set A is a collection of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A2 = A × A. Common relations include divisibility between two numbers and inequalities. A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x2. The output of a function f corresponding to an input x is denoted by f(x) (read "f of x"). In this example, if the input is −3, then the output is 9, and we may write f(−3) = 9. The input variable(s) are sometimes referred to as the argument(s) of the function. === Slopes and trigonometry === The slope of a line is a number that describes both the direction and the steepness of the line. Slope is often denoted by the letter m. Trigonometry is a branch of mathematics that studies relationships involving lengths and angles of triangles. The field emerged during the 3rd century BC from applications of geometry to astronomical studies. == United States == In the United States, there has been considerable concern about the low level of elementary mathematics skills on the part of many students, as compared to students in other developed countries. The No Child Left Behind program was one attempt to address this deficiency, requiring that all American students be tested in elementary mathematics. == References == === Works cited === Halmos, Paul R. (1970). Naive Set Theory. Springer-Verlag. ISBN 978-0-387-90092-6.
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https://en.wikipedia.org/wiki/Elementary_mathematics
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