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'Taking calculus? Then you need the Wolfram Calculus Course Assistant. This definitive app for calculus--from the world...
see more
'Taking calculus? Then you need the Wolfram Calculus Course Assistant. This definitive app for calculus--from the world leader in math software--will help you work through your homework problems, ace your tests, and learn calculus concepts. Forget canned examples! The Wolfram Calculus Course Assistant solves your specific Calculus problems on the fly including step-by-step guidance for derivatives, integrals, and much more.This app covers the following topics applicable to Calculus, AP Calculus AB, AP Calculus BC, Calculus I, and Calculus II:- Evaluate any numeric expression or substitute a value for a variable.- Plot basic, parametric, or polar plots of the function(s) of your choice.- Determine the limit of a function as it approaches a specific value.- Differentiate any function or implicit function.- Find the critical points and inflection points of a function.- Identify the local and absolute extrema of a function.- Integrate a function, with or without limits.- Sum a function given a lower and upper bound.- Find the closed form of a sequence or generate terms for a specific sequence.'This app costs $3.99
'Taking discrete mathematics? Then you need the Wolfram Discrete Mathematics Course Assistant. This app for discrete...
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'Taking discrete mathematics? Then you need the Wolfram Discrete Mathematics Course Assistant. This app for discrete math--from the world leader in math software--will help you work through your homework problems, ace your tests, and learn discrete math concepts. The Discrete Mathematics Course Assistant solves your specific discrete math problems on the fly, providing answers to a broad range of subjects. - Do function calculations like domain and range, image and preimage, and inverse and growth - Compute logic problems like minimal forms, implications, propositions, and bitwise operations - Calculate set functions like power set, basic set operations, complement, and Venn diagrams - Use the Number Theory section for division, modular arithmetic, prime numbers, special numbers, and integer functions - Do sequence computations like summation, product, and limit of a sequence - Compute permutation and combinatorics questions, including derangements and permutations of list or finite relations and Pascal's triangle - Use the discrete probability section for Bernoulli trial equations and view statistics on coin and dice probabilities or view various distribution given the probability of success - View information on basic, named, or custom graphs in our Graph Theory section'This app costs $4.99
'Like fractals? Want to know more about them? The Wolfram Fractals Reference App is a handy reference you can take with you...
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'Like fractals? Want to know more about them? The Wolfram Fractals Reference App is a handy reference you can take with you wherever you go. It's great whether you're covering fractals in your math course or just want to explore the beautiful shapes and structures of fractals and the math behind them.- Choose from both common fractals and more unusual types- Visualize the Sierpiński gasket, the Koch snowflake, and the Mandelbrot set, as well as over 40 other fractals- Input parameters to customize your fractal type- Learn the rules behind the fractal construction- Explore hundreds of possibilities, including line and shape replacement fractals, space-filling curves, Blancmange function, Mandelbrot and Julia sets, and 3D fractals'This app costs $0.99
'Learning fractions? Then you need the Wolfram Fractions Reference App. Whether adding, subtracting, or converting fractions,...
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'Learning fractions? Then you need the Wolfram Fractions Reference App. Whether adding, subtracting, or converting fractions, the Wolfram Fractions Reference App will help you with your specific fraction problems. - Visualize fractions on a number line or pie chart - Convert a fraction to a decimal or percent, or vice versa - Get help with arithmetic including addition, subtraction, multiplication, and division - Reduce fractions to their simplest forms'This app costs $0.99
'Taking multivariable calculus? Then you need the Wolfram Multivariable Calculus Course Assistant. This definitive app for...
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'Taking multivariable calculus? Then you need the Wolfram Multivariable Calculus Course Assistant. This definitive app for multivariable calculus--from the world leader in math software--will help you work through your homework problems, ace your tests, and learn calculus concepts. Forget canned examples! The Wolfram Multivariable Calculus Course Assistant solves your specific multivariable problems on the fly, providing step-by-step guidance for limits, derivatives, integrals, and much more.This app covers the following topics applicable to Multivariable Calculus, Advanced Calculus, and Vector Calculus:- Evaluate any numeric expression, or substitute a value for a variable- Plot 2D or 3D functions of your choice- Determine the limit of a function as it approaches a specific value or values- Differentiate any single or multivariable function- Find the critical points and saddle points of a function- Calculate the gradient of a function- Identify the local extrema of a function- Find the single, double, or triple integral of a function- Determine the dot or cross product of two vectors- Calculate the divergence or curl of a vector fieldStay up to date with the latest version, and see the additions of directional derivatives, line integrals, surface integrals, arc length, and curvature!'This app costs $4.99
'Taking pre-algebra? Then you need the Wolfram Pre-Algebra Course Assistant. This definitive app for pre-algebra--from the...
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'Taking pre-algebra? Then you need the Wolfram Pre-Algebra Course Assistant. This definitive app for pre-algebra--from the world leader in math software--will help you work through your homework problems, ace your tests, and learn pre-algebra concepts. Forget canned examples! The Wolfram Pre-Algebra Course Assistant solves your specific pre-algebra problems on the fly.This app covers the following pre-algebra topics:- Find the divisors and prime factorization of a number- Calculate the GCD and LCM of two numbers- Determine the percent change- Reduce and round numbers- Evaluate expressions- Solve equations and simplify expressions- Convert units of length, area, volume, and weight- Compute the mean, median, and mode of a dataset- Plot equations on the coordinate plane- Graph inequalities on a number line- Calculate the area, surface area, or volume of a geometric figure- Find the midpoint, slope, and distance between two pointsThe Wolfram Pre-Algebra precalculus? Then you need the Wolfram Precalculus Course Assistant. This definitive app for precalculus--from the...
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'Taking precalculus? Then you need the Wolfram Precalculus Course Assistant. This definitive app for precalculus--from the world leader in math software--will help you work through your homework problems, ace your tests, and learn calculus concepts. Forget canned examples! The Wolfram Precalculus Course Assistant solves your specific precalculus problems on the fly, including solving equations, vector arithmetic, statistics, and much more.This app covers the following topics applicable to precalculus and trigonometry:- Evaluate any numeric expression or substitute a value for a variable- Solve a single equation or a system of equations- Plot functions on the x-y plane or draw a parametric or polar plot- Determine the sine, cosine, and tangent of a specific angle in a right triangle- Simplify, expand, or factor trigonometric functions- Find the partial fraction decomposition of an expression- Calculate the dot product, cross product, and magnitude of two vectors- Identify the mean, median, mode, and standard deviation of a set of data- Calculate permutations and combinationsThe Wolfram Precalculus statistics? Then you need the Wolfram Statistics Course Assistant. This definitive app for statistics--from the world...
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'Taking statistics? Then you need the Wolfram Statistics Course Assistant. This definitive app for statistics--from the world leader in math software--will help you work through your homework problems, ace your tests, and learn statistics concepts. Forget canned examples! The Wolfram Statistics Course Assistant solves your specific problems on the fly, covering descriptive statistics, distributions, and much more.This app covers the following topics applicable to Statistics and Introduction to Statistics:- Create a bar chart, histogram, or scatter plot of any set of data- Find the mean, median, mode, standard deviation, quartiles, and interquartile range of a dataset- Calculate normal probabilities and find information about the normal distribution- Calculate binomial probabilities and find information about the binomial distribution- Compute probabilities based on dice rolls and coin flips- Find the best-fit line of a set of data points- Select random integers or random real numbersThe Wolfram Statistics Course Assistant is powered by the Wolfram|Alpha computational knowledge engine and is created by Wolfram Research, makers of Mathematica—the world's leading software system for mathematical research and education.'This app costs $1.99
'Wolfram|Alpha: Get answers. Access expert knowledge. Wherever you are.Remember the Star Trek computer? It's finally happening--with Wolfram|Alpha. Building on 25 years of development led by Stephen Wolfram, Wolfram|Alpha has rapidly become the world's definitive source for instant expert knowledge and computation.Across thousands of domains--with more continually added--Wolfram|Alpha uses its vast collection of algorithms and data to compute answers and generate reports for you.Parts of Wolfram|Alpha are used in the Apple Siri Assistant; this app gives you access to the full power of the Wolfram|Alpha computational knowledge engine. Domains covered by Wolfram|Alpha include: MATHEMATICS, STATISTICS & DATA ANALYSIS, PHYSICS, CHEMISTRY, ENGINEERING, ASTRONOMY, and many more.The cost of this app is $3.99
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First Course in Mathematics Modeling - Text Only - 3rd edition
Summary: This text provides an introduction to the entire modeling process. Throughout the book, students practice key facets of modeling, including creative and empirical model construction, model analysis, and model research. The authors apply a proven six-step problem solving process to enhance a student's problem solving capabilities. Rather than simply emphasizing the calculation step, the authors first ensure that students learn how to identify problems, construct or se...show morelect models, and figure out what data needs to be collected. By involving students in the mathematical process as early as possible, beginning with short projects, the book facilitates their progressive development and confidence in mathematics and modeling. ...show less
"The authors keep a good balance of theory and practice, maintaining fidelity to the ideal of developing experience and skills in the modeling process, rather than overconcentrating on the mathematics of modeling. The revisions are thoughtful and strengthen the text, tying together more effectively the good selection of methods and applications contained in previous editions."
--Charles Landraitis, Boston College
"The approach to modeling is very solid, and corresponds with what I have seen as useful in teaching modeling at all levels for 25 years."
--Stephen J. Merrill, Marquette University
"The examples, projects and exercises are excellent. Very varied and interesting, with a good mix of topics. It is great to be able to pick and choose from among the topics and examples. At the same time there is nothing superfluous about the coverage
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60 - Differential Equations
Study of first order differential equations, higher order linear equations, and systems of differential equations and their applications. Solution techniques include various analytical methods, Laplace transforms, and numerical methods. The use of mathematical software is an integral part of the course.
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Essentials of Precalculus - 06 edition
Summary: This new text from the author team of Aufmann and Nation offers the same engaging style and support for students as the Aufmann College Algebra series, all in a brief format that covers the entire course in a single semester. Interactive learning techniques incorporated throughout the text help students better understand concepts, focus their study habits, and achieve greater success.
In this First Edition, the authors have also integrated many components i...show morento the textbook to help students diagnose and remediate weak algebra skills. Prerequisite review in the textbook and supporting materials allows students to fill in gaps in their mathematical knowledge, and keeps instructors from having to spend time on review. Review Notes next to examples and Prepare for the Next Section exercises provide point-of-use review. Extra support also comes from the Aufmann Interactive Method, featuring Try Exercises that allow students to practice math as it is presented and to more easily study for tests.
Prepare for the Next Section Exercises appear at the end of exercises and are specifically written to review prerequisite skills the student will need in the next section. Answers at the end of the text and a reference section help students review if they get a wrong answer.
Review Notes cover prerequisite skills to help students without the necessary knowledge to understand important concepts. These example-specific notes direct students to the appropriate pages where they can practice and review the skill, thus decreasing frustration and increasing success.
Interactive Reading Support Questions engage students in learning mathematics and encourage them to think critically.
Visualize the Solution graphics are often paired with Algebraic Solutions to assist visual learners in understanding concepts.
Focus on Problem Solving features at the beginning of each chapter review then demonstrate various strategies used by successful problem solvers. This builds students' comfort level with problem solving and leaves them with a collection of tips and strategies to refer to throughout the course.
Eduspace Houghton Mifflin's online learning tool powered by Blackboard, is a customizable, powerful and interactive platform that provides instructors with text-specific online courses and content. See the product supplements for more information
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Algebra I - 01 edition
Summary: Covers all the traditional topics teachers want in an algebra curriculum - Introduces all of the field properties along with the properties of equality early and encourages students to use these properties as justifications for solving equations. Provides complete coverage of polynomial operations and all factoring techniques to prepare students for work with rational expressions and quadratic equations later in the course. Thoroughly covers all traditional Algebra 1...show more topics, including work with rational and radical expressions. Optional coverage of proof is also
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Mathematics is the basic foundation course for all Engineering students. This edition covers the topics of numerical methods, matrices, Fourier Series and Fourier transforms along with Partial differential equations and Z-transforms. The subject matter has been presented in detailed and simple lucid way. The theory aspect is explained with illustrations... more...
The development of mathematical competence -- both by humans as a species over millennia and by individuals over their lifetimes -- is a fascinating aspect of human cognition. This book explores a vast range of psychological questions related to mathematical cognition, and provides fascinating insights for researchers and students of cognition and... more...
This book introduces the important concepts of finite-dimensional vector spaces through the careful study of Euclidean geometry. In turn, methods of linear algebra are then used in the study of coordinate transformations through which a complete classification of conic sections and quadric surfaces is obtained.
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9780471368762 Algebra and Trigonometry with Applications
Introductory Algebra and Trignometry with Applications by Paul Calter and Carol Felsinger Rogers This textbook introduces all the important topics for a student who needs preparatory, review, or remedial work in mathematics. Adapted from Calter's Technical Mathematics, it uses an intuitive approach and gives information in very small-segments. Careful page layout and numerous illustrations make the material easy to follow. Features of Introductory Algebra and Trigonometry with Applications include the following.Graphing Calculator: The graphing calculator has been fully integrated throughout the text, and calculator problems are given in the exercises. The book does not present any particular calculator. Keystrokes are shown in the early chapters, with verbal descriptions given thereafter.Common Error Boxes: Many of the mistakes that students repeatedly make have been identified and are presented in the text as Common Error boxes.Summary of Facts and Formulas: All important formulas are boxed and numbered in the text and are listed in the Summary of Facts and Formulas at the end of the book.Examples: The many fully worked examples are specifically chosen to help the student do the exercises. Exercises: A large number of exercises is given after each section, graded by difficulty and grouped by type.Chapter Review Exercises: Every chapter ends with a set of Chapter Review Exercises. In contrast to the exercises, most are scrambled as to type and difficulty, requiring the student to be able to identify type.Applications: Applications drawn from many fields are included in the examples, the exercises, and the Chapter Review.Writing Questions: The "writing-across-the-curriculum" movement urges writing in every course as an aid to learning. In response, this text provides a writing question at the end of every chapter.Team Projects: As an aid to collaborative learning, a team project is included at the end of most chapters.Thorough Support Material: Among valuable components found at the end of the book are the Summary of Facts and Formulas, Conversion Factors, Answers to Selected Exercises, Index to Applications, Index to Writing Questions, Index to Team Projects, and General Index.For the Instructor: An Instructor's Manual contains worked-out solutions to every even-numbered problem in the text. This most valuable supplement is available to any instructor using the textbook.For more information on this book or any of Prentice Hall's other new technology titles, visit our Web site at prenhall.com
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College Trigonometry / With CD-ROM - 4th edition
Summary: The Fourth Edition of College Trigonometry continues to promote student success by engaging students in mathematics, thus helping them see the dynamic link between concepts and applications. The authors' hallmark approach, the Aufmann Interactive Method, encourages students to interact with math by presenting an annotated example, then guiding students with a Try Exercise, and finally presenting a worked-out solution for immediate reinforcement of the concept. A weal...show moreth of new features designed to enhance learning include more in-text guidance as well as special web-based resources, and an unparalleled Instructor's Annotated Edition facilitates teaching.
New! An Instructor's Annotated Edition, unlike any other offered for this course, features reduced student text pages with special instructor resources in the margins: teaching tips, extra examples, ideas for reinforcing concepts, discussion suggestions, highlighted vocabulary and symbols, challenge problems, quizzes, suggested assignments, and references to transparencies that may be found both in the Instructor's Resource Manual and on the web site.
New! Side-by-Side Solutions to examples pair an algebraic solution and a graphical representation to accommodate different learning styles.
New! Integrated web resources include selected Take Note boxes (identified by a special web icon) which direct students to an interactive example or a downloadable file on the web site. These special resources can be used by instructors for presentation purposes or can be assigned to students to help them 'visualize' a concept.
New! Concept Lists now prominently feature all the major topics at the beginning of each section, preparing students for the concepts to follow.
Exploring Concepts with Technology, a special end-of-chapter feature, expands on ideas introduced in the text by using technology to investigate extended mathematical applications or topics.
Projects at the end of each exercise set are designed to encourage students (or groups of students) to research and write about mathematics and its applications. Additional Projects are included in the Instructor's Resource Manual and on the book's web site.
Topics for Discussion, conceptual exercises included at the end of each section, can be used for discussion or writing assignments.
Take Note and Math Matters (formerly called Point of Interest) margin notes alert students about interesting aspects of math history, applications, and points that require special attention91
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Math Parther Engine
A parser that understand the mathematical equations.Just enter the equation and you will get the result
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More About
This Textbook
Overview
Mathematics for the Technical Trades is a complete math book geared toward those in technical trades such as electronics, construction, automotive, machining, welding, drafting, plumbing, and printing. This easy-to-understand text begins with fractions and decimal numbers and proceeds to build a solid foundation in exponents, the metric system, algebra, geometry and trigonometry. For those in the technical trades who want to learn, review, or reinforce the math skills that are essential to their trades.
Related Subjects
Read an ExcerptTable of Contents
Preface
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Application of Derivatives -Important Questions & Preparation Tips
This is the CBSE Class 12th Chapter, Application of Derivatives. Experts of Jagranjosh.com offer the best practice material that covers all important questions so that students will not miss any portion while preparing for board exams or competitive exams. Consider the mentioned terms/questions at the time of studying. Revise the important formulae and then practice the important questions.
The important discussions in Application of Derivatives are as follows:
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Algebra for College Students - Text - 8th edition
Summary: Kaufmann and Schwitters have built this text's reputation on clear and concise exposition, numerous examples, and plentiful problem sets. This traditional text consistently reinforces the following common thread: learn a skill; use the skill to help solve equations; and then apply what you have learned to solve application problems. This simple, straightforward approach has helped many students grasp and apply fundamental problem solving skills necessary for future mathematics course...show mores in an easy-to-read format. The new Eighth Edition of ALGEBRA FOR COLLEGE STUDENTS includes new and updated problems, revised content based on reviewer feedback and a new function in iLrn. This enhanced iLrn homework functionality was designed specifically for Kaufmann/Schwitters' users. Textbook-specific practice problems have been added to iLrn to provide additional, algorithmically-generated practice problems, along with useful support and assistance to solve the problems
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The key to success in mathematics is to understand that all sub-subjects (algebra, trigonometry, geometry, calculus, differential/difference equations, statistics, probability) are really a LANGUAGE. And more than any spoken language, mathematics is truly
THE universal language. It is also key to understand the PROCESS or STEPS: how to take the problem at hand, break it down into its individual parts, and work through the steps to achieve the correct answer. Like any sport, or as in driving, mathematics involves
following a series of simple RULES and applying the theory to the real world. Once the rules are followed, all that is required is PRACTICE! So, remember: it's a language, which involves understanding steps, following rules, applying the concepts to the real
world, and then . . . the hardest part! :) . . . . practice, practice, practice! You CAN do it!
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Thinking Mathematically - With 2 CDs - 4th edition
Summary: This general survey of mathematical topics helps a diverse audience, with different backgrounds and career plans, to understand mathematics. Blitzer provides the applications and technology readers need to gain an appreciation of mathematics in everyday life. Demonstrates how mathematics can be applied to readers' lives in interesting, enjoyable, and meaningful ways. Features abundant, step-by-step, annotated Examplesthat provide a problem-solving approach to reach the ...show moresolution; annotations are conversational in tone, explaining key steps and ideas as the problem is solved. Begins each section with a compelling vignette highlighting an everyday scenario, posing a question about it, and exploring how the chapter section subject can be applied to answer the question. A highly readable reference for anyone who needs to brush up their mathematics skillsGood
Campus_Bookstore Fayetteville, AR
Used - Good Hardcover. With CD! 4th2.41 +$3.99 s/h
Acceptable
MotorCityBooks Brownstown, MI
With pride from Motor City. All books guaranteed. Best Service, Best PricesAcceptable
Yankee Clipper Books Windsor Locks, CT
Sail the Seas of ValueCD Missing
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Algebra 1: Linearity, Slope, & Direct Variation
Discover how everyday experiences are connected to Math. Understand how quickly a scuba diver gets from reef to rock! Use what you know, and experience what you don't. Open up your world to a new way of learning with AC VBook apps.
"AC VBooks is a real game changer in educational content. It is a new generation of e-Books; it is high-quality, digital content, and study path all at once."
Gary Bitter,
Executive Director of TBLR, ASU
Have you ever wondered why mass and weight are not the same thing? These concepts, and more, open up and come to life through a tablet or PC.
Considered turbo-charged e-Books, AC VBooks blend a variety of instructional activities, from explorations and visual explanations to hands-on, web-based exercises. e-Books are words on a screen, AC VBooks are an interactive world of learning on a screen.
Get engaged with game-like simulations and real-world scenarios that bring everyday meaning to tough Math concepts.
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9780321559852Bob Blitzerrs"sunique background in mathematics and behavioral sciences, along with his commitment to teaching, inspired him to develop a precalculus series that gets readers engaged and keeps them engaged. Presenting the full scope of the mathematics is just the first step. Blitzer draws in the reader with vivid applications that use math to solve real-life problems. These applications help answer the question "When will I ever use this?" Readers stay engaged because the book helps them remain focused as they study. The three-step learning systemSee It, Hear It, Try Itmakes examples easy to follow, while frequent annotations offer the support and guidance of an instructorrs"s voice. Every page is interesting and relevant, ensuring that readers will actually use their textbook to achieve success! Prerequisites: Fundamental Concepts of Algebra; Equations and Inequalities; Functions and Graphs; Polynomial and Rational Functions; Exponential and Logarithmic Functions; Trigonometric Functions; Analytic Trigonometry; Additional Topics in Trigonometry; Systems of Equations and Inequalities; Matrices and Determinants; Conic Sections and Analytic Geometry; Sequences, Induction, and Probability For all readers interested in college algebra.
Author Biography
Bob Blitzer is a native of Manhattan and received a Bachelor of Arts degree with dual majors in mathematics and psychology (minor: English literature) from the City College of New York. His unusual combination of academic interests led him toward a Master of Arts in mathematics from the University of Miami and a doctorate in behavioral sciences from Nova University. Bob is most energized by teaching mathematics and has taught a variety of mathematics courses at Miami-Dade College for nearly 30 years. He has received numerous teaching awards, including Innovator of the Year from the League for Innovations in the Community College, and was among the first group of recipients at Miami-Dade College for an endowed chair based on excellence in the classroom. Bob has written Intermediate Algebra for College Students, Introductory Algebra for College Students, Essentials of Intermediate Algebra for College Students, Introductory and Intermediate Algebra for College Students, Essentials of Introductory and Intermediate Algebra for College Students, Algebra for College Students, Thinking Mathematically, College Algebra, Algebra and Trigonometry, and Precalculus, all published by Pearson Prentice Hall.
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Peer Review
Ratings
Overall Rating:
Maths Online is a medium-sized collection of interactive material at the lower division college mathematics level. The material originated with various projects coordinated at the University of Vienna and is perhaps not as well known as some of the larger US sites. The site includes a gallery of java applets with an accompanying set of interactive tests, a puzzle creation page, an extensive collection of online java math tools that open in separate browser windows for simultaneous use with other site pages, and an excellent collection of links to other math learning materials and collections of resources. Classroom suggestions, project worksheets, and the ability to provide feedback to the authors are provided. In addition, an online HTML formula tool is given along with other ideas about how to render math symbols in web browsers.
The authors describe their goal as promoting new ways of learning and understanding mathematics ? particularly in regard to abstract structures. Interaction rather than explanation is the primary objective
Target Student Population:
The materials here range from basic mathematics through calculus and linear algebra.
Prerequisite Knowledge or Skills:
No specific prerequisites are needed other than standard background for the level of mathematics selected. All topics are lower division college mathematics.
Type of Material:
Mainly interactive java applets.
Recommended Uses:
These applets would be appropriate for use in student discovery activities.
Technical Requirements:
Java enabled browser. As usual there are some compatibility difficulties with different operating systems and browsers of different ages. The site includes a page that mentions some of the known side effects of different configurations. There are several mirror sites for this material.
Evaluation and Observation
Content Quality
Rating:
Strengths:
The site has won many web awards. As well as its own material, the site includes a comprehensive list of other available tools and sites.
The gallery section includes over 50 dynamical diagrams that react to user input and are designed to facilitate understanding ? it includes applets, graphics and other programs organized by broad mathematical topics, e.g., sets, polar coordinates, sequences and series, functions, differentiation, integration, etc.
The interactive tests section includes multiple choice tests, puzzles, and other interactive tests for over 25 items such as sets, variables, equations, functions, limits, derivatives and integration.
The online tools section includes dozens of simple and effective java tools from Maths Online, the MathServe Project at Vanderbilt University, and other sources.
The links section includes a number of links to other web resources for mathematics ordered by topic such as numbers, geometry, trigonometry, linear algebra, fractals, etc.
The collections section includes links to a number of large collections of math resources such as Math Forum, UTK Math Archives, The Geometry Center, Java Sketchpad, GEONET, and others U.S. and international sites.
The puzzle workshop allows creation of your own mathematical puzzles by use of preformatted java.
The site lists a large group of university and K-12 collaborators plus several governmental and corporate sponsors.
Concerns:
There is limited explanation of the underlying mathematics ? more complete explanations are available in German.
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
The java applets provide a wide range of opportunities for interactive learning. Students may observe the effect of changes in coefficients in polynomial graph plots,
in the derivatives and integrals of functions, and much more. The applets are simple and effective and would certainly enhance the teaching/learning process.
The site includes many opportunities for feedback, including email, web forms, and regular mail. The authors appear eager for feedback and maintain an online archive of user comments. Many of the links are to sites different from those normally encountered by an American user. The ability to create your own simple puzzles is a nice feature.
Concerns:
Users desiring explanation of the underlying mathematics will need to explore other resources ? but, given the goal of encouraging interaction, this is acceptable.
Ease of Use for Both Students and Faculty
Rating:
Strengths:
Site navigation is excellent; java applets pop up in separate browser windows. Most of the applets work effectively in a variety of MAC and Windows environments and the controls are relatively simple.
The authors make the entire site available for download (as a zip file) for offline viewing for those who may have slow or inaccessible internet connections.
The authors provide a Java functionality test that users can perform to determine whether their computer is able to run the Java applets on the site.
Concerns:
The use of English may be somewhat formal for some American students but this should not affect the ability to understand the material. A German language version is available. As usual, operating system and browser compatibility is of some concern.
In some browser configurations, a number of the java applets popped ?under?, which may be confusing to novice web users
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To log in and use all the features of Khan Academy, please enable JavaScript in your browser.
Algebra I
Algebra is the language through which we describe patterns. Think of it as a shorthand, of sorts. As opposed to having to do something over and over again, algebra gives you a simple way to express that repetitive process. It's also seen as a "gatekeeper" subject. Once you achieve an understanding of algebra, the higher-level math subjects become accessible to you. Without it, it's impossible to move forward. It's used by people with lots of different jobs, like carpentry, engineering, and fashion design. In these tutorials, we'll cover a lot of ground. Some of the topics include linear equations, linear inequalities, linear functions, systems of equations, factoring expressions, quadratic expressions, exponents, functions, and ratios.
Did you realize that the word "algebra" comes from Arabic (just like "algorithm" and "al jazeera" and "Aladdin")? And what is so great about algebra anyway?
This tutorial doesn't explore algebra so much as it introduces the history and ideas that underpin it.
Wait, why are we using letters in math? How can an 'x' represent a number? What number is it? I must figure this out!!! Yes, you must.
This tutorial is great if you're just beginning to delve into the world of algebraic variables and expressions.
Using the combined powers of Chuck Norris and polar bears (which are much less powerful than Mr. Norris) to better understand what expressions represent and how we can manipulate them.
Great tutorial if you want to understand that expressions are just a way to express things!
All the symbols you write in math are just a language or short-hand to represent real-world ideas. In this tutorial, we'll get experience writing algebraic expressions to elegantly represent real-life ideas.
Algebraic expressions can be composed of pretty much any operation, including fractions. Here we'll explore how to manipulate fractions algebraically. In some ways this is just a review of adding, subtracting, multiplying and dividing fractions, but now we are doing it with variables!
Much of algebra seems obsessed with "doing the same thing to both sides". Why is this? How can we develop an intuition for which algebraic operations are valid and which ones aren't?
This tutorial takes a high-level, conceptual walk-through of what an equation represents and why we do the same thing to both sides of it.
This tutorial is a survey of all the core ideas in a traditional first-year algebra course. It is by no means comprehensive (that's what the other 600+ videos are for), but it will hopefully whet your appetite for more algebra!
The core underlying concepts in algebra are variables, expressions, equations and inequalities. You will see them throughout your math life (and even life after school).
This tutorial won't give you all the tools that you'll later learn to analyze and interpret these ideas, but it'll get you started thinking about them.
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we can see, in vector, we use a lot of algebraic expressions. The above example is only one example. There are more examples of the connection between the linear equation chapter in form 1 and the vector chapter in additional mathematics for form 5.
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This is a set of materials developed at the National University of Singapore concerning the connections between mathematics...
see more
This is a set of materials developed at the National University of Singapore concerning the connections between mathematics and art and architecture. The author emphasizes that mathematics is not just about formulas and logic, but about patterns, symmetry, structure, shape and beauty. There are powerpoint tutorials, text and graphics descriptions, and a wealth of links to other valuable resources.
This is a subpage of the Maths Online collection of interactive material at the lower division college mathematics level....
see more site contains a collection of fully developed high school curriculum modules that use the Internet in significant ways. ...
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This site contains a collection of fully developed high school curriculum modules that use the Internet in significant ways. There are currently 15 modules in Mathematics and 6 modules in Science; also, there are approximately two dozen additional modules that have been created by instructors and/or Education students.The learning modules here are web-based, technology intensive lessons focusing on mathematics and science in an applied context. They have been developed for teachers, by teachers, aligned with the Illinois State Learning Standards and the National Council for Teachers of Mathematics (NCTM) Standards. Some of the lessons are designed to last over several days, some only for a class period.
The MSTE lessons site contains a collection of excellent high school/lower college division math lessons (and a limited...
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The MSTE lessons site contains a collection of excellent high school/lower college division math lessons (and a limited number of science lessons) that use the Internet in significant ways. The lessons have been developed with descriptions of the problem, connections to standards, examples of use, references, and more. Java source codes are often available. The Office for Mathematics, Science, and Technology Education (MSTE) is a division of the College of Education at the University of Illinois at Urbana-Champaign.
The goal of this study was to determine whether students' achievement in Calculus courses could be improved using the online...
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The goal of this study was to determine whether students' achievement in Calculus courses could be improved using the online assessment system WeBWorK, with or without interactive classroom support. Three instructional designs (C1, C2 and C3) were compared, all using lecture format classes and standard content, but with differences in assignment delivery: C1, paper; C2, WeBWorK with unlimited tries; C3 differed from C2 only because 20% of class time was spent with students working on assignments, interacting with the teacher and each other. There were no differences in student achievement, as measured by independent coding of student protocols, or motivation between C1 and C2. C3 students outperformed other students and exhibited more effort. The self-efficacy of all students decreased pre- to post-instruction with the exception of women in C3 classes. Importantly, the C3 design has now been adopted by a majority of instructors at the research site.
A java application that lets you investigate the problem of creating a phylgenetic tree. there is some explanation of the...
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A java application that lets you investigate the problem of creating a phylgenetic tree. there is some explanation of the problem of drawing phylogenetic trees and a couple of versions of the applet. The applets let you randomly generate trees and also let you infer a phylogenetic tree with a couple of different methods. Number of species, mutation rate and the method for calculating the distance matrix can all be varied.
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Quick Review Math Handbook hot words hot topics
9780078601262
ISBN:
0078601266
Pub Date: 2004 Publisher: McGraw-Hill Higher Education
Summary: "Quick Review Math Handbook: Hot Words, Hot Topics" (available in English and Spanish) provides students and parents with a comprehensive reference of important mathematical terms and concepts to help them build their mathematics literacy. This handbook also includes short-instruction and practice of key standards for Middle School and High School success.
Glencoe McGraw-Hill Staff is the author of Quick Rev...iew Math Handbook hot words hot topics, published 2004 under ISBN 9780078601262 and 0078601266. Two hundred twenty seven Quick Review Math Handbook hot words hot topics textbooks are available for sale on ValoreBooks.com, one hundred seventy one used from the cheapest price of $0.01
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200 Level Math Courses
MA 203, Foundations of Elementary Mathematics I 204, Foundations of Elementary Mathematics II, will also be of value for any student who wants a better understanding of these ideas. Focus on understanding and exploring the mathematics through problem solving, projects, group explorations, use of manipulatives, and some use of technology. MA 203 concentrates on problem solving, whole number arithmetic and theory, discrete math, integers, fractions, decimals, and algebraic concepts. MA 203 does not count towards the mathematics major or minor requirements.
Text: Mathematics for Elementary School Teachers, Textbook and Explorations, by Tom Bassarear.
MA 204, Foundations of Elementary Mathematics II 203, Foundations of Elementary Mathematics I, will also be of value for any student who wants a better understanding of these ideas. Focus on understanding and exploring the mathematics through problem solving, projects, group explorations, use of manipulatives, and some use of technology. Topics in MA 204 include fractions, ratios and percents, data analysis, counting and probability, geometry of shape, measurement, and measurement geometry (perimeter, area, surface area, volume). MA 204 does not count towards the mathematics major or minor requirements.
MA 219, History of Mathematics
Development of mathematical concepts from primitive counting methods through the invention of calculus including the history of computers and computing. Prerequisite: Mathematics 126, passed with a grade of "C-" or higher.
MA 237, Programming in Mathematics
Provides an introduction to the use of technology as it applies to mathematics. A major component of the course will be to build a solid foundation in the skills needed to apply mathematical concepts to programming. In addition, the use of technology in presentations, scholarly searches, and its role and limitations in computer and internet security will be covered. Students will gain an appreciation of the important ethical and social issues involving the use of technology. Prerequisites: MA-120, MA-125, and MA-126, each passed with a "C-" or higher and a passing score on Gateway Exam 2. Co-requisite: MA-221 or MA-211 or MA-225.
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Applied Mathematics
Why SVSU?
Applied mathematicians with skills in computer science, electronic design and theory, statistics and probably are in demand in government, industry, research and education. The program includes courses in calculus, discrete mathematical structures, applied probability and statistics and a computer science course. The Math Resource Center provides free tutoring for MATH 081- MATH 261, as well as help with individual assignments.
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Calculus of a Single Variable
Browse related Subjects
This text combines the theoretical instruction of calculus with current best-practise strategies.This text combines the theoretical instruction of calculus with current best-practise strategies
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More About
This Textbook
Overview
Minimal prerequisites make this text ideal for a first course in number theory. Written in a lively, engaging style by the author of popular mathematics books, it features nearly 1,000 imaginative exercises and problems. Solutions to many of the problems are included, and a teacher's guide is available. 1978
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Student Activity Book exercises help reinforce the lessons from the student text and provide a matrix for assessment. Chapter reviews, cumulative reviews, math history, dominion mandate, and lesson-based practices are included.
The accompanying activity manual teacher's guide includes full-page reproductions of the student pages have the correct answers overlaid in magenta ink; page-numbers to where the answers may be found within the student textbook are not included. 318 pages, softcover, spiral-bound. The CD-ROM includes worked-out solutions in PDF files.
Evaluate student progress and comprehension with this set of tests have glue bindings for easy removal; tests for each chapter are included. The test answer key includes full-page reproductions of the student tests with the correct answers overlaid in pink ink; pages are loose-leaf and three-hole-punched.
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Intermediate Algebra - 2nd edition
Summary: This student-focused text addresses individual learning styles through the use of a complete study system that starts with a learning styles inventory and presents targeted learning strategies designed to guide students toward success in this and future college-level courses.
Students who approach math with trepidation will find that Intermediate Algebra, Second Edition, builds competence and confidence. The study system, introduced at the outset and used c...show moreonsistently throughout the text, transforms the student experience by applying time-tested strategies to the study of mathematics. Learning strategies dovetail nicely into the overall system and build on individual learning styles by addressing students' unique strengths. The authors talk to students in their own language and walk them through the concepts, showing students both how to do the math and the reasoning behind it. Tying it all together, the use of the Algebra Pyramid as an overarching theme relates specific chapter topics to the 'big picture' of algebra99 +$3.99 s/h
Good
HPB-1960
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Summary: These popular and proven workbooks help students build confidence before attempting end-of-chapter problems. They provide short problems and exercises that focus on developing a particular skill, often requiring students to draw or interpret sketches and graphs, or reason with math relationships. New to the Second Edition are exercises that provide guided practice for the textbook's Problem-Solving Strategies, focusing in particular on working symbolically55 +$3.99 s/h
Good
Helping Hands Global Kansas city, MO
2009 Paperback This book is in good condition with minimum amount of wear. Same day shipping. Thank you94 +$3.99 s/h
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Trade Used-Like New We are a Howard Co., Maryland-based brick-and-mortar store with over 75, 000 volumes. Satisfaction Guaranteed! !5011.94
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Optimization Approaches for Solving String Selection Problems provides an overview of optimization methods for a wide class of genomics-related problems in relation to the string selection problems. This class of problems addresses the recognition of similar characteristics or differences within biological sequences. Specifically, this book considers... more...
Comprehensive and thorough development of both probability and statistics for serious computer scientists; goal-oriented: "to present the mathematical analysis underlying probability results" Special emphases on simulation and discrete decision theory Mathematically-rich, but self-contained text, at a gentle pace Review of calculus and linear algebra... more...
Modern development of science and technology is based to a large degree on computer modelling. To understand the principles and techniques of computer modelling, students should first get a strong background in classical numerical methods, which are the subject of this book. This text is intended for use in a numerical methods course for engineering... more...
MULTIPLY your chances of understanding DISCRETE MATHEMATICS If you're interested in learning the fundamentals of discrete mathematics but can't seem to get your brain to function, then here's your solution. Add this easy-to-follow guide to the equation and calculate how quickly you learn the essential concepts.
Written by award-winning math professor... more...
The Basics of Computer Arithmetic Made Enjoyable and Accessible-with a Special Program Included for Hands-on Learning "The combination of this book and its associated virtual computer is fantastic! Experience over the last fifty years has shown me that there's only one way to truly understand how computers work; and that is to learn one computer and more...
About the Book: The book `Fundamental Approach to Discrete Mathematics` is a required part of pursuing a computer science degree at most universities. It provides in-depth knowledge to the subject for beginners and stimulates further interest in the topic. The salient features of this book include: Strong coverage of key topics involving recurrence... more...
The field of discrete calculus, also known as 'discrete exterior calculus', focuses on finding a proper set of definitions and differential operators that make it possible to operate the machinery of multivariate calculus on a finite, discrete space. In contrast to traditional goals of finding an accurate discretization of conventional multivariate... more...
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The course will
cover selected material in Chapters 1 through 5 of the text.The topics emphasize the basic principles of exponential and logarithmic
functions, introduction to limits and derivatives, computation and application
of derivatives, and the basic concept of the integral.
CLASS POLICY
Student Learning Outcomes:Upon completion of this course, the student should be able to:
Display a sound understanding of limits and continuity
Display a sound understanding of derivatives of
algebraic and transcendental functions
Apply the concepts of differential calculus to a
variety of applications
Display a sound understanding of basic integrals
Tests:Five chapter tests
will be given over the term along with a comprehensive final exam.The Final Exam may replace your lowest test score.The average of the five tests will represent
60% of the class grade.
Test 1Chapter 1 (Functions)
Test 2Chapter 2 (Limits)
Test 3Chapter 3 (Differentiation)
Test 4Chapter 4 (Applications)
Test 5Chapter 5 (Integrals)
Final Exam:The Final Exam is a comprehensive exam that will represent
20% of the class grade.
The Final Exam is currently scheduled for:Monday, May 2, 2011 (10:30 am -
12:30 pm)
Quiz / Homework:Quizzes will be given weekly.Make-up quizzes are not given, but the lowest quiz score will be dropped.Homework will be assigned daily and discussed the following class period.
The quiz average represents 20% of the class grade.
Final
Grades:The course grade will be based on the comprehensive
final exam (20%), quiz/homework average (20%), and class test average (60%).
Note:
If the Final Exam is better than your lowest test
score, the Final Exam will replace that score.
Grade AverageCourse Grade
90 - 100A
80 - 89B
70 - 79C
60 - 69D
Below 60F
Calculators: A scientific or
graphing calculator that does not have symbolic differentiation or integration
capabilities is recommended, and may be used on all exams.
OTHER INFORMATION
Attendance:If you are absent from a class, you are responsible for all
material covered and all announcements made.No make-up tests or quizzes will be given for any reason.If you know that you will be out on a test date due to prior obligations,
then you may make an appointment to take the test early.If you are absent from a test, the final exam will replace your missed
test score (final exam replaces lowest test score).Only one missed test can be replaced; a second or third missed test will
be given a grade of zero.
Honesty:Every student is expected and required to do his or her own work
in this course and all other courses at Dalton State College.Any instances of cheating will result in a minimum penalty of dismissal
from the course with a grade of "F".
Visitors: College policy allows
only those students registered for a class to attend that class. You may not
bring guests or children to class.
Etiquette: Talking in class
should be restricted solely to questions and comments pertaining to the material
at hand and intended for me and the whole class to hear.Persistent disruptive talking will result in a new seating arrangement
for the talkers.
Math Lab:The
math lab will be available throughout the day for your assistance.It is located in Sequoya, Room 155 and operating hours will be posted on
the door.
DROP / WITHDRAWAL
The last day to drop this class without penalty is
Monday March 21, 2011. You will be
assigned a grade of W.After this date, withdrawal without penalty is permitted only in cases of
extreme hardship as determined by the Vice President for Academic Affairs;
otherwise a grade of WF will be issued.The
proper form for withdrawing from all classes at the college after the official
drop/add period but before the published withdrawal date is the Schedule
Adjustment Form.Students who are
assigned to the Academic Advising Center for advisement must meet with an
advisor or staff member at the Academic Advising Center (107 Liberal Arts
Building) to initiate the withdrawal process.All other students must meet with a staff member or advisor at the Office
of Academic Resources in the PopeStudent
Center
to initiate the withdrawal process.
After meeting with the staff member or advisor, all students will then finalize
the withdrawal process in the Financial Aid Office.Students who fail to complete the official drop/withdrawal procedure will
receive the grade of F.Withdrawal from class is a student responsibility.The grade of W counts as hours attempted for the purposes of financial aid.
WORKFORCE DEVELOPMENT
If a student receiving aid administered by the DSC
Workforce Development Department drops this class or completely withdraws from
the College, the Schedule Adjustment Form must be taken to the Workforce
Development Office located in Room 214 of the TechnicalEducationBuilding. The Office is
open on the following schedule:
Students with disabilities or special needs are encouraged
to contact Disability Support Services in Academic Resources.In order to make an appointment to obtain information on the process of
qualifying for accommodations, it is the
student's responsibility to contact the Disability Support Specialist.
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Mike Sullivan's time-tested approach focuses students on the fundamental skills they need for the course: preparing for class, practicing with homework, and reviewing the concepts. In the Ninth Edition, College Algebra has evolved to meet today's course needs, building on these hallmarks by integrating projects and other interactive learning tools for use in the classroom or online.
Note : Access codes and supplements are not guaranteed with rentals.
Editorial reviews may belong to another edition of this title.
Customers Who Bought This Item Also Bought:
College Algebra (9th Edition): Search Results1024910250
Book Description:Pearson, 2011. Book Condition: New. Brand New, Unread Copy in Perfect Condition. A+ Customer Service! Summary: Mike Sullivan's time-tested approach focuses students on the fundamental skills they need for the course: preparing for class, practicing with homework, and reviewing the concepts. In the Ninth Edition , College Algebra has evolved to meet today's course needs, building on these hallmarks by integrating projects and other interactive learning tools for use in the classroom or online. Bookseller Inventory # ABE_book_new_0321716817121
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GCSE Mathematics: Revision and Practice: Homework Answer Book
Browse related Subjects
This book contains all the answers to all the exercises in the Higher and Foundation GCSE Mathematics: Revision and Practice Homework books in a clear, easy-to-read style.This book contains all the answers to all the exercises in the Higher and Foundation GCSE Mathematics: Revision and Practice Homework books in a clear, easy-to-read
| 677.169 | 1 |
College Algebra
Browse related Subjects
...Read More help students learn to think mathematically and to develop genuine problem-solving skills. Comprehensive and evenly-paced, the text has helped hundreds of thousands of students. Incorporating technology, real-world applications, and additional useful pedagogy, the sixth edition promises to help more students than ever build conceptual understanding and a core of fundamental skills
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Different Versions of Math 095
There are several options available for students who wish to take Math 095. The course is offered in the following formats:
In a traditional classroom setting meeting three days per week for 50 minutes per class meeting;
In a computer lab five days per week for 50 minutes per class meeting using the ALEKS software;
In conjunction with Math 090 in a computer lab, meeting 5 days per week, twice a day (75 minutes in the morning and 50 minutes in the afternoon);
In conjunction with Math 105 in a computer lab, meeting 5 days per week, twice a day (75 minutes in the morning and 50 minutes in the afternoon);
In a hybrid format, meeting face-to-face for only one 50 minute class meeting per week;
In a completely online format with no face-to-face meetings.
1. Traditional
The first version is the familiar one and needs no further explanation. However, all students who take 095 in the traditional setting are now required to complete homework online and fulfill the expectations of the Basic Skills Testing Program. Be sure you understand the Basic Skills Tests. More information can be found in the section on Basic Skills Tests.
2. ALEKS
In the second format, students attend class meetings in a computer lab five days per week and work with computer adaptive testing software, called ALEKS, to monitor their mastery of the course material. This style is ideal for the highly motivated student who has experienced some success with beginning algebra and who is looking for a class format that will allow that student to focus on those parts of the material that the student has previously found difficult. In addition to doing homework and assessments via the internet, students are also required to turn in written work. Assessments are taken in class in a monitored format.
3. Combined 090/095
In the third option students are given the opportunity to complete both Math 090 and Math 095 in the same semester. Classes meet twice a day, every day, and are taught using a combination of small group instruction and individual tutoring in conjunction with computer adaptive testing software from ALEKS. This format is ideal for the highly motivated student who is looking to complete the developmental mathematics sequence in one semester in order to begin college-level work sooner. Students who want to enroll in these sections will actually register for the new course number Math 094. These sections have mandatory attendance and homework policies.
4. Combined 095/105
In the fourth version students are afforded the opportunity to complete both Math 095 and Math 105 in the same semester. Classes meet twice a day, every day, and are taught using a combination of small group instruction and individual tutoring in conjunction with computer adaptive testing software from ALEKS. This style is ideal for the highly motivated student who needs to complete Math 105 in order to take further courses in Mathematics, Chemistry, etc. It is not recommended for students who will take Math 105 for the sole purpose of completing the General Education Requirement in mathematics. Students who register for these sections must also register for the corresponding sections of Math 105. These sections have mandatory attendance and homework policies.
5. Hybrid Online/Traditional
In the fifth option, students attend class meetings in a regular classroom. However, due to the reduced face-to-face time, students are expected to do most of the learning on their own. Students use the university course management system, Desire to Learn (D2L) for online discussions and the ALEKS software for mastering the mathematical content. This type requires that students be highly motivated and have good time management skills since so much of the work is on their own.
6. Online Only
In addition to the above five choices, a completely online version of Math 095 was offered for the first time in the fall of 2009, also using the ALEKS software. This format is similar to the hybrid course but there are no face-to-face meetings. In particular, students use the university course management system, Desire to Learn (D2L) for online discussions and the ALEKS software for mastering the mathematical content. This type requires that students be highly motivated and have good time management skills since all of the work is on their own.
These different versions have been developed to offer students options for completing the Math 095 course. The objective for all of these courses is not to "get the students through the material" as is often thought, but rather to have students master the material of the course. (All students have at least one more math course they will have to take after completing Math 095.) Students have different learning styles and can achieve this mastery in different ways and in differing amounts of time. By offering these various options for the course, we hope that each student can find a version that is best for her/him to actually learn the material of the course.
Students interested in any of the last three options are strongly encouraged to complete a free trial of the ALEKS software by going to before registering for any sections using ALEKS. However, students should not purchase any ALEKS access without consulting with Mrs. Kohlmetz, or Professor Eric Key (ericskey@uwm.edu).
Instructors who are interested in teaching with ALEKS should contact the Course Coordinator or Professor Eric Key. We are always looking for instructors to teach these courses!
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...Algebra 2 builds strongly on the skills acquired in Algebra 1. I math courses.
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Free Math Video Lessons and Tutorials
Free Math Video Lessons & Tutorials
Looking for math help? We have great collection of free math video lessons and self-help tutorials from around the web in almost every high-school math subject. Updated regularly, these video lessons are perfect for students looking for extra math help. They are also great for teachers and home-school parents seeking additional ideas or teaching strategies.
We check all the popular video sharing sites for new math videos on a regular basis, so our math video collection is always up to date. You found your one stop site for access to the web's best free math video tutors and lessons!
Hundreds of free Algebra video lessons and tutorials. Find math tutors and teachers showing you how to solve a variety of different algebra problems. Great for both students for extra practice and teachers looking for lesson ideas.
Pre-Algebra students and teachers will love our collection of free Pre-Algebra video lessons from teachers covering a variety of topics from positive and negative integers and ordering of number to variable expressions and equations.
Angles, Circles, Secants, and Proofs. Browse through hundreds of Geometry video lessons from around the web. Find math teachers and geometry tutors giving help in everything from basic angles to complicated geometric proofs.
Limits, Derivatives, Integrals, and everything Calculus has to offer. What better way to get help with your Calculus homework than to watch teachers and tutors work through complex calculus problems and concepts utilizing free tutorials?
A wonderful collection of free statistics videos and probability lessons. Statistics and Probability concepts can be tough to grasp for many students. These free video lessons are a great way to gain a deeper understanding on topics.
If you find you learn better by viewing video lessons, check out these complete Math Courses on DVD. DVDs cover all topics taught in most Algebra, Geometry, Calculus, Trigonometry, and other high school math courses.
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Collegeocusing on helping students to develop both the conceptual understanding and the analytical skills necessary to experience success in mathematics, we present each mathematical topic in this text using a carefully developed learning system to actively engage students in the learning process. We have tried to address the diverse needs of today's students through a more open design, updated figures and graphs, helpful features, careful explanations of topics, and a comprehensive package of supplements and study aids. Students planning to continue their study of mathematics in calculus, trigonometry, statistics, or other disciplines, as well as those taking college algebra as their final mathematics course, will benefit from the text's student-oriented approach. We believe instructors will particularly welcome the new Annotated Instructor's Edition, which provides answers in the margin to almost all exercises, plus helpful Teaching Tips.
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More About
This Textbook
Overview
The Heart of Mathematics addresses the big ideas of mathematics (many of which are cutting edge research topics) in a non-computational style intended to be both read and enjoyed by students and instructors, as well as by motivated general readers. It features an engaging, lively, humorous style full of surprises, games, mind-benders, and all without either sacrificing good mathematical thought or relying on mathematical computation or symbols.
The authors are award-winning authors, holding awards such as: Distinguished Teaching Award (Burger, from the Mathematical Association of America); Chauvenet Prize (the best expository mathematics writer in the world, Burger, from the MAA) 10, 2004
Beauty of Mathematics
The primary emphasis of this textbook is to convey some of the great ideas of mathematics and, in addition, to teach effective thinking. A diverse number of topics are covered such as numbers, infinity, geometry, contortions of space, chaos and fractals, uncertainty, and decision making. Numerous illustrations are used to explain key ideas. The writing style is very informal and allows the reader to more easily grasp complex mathematical concepts. Text would be ideal for a liberal arts mathematics course, an enrichment course for high school or middle school teachers, or as a course for advanced high school students. Text comes with 3D glasses and a interactive explorations CD. In summary, the authors have produced a reader/learner friendly text which does a nice job of conveying the beauty of mathematics and effective thinking strategies.
1 out of 1 people found this review helpful.
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| 677.169 | 1 |
Shipping prices may be approximate. Please verify cost before checkout.
About the book:
The majority of students who take courses in number theory are mathematics majors who will not become number theorists. Many of them will, however, teach mathematics at the high school or junior college level, and this book is intended for those students learning to teach, in addition to a careful presentation of the standard material usually taught in a first course in elementary number theory, this book includes a chapter on quadratic fields which the author has designed to make students think about some of the "obvious" concepts they have taken for granted earlier. The book also includes a large number of exercises, many of which are nonstandard.
Hardcover, ISBN 0841010145 Publisher: Markham Pub. Co 28
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Notes
Price
1.
Works on Paper via United States
Hardcover, ISBN 0841010145 Publisher: Markham Pub Co, Chicago, 1970 Used - Very Good. A very good copy of the hard cover edition in a like (not price-clipped) dust-jacket. Previous owner's name and date modestly in ink atop the front free endpaper, else the text is wholly unmarked, pristine, and the binding and jacket are bright and fresh in appearance, with a couple of miniscule chips missing along the base of the jacket. A sharp copy.; includes dustjacket
Hardcover, ISBN 0841010145 Publisher: Markham Pub. Co, 197041010145 Publisher: Markham Pub. Co, 1970 Used - Good, Usually dispatched within 1-2 business days, This Book is in Good Condition. Used Copy With Light Amount of Wear. 100% Guaranteed.
| 677.169 | 1 |
SESSION – II
(Two Sections– Two hours – 100 Marks)
Section – D: Quantitative Aptitude (50 Marks )
Level of Knowledge :
Objective . . .
To test the grasp of elementary concepts in Mathematics and Statistics and application of the same as useful quantitative tools.
Contents . . .
Ratio and proportion, Indices, Logarithms.
Equations Linear – simultaneous linear equations up to three variables, quadratic and cubic equations in one variable, equations of a straight line, intersection of straight lines, graphical solution to linear equations.
| 677.169 | 1 |
Algebra Concepts is an interactive learning system designed to provide instruction in mathematics at the 7th grade enrichment through adult levels. The instructional goals for Algebra Concepts includeAlgebra Concepts is a tool for introducing many of the difficult concepts that are necessary for success in higher level math courses. This program includes a special feature, the Algebra Tool Kit, whThe Cramers Rule App will help you solve a system of equations in two or three variables using the Cramer's Rule method. In addition to providing the results, this app provides all intermediate steps ...If you have a checkerboard that is 50x50 with small squares inside it, how many squares will there be all together? Students use a Java applet from the Freudenthal Institute to think about the ques
| 677.169 | 1 |
According to Student PIRGS, "Book of Proof is an introduction to the language and methods of mathematical proofs. The text is...
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According to Student PIRGS, "Book of Proof is an introduction to the language and methods of mathematical proofs. The text is meant to bridge the computational courses that students typically encounter in their first years of college (such as calculus or differential equations) to more theoretical, proof-based courses such as topology, analysis and abstract algebra. Topics include sets, logic, counting, methods of conditional and non-conditional proof, disproof, induction, relations, functions and infinite cardinality.Although this book may be more meaningful to the student who has had some calculus, there is no prerequisite other than a measure of mathematical maturity. The text is an expansion and refinement of the author's lecture notes developed over ten years of teaching proof courses at Virginia Commonwealth University. The text is catered to the program at VCU to an extent, but the author kept the larger audience of undergraduate mathematics students in mind.
'This short text is designed more for self-study or review than for classroom use; full solutions are given for nearly all...
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'This short text is designed more for self-study or review than for classroom use; full solutions are given for nearly all the end-of-chapter problems.''The focus is mainly on integration and differentiation of functions of a single variable, although iterated integrals are discussed. Infinitesimals are used when appropriate, and are treated more rigorously than in old books like Thompson's Calculus Made Easy, but in less detail than in Keisler's Elementary Calculus: An Approach Using Infinitesimals.Numerical examples are given using the open-source computer algebra system Yacas, and Yacas is also used sometimes to cut down on the drudgery of symbolic techniques such as partial fractions. Proofs are given for all important results, but are often relegated to the back of the book, and the emphasis is on teaching the techniques of calculus rather than on abstract results.'
This is a free, online wikibook, so the content is continually being updated and refined. According to the authors, "This...
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This is a free, online wikibook, so the content is continually being updated and refined. According to the authors, "This wikibook aims to be a quality calculus textbook through which users may master the discipline. Standard topics such as limits, differentiation and integration are covered as well as several others.״
The emphasis in this free, online textbook is on problems - calculations and story problems. "The more problems you do, the...
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The emphasis in this free, online textbook is on problems - calculations and story problems. "The more problems you do, the better you will be at doing them, as patterns will start to emerge in both the problems and in successful approaches to them.״
'This is a four unit module. The first two units cover the basic concepts of the differential and integral calcualus of...
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'This is a four unit module. The first two units cover the basic concepts of the differential and integral calcualus of functions of a single variable. The third unit is devoted to sequences of real numbers and infinite series of both real numbers and of some special functions. The fourth unit is on the differential and integral calculus of functions of several variables.Starting with the definitions of the basic concepts of limit and continuity of functions of a single variable the module proceeds to introduce the notions of differentiation and integration, covering both methods and applications.Definitions of convergence for sequences and infinite series are given. Tests for convergence of infinite series are presented, including the concepts of interval and radius of convergence of a power series.Partial derivatives of functions of several variables are introduced and used in formulating Taylor's theorem and finding relative extreme values.'״Here are my online notes for my Calculus I course that I teach here at Lamar University. Despite the fact that these are my...
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״Here are my online notes for my Calculus I course that I teach here at Lamar University. Despite the fact that these are my "class notes", they should be accessible to anyone wanting to learn Calculus I or needing a refresher in some of the early topics in calculus." The site also includes reviews and cheat sheets as extra material.
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Calculus for Biology and Medicine, Books a la Carte edition features the exact same content as the traditional text in a convenient, three-hole- punched, loose-leaf version. Books agrave; la Carte also offer a great valuethis format costs significantly less than a new textbook. Calculus for Biology and Medicine, Third Edition, addresses the needs of readers in the biological sciences by showing them how to use calculus to analyze natural phenomenawithout1. Preview and Review
1.1 Preliminaries
1.2 Elementary Functions
1.3 Graphing
2. Discrete Time Models, Sequences, and Difference Equations
2.1 Exponential Growth and Decay
2.2 Sequences
2.3 More Population Models
3. Limits and Continuity
3.1 Limits
3.2 Continuity
3.3 Limits at Infinity
3.4 The Sandwich Theorem and Some Trigonometric Limits
3.5 Properties of Continuous Functions
3.6 A Formal Definition of Limits (Optional)
4. Differentiation
4.1 Formal Definition of the Derivative
4.2 The Power Rule, the Basic Rules of Differentiation, and the Derivatives of Polynomials
4.3 The Product and Quotient Rules, and the Derivatives of Rational and Power Functions
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More About
This Textbook
Overview
For courses in algebra and trigonometry.
Visualize. Interact. Succeed.
Beecher, Penna, and Bittinger's Algebra and Trigonometry is known for enabling students to "see the math" through its focus on visualization and early introduction to functions. With the Fifth Edition, the authors continue to innovate by creating and positioning review material to provide a more effective tool for teachers and students.
25 Just-In-Time review topics are placed throughout the text and MyMathLab to help students right when they need it most. This, along with the existing Mid-chapter Mixed Review exercises, Study Guide summaries, and the new MyMathLab with Integrated Review course, students have an unparalleled amount of review resources to help them be successful in the course.
Also available with MyMathLab®
MyMathLab is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts. With this edition, the authors focused on developing MyMathLab features that help better prepare students and get them thinking more visually and conceptually.
Product Details
ISBN-13: 9780321693983
Publisher: Pearson
Publication date: 2/11/2011
Edition number: 4
Pages: 1120
Sales rank: 349,910
Product dimensions: 8.30 (w) x 10.20 (h) x 1.60 (d)
Meet the Author
Judy Beecher has an undergraduate degree in mathematics from Indiana University and a graduate degree in mathematics from Purdue University. She has taught at both the high school and college levels with many years of developmental math and precalculus teaching experience at Indiana University—Purdue University Indianapolis (IUPUI). In addition to her career in textbook publishing, she enjoys traveling, spending time with her grandchildren, and promoting charity projects for a children's camp.
Judy Penna received her undergraduate degree in mathematics from Kansas State University and her graduate degree in mathematics from the University of Illinois. Since then, she has taught at Indiana University—Purdue University Indianapolis (IUPUI) and at Butler University, and continues to focus on writing quality textbooks for undergraduate mathematics students. In her free time she likes to travel, read, knit and spend time with her children.
Marvin Bittinger has been teaching math at the university level for more than thirty-eight years. Since 1968, he has been employed at Indiana University—Purdue University Indianapolis (IUPUI),1. Graphs, Functions, and Models.
Introduction to Graphing.
Functions and Graphs.
Linear Functions, Slope, and Applications.
Equations of Lines and Modeling.
More on Functions.
Symmetry and Transformations.
7. Applications of Trigonometry.
The Law of Sines.
The Law of Cosines.
Complex Numbers: Trigonometric Form.
Polar Coordinates and Graphs.
Vectors and Applications.
Vector Operations.
8. Systems of Equations and Matrices.
Systems of Equations in Two Variables.
Systems of Equations in Three Variables.
Matrices and Systems of Equations.
Matrix Operations.
Inverses of Matrices.
Determinants and Cramer's Rule.
Systems of Inequalities and Linear Programming.
Partial Fractions.
9. Conic Sections.
The Parabola.
The Circle and the Ellipse.
The Hyperbola.
Nonlinear Systems of Equ
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121,192FOR STUDENTS REQUIRING ADDITIONAL ASSISTANCE WITH THEIR STUDY FOR THE FINAL EXAM. THIS SEGMENT WILL INCLUDE SOLVING SYSTEMS OF EQUATIONS, GRAPHING, RECOGNIZING THE EQUATION OF A GRAPH, SOLVING EQUATIONS, LINEAR AND QUADRATIC, LONG AND SYNTHETIC DIVISION, FACTORING TO SOLVE, COMPLETING THE SQUARE TO SOLVE EQUATIONS, FINDING THE VERTEX USING COMPLETING THE SQUARE AND A SIMPLER METHOD, USING THE SQUARE ROOT PROPERTY, PROPERTIES OF EXPONENTS AND RADICALS, SOLVING COMPLEX FRACTIONS, SOLVING RATIONAL EQUATIONS, SIMPLIFYING RATIONAL EXPRESSIONS, ADDING AND SUBTRACTING RATIONAL EXPRESSIONS. FOILing, FINDING THE X- AND Y-INTERCEPT, DIFFERENCE OF 2 SQUARES, SUM OR DIFFERENCE OF 2 CUBES, BASIC GEOMETRY, AND MUCH, MORE BASED ON STUDENTS CALLING IN .
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Topology is generally considered to be one of the three linchpins of modern abstract mathematics (along with analysis and...
see more
Topology is generally considered to be one of the three linchpins of modern abstract mathematics (along with analysis and algebra). Recently, topology has an important components of applied mathematics, with many mathematicians and scientists employing concepts of topology to model and understand real-world structures and phenomena. Topology is the study of shapes:Including their properties, Deformations applied to them, Mappings between them and Configurations composed of them. Here we can learn this course with the help of provided study material
This module (eCourse) is designed to stand alone as an instructional tool to cover the topic of Variable Expresions using...
see more
This module (eCourse) is designed to stand alone as an instructional tool to cover the topic of Variable Expresions using properties of real numbers and rules of exponentiation. Learners would benefit by reviewing modules in sequence for the related course in Beginning Algebra.
This module (eCourse) is designed to stand alone as an instructional tool to cover the topic of Variable Expressions....
see more
This module (eCourse) is designed to stand alone as an instructional tool to cover the topic of Variable Expressions. Learners would benefit by reviewing modules in sequence for the course Beginning Algebra.
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This subreddit is responsible for answering questions about careers in Computer Science, Computer Engineering, Software Engineering, and other related fields. Respect the reddiquette, and reserve this space for questions concerning careers and degrees only. Please keep the conversation professional.
It was called Foundations in Computer Science in my school. Discrete math covers a broad range of topics, each of which can exist as a standalone detailed course in any maths curriculum. In my school, it had a high fail rate mainly because the teaching standard was poor and more generally, because the subject material covers a lot of ground. Just on the top of my head, topics included: propositional logic, boolean algebra, combinatorics & probability, recurrence relations, big Oh complexity, graph theory, formal proofs. Its essentially all the applied math you'd generally come across in any future CS subject.
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Buy The Joel McHale Handbook - Everything you need to know about Joel McHale by Smith, Emily and Read this Book on Kobo's Free Apps. Discover Kobo's Vast Collection of Ebooks Today - Over 3 Million Titles, Including 2 Million Free Ones!
On-Core Mathematics is a supplemental program that can be used with any math curriculum to provide complete coverage of the Common Core State Standards in Math. Step-by-step instruction and modeling helps students to understand the concepts presented, while progressively difficult practice exercises continue to build fluency. Problem-solving activities are also integrated into every lesson to help students synthesize and apply newly-learned concepts and skills. This Grade 4 Student Workbook covers place value, round numbers, remainders, multiples, common denominators, equivalent fractions, line plots, perimeter, area, prime and composite numbers, and more. Problems are presented in a variety of ways, including through fill in the blanks, charts, tables, pictures, and traditional problems...
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TECHNICAL MATHEMATICS provides a thorough review of pre calculus topics ranging from algebra and geometry to trigonometry and analytic geometry, with a strong emphasis on their applications in specific occupations. The text's breadth of coverage and practical focus will prepare you well for a technical, engineering technology, or scientific career, while integrated calculator and spreadsheet examples teach you to solve problems the way professionals do on the job. Written in an easy-to-understand manner, this comprehensive text complements core content with numerous application- oriented exercises and examples to help you apply your knowledge of mathematics and technology to situations you may encounter in your future work. The Fourth Edition of this proven text includes abundant new
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Prealgebra
Browse related Subjects
...Read More mathematical situations.This prealgebra text, as a part of the Lial/Hornsby/Miller developmental worktext series, focuses on students by helping them reduce their confusion of symbols for subtraction with negative numbers. The text also clearly demonstrates why the product of two negative numbers is a positive number and explains why letters instead of numbers are used in algebra. This text helps students solve applied problems and increases their proficiency in solving fraction and percent problems.Read Less
New. 0321266625
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Mathematical Modelling with Case Studies: Using Maple? and MATLAB « , Third Edition provides students with hands-on modelling skills for a wide variety of problems involving differential equations that describe rates of change. While the book focuses on growth and decay processes, interacting populations, and heating/cooling problems, the mathematical... more...
Explore Theory and Techniques to Solve Physical, Biological, and Financial Problems
Since the first edition was published, there has been a surge of interest in stochastic partial differential equations (PDEs) driven by the LÚvy type of noise. Stochastic Partial Differential Equations, Second Edition incorporates these recent developments... more...
"Krantz is a very prolific writer. He ? creates excellent examples and problem sets." ?Albert Boggess, Professor and Director of the School of Mathematics and Statistical Sciences, Arizona State University, Tempe, USA
Designed for a one- or two-semester undergraduate course, Differential Equations: Theory, Technique and Practice, Second Edition... more...
Approximate Analytical Methods for Solving Ordinary Differential Equations (ODEs) is the first book to present all of the available approximate methods for solving ODEs, eliminating the need to wade through multiple books and articles. It covers both well-established techniques and recently developed procedures, including the classical series solution... more...
Integral Transforms and Their Applications, Third Edition covers advanced mathematical methods for many applications in science and engineering. The book is suitable as a textbook for senior undergraduate and first-year graduate students and as a reference for professionals in mathematics, engineering, and applied sciences. It presents a systematic... more...
provides an accessible introduction to the principles and tools for modeling, analyzing, and synthesizing biomolecular systems. It begins with modeling tools such as reaction-rate equations, reduced-order models, stochastic models, and specific models of important core processes. It then describes in detail the control and dynamical systems... more...
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Gauss.acatlan1603373. This site has a good Pagerank(2/10).
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books.google.com - Most students taking this course do so to fulfill a requirement, but the true benefit of the course is learning how to use and understand mathematics in daily life. This quantitative reasoning text is written expressly for those students, providing them with the mathematical reasoning and quantitative... and Understanding Mathematics
Using and Understanding Mathematics: A Quantitative Reasoning Approach
Most students taking this course do so to fulfill a requirement, but the true benefit of the course is learning how to use and understand mathematics in daily life. This quantitative reasoning text is written expressly for those students, providing them with the mathematical reasoning and quantitative literacy skills they' ll need to make good decisions throughout their lives. Common-sense applications of mathematics engage students while underscoring the practical, essential uses of math.
About the author (2005)
Jeffrey O. Bennett s academic home is the University of Colorado at Boulder, where he has been teaching on and off since 1983 and from which he received his Ph.D. in Astrophysics in 1987. During this time, he s taught more than 50 college courses in subjects including mathematics, astronomy, physics, environmental science, and science education. He began work on Using and Understanding Mathematics because he is particularly interested in helping students overcome difficulties with mathematics. For similar reasons, he has recently completed a textbook for introductory astronomy (The Cosmic Perspective, with M. Donahue, N. Schneider, and G.M. Voit, Addison Wesley Longman, 1999).
He is also working on several books about mathematics and science for the general public. In addition, he is now working on science books for children. Jeff is perhaps best known for his role in creating the Voyage Scale Model Solar System on the National Mall in Washington, DC (opening October 2001); he proposed the project and worked on the team that developed it as a collaborative effort between the Challenger Center for Space Science Education, the Smithsonian Institution, and NASA.
When not working, he enjoys participating in masters swimming and hiking the trails of Boulder, Colorado, with his family.
William L. Briggs has been on the mathematics faculty at the University of Colorado at Denver for 17 years. He teaches throughout the undergraduate and graduate curriculum with a special interest in teaching mathematical modeling as it applies to problems in biology and medicine. He developed the quantitative reasoning course for liberal arts students at CU-Denver supported by the textbook Using and Understanding Mathematics, which he co-authored with Jeff Bennett. He has written two other tutorial monographs, The Multigrid Tutorial and The DFT: An Owner's Manual for the Discrete Fourier Transform.
He is a University of Colorado President's Teaching Scholar, an Outstanding Teacher awardee of the Rocky Mountain Section of the MAA, and the recipient of a Fulbright Fellowship to Ireland. Bill lives with his wife, Julie, his daughter, Katie, and two dogs, Midnight and Seamus, in Boulder, Colorado. He loves to bake bread, as well as run trails and rock climb in the mountains near his home.
Bibliographic information
Title
Using and Understanding Mathematics: A Quantitative Reasoning Approach
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Basic College Mathematics
Browse related Subjects
...Read More skills and concepts. Martin-Gay enhances readers' perception of math by exposing them to real-life situations through graphs and applications and ensures that readers have an organized, integrated learning system at their fingertips. The integrated learning resources program features book-specific supplements including Martin-Gay's acclaimed tutorial videotapes, CD videos, and MathPro 5. This book covers topics such as multiplying and dividing fractions, decimals, ratios and proportion, percent, geometry, statistics and probability, as well as an introduction to algebra. For anyone who wishing to brush up on their basic mathematical skills.Read Less
Fair. Paperback. All text is legible, may contain markings, cover wear, loose/torn pages or staining and much writing. SKU: 978032164940949409.
Fair. 1256334472 Your purchase benefits those with developmental disabilities to live a better quality of life. Your purchase benefits those with developmental disabilities to live a better quality of life. wear on edges and corners markings/ stains on edges creasing writing on inside cover highlighting or writing on some pages Labels/sticker on cover water stained/damaged on some pages minimal wear on some pages.
Good. Looseleaf. May include moderately worn cover, writing, markings or slight discoloration. SKU: 97803216925421692542.
Fair. Paperback. All text is legible, may contain markings, cover wear, loose/torn pages or staining and much writing. SKU: 9781256334477-5-0-3 Orders ship the same or next business day. Expedited shipping within U.S. will arrive in 3-5 days. Hassle free 14 day return policy. Contact Customer Service for questions. ISBN: 9781256334477
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Authorized users only:
Added 12/01/2009
This toolkit functions as a complex graphing calcuator, but also has applications where the student can explore what a tangent line is, the meaning of concavity, the max and min of a function, and others topics.
Added 12/07/2009
Limits: JAVA Applets for Math Applications-
This is an applet that generates a table of nearby values of c for any c. Great for demonstrating the tabular approach to limits.
Added 12/07/2009
Definition of the Derivative: Mathematical Visualization Toolkit
The MVT is an application that allows for graphics plotted and features several learning activities. The Tangent Slider App will graph any function and allows the student to view the tangent line and secant line using sliders that move the point an the "h".
Added 12/07/2009
Derivative Rules -- MathQ's (applets for calculus)
We need to use the Chain Rule section of this site. Description from the MERLOT site: The aim of these investigations is not to provide drill (although links to other resources on the web that do have been included in places), but to encourage students to think about why things happen the way they do in calculus. Such an understanding can be greatly useful both when rote memorization fails and when studying a new concept. Indeed, many concepts from the single variable calculus studied in APSC 171 form the foundations of later courses. The investigations have been designed to be quick and self-contained and should take at most ten or fifteen minutes each to complete.
Added 12/07/2009
Derivatives and Graphing: Larry Green's JAVA Applets
This is an activity where a graph is presented. Using a mouse, the student is challenged to sketch the graph of the derivative. The computer lags behind sketching the actual graph of the derivate so that the student can observe how accurate the student's sketch is as the sketch is being created.
Added 12/07/2009
Definition of the Derivative: Mathematical Visualization Toolkit
The MVT is an application that allows for graphics plotted and features several learning activities. The Root Finding App will graph any function and goes through the iterations of Newton's Method, showing the graphics until it finds an approximate solution.
Added 12/07/2009
Numerical Integration and Area: Riemann Sums
This an applet that allows the user to enter any function and bounds and have the computer approximation of the integral using each of the numerical methods from calculus. The rectangles or other appropriate shapes for the approximation are also generated.
Added 12/07/2009
Fundamental Theorem of Calculus -- MathQ's (applets for calculus)
We need to use the Introduction to Integration and the Fundamental Theorem of Calculus section of this site. Description (quoted from the site): In this learning object you will review the construction of the definite integral, and then observe that if you change one endpoint of the integration, the function that takes that endpoint as input and the value of the integral as input is an anti-derivative of the integrand.
Added 12/07/2009
Fundamental Theorem of Calculus: Calculus of the Dinner Table—Mathematical Modeling
Calculus students are presented with a write-pair-share activity that initially involves the construction of a model based on direct variation and later involves the use of calculus as a means by which to analyze the model. Suitable for either Calculus I or Calculus II students.
Added 12/07/2009
Fundamental Theorem of Calculus: Fundamental Theorem of Calculus--An Investigation
Calculus students are presented with a write-pair-share activity that leads them to a practical understanding of the Fundamental Theorem of Calculus. The activity involves analyzing a function that describes eating speed in a hypothetical dinner table experience. Suitable for either Calculus I or Calculus II students.
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Prentice Hall Math Course 1 Student Workbook 2007c
Browse related Subjects
...Read More understanding of rational number operations preparing them to apply these skills to algebraic equations. Activity Labs throughout the text provide hands-on, minds-on experiences reaching all types of learners.Read Less
Good. Shows some signs of wear, and may have some markings on the inside. Fast &
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Calculus Problem Solver - 95 edition
Summary: The Problem Solvers are an exceptional series of books that are thorough, unusually well-organized, and structured in such a way that they can be used with any text. No other series of study and solution guides has come close to the Problem Solvers in usefulness, quality, and effectiveness. Educators consider the Problem Solvers the most effective series of study aids on the market. Students regard them as most helpful for their school work and studies. With these bo...show moreoks, students do not merely memorize the subject matter, they really get to understand it. Each Problem Solver is over 1,000 pages, yet each saves hours of time in studying and finding solutions to problems. These solutions are worked out in step-by-step detail, thoroughly and clearly. Each book is fully indexed for locating specific problems rapidly. Covers topics usually given in Calculus I, II, and III. Differentiation and integration are illustrated with detailed algebraic and trigonometric operations. Different fields of applications are thoroughly covered with numerous illustrations. ...show less
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Precise Calculator has arbitrary precision and can calculate with complex numbers, fractions, vectors and matrices. Has more than 150 mathematical functions and statistical functions and is programmable (if, goto, print, return, for).
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application of mathematical modelling to physical, economic, and social systems is growing rapidly. This book describes the more important techniques of mathematical modelling, and shows how to apply these techniques to a variety of problems. Each chapter covers a different mathematical technique, discusses the kinds of situations in which it is useful, and shows how to apply the technique to different fields. Examples are drawn from many subjects, including physics, chemistry, economics, demography, biology, medicine, ecology, traffic flow, and others.
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Begin by getting a general idea of some of the things that Mathematica can do by looking at and running some short and simple prepared Mathematica programs that do things that are related to high school mathematics
Learn a few basic facts about Mathematica syntax to help you to avoid mistakes when you begin writing your own Mathematica programs. (You will still make simple mistakes that are annoying but this step will help to reduce the number of mistakes that you make and to find and correct the ones that do occur)
Write some very simple programs to do things that would be useful to you in one of your current classes. Often, you can do this by suitably modifying some program that you have seen in Steps 1 or 2
Learn how to do some basic procedures that are common ingredients to many classroom projects created with Mathematica such as: writing and displaying text and formulas attractively, creating and running animations, creating lists and tables, entering and using functions, and enhancing graphics so that they are more attractive and informative
Select and begin a classroom project that you would like to do for one of the classes that you teach. We will provide you with a file that contains many such projects that have been done by high school mathematics teachers who were Mathematica beginners just a few days before they prepared these projects. You can use these sample projects as a souce of ideas for your own project. You can also use these sample projects as a source of Mathematica programs that you can copy and modify to suit your own purposes.
Materials
Course materials are provided as downloadable notebooks. Students will have to purchase a copy of Mathematica to take the course.
Description
This module is designed for mathematics teachers at the 9 - 14 grade levels who are beginners with Mathematica and who want to learn to use this software package to create transparencies and handouts, computer demonstrations, and interactive student lessons for their mathematics classes. This module is available for both Version 2.2 and Version 3 of Mathematica. Using Mathematica in High School Mathematics Instruction was written by Tony Peressini and Debra Woods of the University of Illinois during October 1997.
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9780547197975 10/28Based on the best-selling series by the Aufmann team, this hardcover text for the This special MEDIA ENHANCED EDITION now comes with Enhanced WebAssign and flash videos for every end of chapter test question available online through the student website.
Table of Contents
Review of Real Numbers
Introduction to Real Numbers
Operations on Rational Numbers
Variable Expressions
Verbal Expressions and Variable Expressions
First Degree Equations and Inequalities
Equations in One Variable
Coin, Stamp, and Integer Problems
Value Mixture and Motion Problems
Applications: Problems Involving Percent
Inequalities in One Variable
Absolute Value Equations and Inequalities
Linear Functions and Inequalities in Two Variables
The Rectangular Coordinate System
Introduction to Functions
Linear Functions
Slope of a Straight Line
Finding Equations of Lines
Parallel and Perpendicular Lines
Inequalities in Two Variables
Systems of Equations and Inequalities
Solving Systems of Linear Equations by Graphing and by the Substitution Method
Solving Systems of Linear Equations by the Addition Method
Solving Systems of Equations by Using Determinants and by Using Matrices
Application Problems
Solving Systems of Linear Inequalities
Polynomials and Exponents
Exponential Expressions
Introduction to Polynomials
Multiplication of Polynomials
Division of Polynomials
Factoring Polynomials
Special Factoring
Solving Equations by Factoring
Rational Expressions
Introduction to Rational Functions
Operations on Rational Expressions
Complex Fractions
Rational Equations
Proportions and Variation
Literal Equations
Rational Exponents and Radicals
Rational Exponents and Radical Expressions
Operations on Radical Expressions
Radical Functions
Solving Equations Containing Radical Expressions
Complex Numbers
Quadratic Equations and Inequalities
Solving Quadratic Equations by Factoring or by Taking Square Roots
Solving Quadratic Equations by Completing the Square and by Using the Quadratic Formula
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This course is a three (3) hour noncredit course that does not carry credit for graduation. It is designed to prepare students for college level mathematics by increasing their awareness of the structure of elementary mathematics. Emphasis is on principles, techniques, and applications of basic algebra. Topics include polynomials, rational expressions, exponents, radicals, calculator usage, linear equations and inequalities, quadratic equations, and graphs of equations in two variables.
| 677.169 | 1 |
Abstract: The NCTM Algebra Standard suggests that students use technology to explore the effects of varying the parameters in y = ax2 + bx + c. This article discusses an extension of this task that incorporates dynamic geometry software to engage students in generating, testing, and proving mathematical conjectures.
The National Council of Teachers of Mathematics is the public voice of mathematics education, supporting teachers to ensure equitable mathematics learning of the highest quality for all students through vision, leadership, professional development, and research.
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Summary: Focusing on the important ideas of geometry, this book shows how to investigate two- and three-dimensional shapes with very young students. It introduces methods to describe location and position, explores simple transformations, and addresses visualization, spatial reasoning, and the building and drawing of constructions. Activities in each chapter pose questions that stimulate students to think more deeply about mathematical ideas. The CD-ROM features fourteen arti...show morecles from NCTM publications. The supplemental CD-ROM also features interactive electronic activities, master copies of activity pages for students, and additional readings for teachers. ...show less
Edition/Copyright:01 Cover: Paperback Publisher:National Council of Teachers of Mathematics Year Published: 2001
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Algebra 1: An Incremental Development, by
John Saxon. Second Edition, 11th printing, 1999. HC, glossy boards, no jacket,
as issued. Cover is moderately worn and corners are bumped. Image used is of actual copy of book for sale, not a stock image. For more condition details, most current pricing, or purchase, please follow title link above. BTH-5968. $9.99
Beginning Algebra with Applications by Vincent K Smith and Linda L Exley. Prentice Hall Second Edition; First Printing, 1994. Hardcover. This book reviews arithmetic and geometry and then teaches beginning algebra. It is designed to be easy to understand. Methods and techniques are illustrated with worked examples whenever possible. Careful mathematics is stressed. The heart of the book is contained in over 5500 carefully selected exercises that develop and illustrate the ideas of algebra in a modern setting. There are extensive problems sets at the end of each section. Each of these starts with "warm-ups " which are keyed to worked examples in the text. These are followed by "Practice Exercises". These are not keyed to worked examples. There are also a few "Challenge Problems" which allow the student to probe into the natural extensions of the ideas presented in the text. All new material and teaching points of each section contain worked and annotated examples. Problem solving steps are identified and explained. Students see what is to be done and how to do it. Students never have to use a concept that has not yet been developed, since the student progresses through the books developing skills as they are needed. Answers are given for odd-numbered problems in the problem sets. 568 pages. Image used is of actual copy of book for sale, not a stock image. For condition details, most current pricing, or purchase, please follow title link above. BTH-5972. $25.95
Student Solutions Manual for Beginning Algebra with Applications (The book listed above.) by Virginia Parks. Prentice Hall Second Printing, 1990. Softcover. This book contains the solutions to every odd-numbered exercise and all the problems in the Chapter Tests for Beginning Algebra with Applications by Linda Exley and Vincent Smith. Punched for three-hole binder.Image used is of actual copy of book for sale, not a stock image. For condition details, most current pricing, or purchase, please follow title link above. BTH-5973
Business Mathematics: A College Course. Third Edition. South-Western
Publishing Co., 1984. By Loyce Gossage. Very good condition, clean inside (no writing),
light wear to edges and corners. Original price stamped on first page. Cover has
a few light marks and scratches, and edges have a couple of spots.
Contains index and answers to odd-numbered problems. This is a good basic
text on College Business Mathematics. It includes the math needed by business
owners for figuring profits and understanding the terms on the tax and
accounting forms. 596 pages. BTH-5149. $3.50
Geometry the Easy Way by Lawrence S. Leff.
Barron's Educational, 1984, 11th printing. This book is an
ideal student self-help supplement. It offers valuable overviews of course work
and extra help with difficult subject areas. Covers the "how" and "why" of
geometry. Includes hundreds of examples and exercises with solutions. Includes
more than 700 drawings, graphs, and tables. Paperback / 343Pages / 7-13/16" x
10-7/8" BT-3503. $6.00-U B
How Children Learn Mathematics: Teaching Implications of
Piaget's Research by Richard W. Copeland. Macmillan, 1970, first edition
hardcover with dust jacket. 310 pages. This book differs from other math methods
course books by concentrating more on how children learn math rather than on how
teachers teach it. The author suggest the teacher take the role of skillful
interviewer and use manipulative materials to help children learn mathematical
concepts. Learning theories are discussed, especially Piaget's theory of
cognitive development. Various applications of the theory with regards to math
instruction, including the first experiences children should have, the
development of concepts of number, and how children's geometrical concepts
develop, are discussed through the rest of the book. Condition: Reading copy.
Book is in good condition with name label on front free end paper. Previous
owner name on fore edge in black marker. Another name is in ink on top edge.
Dust jacket has several tears and parts missing but both flaps are intact and it
stays on and mostly covers the book. BTH-3467. $7.50-U (B)
Intermediate Algebraby Raymond W. Brink. Appleton-Century-Crofts Second Edition, 1951. Hardcover, near very good, with no dust jacket. Contains anything a student would need to know about second year algebra. 295 page. Contains tables and answers to odd-numbered problems at the back. Image used is of actual copy of book for sale, not a stock image. For condition details, most current pricing, or purchase, please follow title link above. BTH-5971. $11.95
Math 2 for Christian Schools, Home Teacher's Edition, 2nd Edition. Bob Jones University Press, 1996 Tests with Test Answer Keys are included. Spiral bound with stiff paper covers. Spirals aren't all perfectly shaped, but inside is in very good condition. Tests and test answers are included -- they are 3-hole punched for binders, as from publisher. Item #099549, 063784 &063768. BTH-5964 $17.25
Math for Christian Schools, Grade Four, 1980 Edition Set of Student and Teacher Edition. Hardcover.
Book beginsby explaining why it's important to study math. Each unit begins with an exciting story that imparts a spiritual reminder. Content includes basic operations at grade 4 level, fractions nd decimals, measurement , and problem solving. There is a railroad theme pervading the book. Student book seems to have doubled as a sketch book and some of the doodles are pretty good. Cover has light edge and
corner wear. Teacher's Edition, 1980, in binder, is in very good condition. Image used is of actual copy of sets for sale, not a stock image. For more condition details, most current pricing, or purchase, please follow title link above. Set is $25.00-U . BTH-5966.
Mathematics is a Verb: Options for Teaching, a Book of
Readings by C.W. Schminke and William R. Arnold. Dryden Press, 1971,
first edition. 365 pages. In the authors' words, "The purpose of this book is
to provide the teacher with a functional, substantive, and pedagogical
reference for those concepts children must learn in elementary school
mathematics. " Condition: Very good, except for some fading and small wrinkles
on the spine. Image used is of actual copy of book for sale, not a stock image. For condition details, most current pricing, or purchase, please follow title link above. BTH-3267. $9.95-U
Mathematiques
5, Collection Pythagore by Bonnefond, Daviaud, and Revranche. Hatier,
1987. Hardcover, no dust jacket. Since this book is in French, I can't tell you
much about it except that I love the crisp, clean look of the text and the
clarity of the color illustrations. it seems to deal with a bit of algebra and
lots of geometry and appears to be at the teen level, since many illustrations
deal with topics such as cars, computers, and sports. The illustrations also
indicate that measurements, fractions, and percentages are dealt with, and there
seems to be an abundance of word problems, graphs, and even maps. So I'd guess
this is a text with lots of applied math, and although if it were an American
book it's markings would indicate Grade 5, I can't believe any American fifth
grader could handle this material. The book has 15 chapters which are organized
into three parts: (1) Travaux numériques (2) Gestion de
données (3) Travaux géométriques. Each chapter
includes: Des activités pour s'initier; L'essentiel; Les exercices. Very good
condition. Corners are bumped. 223 pages. ISBN#2218078686.
BTH-2991. $15.00-U (C)
Measurement
Investigations by Tamara J. Drean and Randall J. Souviney. A Dale
Seymour Publication, 1992. This book provides detailed descriptions of
measurement activity sequences for both primary and intermediate grade (4-6)
students. These students will learn to relate math and measurement to their own
environment as they learn to define measurable attributes through direct
comparison, communicate attributes via identifiable nonstandard units, and
develop a thorough understanding of measurement concepts and the need for
adopting customary or metric units for standard measurement. The book includes
warm-up activities, sequenced activities, extension ideas, games, record sheets,
squared paper and other tools, and blackline masters. Customary and metric
tables are provided, as are bibliographies. Very good condition with some shelf
wear. 134 pages. BTH-3068. 15.99-U
Prealgebra, by Van Dyke, Rogers, and Barker,
Harcourt Brace, softcover worktext. Junior college level. Answers to odd-numbered problems
at back. Fair condition. 870 pages + Supplements for Plane Geometry and Special Equations
and 7 appendices. Image used is of actual copy of book for sale, not a stock image. For condition details, most current pricing, or purchase, please follow title link above. BTH-5967. $5.99
The Secondary School Mathematics Curriculum 1985 Yearbook,
by Christian Hirsch and Marilyn Zweng. National Council of Teachers of
Mathematics, 1985. This book contains essays and lectures on curriculum planning
issues, new curricular directions in secondary mathematics, innovative courses,
programs for talented students, and various three and four year programs
including an three-year applied math course for non-college-bound students and
courses integrating computers into math instruction. 250 pages. Book is like
new. No dust jacket, as issued BTH-3468. $10.00
Understanding Numbers 6: Mathematics for
Christian Living Series, Rod and Staff, 1985. Covers basic operations, problem solving, percent, banking, measurement, fractions, and graphs on a Grade 7 level. Each unit is followed by review pages and an interesting math-related fact or hint. The Christian world view permeates the pages, and the illustrations portray a Mennonite lifestyle. Hardcover book shows moderate wear. Text pages are mostly clean, but someone has circled problem numbers on some pages in pencil. Image used is of actual copy of book for sale, not a stock image. For condition details, most current pricing, or purchase, please follow title link above. 487 pages. BTH-5969. $7.99
Arithmetic Enrichment Activities for Elementary School
Children: A collection of practical classroom procedures and activities for the enrichment
of arithmetic learning byJoseph Crescimbeni. Parker Publishing1971, 1965. Ninth printing. Hardcover. Contains hundreds of enrichment activities for arithmetic for use in lessons or recreation. Geared to reach students at all learning levels. Arranged by grade for easy reference.VG/G. Owner's name on ffep.. Jacket has chipping and small tears around the edges, some writing on the front, and some rubbing and smears on white background. Cover has light edge and corner wear. Bottom of spine is lightly bumped. Front paste-down is wrinkled at hinge. Text pages are clean and bright. 224 indexed pages. Text has lots of white space for easy-on-the-eyes reference. Numerous drawings and diagrams enhance the text. BTH-5970. $9.95
Books
You Can Count On: Linking Mathematics and Literature by Rachel Griffiths
and Margaret Cline. Heinemann Educational Books, 1992. Workbook size paper. This
teaching resource for primary teachers provides a wide range of ideas for using
literature to teach mathematics. It includes a mathematical overview, background
information , and notes on classroom organization, assessment, and evaluation.
It provides lesson outlines based on forty different stories ad poems. For each
activity there is a synopsis, preparation for teaching, mathematical goals, ,
evaluation notes, and ideas for extension. Some of the books used are Ten Nine
Eight; The Very Hungry Caterpillar; Teddybears Go Shopping; 1 Hunter; A Lion in
the Night; A Bag Full of Pups; The Doorbell Rang; When the King Rides By;
Grandma Goes Shopping; The Shopping Basket; The Very Busy Spider; Ten Apples Up
on Top; Anno's Mysterious Multiplying Jar; The Twelve Days of Christmas; Anno's
Counting Books; and many more. 100 pages. Very good condition: Light wear to
edges and corners. Previous owner labels on both sides of front cover. The are
some indentations in a few top page margins where the previous owner used a
paperclip to mark the place. Image used is of actual copy of book for sale, not a stock image. For most current pricing, or purchase, please follow title link above.BTH-2990. 13.95-U (B)
Great Book of Math Puzzlesby Philip Heafford.
Trade paper, 1st edition. A volume of math teasers, twisters, traps and tricks to puzzle,
delight and drive math buffs crazy. This book will take them through math history,
symbols, circles, triangles, units, measures, series, permutations, and a whole assortment
of number puzzles. Very good condition with minor defects. Image used is of actual copy of book for sale, not a stock image. For condition details, most current pricing, or purchase, please follow title link above. . BTH-5975. $4.99
Read Any
Good Math Lately? Children's Books for Mathematical Learning, K-6 by David J. Whitin and Sandra Wilde. Forward by Kenneth S. Goodman. Heinemann, 1992. Soft cover. This book shows teachers how to use children's literature to teach mathematical topics such as place value, estimation, large numbers, geometry, measurement, fractions, classification, addition, subtraction, multiplication, division, and games and puzzles. Illustrations include examples of student work. 206 pages. Good condition, with moderate wear to cover, mostly at corners and ends of spine. Previous owner name labels on inside front cover and six words in ink on the half-title page. Image used is of actual copy of book for sale, not a stock image. For most current pricing, or purchase, please follow title link above.BTH-4090. $9.99
The Write Equation: Writing in the Mathematics Classroom
by John and Dorothy Carter. Dale Seymour, softcover, 1994. 65
pages. The authors show how journals, essays, and research projects help
students learn by putting mathematical ideas into words. These methods help
teachers evaluate by giving them insight into student thinking processes. This
book will help in getting a mathematics writing program started, suggest ideas
for writing topics in middle and high school, provide student writing samples,
offer techniques for evaluating writing, provide ready-to-use checklists, and
show an example of a unit which integrates writing with other teaching methods
for complete learning and assessment. Good condition: Moderate edge and corner
wear to wraps, especially on the top. Top corner is dog-eared. This is not a
previously owned book, but a store display copy. BT-3213. $12.50-U (A)
Young Children Reinvent
Arithmetic: Implications of Piaget's Theory by Constance K. Kamii.
Teachers College Press, 1985. Paper. 269 pages. The author demonstrates that at
the end of first grade, children who have been encouraged to use arithmetic in
their daily lives and in math games do better with numbers than those taught
traditionally with worksheets, drills, and flashcards. She has "translated"
Piaget's theory into a concrete program of games and activities that will appeal
to both children and their teachers. The main focus of the book is a discussion
of these games and activities -- how to make and use them and also the reasons
and objectives behind them. There is also an account of a real first grade
teacher who switched from teaching traditional math to a program where the
children "reinvented" math. This book is aimed at teachers, curriculum
specialists, and administrators. Used book with moderate wear, mostly to the
cover. No underlining. BTH-2541. $9.99
If you didn't find what you need here,
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| 677.169 | 1 |
More About
This Book
Algebra II Workbook For Dummies, 2nd Edition helps you learn Algebra II by doing Algebra II. Author and math professor Mary Jane Sterling walks you through the entire course, showing you how to approach and solve the problems you encounter in class. You'll begin by refreshing your Algebra I skills, because you'll need a strong foundation to build upon. From there, you'll work through practice problems to clarify concepts and improve understanding and retention.
Revisit quadratic equations, inequalities, radicals, and basic graphs
Master quadratic, exponential, and logarithmic functions
Tackle conic sections, as well as linear and nonlinear systems
Grasp the concepts of matrices, sequences, and imaginary numbers
Algebra II Workbook For Dummies, 2nd Edition includes sections on graphing and special sequences to familiarize you with the key concepts that will follow you to trigonometry and beyond. Don't waste any time getting started. Algebra II Workbook For Dummies, 2nd Edition is your complete guide to 2010
Wrong answers!
There are at least three errors in the answers provided through the first five chapters of the workbook. The concept of the book is excellent, but the execution definitely leaves something to be desired.
2 out of 2 people found this review helpful.
Was this review helpful? YesNoThank you for your feedback.Report this reviewThank you, this review has been flagged.
| 677.169 | 1 |
Connecting Meaning and Mathematics
Students often do not (for lack of time, motivation, skills, reward) connect their mathematical work to their conceptual understanding. This page will house a collection of curricular pieces and references that guide students to connect meaning and mathematics in physics courses.
Most of these pieces were written for the upper level undergraduate classical mechanics course on the level of Marion and Thorton or Cassiday and Fowles. We refer the interested instructor to Intermediate Mechanics Tutorials for other useful curricular pieces for the same class. Some of the tutorials below assume students have done specific IMT tutorials already; this will be in the "notes" column. All of these have been class-tested with 2-3 groups of 15-20 students.
Level
Topic and format
Notes
Files
Introductory
Electric field due to a bar of charge; guided inquiry tutorial and homework
Helps students become develop a view of integration as a sum of physical quantitities.
To show how to use the eigenvalues and eigenvectors of a coupled, linear differential equation can be used to understand the organization of phase space of a damped harmonic oscillator. This piece assumes students understand phase space rules at the level of theIMT tutorial on "phase space - simple harmonic motion."
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Survey of Mathematics with Applications
9780321501073
ISBN:
0321501071
Pub Date: 2007 Publisher: Pearson
Summary: This best-selling text balances solid mathematical coverage with a comprehensive overview of mathematical concepts as they relate to varied disciplines. The text provides an appreciation of mathematics, highlighting mathematical history, and applications of math to the arts and sciences. It is an ideal book for students who require a general overview of mathematics, especially those majoring in liberal arts, the soci...al sciences, business, nursing and allied health fields. Let us introduce you to the practical, interesting, accessible, and powerful world of mathematics today-the world ofA Survey of Mathematics with Applications,8e.
Angel, Allen R. is the author of Survey of Mathematics with Applications, published 2007 under ISBN 9780321501073 and 0321501071. Three hundred seven Survey of Mathematics with Applications textbooks are available for sale on ValoreBooks.com, one hundred thirty five used from the cheapest price of $0.34, or buy new starting at $3
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See What's Inside
Product Description
The monograph series is published by NCTM as a supplement to the Journal for Research in Mathematics Education (JRME). Each monograph has a single theme related to the learning or teaching of mathematics.
Number 10 in the JRME monograph series. Funded by the
National Science Foundation, the purpose of the LOGO Geometry Project was to
develop a research-based grades K–6 geometry curriculum that addressed the
deficits of the current curriculum. In addition to introducing the project and
its rationale, this monograph details the research, results, and implications of
the study.
Related Products
This volume considers the background of constructivism, explores what it
means to carry out the process of mathematical thinking, and describes how
children engage in mathematical activity and how teachers can promote this
activity.
The chapters in this book, all research articles from NCTM's Journal for Research in Mathematics Education, have been recast specifically to reach the teacher audience and provide commentary that highlights the value of each.
This book focuses on algebra as a language of process, expands the notion
of variable, develops ideas about the representation of functions, and extends
students' understanding of algebraic equivalence and change.
This provocative collection challenges teachers to consider their role in ensuring equity in mathematics education for girls and women and offers exemplars of interventions that encourage young women in mathematics.
The National Council of Teachers of Mathematics is the public voice of mathematics education, supporting teachers to ensure equitable mathematics learning of the highest quality for all students through vision, leadership, professional development, and research.
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Algebra Nspirations & Applications
Inequalities: Solving Linear Inequalities (#104)
This program explores one of Algebra's fundamental building blocks, inequalities. Concepts of equations and inequalities, as well as real-world contexts are discussed in this program including solving problems using the TI-Nspire. [27 minutes]
This episode has not aired in the past few months on Iowa Public Television.
Series Description: This brilliant series, developed by math experts, integrates guided instruction through Algebraic processes with real life applications of these operations, taking students step-by-step through key curricular topics, illustrating how these processes are used in scientific, technological, finance and other practical applications.
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Don't just tell students "Algebra helps you to think in the abstract". That's a great tool, but many people need an application. They may be creative, but not as good with abstract concepts. Give them examples of what Algebra does and what it's used for. That would keep a lot of them from dropping the class, out of school and falling through the cracks. I really, really needed to be great with Algebra for my college major, even if it wouldn't have been needed after graduation.
| 677.169 | 1 |
In this volume the author gives a unified presentation of some of the basic tools and concepts in number theory, commutative algebra, and algebraic geometry, and for the first time in a book at this level, brings out the deep analogies between them. The geometric viewpoint is stressed throughout the book. Extensive examples are given to illustrate each new concept, and many interesting exercises are given at the end of each chapter. Most of the important results in the one-dimensional case are proved, including Bombieri's proof of the Riemann Hypothesis for curves over a finite field. While the book is not intended to be an introduction to schemes, the author indicates how many of the geometric notions introduced in the book relate to schemes which will aid the reader who goes to the next level of this rich subject.
Readership
Graduate students and research mathematicians interested in number theory.
Reviews
"Extremely carefully written, masterfully thought out, and skillfully arranged introduction ... to the arithmetic of algebraic curves, on the one hand, and to the algebro-geometric aspects of number theory, on the other hand. Detailed discussions, full proofs, much effort at thorough motivations, a wealth of illustrating examples, numerous related exercises and problems, hints for further reading, and a rich bibliography characterize this text as an excellent guide for beginners in arithmetic geometry, just as an interesting reference and methodical inspiration for teachers of the subject ... a highly welcome addition to the existing literature."
-- Zentralblatt MATH
"In order to come straight to the point: this book represents an excellent introduction to Algebraic Number Theory and to Algebraic Curves as well by viewing both theories as part of Commutative Algebra ... all proof are given in full detail and its concept as well thought-out."
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Daniel Kaplan, Randall Pruim, Eric Marland, and Nicholas Horton
Registration Fee: $225 ($300 for registrations received after May 28, 2012)
Modeling is an important mathematical skill, yet instructors are often at a loss when it comes to teaching it. This workshop will help you teach modeling in a way that strengthens your students' development of mathematical concepts, interest in mathematics, and appreciation for the uses of mathematics. Based on ideas and materials developed as part of the NSF-supported Project MOSAIC, whose aim is to create stronger connections among modeling, statistics, computation and calculus, the workshop will share existing materials for teaching modeling-based calculus from the introductory level through differential equations. As part of the workshop, you will develop a syllabus for integrating modeling into one of your own courses and a modeling case study. Come see how modeling can be your ally in teaching undergraduate calculus.
More details information about the schedule of the workshop will be posted as they become available.
dahl.calvin.edu hosts Sage and RStudio servers we will be using. You should have received email with instructions for accessing your accounts.
Arrival and Departure
The workshop will begin with dinner in the Prince Conference Center at 6:30 pm on Monday, July 9. Dinner will be followed by an introduction to the workshop and its participants. The workshop will end with lunch on Friday, July 13. Those flying to the workshop can book flights to the Gerald R Ford International Airport in Grand Rapids, MI (GRR). The airport is approximately 10 minutes from campus by car. The Prince Conference Center provides a free shuttle if they are provided with flight information in advance.
Lodging and Local Arrangements
Workshop sessions will take place in computer laboratories in the Science and Mathematics Complex at Calvin College, in Grand Rapids, MI.
Lodging (double occupancy) for workshop participants will be provided at the Prince Conference Center, located on Calvin's campus, about a 10-minute walk from the Science Complex. For an additional $50/night, participants can book a single room or share a room with family members. Room charges include breakfast for up to four guests staying in a room.
Additional meals (lunches and dinners) will be provided for workshop attendees. Guests and family members are welcome to join us for any excursions or social events (sometimes at a nominal charge).
| 677.169 | 1 |
Mathematical Proofs: Transition To Advanced Mathematics - 2nd edition
Summary: Mathematical Proofs: A Transition to Advanced Mathematics, 2/e,prepares students for the more abstract mathematics courses that follow calculus. This text introduces students to proof techniques and writing proofs of their own. As such, it is an introduction to the mathematics enterprise, providing solid introductions to relations, functions, and cardinalities of sets.KEY TOPICS: Communicating Mathematics, Sets, Logic, Direct Proof and Proof by Contrapositive, More on Direct Proof an...show mored Proof by Contrapositive, Existence and Proof by Contradiction, Mathematical Induction, Prove or Disprove, Equivalence Relations, Functions, Cardinalities of Sets, Proofs in Number Theory, Proofs in Calculus, Proofs in Group Theory.MARKET: For all readers interested in advanced mathematics and logic. ...show less
0. Communicating Mathematics Learning Mathematics What Others Have Said About Writing Mathematical Writing Using Symbols Writing Mathematical Expressions Common Words and Phrases in Mathematics Some Closing Comments about Writing93 +$3.99 s/h
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Penntext Downingtown, PA
Excellent Condition. No wear/tear. Please contact us if you have any Questions.
$31.21 +$3.99 s/h
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BookCellar-NH Nashua, NH
032139053955Used - Very Good Book. Shipped from US within 4 to 14 business days. Established seller since 2000
$64.41 +$3.99 s/h
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| 677.169 | 1 |
Developmental Mathematics - MyWorkBook - 8th edition
Summary: Worksheets for Classroom or Lab Practice offer extra practice exercises for every section of the text, with ample space for students to show their work. These lab- and classroom-friendly workbooks also list the learning objectives and key vocabulary terms for every text section, along with vocabulary practice problemsTextbooksPro Dayton, OH
Book is in acceptable condition. Cover shows considerable wear and tear but pages have minimal marks. Some water damage causing pages to stain. Does not affect the text. Definitely not pretty but sti...show morell usable
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Math is a special and important learning in education. Even though Math is hard to some people, it is not hard to learn if you follow a good guide. This book is a good guide that will help high/middle school students learn basic and advanced skills with important concepts and skills carefully designed into questions and solution for students to master. This book will escort you to your success.
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Informal Course Descriptions
MATH 151—Calculus I
Slope tells something about the rate of change in a line. This is an extremely useful
concept, but has the shortcoming of only being applicable to lines. In Calculus I this
problem is overcome by the derivative, essentially a concept of slope that can be applied
to functions other than lines. Armed with the derivative, we can answer questions about
the rate of change of many functions, allowing us to find maxima or minima of functions,
study velocity and acceleration of physical bodies, chemical reactions and population
growth. We can graph complex curves and describe the relative efficiency of rival
computer algorithms. Indeed, the calculus provides a universal language to precisely
describe and compute rates of growth and corresponding changes in amount.
MATH 152—Calculus II
Nearly everyone knows that the area of a circle is r 2 , and so on. But few think about
where these formulas come from. In Calculus II we use the concept of the integral to
study the area under curves. This naturally generalizes to the study of volumes of solids
in space. But this same concept, combined with the derivative (from Calculus I) can be
used in many unexpected and powerful ways. Quantities as diverse as the GNP (gross
national product) and total run time of a computer program can be described as an area
under a curve on a graph. Calculus II provides tools to compute these quantities and
relate them to the functions that describe their rates of change.
It is possible for infinitely many numbers to sum to a finite value. For example, it can be
1 1 1 1
shown that ... 1 . The integral and derivative are used as tools to help
2 4 8 16
us understand such infinite series. In turn, these series help us to understand several
functions better. For example, cos x and ln x can be written as infinitely long
polynomials and can be approximated reasonably well by, say, polynomials of degree
four or five.
Math 203 – History of Mathematics
Often, when we learn mathematics, we learn it without the story of who developed it, and
when and why. In the History of Mathematics, we look at the stories behind the
mathematics.
These stories take us to many places on the earth and through a long period of time. We
begin about 4000 years ago with the ancient civilizations of Egypt and Mesopotamia,
where there was already a good deal of mathematics known, particularly algebra and the
art of computation. We also explore the early mathematical discoveries of China and
India. Next we go to the amazing flowering of mathematics that occurred in ancient
Greece: geometry, astronomy, trigonometry and much more.
We see some more development of algebra with the Arabic mathematicians of Medieval
times; in fact our word, algebra, is from the Arabic. We next move to Europe to see
algebra in Italy, analytic geometry in France, logarithms in Scotland and the beginnings
of calculus almost everywhere. We follow the development of calculus and see how it
changed from around 1600 to around 1800. We then look at the surprising story of non-
Euclidean geometry in the 1800's. We can only survey more recent discoveries briefly
because they are more difficult and there are so many of them.
We study the biographies of a number of mathematicians, and look at the special
problems encountered by women mathematicians. Many of the students in this class
intend to become mathematics teachers so we examine the histories of specific areas of
mathematics taught in the schools, such as number systems, algebra, geometry and
trigonometry.
MATH 245-Discrete Structures
The possession of logical reasoning skills is essential for anyone interested in computer
science. In this class, students enhance these skills by studying a variety of mathematical
topics related to the study of computer science, which may include propositional logic,
set theory, relations, functions, combinatorics, graph theory, and applications of these
topics. Students also learn proof-techniques such as induction (a ―domino‖ technique
that allows one to prove that a statement relating to a variable n is true for all positive
integers n) and proof by contradiction (in which one proves a desired result by showing
that if it isn't true, nonsensical things happen), thereby increasing their mathematical
maturity and their ability to make reasoned arguments, prerequisites for programming.
Topics vary from term to term, and may depend on student interest. Here is a sample of
things students may learn in this class:
(1) The logical difference between the statements, Not all people have red hair and All
people do not have red hair;
(2) How to show that 1+2+3+…+n= n(n+1)/2, for any positive integer n;
(3) How to show that the set of integers and the set of rational numbers have the same
―size‖, but the set of real numbers is ―bigger‖;
(4) How to compute the probability of getting a royal flush in poker.
The course is intended primarily for computer science majors and math majors.
Note: though this class has Math 152 as a prerequisite, to ensure the mathematical
preparedness of its students, its material is not directly related to that learned in the
calculus sequence.
MATH 253—Calculus III
Most things are related to more than just one factor. For example, your minimum
monthly credit card payment depends on the total you owe and your interest rate. The
amount you actually pay depends on the minimum payment due and the amount you have
available to pay. The growth rate of a deer population depends on the size of the
population, its age distribution, the food supply and predation. The pressure exerted by
gas in a cylinder depends on the amount of gas, its temperature and the volume of the
cylinder.
Other functions may only depend on one variable, but give an output that is more than
just one number. For example, a person traveling around the world has, at any given time,
a latitude and a longitude (and perhaps an altitude too if s/he is in an airplane). Thus
position can be considered a function of time but it cannot be represented by a single
value; it must be given as a doublet (or triplet) of numbers representing latitude and
longitude (and altitude). Such a doublet or triplet can be represented as a vector.
Calculus III extends the ideas of Calculus I and II by considering derivatives and
integrals of functions with more than one variable, or of vector-valued functions. Along
the way, other possible coordinate systems (such as polar coordinates) are discussed.
MATH 317—Introduction to Proof in Mathematics
In mathematics we accept a statement as true only if we have a proof that it is true. Since
the method of proof is so basic to mathematics, anyone who seriously wants to learn
mathematics beyond a fairly elementary level must be able to understand proofs and be
reasonably proficient at constructing them. The purpose of this class is to teach you how
to understand proofs and to develop your skills at constructing proofs. Skill at proving
develops over a long period of time; this class is only a beginning. The best way to learn
to do proofs is to do them, so you will be given plenty of opportunity to practice proving
things.
We will begin with an introduction to logic. Logic is a tool that we will use to analyze
proofs to see if they are correct and to help us to construct proofs. We will practice
writing proofs in a number of areas of mathematics: set theory, including infinite sets,
inequalities and functions. We will study the whole numbers using mathematical
induction. In addition to the usual lecture format, a good deal of class time will be spent
with students presenting their proofs to the class or constructing proofs together.
This class is good preparation for Linear Algebra (MATH 331), Abstract Algebra
(MATH 433), Analysis (MATH 455) and other advanced mathematics classes.
MATH 321—Geometry
The geometry most of us learned in high school is based on Euclid's famous 5 Postulates
and works well for describing things in or on a flat surface. However, the surface of our
world is not flat and any pilot or ship's navigator must understand the rules of spherical
geometry.
The discovery of two-dimensional non-Euclidean geometries early in the nineteenth
century by Gauss, Bolyai and Lobachevski allowed us to ask for the first time, ―Could the
geometry of the three-dimensional universe in which we live also be non-Euclidean?‖
The work of Riemann and, later, Minkowski provide a geometric structure for Einstein's
theory of relativity and modern theories of cosmology where the ultimate collapse or
expansion of the universe is related to the curvature of space itself.
The discovery of two-dimensional non-Euclidean geometries also initiated a momentous
shift in our view of the entire mathematical enterprise. The question of axiomatic
foundations raised by the non-Euclidean geometries now pervades all branches of the
subject and forms the acid test of mathematical validity.
This class examines the foundations of geometry that lead to Euclid's geometry in the
plane and to other possible geometries, most notably spherical and hyperbolic, and
concentrates on exploring the rules of geometric logic that are universal.
MATH 331—Linear Algebra
Why algebra? Algebra was invented because of the limitations of our geometric intuition.
In applications ranging from business to engineering to the social sciences, it is often
useful to work with data that naturally correspond to points in the plane, or in three-
dimensional space, or even in fifty-dimensional space. Certainly we could draw pictures
or build models to avoid algebra for points in the plane or in three-dimensional space, but
what pictures or models could help us to ―see‖ in fifty dimensions? This obstacle
motivates the development of vectors and the development of algebraic rules and
techniques for manipulating them. In this course we pursue two intimately related
subjects: matrix theory and linear algebra.
Matrix theory is concerned with vectors and matrices. Vectors are the n-dimensional
generalizations of the ordered pairs representing points in the plane. We will investigate
how our geometric concepts naturally imbed in algebraic concepts. We will learn how the
geometry of lines and planes, lengths and angles is replaced by systems of equations and
operations on vectors. Further, we will see how systems of equations can be analyzed in
terms of the properties of a single algebraic object: the matrix.
Linear algebra is the study of sets of vectors and how operations on individual vectors
can be applied to entire sets. Linear algebra is the abstraction of the fundamental
properties displayed by vectors and matrices. This abstraction allows us to use the
knowledge and skills developed working with vectors and matrices to answer questions
about the behavior of wave functions in Fourier analysis or about the nature of solutions
to important families of differential equations.
This course is very different from calculus. In calculus there are relatively fewer
theoretical ideas, and most of the course is devoted to applying those ideas and the
associated techniques to specific computations. In MATH 331 students learn a large
variety of new ideas and, while calculations are important, they are primarily tools for
understanding the examples that motivate the theory. Consequently much of the work in
this course is focused on explaining why certain relationships between ideas are true or
why certain sets have specified properties rather than on simply producing a slope or an
integral or a number. Calculus is a prerequisite for this course primarily because students
rarely have adequate facility with mathematical thinking, working with equations,
working extensively with symbols, thinking about exceptions or using technical
language—prior to completing the calculus sequence.
MATH/STAT 341—Introduction to Mathematical
Statistics
As the title suggests, we will apply mathematical techniques to develop some of the
fundamental ideas of statistics. So just what is statistics? Statistics is the art of extracting
patterns from data. This might consist of summarizing complicated data, whether
numerically, graphically or by constructing a simple mathematical model that connects
pieces of data to one another. Whereas mathematics uses a language of certainty,
theorems and proofs, statistics has developed precisely to deal with uncertainty,
estimates, bounds and probabilities.
In this course we will examine answers to several important questions in statistics. How
do you describe a data set so as to capture its ‗center' and its variation? This will lead to
topics such as the mean and the variance of a sample. What is probability and how do we
model it mathematically? This will lead to the classical distributions: binomial, Poisson,
exponential and normal. How do you decide whether your preconceptions about a large
population are in agreement with the data obtained from a sample? This will lead us to
confidence intervals and hypothesis testing.
Throughout the course we will see that statistics is much more that just the application of
mathematical techniques. We will see that, before we can apply the mathematics, we
must have good data and reasonable models. After we have done our mathematical
analysis, we must still decide whether we have enough certainty to make conclusions. In
short, we will be the lawyers, judge and jury in the court of data analysis.
We will apply the techniques of algebra and calculus to investigate probability, to
develop models and to explore their properties and understand why some estimation
techniques have better properties than others do. We will apply Minitab statistical
software to real world data sets and to simulated data sets.
Successful completion of MATH 152 is a prerequisite for this course. This course is
cross-listed under both mathematics and statistics. Students can take this course for the
mathematics major and minor, the statistics minor and the actuarial science minor.
MATH/STAT 342—Probability and Statistical Theory
This is a continuation of MATH/STAT 341 (Introduction to Mathematical Statistics). In
this class, students will expand their basic knowledge from 341 into broader and deeper
probability and statistics theory. For instance, students will learn about conditional
distributions of multiple random variables, limiting distributions, moment generating
functions and higher moments than mean and variance. Students will learn more methods
for testing statistical hypotheses, such as the two-sample T test, the F-test and non-
parametric methods. There will also be an introduction to analysis of variance (ANOVA).
To insure that students learn more than just theoretical ideas a term project applying class
knowledge to solving real world problems is usually assigned. Minitab will be used for
the data analysis.
Students are required to complete MATH/STAT 341 prior to enrolling in this class.
MATH/STAT 342 is cross listed under mathematics and statistics. Students can take it
for the mathematics major (or minor), the statistics minor and the actuarial science minor.
MATH/STAT 348—Applied Regression Analysis and
ANOVA
Regression analysis of data is a powerful statistical tool that is widely used in biology,
psychology, management, engineering, medical research, government and many other
fields. It provides a technique for building a reasonable mathematical model that relates
the mean value of a response (e.g., profit) to various independent variables or predictors
(e.g., advertising budgets, size of inventory, etc.).
Any prediction or estimation based on a random sample of data will contain a certain
unknown error. In this course, students will learn various methods to build a best
regression model for a given set of data under certain constraints so that the error is
minimized.
When the relation between the dependent and independent variables is linear, we call it
linear regression. Students will also learn about nonlinear regression, where there can be
a nonlinear relationship (such as quadratic or exponential). Real world problem solving
skills are emphasized. Minitab is used extensively for the data exploration and data
analysis. A term project (with open topics) is normally assigned for students to explore
knowledge beyond the classroom.
Students are required to complete MATH/STAT 341 prior to enrolling in this class.
MATH/STAT 348 is cross-listed under mathematics and statistics. Students can take it
for the mathematics major (or minor), the statistics minor and the actuarial science minor.
MATH 351 Differential Equations
Differential equations are a powerful tool in constructing mathematical models for the
physical world. Their use in industry and engineering is so widespread and they perform
so well that they are among the most successful of modeling tools.
For example, a cup of hot coffee is initially at 170F and is left in a room with an
ambient temperature of 70F . Suppose that initially it is cooling at a rate of 20 per
0.2T 70 . This is an
dT
minute. Then the model for the cup's temperature is
dt
example of a differential equation. We are interested in predicting the temperature, T, of
the coffee at any time t. We can also ask, ―How long does it take the coffee to cool to a
temperature of, say, 110F ?"
MATH 356—Numerical Analysis
When one pushes the square root button on a calculator to compute the square root of 2,
one should ask, ―How does the calculator do it?‖ Numerical analysis deals with
implementing numerical methods to answer questions like this one.
While numerical methods have always been useful, since the invention of computers, the
role of numerical methods in scientific research has become essential. No modern applied
mathematician, physical scientist or engineer can be properly trained without some
understanding of numerical methods. There is more involved here than just knowing how
to use the methods. One needs to know how to analyze their accuracy and efficiency.
Numerical analysis is a broad and challenging mathematical activity, whose central
theme is the effective constructability of various kinds of approximations.
MATH 433—Abstract Algebra
If you can tell time, you already know some abstract algebra: you just don't know you
know it! Suppose you have lunch every day at 1:00pm. Then you'll have lunch at 1:00pm
today and at 1:00pm tomorrow. We just called both of those times ‗1:00pm', but they're
not really the same moment in time, since they're occurring on different days! It turns out
they both can be thought of as representatives of a coset of 24 Z in R ; this coset, in turn,
is an element of the factor group R / 24Z .
Huh, you ask? What's a coset? What's Z ? What's R ? What's a factor group?! Take this
class and find out! Abstract algebra is the study of algebraic structures such as groups,
rings and fields. (You don't know what these objects are yet, but if you take this class
you will!) You encounter such objects everywhere in math: the coordinate plane is an
example of a group; the set of all 2 x 2 matrices over the real numbers is an example of a
ring; the set of all real numbers is a field. By studying these structures abstractly, we can
give one proof for many results that hold for wildly different objects, instead of proving
each result for each object separately.
Abstract algebra is a beautiful and powerful area of mathematics and it is an essential part
of any mathematics curriculum. It has applications in many sciences, from physics to
chemistry, in addition to having extremely important uses in areas such as cryptography.
While the concepts in this class require minimal prerequisite knowledge of topics such as
calculus, this class is heavily proof-based and requires a large amount of mathematical
maturity. The ability to write grammatically and make logical arguments is extremely
important, while the ability to differentiate will be of little, if any, use. Conceptual
understanding, not a calculator, is at the heart of this course!
MATH/EDUC 446—Mathematics in the Secondary School
This course has been designed for prospective teachers of middle school and high school
mathematics and reflects the recommendations of the National Council of Teachers of
Mathematics (NCTM). The following excerpt is from the NCTM Principles and
Standards book:
―The Teaching Principle
Effective mathematics teaching requires understanding what students know and need to
learn and then challenging and supporting them to learn it well.
Teachers need to know and use ‗mathematics for teaching' that combines mathematical
knowledge and pedagogical knowledge. They must be information providers, planners,
consultants and explorers of uncharted mathematical territory. They must adjust their
practices and extend their knowledge to reflect changing curricula and technologies and
to incorporate new knowledge about how students learn mathematics. They also must be
able to describe and explain why they are aiming for particular goals.‖
The course takes the art of teaching through a series of motivational ideas suitable for
many grade levels and abilities and includes a discussion of activities, materials and
manipulatives suitable for classroom use. Problem solving and heuristics is a major
theme in the course. Other topics covered include cooperative learning, questioning
techniques, technology, lesson planning, homework options, mini-discovery lessons and
technology lessons.
MATH 455 Mathematical Analysis
Why does calculus work? In this course we examine the foundations of calculus. What
properties of the real numbers distinguish them from the rational numbers? What role do
these differences play in the development of such fundamental concepts as limits and
convergence? What does continuity really mean, and why do we need it? Along the
way, we will study sequences, series and limits, first of numbers, and then of functions.
One consequence of our study will be a better appreciation of the central role of power
series in many of the results of calculus.
This course is strongly recommended for anyone considering a graduate degree in pure or
applied mathematics, statistics, theoretical physics or operations research. Surprisingly, a
deep understanding of the theoretical underpinnings of calculus is necessary to make
progress in such applied areas as optimization, numerical analysis, financial modeling,
probability and differential equations.
This course is almost entirely focused on formal definitions and rigorous proofs.
Students are encouraged to have as much exposure to proofs as possible prior to enrolling
in this course.
9/16
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Precalculus: Graphs and Models - 5th edition
Summary: The Graphs and Models series by Bittinger, Beecher, Ellenbogen, and Penna is known for helping students ''see the math'' through its focus on visualization and technology. These texts continue to maintain the features that have helped students succeed for years: focus on functions, visual emphasis, side-by-side algebraic and graphical solutions, and real-data applications. With the Fifth Edition, visualization is taken to a new level with technology. The authors also in...show moretegrate smartphone apps, encouraging readers to visualize the math. In addition, ongoing review has been added with new Mid-Chapter Mixed Review exercise sets and new Study Guide summaries to help students prepare for tests1783964 Does not contain ACCESS CODE-Acceptable Condition - Book may have excessive writing or highlighting May contain some highlighting, underlining, general markings. Will NOT include CDs, acc...show moreess WILL NOT CONTAIN SUPPLEMENTS,100.00 +$3.99 s/h
Good
Recycle-A-Textbook Lexington, KY
03217839
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Connected Mathematics 2 : Growing, Growing, Growing - 06 edition
Summary: * New Unit: The Shape of Algebra focuses on the strong connections between algebra and geometry to extend students' understanding and skill in key aspects of algebra and geometry* New resource: CMP Strategies for English Language Learners * Video Tutors available on-line * Academic vocabulary support added in each Student Unit
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Calculus : Single and Multivariable - 4th edition
Summary: Calculus, Fourth Edition brings together the best of both new and traditional curricula to meet the needs of even more instructors teaching calculus. The author team's extensive experience teaching from both traditional and innovative books and their expertise in developing innovative problems put them in an unique position to make this new curriculum meaningful to students going into mathematics and those going into the sciences and engineering. This edition will wo...show morerk well for those departments who are looking for a calculus book that offers a middle ground for their calculus instructors.
Calculus, Fourth Edition exhibits the same strengths from earlier editions including the Rule of Four, an emphasis on modeling, exposition that students can read and understand and a flexible approach to technology. The conceptual and modeling problems, praised for their creativity and variety, continue to motivate and challenge students. ...show less3.14
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PSYC 326 Behavioral Neuroscience Fall 2008 Page 1 This course is an introduction to the biological bases of behavior. We will use the topic of learning and memory as ...
father lopez catholic high school textbook list 2010-2011 course name isbn number title publisher required or optional must buy new english ii honors 0-8219-1563-0 literature and ...
u0022Several schools including ours offer the PSAT to 9th, 10th and 11th grade rs. This year we noticed that our 9th graders tended to score higher in the mathematics than ...
Challenges in Secondary Math If students donu0027t perceive they have the ability to learn math, they wonu0027t put forth the efforts necessary to master math concepts and skills.
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Linear Feedback Control: Analysis and Design with MATLAB
Written for undergraduate courses in control systems, this book provides an introduction to linear feedback controls using MATLAB. The book begins with a summary of the properties of linear systems and addresses modeling and model reduction issues. Later chapters provide in-depth coverage of time domain, complex plane, and frequency domain techniques. Topics covered include model-based controller designs, PID controllers, and robust control designs.
MATLAB, Simulink, and the Control System Toolbox are used throughout the book to solve numerous real-world application examples. In addition, a supplemental set of MATLAB M-files is available for download.
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CHEGG TEXTBOOK SOLUTIONS FOR
An Introduction to the Finite Element Method3rd Edition
Chapter
Problem
New Problem 3.2: Develop the weighted-residual finite element model (not weak-form finite element model) of the following pair of equations:
Assume the following approximations of the form
The finite element equations should be in the form
(a) Define the coefficients and in terms of the interpolation functions, known data, and secondary variables, and (b) comment on the choice of the interpolation functions (what type, Lagrange or Hermite, and why
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When to Take Notes
To become a better note-taker you must know when to take notes and when not to
take notes. The instructor will give cues that indicate what material is
important Some such cues include:
presenting usual facts or ideas
writing on the board • summarizing
pausing
repeating statements
enumerating; such as, "1, 2, 3" or "A, B, C"
working several examples of the same type of problem on the black- board
saying, "This is a tricky problem. Most students will miss it." For example,
510 is "undefined" instead of "zero."
saying, "This is the most difficult step in the problem."
indicating that certain types of problems will be on the test, such as coin-
or age-word problems
explaining bold-print words
You must learn the cues your instructor gives indicating important material. If
you are in doubt about the importance of the class material, do not hesitate to
ask the instructor about its importance.
While taking notes, you may become confused about math material. At that point,
take as many notes as possible, and do not give up on note-taking.
As you take notes on confusing problem steps, skip lines; then go back and fill
in information that clarifies your misunderstanding of the steps in question.
Ask your tutor or instructor for help with the uncompleted problem steps, and
write down the reasons for each step in the space provided.
Another procedure to save time while taking notes is to stop writing complete
sentences. Write your main thoughts in phrases. Phrases are easier to jot down
and easier to memorize.
Abbreviations
E.G.
for example
D
shows disagreement with statement or passage
CF.
compare, remember in context
REF
reference
N.B.
note well, this is important
et al
and others
\
therefore
bk
book
Ñ
because
P
page
Ì
implies, it follows from this
etc.
and so forth
>
greater than
V
see
<
less than
VS
see above
=
equals, is the same
SC
namely
¹
does not equal, is not the same
SQ
the following
( )
parentheses in the margin, around a sentence or group of
sentences indicates an important idea
Comm.
Commutative
?
used to indicate that you do not understand the material
Dis.
Distributive
0
a circle around a word may indicate that you are not
familiar with it; look it up
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Constructivist and Interactionist Theories of Mathematical Development
9048143977
9789048143979
Learning Mathematics:The common theme that links the six contributions to this volume is the emphasis on students' inferred mathematical experiences as the starting-point in the theory-building process. The focus in five of the chapters is primarily cognitive and addresses the processes by which students construct increasingly sophisticated mathematical ways of knowing.
Back to top
Rent Learning Mathematics 1st edition today, or search our site for Paul textbooks. Every textbook comes with a 21-day "Any Reason" guarantee. Published by Springer.
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Seven The Pre-Algebra course is designed to provide nu...
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The connection of the physical to the mathematical representations can also be a
distraction or confusing for some students. It is possible to focus on the
mathematical properties of the graphs (steepness, angle, intersection, etc.)
without making the physical connection.
One somewhat related example is the discussion we had here about the concept of
step size and its relation to slope. Another was the question of position vs.
distance and whether one can draw conclusions about where the runners actually
are relative to each other. Does the intersection of the graphs really indicate
that the runners have to meet/pass by each other?
These are all opportunities for good discussion, but depending on the objectives
and the point at which this is being used, it can introduce complications
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This course is useful for students interested in a career in (among other areas) mathematics, operations research, physics, engineering, or teaching secondary school math.
TRANSFERABILITY
UBC, SFU, UVic, Open University, TWU.
ALL THIS AND BEAUTY, TOO.
Linear algebra is an incredibly powerful set of tools with applications in many widely differing areas, including computer graphics, cryptography, physics, engineering, biology, chemistry, economics, commerce, and most areas of modern mathematics.
JOIN US IN VECTOR SPACE – DEFINE YOUR OWN SUBSPACE.
This course is generally considered a student's first "abstract" course. It provides a bridge between the intuitive, computational approach used in first-year calculus and the more sophisticated, formal approach used in upper-level courses. You can expect to think about questions you've never considered before, such as "When does AB not equal BA?", "What exactly is an algebra?", and "How do I know when I've proved something?" You can expect to wrestle with proofs and with the difficulties of expressing yourself clearly and concisely. You can also expect to be amazed at how seemingly bizarre constructions produce useful results for a wide variety of applications.
The sophistication that you develop during this course is extremely important for your success in future mathematics courses. The mathematics that you learn in the course will turn up over and over again in all kinds of courses.
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주 메뉴
Common Core and NCTM Standards
Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.
Define appropriate quantities for the purpose of descriptive modeling.
Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
Modeling: When making mathematical models, technology is valuable for varying assumptions, exploring consequences, and comparing predictions with data.
Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.
Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
a. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.
b. Informally assess the fit of a function by plotting and analyzing residuals.
c. Fit a linear function for a scatter plot that suggests a linear association.Interpret linear models
Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
Compute (using technology) and interpret the correlation coefficient of a linear fit.
Distinguish between correlation and causation.
NCTM Standards and Expectations:
Algebra 6-8
Use graphs to analyze the nature of changes in quantities in linear relationships.
Explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope.Algebra 9-12Use symbolic algebra to represent and explain mathematical relationships.
Approximate and interpret rates of change from graphical and numerical data.
Data Analysis & Probability 6-8
Select, create, and use appropriate graphical representations of data, including histograms, box plots, and scatterplots.
Make conjectures about possible relationships between two characteristics of a sample on the basis of scatterplots of the data and approximate lines of fit.
Data Analysis & Probability 9-12
Identify trends in bivariate data and find functions that model the data or transform the data so that they can be modeled.
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Te tau(
Book
)
5
editions published
between
2002
and
2004
in
Maori
and held by
55
libraries
worldwide
Provides exercises, activities, and games to help understand various number systems, including place values, counting systems, fractions and decimal numbers. Designed to support Mathematics in the New Zealand curriculum. Suggested level: primary, intermediate
Te tauanga(
Book
)
5
editions published
between
2002
and
2009
in
Maori
and held by
41
libraries
worldwide
Exercises, activities, and games introduce the understanding of statistical concepts, including gathering information, presenting and interpreting data. Designed to support Mathematics in the New Zealand curriculum. Suggested level: primary, intermediate
Te taurangi(
Book
)
4
editions published
between
2002
and
2007
in
Maori
and held by
40
libraries
worldwide
Provides exercises, activities and games to assist students with understanding the concepts of algebra. Designed to support mathematics in the New Zealand curriculum. Suggested level: primary, intermediate
Te ine(
Book
)
4
editions published
between
2002
and
2007
in
Maori
and held by
39
libraries
worldwide
Provides exercises, activities, and games to help understand the mathematical concepts of length, weight, quantity, volume, area, and time. Designed to support Mathematics in the New Zealand curriculum. Suggested level: primary, intermediate
Te Āhuahanga(
Book
)
4
editions published
between
2002
and
2007
in
Maori
and held by
36
libraries
worldwide
Provides exercises and activities that introduce the basic principles of geometry. Designed to support mathematics in the New Zealand curriculum. Suggested level: primary, intermediate
Algebra(
Book
)
3
editions published
between
2000
and
2003
in
English
and held by
34
libraries
worldwide
Provides exercises, activities and games to assist students with understanding the concepts of algebra. Designed to support mathematics in the New Zealand curriculum. Suggested level: primary, intermediate
Geometry by New Zealand(
Book
)
3
editions published
between
2000
and
2004
in
English
and held by
34
libraries
worldwide
Provides exercises and activities that introduce the basic principles of geometry. Designed to support mathematics in the New Zealand curriculum. Suggested level: primary, intermediate
Ngā meka matua(
Book
)
3
editions published
between
2002
and
2004
in
Maori
and held by
33
libraries
worldwide
Provides exercises, activities, and games for students to practise addition, subtraction, multiplication and division. Designed to support Mathematics in the New Zealand curriculum. Suggested level: primary, intermediate
Number(
Book
)
3
editions published
between
2000
and
2002
in
English
and held by
33
libraries
worldwide
Provides exercises to help understand various number systems, including place values, counting systems, fractions and decimal numbers. Designed to support mathematics in the New Zealand curriculum. Suggested level: primary, intermediate
Statistics(
Book
)
3
editions published
between
2000
and
2008
in
English
and held by
32
libraries
worldwide
Exercises, activities, and games introduce the understanding of statistical concepts, including gathering information, presenting and interpreting data. Designed to support mathematics in the New Zealand curriculum. Suggested level: primary, intermediate
Measurement by New Zealand(
Book
)
2
editions published
between
2000
and
2001
in
English
and held by
30
libraries
worldwide
Provides exercises and activities designed to reinforce students' understanding of mensuration, with problems involving length, weight, quantity, volume, area, and time. Suggested level: primary, intermediate
Te whakaoti rapanga(
Book
)
3
editions published
between
2002
and
2004
in
Maori
and held by
30
libraries
worldwide
Provides exercises, activities, and games for students to practise applying problem-solving strategies. Designed to support Mathematics in the New Zealand curriculum. Suggested level: primary, intermediate
Problem solving(
Book
)
2
editions published
between
2000
and
2001
in
English
and held by
29
libraries
worldwide
Provides exercises for students to practise applying problem-solving strategies. Designed to support mathematics in the New Zealand curriculum. Suggested level: primary, intermediate
Number(
Book
)
3
editions published
between
2002
and
2004
in
English
and held by
29
libraries
worldwide
Provides exercises, activities, and games to help understand the concepts of number. Designed to support Mathematics in the New Zealand curriculum
Multiplicative thinking by Vince Wright(
Book
)
2
editions published
in
2006
in
English
and held by
26
libraries
worldwide
Provides exercises, activities and games for students to practice multiplication, and to develop strategies for solving problems using arithmetic. Suggested level: primary, intermediate
Basic facts(
Book
)
2
editions published
between
2000
and
2001
in
English
and held by
25
libraries
worldwide
Provides exercises, activities, and games for students to practise addition, subtraction, multiplication and division. Designed to support mathematics in the New Zealand curriculum. Suggested level: primary, intermediate
Number sense(
Book
)
2
editions published
in
2003
in
English
and held by
20
libraries
worldwide
Number(
Book
)
2
editions published
between
2002
and
2004
in
English
and held by
17
libraries
worldwide
Provides exercises, activities, and games designed to reinforce students' understanding of various number systems, including place values, counting systems, fractions and decimal numbers, and their application in problem solving. Suggested level: primary, intermediate
Sport(
Book
)
1
edition published
in
2001
in
English
and held by
15
libraries
worldwide
Provides exercises, activities and games based around the theme of sport, and designed to reinforce students' understanding and application of mathematical concepts, including problem solving, geometry, arithmetic and mensuration. Suggested level: primary, intermediate
| 677.169 | 1 |
Abstract: Edited by Kathleen Lynch-Davis and Tracy Goodson-Espy. GeoGebra is a free multiplatform software application that allows students to explore a wide variety of algebra and geometric concepts through hands-on manipulation of graphs, tables, formulas, and shapes. It is also a convenient and easy way to generate graphics and visuals for presentations, test questions, and homework problems.
The National Council of Teachers of Mathematics is the public voice of mathematics education, supporting teachers to ensure equitable mathematics learning of the highest quality for all students through vision, leadership, professional development, and research.
| 677.169 | 1 |
The reflections which will be presented here, result partly from experimental
teaching sequences of geometry for the first year of French senior high school
(15-16 year old students), and from research carried out in several countries
about the use of Cabri-geometry, in particular from case studies of students
solving mathematical tasks in a Cabri-geometry environment.
Experimental teaching sequences
They have been designed and carried out in classroom for three years. They
are based on the use of Cabri-geometry (software version and application of
the TI 92). The students were given a TI 92 for the whole academic year. It
implies that they could use it at home and not only for geometry. They also
worked for some activities on computers in a specific computer room during part
of the maths hours. The fact that more or less the same dynamic geometry program
was available in both environments (computer and calculator) allowed this double
use of technology. The availability of the geometry application on a hand held
device certainly contributed to its integration under several aspects : the
students could decide on their own to use it , the teacher could give home work
or class assignment to be done on the TI 92 (the files were easily transferred
and collected on the calculator of the teacher).
It must be stressed that these students were not involved in a mathematics
oriented class. At this level of schooling the classes gather all students independently
of their achievement in any subject matter. The choice of a major is made on
the following year when students are 16-17 year old.
I - Why integrating new technology in the teaching of maths ?
The philosophy of such an integration is not the use of technology for itself
but for supporting, improving and changing the learning of geometry through
various possibilities of computers which have very often been presented: exploration
of a great number of cases, possible variations on the parameters of the problem,
visual or numerical feedback from computer.
The computer may work as a catalyst for generating questions ("what if
?"), for creating counterexamples, in a word it may foster a more
scientific approach from students. The computer allows the design of new kinds
of tasks revealing well the meaning of theoretical objects.
An additional aimof integrating new technology is to develop the students'
ability of choosing the relevant tool to use it in a relevant way for solving
a problem.
The case of dynamic geometry software
Dynamic geometry software based on direct manipulation offer a microworld in
which theoretical objects and relations (sometimes very complex from a conceptual
point of view) can be visualized and physically manipulated. Such kind of environments
offers the possibility for students of constructing knowledge in action and
not only by having recourse to language:
For example, a geometrical transformation like point symmetry can be used as
a tool for constructing a parallelogram. When students are given the task of
constructing a parallelogram, they all do it by using parallel lines and the
parallelogram collapses when moving a vertex until three vertices are collinear.
The construction by point symmetry appears as more powerful because preserving
the parallelogram even when it is flat. The environment Cabri-geometry reveals
thus the power of point symmetry under two aspects : the operational aspect
as a construction tool and the generality of this tool allowing a construction
resisting to a limit case.
The property of symmetry of the parallelogram in a paper and pencil environment
is mainly used for proving, dynamic geometry software allows the students to
experience this property in action before using it at a more formal level (Laborde
1995).
Dynamic geometry software may be used for creating intriguing visual phenomena
which are not expected by students. The only way of explaining those phenomena
is the recourse to theory. Prediction activities are from this point of view
also interesting: the student may become aware of the inadequacy of his/her
expectations when confronting his/her prediction with the observed result on
the computer. Ex : what will happen to the image of a polygon through a translation
if you move the vector of translation ? or how to modify the vector of translation
so that a circle and its image become tangent ?
This brief description of possible uses of technology in mathematics teaching
reveals the importance of the design of tasks in which the computer is used.
This leads us to attempt at defining more precisely the idea of integration.
II - What does mean integration of new technology in mathematics teaching?
Integration may be realized in several ways to a more or less extent. We would
propose a gradation in the extent of integration in a increasing order of integration
:
- scarce use of technology for activities not really related to the teaching content: it may happen that teachers use computers for creating sessions on open problem solving, three or four times the year but these sessions are not part of the course and quite no reference is made to these sessions during the ordinary lessons;
- use of computers for sessions of activities on previously introduced notions: the computer offers opportunities of "hands on" sessions in which students are more autonomous ; but the notions which are objects of teaching have been introduced in an usual way in a paper and pencil environment;
- the teacher introduces mathematical content through technology and not only using technology on previously introduced mathematical notions : it implies that reference situations based on technology are created which may affect strongly the meaning of these notions.
- in addition of content introduced through technology, the teacher "institutionnalizes" the notions to be memorized by referring to some elements of the computer environment
It is clear that the latter ways of integrating computers require a long term use of technology. There must be no need for the teacher to repeat how to use some or some command.
A greater degree of integration is fulfilled if the student on his/her own may have recourse to technology to solve a problem given outside the computer/calculator context.
III — The process of integration
III.1- A long process
Our experience of designing scenarios based on Cabri and integrating them in the regular course of the teaching shows that it takes a long time before reaching the adequate tasks taking advantage of the computer environment and finding the good time management in the classroom. It turned out that the composition of the team of teachers involved in the project revealed well the difficulties and successive phases of integration since those teachers presented various degrees of experience in either teaching mathematics or using technology.
We propose to describe the process of integration in terms of equilibrium processes according to a Piagetian metaphor. Integrating technology introduces perturbations in the teaching system. By teaching system we understand the system made of several
elements mutually interacting, around three poles, the teacher, the students and knowledge. We assume that the teaching system is subject to several constraints (time, societal choices regarding curriculum, inner structure of the mathematical domain of knowledge, conceptions and ideas of students ) and that it evolves from an equilibrium state to another one by making choices. When a new element is introduced, the system is perturbed and is lead to make new choices for insuring a new equilibrium. Following Piaget who proposes three kinds of reactions of an individual to cognitive perturbations, we propose the following reactions
- reaction alpha : ignoring the perturbation
- reaction beta : integrating the perturbation into the system by means of partial changes
- reaction gamma : the perturbation is overcome and looses its perturbing character.
We consider that there is a real integration of technology when the teachingsystem is reacting according to the gamma reactions. But our claim is that the process leading to this kind of reaction is a long term process depending on several factors. Some of them play an important role. Let us mention two of them: the features of the computer environment, the tacit learning hypotheses and beliefs of the teacher.
III.2 - The role of the computer environment
Numerous research papers stress how the context shapes the students' solving strategies when they are faced with a problem. Sharing this point of view, we also claim that the problem itself is shaped by the context. Features of a computer environment may play a crucial role on the type of task the students have to solve and affect thus the possible strategies and the cognitive outcome of the task.
Let us give an example taken from our own experience of writing tasks in a computer environment.
One of the first work sheets designed by one of the teachers involved in the project dealt with the sum of the angles of a convex quadrilateral. It is interesting to note that this is not part of the French syllabus. When starting using Cabri, this teacher chose to address a point slightly external of the curriculum (behavior partly belonging to reaction alpha). Because of the type of computers available in his school he had to use Cabri-geometry 1.He gave the following task to the students:
"Construct any convex quadrilateral ABCD. Mark
and measure the interior angles of this quadrilateral by means of the menu
items "Mark an angle" and"Measure"
of the menu "Miscellaneaous". Note the measures in the table below.
Calculate the sum of the four angles and note the result in the table. Move
A, B, C or D and note the new measures, then calculate the sum. Repeat it
several times. What do you notice ? Make a conjecture and prove it"
In this activity, the computer is only used for discrete measures. The student
must add the measures on his sheet as soon as he moves one of the vertices of
the quadrilateral because there was no calculating facility on Cabri 1. The
statement of the task did not offer an opportunity of analyzing the behavior
of the quadrilateral when one of its vertices was continuously dragged. The
computer was used as a box from which quadrilaterals could be randomly taken
each one after the other. It could be easily be replaced by a table of values
of angle measures of quadrilaterals. The change brought by the use of a computer
is reduced to almost nothing.
If Cabri II or its implementation on the TI 92 is used, it is possible to compute
and display the sum of the angle measures. The student may be asked for observing
what remains invariant in the diagram in the drag mode. He/she may thus observe
that not only the sum remains constant but also that three vertices remain invariant
when one of them moves. This is the starting point of establishing a relation
between the invariance of the sum and a geometrical analysis of the quadrilateral.
Recognizing an invariant triangle in the quadrilateral may prompt the use of
the property of the sum of the angles of a triangle. One can notice how the
drag mode in the second context may be the source of linking a numerical invariant
and a geometrical one and how this calls for previous knowledge of the student.
For these reasons we consider that the computer is more integrated in the second
case.
Following Kaput (1994) we think that "technology without curriculum is
only worth the silicon it is written on" but we would add that curriculum
with inadequate use of technology is only worth the text processor it is written
with.
But again finding the adequate environment and elaborating an adequate use
for a specific learning aim is not trivial and needs a deep knowledge of the
environment.
III.3 — Learning hypotheses — Epistemological beliefs
When designing teaching based on the use of technology, the teacher or the
researcher may not be able to predict as he does in traditional environments
the possible outcome of the situations proposed to students. According to the
learning hypotheses or teachers implicit beliefs underlying the design of teaching,
it may lead to various deviations.
Let us present two extreme cases:
i) Case of constructivist hypotheses, such as:
- Students learn when they are faced with tasks for which math notions are
efficient tools of solutions
- Feedback coming from the situation may favor an evolution of solving strategies
more than a judgement coming from the teacher
Feedback of dynamic geometry software may be from this point of view very rich
in that it allows an interaction between the visual and the theoretical aspects
of geometry.
The teacher may rely too much on feedback of computer or give a too large place
to activities in which students work on computer, and propose tasks of a greater
complexity with respect to corresponding paper and pencil tasks.
The teacher underestimates the complexity of the task, the time needed for
the student to solve the task because he has no reference point in his past
experience. He overestimates the possibility of interpretations by the student
of feedback given by the software.
ii) Epistemological view of geometry as intrinsically linked to paper and pencil
The teacher does not rely on computer based activities as allowing learning
of geometry and in addition to computer activities proposes similar paper and
pencil tasks without being aware that sometimes a paper and pencil task is less
demanding in terms of knowledge and allows perceptive strategies instead of
strategies based on theoretical properties. We encountered this situation in
our teachers group. One of them, who was an experienced teacher but novice in
using technology in her teaching designed a scenario for introducing the students
to a new geometrical transformation: "dilation". This was a great
change for her but she reduced the effects of the change by two behaviors :
- giving only problems which could be given in a paper and pencil environment
- systematically asking twice the same construction task, the construction
in Cabri then in paper and pencil environment. Her behavior can be assigned
to a beta reaction: she reduced the effects of the perturbation by performing
only partial changes in the teaching.
This behavior is often linked with the conception of a paper and pencil environment
as not a context. Knowing how to perform something in paper and pencil environment
would be the warrant of a decontextualized knowledge. Noss and Hoyles (1996,
p. 48) propose an alternative view of abstraction as not necessarily linked
to decontextualisation and "as a process of connection rather than ascension".
They add that the "situated, the activity based, the experiential can contain
within it the seeds for something more general" (p.49).
Another reason for such a behavior may be also explained by the institutional
context. Even if all kinds of calculators are allowed in our French national
evaluation, all tasks are given in a paper and pencil environment. The teacher
sticks at this context to be sure that students are able to perform the tasks
in this latter environment.
IV — Evolution of choices in the design of scenarios
IV.1 Evolution of the tasks
During the last three years, successive versions of the same scenarios have
been written after they have been achieved in classroom. The evolution of their
features can be summarized as follows.
The first versions called often for immediate visual observations and generalization
by inductive reasoning. The need for proof was less important than in a paper
and pencil environment. The first versions gave a great role to measuring. For
example the first version of the scenario "Dilation" asked the student
to construct the image of a segment by a dilation with given ratio and to compare
the length of the image and of the initial segment; this was to be done with
several ratios. Again as in the case of the quadrilateral, the activity called
only for discrete measuring and did not use the animation facility of the numerical
display of the ratio.
The later versions introduced two new kinds of tasks :
- tasks in which the environment allows efficient strategies which are not possible to perform in a paper and pencil environment
- tasks raised by the computer context, i.e. tasks which can be carried out only in the computer environment.
Example of the first kind of tasks in the scenario "Vectors" : "Construct a triangle ABC from the given points B, C and G centroid of triangle ABC." A can be constructed as satisfying the vectorial relation :
vector GA + vector GB + vector GC = vector 0. (1)
Fig. 1 - Construction of the image of A' through a point symmetry around G.
Fig.2 — Result of the construction
A is constructed as the symmetrical point with respect to G of the endpoint of the vector sum of the two vectors GB and GC (Fig. 1 & 2).
Cabri contributes to linking the algebraic aspects of vectors to the geometrical aspects Relation (1) is restricted in paper and pencil environment to algebraic calculations while in Cabri it also receives a geometrical meaning since it is a tool of construction. It offers a new connection in the conceptual field of vectors (Vergnaud) or in theweb of vectors (Noss & Hoyles, op.cit.).
The second kind of tasks involves mainly two categories of tasks :
- the "black box" situations
- the prediction tasks
In the black box situations, the students are given a diagram on the screen
of the computer and they are asked qustions about it. This kind of situations
was used in our scenarios for introducing new transformations. A point P and
its image P' through the unknown transformation were given to the students.
They could move P and observe the subsequent effect on P'. Students were
asked to find the properties of the unknown transformation by means of this
black box. In such a task students must themselves ask questions about the transformation
:
Does it preserve collinearity ? Does it preserve distance ? Does it have invariant
points ?
Cabri can be used to design experiments and get empirical answers. For example,
one may redefine P as belonging to any given straight line and obtain the image
of this line as the Locus of P' depending on the variable point P. Two
specific tools of Cabri are used "Redefinition" and "Locus".
It presupposes that the students not only master their use but also decide to
use them. This decision actually involves mathematical knowledge : the fact
that the image of a figure is the set of images of points of a figure; this
is often completely implicit in our curricula but it presents a conceptual cut
(even obstacle probably from both cognitive and didatical origin) with the view
of a figure as an entity and not as a set of points.
Fig.3 — Redefining the given point P
Fig.4 - as a point on Fig.5 —
a line
Fig.6 —Locus of P' when P is moving on the line
Fig.7 — Locus of P' when P is moving on a circle
Such a task offers a very different point of view on the notion of geometrical
transformation. Instead of studying the effects of a known transformation, students
are asked to characterize the transformation by means of its properties. Of
course this may be an attractive task only if some exotic transformations and
not only the usual ones are given to students. Theorems of invariance receive
a new meaning in this kind of task : they are tools for identifying the category
which the unknown transformation belongs to. An effect of this kind of task
is that students may understand why to study all these theorems about invariant
elements of transformations. The invariance properties become remarkable phenomena
instead of being the routine.
Prediction tasks are also specific to computer environment. Where should be
the center of dilation for obtaining the image of a given circle tangent to
this circle ? When the prediction of the students turns out to be wrong, this
is a good opportunity of asking "why is it so ?" and calling for proof.
The design of scenarios revealed us that there are ways of integrating the
computer in the problems given to students. The computer is an essential part
of the meaning of the problem. At the beginning of our work, technology was
mainly used as illustrating mathematical facts. It is only in a second phase
that teachers used it as source of problems. This is not without raising problems
for teachers:
- the possibility of going beyond the usual curricula
- the tension between the mathematical and the instrumental
- problems of time management
IV.2 - Tension between the mathematical and the instrumental
A computer based teaching involves mathematical knowledge but also knowledge of how to use the software, to perform operations on the software. There is a tension between both kinds of knowledge (Artigue 1997). The teacher is faced with questions as : to what extent must the statement of the task refer to what is to be done in terms of technical operations in order to avoid time consuming on technical aspects ? or should the task statement not refer to the technical aspects in order to allow students' autonomy ?
Does the student fail because of mathematics or of the technical aspects ? This tension may be solved only if the use of technology is a long term use. In this latter case, the use of the environment may become an object of teaching in relation to mathematical teaching. Of course the strength of the interaction between mathematics and using the software depends very much on the features of the software.
Our teachers introduced the tool "Trace" as a tool for easily giving evidence of an invariant point. For example when a variable line is passing through a fixed point, the trace of this line shows clearly this point. This is for example a good way of displaying that the sum MC of two vectors MA and MB is passing through the midpoint segment AB for any point M.
Fig.8 — Trace of the sum of the vectors AM and MB when M is moving on the screen
At the end of the year students became able to use on their own the tool Trace for displaying an invariance phenomenon like in the dilation black box task mentioned above.
This lead the teachers to include technology in their synthesis phase. Knowledge pointed out by the teacher could refer to some related aspects of Cabri .
Example in the scenario "Vectors": The notion of direction of a vector is not easy to understand by students. There is a paradox that this notion is understood as soon as the notion of vector is acquired but to acquire the notion of vector, the students need to understand the notion of direction. The use of the two kinds of pointers in Cabri showed to the students that when the vector is moved by the usual pointer , its coordinates remain unchanged while they are changed when the vector is rotated by the pointer "Rotate" although its norm is unchanged. So the teacher introduced the Cabri property : coordinates of a vector are modified by the Rotate pointer which lead to the usual property "coordinates of a vector depend on the direction of the vector". The pointer played a mediation role in vygotskian terms.
In the same way, the degree of freedom of points was introduced by the teachers
as linked to their geometrical status.
IV.3 Time management
Our first versions of scenarios were time greedy. It is a quite usual phenomenon
that any kind of teaching innovation provokes inflation of time. Schneider (1998)
reported on a teaching based on the use of the TI 92 about logarithms and exponentials
which took 40 hours of teaching instead of the usual nine hours. This led us
to seek for simple critical computer based tasks which may be very efficient
in terms of learning and to have less recourse to long and open tasks.
Ex:
Construction of a straight line passing through a given point whose directing
vector is given.
We also attempted to find an optimal balance between what is demonstrated by
the teacher on the LCD display and what is done by students, between what is
ready made and given on the calculators to students and what has to be done
by the students with the software. We preferred after one year to give the macro-construction
of the multiplication of a vector by a number to be explored and interpreted
rather than to be constructed by the students themselves.
After sometime teachers decided to give homework requiring the use of technology.
It not only solved some time problems but also gave a more institutional status
to the use of technology for the students.
When examining the changes occurred over the last three years, it seems that
the use of technology became a more usual and ordinary element of the classroom,
less spectacular, calling for less complex tasks but involved in more events
of the school activities of the student, possibly beyond the only class. So
assessment in the classroom in the last year included tasks in computer based
environments.
V- Mottos for a curriculum integrating new technology
• Technology to design learning situations in which mathematics is constructed
by the student as a way of describing and modeling behaviors (s.c. black box
situations)
| 677.169 | 1 |
MathScape: Seeing and Thinking Mathematically
Navigation
The Language of Algebra: Equations, Tables, and Graphs
Students explore the use of variables and expressions in solving problems
as they work with equations, tables, and graphs. Students learn about variables
and expressions as they consider what they would put into an ideal school.
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NCTM Standard: Algebra
Understand patterns, relations, and functions
Represent and analyze mathematical situations and structures using algebraic
symbols
Use mathematical models to represent and understand quantitative relationships
Analyze change in various contexts
Primary Mathematical Goals
Use variables to write expressions and linear equations
Make predictions based on tables, equations, and graphs
Understand the relationship between tables, equations, graphs, verbal
or written descriptions
| 677.169 | 1 |
9780136007029
ISBN:
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The newly created Essential Mathematical Methods 1&2 CAS text is written specifically for CAS students who plan to study Mathematical Methods 3&4 CAS in their final VCE year.
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Activities (for students) Activities for Students: Biology as a Source for Algebra Equations: The Heart
Virginia Horak
November 2005, Volume 99, Issue 4, Page 296
Abstract: The integration of high school algebra and biology by utilizing opportunities to represent relationships and solve problems in biology using algebra concepts and techniques. Students use an equation to learn about their own heart. Activity sheets included.
The National Council of Teachers of Mathematics is the public voice of mathematics education, supporting teachers to ensure equitable mathematics learning of the highest quality for all students through vision, leadership, professional development, and research.
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Transcript
2.
Chapter 1Getting Started With GeoGebraIn this chapter• Install and start up GeoGebra• Examine basic features• Open and save a GeoGebra fileStarting up GeoGebraGeoGebra can be downloaded for free at can also be accessed through any browser through the above web site (you still click on the "Down-load" button, and look for the web applet option). This is useful if you are using a public computer or acomputer in a lecture hall and do not have download and install permissions.This chapter will familiarize you with various basic features of GeoGebra (pronunced Gee-O-gebra).We will introduce features of GeoGebra as the need arises. When working with the examples given,you should be at a computer with the Geogebra program open.Start up the GeoGebra software. The main buttons are shown below and each button has a drop downmenu associated with it.. Algebra View Geometry View. 1
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2 Guide to GeoGebraDo not be concerned if your screen does not exactly look like the above. When we work our examples,you will be shown which tools must be used and how you can access them via the toolbar.GeoGebra is a software with a wide variety of capabilities.This guide will focus primarily on how towork with functions and their properties using GeoGebra.Graphing a functionThe easiest way to see what GeoGebra is about is by graphing a function. Unlike most graphing soft-ware, GeoGebra allows you to dynamically change the graph with the mouse. That's what sets itapart.Example 1 Graph the function f x = 3x 2 + 1Solution1 In input bar, type f(x)=3x^2+12 Press <Enter> and you'll see the graph.Moving the graphGeoGebra is a dynamic geometry software. That is, the graph that's drawn is not static. It has variousproperties which can be examined individually. A simple property is to just move the graph. To do this,follow these steps.1 Click on the selection tool. . This enables the drag option.2 Point to the graph, then hold down the left mouse button, and move the graph with the mouse.3 As you move the graph, note how the expression for f(x) changes. Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 United States License.
4.
Guide to GeoGebra 3Changing line stylesTo change the line color and/or styles in a plot, right click into the curve you want to change. Click onProperties, and set the options you wish.Points on the graphExample 2 Use the graph of f x = 3x 2 + 1 to find various points on the curve and trace along thecurve.SolutionSteps to trace a point along a graph1 Click on the point tool and choose new point.2 Now click on the selection tool.3 Move mouse until you see the graph highlighted. Left click to place a point on the graph. Move mouse to the point A on the graph, hold down left mouse button and start moving your mouse. You should see the point A tracing along the curve. Your window should be similar to the following.R. Narasimhan
5.
4 Guide to GeoGebra Note that the coordinates of the point A are displayed under Dependent Objects. That's because the point A depends on the function f.Scaling the axesYou can change the scale on the axes by simply clicking on the drawing pad tool . Point themouse to the axis you want to scale. By holding down your mouse button you can stretch or shrink thex or y axes.You can also use the drop down menu from the drwaing pad tool to zoom in or zoom out.Saving GeoGebra files1 Open the File menu and select Save.2 Select a folder where you want to store the file, or create a new folder.3 Type in a name for your GeoGebra file.4 Click Save in order to finish this process. A file with the extension '.ggb' is created. This exten- sion identifies GeoGebra files and indicates that they can only be opened with GeoGebra.Avoid using spaces or special symbols in a file name since they can cause unnecessary problems whentransferred to other computers. Instead you can use underscores or upper case letters within the filename (e.g. First_Drawing.ggb). Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 United States License.
6.
Guide to GeoGebra 5Printing and exporting graphsOnce you've drawn a graph with GeoGebra, you may want to export the graph so that you can use itlater for another purpose.To do this, click on File > Export >Graphics View.... Select the option you prefer. You can save as agraphics file (you will be prompted on the file tye - png, pdf etc.) or save in the Clipboard to paste in adocument..Some Common Errors• To move the graph around, you need to have the selection tool highlighted.R. Narasimhan
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Chapter 2Lines and Linear EquationsIn this chapter• Graph a line and find its equation given two points• Explore the slope triangle• Find distance between two points• Parallel and perpendicular lines• Creating dynamoc graphs with slidersGraphing a line given two pointsA simple way to explore the powerful features of GeoGebra is to plot two points, and draw a line.GeoGebra will automatically determine its equationExample 1 Plot the points (2,3) and (-4,1) and draw a line through them.Solution1 Click on Options > Drawing Pad.. 6
8.
Guide to GeoGebra 72 Use the options here to set up your drawing grid.3 In the Input box, type A=(2,3). Press <ENTER>. Then type B=(-4,1). The two points will be plotted as follows.R. Narasimhan
9.
8 Guide to GeoGebra4 Now choose the line tool . Click on Point A. A line will appear. Guide the line to Point B and click. You should see a graph similar to the one below5 Save the file as line1.ggb. We will use it later in this chapter. Check it out • Click on the selection tool and move the graph. You can translate the graph. See what happens to the points A and B and the equation. • You can also rotate the line around a point. The drop down menu from the selection tool has an option for this.Using the slope triangleUsing GeoGebra, you can visually indicate the slope of the line that you graphed in Example 1. Fur-thermore, you can see how the slope changes as you move one or both of the points. Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 United States License.
10.
Guide to GeoGebra 9Example 2 Use GeoGebra to indicate the slope of the line in Example 1.Solution1 Open the file line1.ggb, created in Example 1. If you were moving the line around, the points A and B may have changed in the file. If so, in the algebra window, double click on B to (-4,1). You can now edit the coordinates of Point B. You can also do this for Point A(2,3).2 Click at the bottom right of the angle button , and choose the slope button.3 Move your mouse to highlight the line and click. The slope triangle and the value of the slope will appear on the graph. and in the algebra window.4 You can also find the slope by typing m=Slope[a] in the Input box. Here, a is the name of the line that was created and m is the letter assigned to the slope.5 You can display the equation of Line a in slope-intercept form by right clicking on its equation and selecting Equation y=mx+b6 Save this file under the original name or to a different name. Check it out • Click on the selection tool, and move Point B. Keep Point A fixed. What do you notice about the slope? • Calculates values of the slope for some different values of Point B and compare to the value given in GeoGebra. • In the algebra window, double click on B. You can now edit the coordinates of Point B. You can also do this for Point A.R. Narasimhan
11.
Finding distance between two pointsYou can use the Distance command in the Input box to calculate the distance between two points.Example 2 Use GeoGebra to find the distance between A(-4,1) and B(3,-2).Solution1 Start up GeoGebra or open a new GeoGebra workspace by choosing File> New.2 In the Input box, type A=(-4,1). Press <ENTER> and then type B=(3,-2).3 In the Input box, type d=Distance[A,B]. Press <ENTER>.The value of the distance is dis- played in the algebra window. Check it out 2 2 • Use the distance formula d = x 2 – x 1 + y 2 – y 1 to verify that the distance given by GeoGebra is correct. • Find the midpoint of points A and B by typing C=Midpoint[A,B] in the Input box • A good use of the distance function is to help you find the perimeter of a polygon whose verti- ces are given by coordinates. Plot the points (1,2), (3,-1) and (-1,-2) in GeoGebra. Connect each pair of points with a line segment by clicking on the Line tool and choosing the segment option.. Find the perimeter of the resulting triangle.Parallel and perpendicular linesUsing GeoGebra, you can examine both the geometric and algebraic relationships between two paral-lel or two perpendicular lines.10
12.
Guide to GeoGebra 11Example 4 Use Geogebra to sketch the line parallel to the line y = – 2x + 3 and passing through(-1,2).Solution1 Start up GeoGebra or open a new GeoGebra workspace by choosing File> New. To see the grid, make sure the menu item View > Grid is checked.23 Now type P=(-1,2) in the Input box. Press <ENTER>. Click on the button with perpendicular lines and then click on the small red arrow. From the submenu, choose Parallel Line.R. Narasimhan
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12 Guide to GeoGebra4 Now select the Point P and the line a. The parallel line passing through P is now drawn and its equation is given.5 Use GeoGebra to find the slope of each line. Type Slope[a] in the Input box. Press <ENTER>. Then type Slope[b] in the Input box. Press <ENTER>. The slopes and the slope triangles are now given. Check these values by hand. Check it out • What do you observe about the slopes of parallel lines? • Find the equation of the parallel line by hand, and check with the one from GeoGebra.. Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 United States License.
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Guide to GeoGebra 13Example 5 Use Geogebra to sketch the line perpendicular to the line y = – 2x + 3 and passingthrough (-1,2).Solution1 Start up GeoGebra or open a new GeoGebra workspace by choosing File> New. To see the grid, make sure the menu item View > Grid is checked.2 To get a square grid, right-click in the graphing area. Select Properties and set xaxis:yaxis ratio to 1:1. Otherwise, perpendicular lines will not appear perpendicular!34 Now type P=(-1,2) in the Input box. Press <ENTER>. Click on the button with perpendicular lines .R. Narasimhan
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14 Guide to GeoGebra5 Now select the Point P and the line a. The perpendicular line b, passing through P, is now drawn and its equation is given.6 Use GeoGebra to find the slope of each line. Type m1=Slope[a] in the Input box. Press <ENTER>. Then type m2=Slope[b] in the Input box. Press <ENTER>. The slopes and the slope triangles are now given. Check these values by hand by examining the slope-intercept forms of the equations. Check it out • Do you observe about the slopes of perpendicular lines are negative reciprocals of each other? • Find the equation of the perpendicular line by hand, and check with the one from GeoGebra. Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 United States License.
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Guide to GeoGebra 15Creating dynamic graphs with slidersIn GeoGebra, you can introduce sliders to make your graph change when its parameters change. Forexample, the equation of a line is given by y = mx + b . You can set the slope, m, and the y-intercept, b,as parameters and then define the line. This allows GeoGebra to change m and b dynamically.Example 6 Use Geogebra to sketch the line y = mx + b , with m = 3 and b= 4. USe a slider tovary m and b.Solution1 Start up GeoGebra or open a new GeoGebra workspace by choosing File> New. To see the grid, make sure the menu item View > Grid is checked.2 In the Input box, type m=3. Press <ENTER>. Then type b=4. Press <ENTER>.3 Now type y=m*x+b in the Input box.4 If you look at the left panel, you will see that the line is dependent on the "objects" m and b. Click on the b = 4 button in the left panel. You will see a slider appear in the graphing area. Do the sameR. Narasimhan
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16 Guide to GeoGebra for the m = 3 button. Your graph should resemble the following. Now move each slider with your mouse and see what happens to the graph. Check it out • As m varies from negative to zero to positive, what do you observe about the slant of the line? • What do you observe about the line as b varies from negative to zero to positive? • You can add a slope triangle to visualize the slope of the line. Refer to Example 2 for instruc- tions. • The default range for the sliders is from -5 to 5. You can change this by right-clicking on the slider and then modifying the range under the slider tab in the properties dialog box. You can also change its color and other properties. Try it!NOTE: This guide is a work in progress. Chapters on different functions, including trig func-tions, and conic section will be added. Your comments are welcome. Please email comments toreva@mymathspace.net(Notes on new features to include: mx+b : parametrize m and b; list view of points and "guess" at line of best fit) Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 United States License.
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Precise Calculator has arbitrary precision and can calculate with complex numbers, fractions, vectors and matrices. Has more than 150 mathematical functions and statistical functions and is programmable (if, goto, print, return, for).
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More About
This Book
Editorial Reviews
Booknews
Intended for advanced undergraduates in engineering, physics, mathematics, and applied sciences, this material can serve as a springboard for studies in continuum mechanics and general relativity. Topics include an introduction to vectors and tensors, general bases and tensor notation, Newton's law and tensor calculus, the gradient, del operator, covariant differentiation, and the divergence theorem. Annotation c. Book News, Inc., Portland, OR (booknews.com)
Table of Contents
I Introduction: Vectors and Tensors.- Three-Dimensional Euclidean Space.- Directed Line Segments.- Addition of Two Vectors.- Multiplication of a Vector v by a Scalar—.- Things That Vectors May Represent.- Cartesian Coordinates.- The Dot Product.- Cartesian Base Vectors.- The Interpretation of Vector Addition.- The Cross Product.- Alternative Interpretation of the Dot and Cross Product. Tensors.- Definitions.- The Cartesian Components of a Second Order Tensor.- The Cartesian Basis for Second Order Tensors.- Exercises.- II General Bases and Tensor Notation.- General Bases.- The Jacobian of a Basis Is Nonzero.- The Summation Convention.- Computing the Dot Product in a General Basis.- Reciprocal Base Vectors.- The Roof (Contravariant) and Cellar (Covariant) Components of a Vector.- Simplification of the Component Form of the Dot Product in a General Basis.- Computing the Cross Product in a General Basis.- A Second Order Tensor Has Four Sets of Components in General.- Change of Basis.- Exercises.- III Newton's Law and Tensor Calculus.- Rigid Bodies.- New Conservation Laws.- Nomenclature.- Newton's Law in Cartesian Components.- Newton's Law in Plane Polar Coordinates.- The Physical Components of a Vector.- The Christoffel Symbols.- General Three-Dimensional Coordinates.- Newton's Law in General Coordinates.- Computation of the Christoffel Symbols.- An Alternative Formula for Computing the Christoffel Symbols.- A Change of Coordinates.- Transformation of the Christoffel Symbols.- Exercises.- IV The Gradient, the Del Operator, Covariant Differentiation, and the Divergence Theorem.- The Gradient.- Linear and Nonlinear Eigenvalue Problems.- The Del Operator.- The Divergence, Curl, and Gradient of a Vector Field.- The Invariance of— · v,— × v, and—v.- The Covariant Derivative.- The Component Forms of— · v,— × v, and—v.- The Kinematics of Continuum Mechanics.- The Divergence Theorem.- Differential Geometry.- Exercises
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Microsoft Mathematics (formerly Microsoft Math) is a freely downloadable educational program, designed for Microsoft Windows, that allows users to solve math and science problems. Developed and maintained by Microsoft, it is primarily targeted at students as a learning tool.
A related freeware add-in, called Microsoft Mathematics Add-In for Word and OneNote, is also available from Microsoft that offers comparable functionality (Word 2007 or higher is required).[1][2]
Microsoft Math has received 2008 Award of Excellence from Tech & Learning Magazine.[3]
Contents
Microsoft Math contains features that are designed to assist in solving mathematics, science, and tech-related problems, as well as to educate the user. The application features such tools as a graphing calculator and a unit converter. It also includes a triangle solver, and an equation solver that provides step-by-step solutions to each problem.
The standalone version of Microsoft Math 3.0 also has support for calculus and Ink Handwriting, allowing the user to write out problems by hand and have them recognized by Microsoft Math.
Microsoft Math 3.0 – Full-featured version available as a standalone purchasable product and a scaled-down version called Encarta Calculator available as part of Microsoft Student 2008. The full-featured standalone version exclusively includes calculus support, digital ink recognition features and a special display mode for video projectors. The standalone version is also the first version of Microsoft Math to require product activation.[4]
Microsoft Mathematics 4.0 – This version was released in 32-bit and 64-bit editions as a free download in January 2011.[5] It features a Ribbon interface.
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MATH 111 Math for the Liberal Arts
A survey course intended to introduce students to several ideas of mathematics, their historical context, and their applications and significance in society. The course will cultivate an appreciation of the significance of mathematics and develop student's mathematical reasoning through selected topics in logic, set theory, probability, statistics, number theory, graph theory, the real number system, and problem solving. Creation: Math. Liberal Arts.
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