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Manhattan, NY Ge quadratic formula is presented, along with an introduction to complex numbers. The laws of exponents are extended to the cases of zero, negative and fractional exponents. The idea of a function and its inverse is introduced
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Calculus Early Vectors
Browse related Subjects
...Read More in their curriculum. Stewart begins by introducing vectors in Chapter 1, along with their basic operations, such as addition, scalar multiplication, and dot product. The definition of vector functions and parametric curves is given at the end of Chapter 1 using a two-dimensional trajectory of a projectile as motivation. Limits, derivatives, and integrals of vector functions are interwoven throughout the subsequent chapters. As with the other texts in his Calculus series, in Early Vectors Stewart makes us of heuristic examples to reveal calculus to students. His examples stand out because they are not just models for problem solving or a means of demonstrating techniques - they also encourage students to develop an analytic view of the subject. This heuristic or discovery approach in the examples give students an intuitive feeling for analysis534493483. This book is in good condition only; used stamp on edge. The book has some cover shelfwear, edgewear, corner wear. Some scattered written notations: most pages are clean. Solid study or reading copy but not for collectors.; 1.9 x 10.1 x 8.5 Inches; 1120
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designed to give elementary education majors the mathematical foundation for early mathematics. Fundamental topics in geometry, measurement, estimation, numeration, number systems, number relations, fractions, decimals, statistics, and probability will be covered. The National Council of Teachers of Mathematics' Curriculum and Evaluation Standards for Grades K-8 and the integration of technology will also be a focus.
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More About
This Textbook
Overview
Joy of Mathematica, Second Edition, is a book and software combination for Windows and Macintosh that makes Mathematica easier to use and learn. The software includes the most common Mathematica operations needed in the first two years of college and university courses. The book is a manual for the software and an introduction to using Mathematica for mathematics and its applications to other fields. It contains material for students in calculus, differential equations, and linear algebra courses. Students and professionals will benefit from this user-friendly, practical guide to Mathematica.
* The CD:
* Runs on both Windows and Power Macintosh platforms
* Is optimized for Mathematica 4.0
* Requires that Mathematica's kernel and front end be on the same computer
* Includes a palette for easy entry of common mathematical notation The Book:
* Contains ready-to-use exercises and labs for the mathematics classroom
* Now includes more coverage of multivariable calculus and differential equations, in addition to single-variable calculus and linear algebra
Audience: For the mathematics professional or interested layperson engaged in learning Mathematica and it's practical applications.
Related Subjects
Table of Contents
A Brief Tour of Joy.
More About Joy.
Graphing in Two Dimensions.
Manipulating Expressions.
Solving Equations.
Working with Functions of One Variable.
Differentiating Functions of One Variable.
Integrating Functions of One Variable.
Working with Sequences and Series.
Graphing in Three Dimensions.
Working with Functions of Several Variables.
Differentiating Functions of Several Variables.
Integrating Functions of Several Variables.
Working with Vector Fields.
Solving Differential Equations.
Working with Vectors and Matrices.
Functions.
Limits and Continuity.
Derivatives in One Variable.
Integrals in One Variable.
Sequences and Series.
Parameterized Curves.
Surfaces and Level Sets.
Derivatives in Several Variables.
Multiple Integrals.
Differential Equations.
Systems of Differential Equations.
Matrices and Linear Equations.
Vector Spaces and Linear Transformations
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Information for Students
The Right Math Course for Me
Whether you are taking a course for a major requirement or for exploring your own interests, we have the right course for you. While making sure that mathematics majors have challenging and interesting courses, we dedicate ourselves to providing meaningful mathematics courses for all students.
Courses for Dabbling
Do you have an interest in mathematics, but you don't want to take calculus? Have you finished a calculus course and want something different to follow up? Are you an exploratory major? The following courses might interest you:
Math 152 (What is Mathematics?): What is the role of mathematics in our world? What does infinity really mean? How small is small? Questions like this (and many more) are explored in this course. We explore what mathematics means to us as individuals and as a culture. This course is offered every semester.
Math 161 (Math and Society): How does we manage credit card debt or choose the right loan? How do we share a cake in a fair way? These questions and many more in this course show us how mathematics helps us function as a society. This course is offered every semester.
Math 185 (Mathematical Experimentation): Experiments in mathematics?What does it mean to discover mathematics? Are you fascinated by patterns and pulling meaning out of these patterns? We use computers to help us model mathematical phenomena and answer these questions does require Calculus II as prerequisite and is offered every fall semester.
Math 220 (Mathematics for Childhood Education): How can Martian numbers help us understand long division? How is Arnold Schwarzenegger connected to fractions? How can elementary-school students help us understand math? Although most people are familiar with how to subtract whole numbers or multiply fractions, many of us don't really understand why they work. In this class, we use alternate number systems, student-generated algorithmsand challenging math problems to explore our number system and ideas of arithmetic. This course is offered every spring semester.
Math 250 (Problem-Solving Seminar): Do you like solving problems? Are you looking for a little taste of the math you love? Is there a way to attack all problems? In this one-credit course, we explore ways to approach solve fun mathematical problems. This course is offered every semester.
Statistics Courses
We live in an increasingly data-driven world, filled with advertising claims, opinion polls, and reported results of medical experiments. Confronted with all of this data, statistics gives us a systematic way of drawing informed decisions about issues that affect our lives.
Math 144 (Stats for Business, Economics, and Management): Statistics are used frequently in the world of business and finance; this class will help you understand where these statistics come from and how to use them yourself. This class is targeted at students in the business school but will be useful for everyone! This course is offered every semester.
Math 145 (Stats for Health/Life Sciences): Similar to Math 144, this class looks at statistics as it's used in the health, life, and natural sciences. This course is offered every semester.
Math 155 (Basic Statistical Reasoning): Statistics are increasingly used in the news and on the internet. This class will help you make sense of all the stats. It's a little less technical than Math 144/145, so it's perfect for students looking for gen ed creditCalculus Courses
Calculus is the study of how things change and is used in the life sciences, physical sciences, and economics. Whether you need calculus for your major or you are interested in application or theory, we have the right calculus course for you.
Math 107 (Fundamentals of Applied Calculus): Calculus is a way of describing how quickly quantities change. This version of calculus is tailored to business and economics students and focuses on modeling data with technology with less emphasis on algebra. This course is offered every semester.
Math 108 (Calculus for Decision Making): Looking for a course in calculus that focuses on applications? This course explores calculus without worrying about the theoretical underpinnings of calculus. Applications include drug concentrations in the body via daily medication, credit card debt, and population growth. This course is offered every semester.
Math 111 (Calculus 1): Roughly 300 years ago, Newton and Leibniz asked three important questions: What is instantaneous rate of change? What is the area under a curve? And what is the amazing relationship between the first two questions? The answers to these questions helps solve problems in fields from physics to economics, from biology to the business world! This course is offered every semester.
Math 112 (Calculus 2): Population growth and differential equations, physics and integrals, finance and series. This and much more is explore as we apply calculus to problems in the real world. This course is offered every semester.
Math 211 (Calculus 3): Differentiate and integrate in three dimensions! Add time for a thrilling fourth dimension! Impress your friends and amaze your acquaintances! This course is offered every semester.
Math 212 (Calculus 4): How do measure the area of a non-regular area? What is a planimeter? How do physicists use calculus? Take calculus four and find out. This course is offered every spring semester.
Intermediate Courses
Have you completed two semesters of calculus and are now ready for the next level? Courses at level 2 are designed with a broad audience in mind while beginning the transition to deeper mathematics.
Math 211 (Calculus 3): Calculus in three, four, and even higher dimensions! Partial derivatives, multiple integrals, and all that good stuff. This course is offered every semester.
Math 214 (Differential Equations): How do populations grow? Is it possible to sustainably harvest fish? How do pilots pursue and intercept enemy aircraft? These questions and more are addressed in the study of differential equations. We learn the how to model real phenomena in order to answer important questions. Using technology and visual techniques, we develop a systematic way of analyzing any differential equation. This course is offered every spring semester.
Math 216 (Introduction to Mathematical StatsMath 231 (Linear Algebra): How are graphics created in video games? How do you model an economy or build a fractal? We study vectors, matrices, and their operations and how these contribute understanding real problems. This course is offered every semester.
Math 270 (Mathematical Reasoning with Discrete Mathematics): How do we prove theorems? This course shows us how to create proofs and explore the various ways of proving mathematical results. This course is offered every spring semester.
Advanced Courses
Are you ready to delve deeply into mathematics? Courses at levels 3 and 4 focus on theory and application of mathematics. While designed for mathematics majors and minors, these courses are open to anyone with an interest.
Math 303 (Abstract Algebra): How can we understand symmetries from a standard frame of reference? How are the integers fully described? This course explores these questions and teaches us how structure can be given to algebraic objects. This course is offered every fall semester.
Math 305 (Introduction to Analysis): We learn how to fully understand limits and how to prove the theorems that we learn in calculus. This course is offered every spring semester.
Math 316 (Probability): Probability is the branch of mathematics concerned with the study of mathematical techniques for making quantitative inferences about uncertainty. This course will develop an understanding of mathematical probability and its applications. Topics include probability systems, properties and distributions of random variables, stochastic processes and applications to several areas. This course is offered every spring semester.
Math 362 (Modern Geometry): Rigorous development of Euclidean and hyperbolic geometry from both a metric and synthetic point of view. Some topics in transformational geometry are also covered. This course is offered every fall semester.
Math 397 (Junior Seminar): Engage in problem-solving with a goal of developing a research project for the Research Experience course.
Math 39810 (Research Experience in Mathematics): Research is designed to give you insight into how mathematicians work and think. In particular, you will gain an enjoyment of discovering and exploring mathematics for yourself. To this end, we highlight that mathematics is a current and vibrant subject. In addition, you will learn to effectively communicate mathematical ideas both through writing and oral presentation. This course is offered every spring.
Math 411 (Complex Analysis): Students explore the theory of functions defined in the complex plane, highlighting the interplay between geometric visualization and analysis. Topics include the geometry of analytic mappings, power series, Cauchy's Theorem, and the Residue Theorem. Connections to other areas of mathematics and to other scientific fields will be explored through applications. This course is offered every other year.
Math 421 (Graph Theory & Combinatorics): Topics in graph theory include basic properties of graphs, Eulerian trails, Hamilton chains, trees, and may include the chromatic polynomial, planar graphs, and the independence number. Topics in combinatorics include the pigeonhole principle, permutations and combinations, the binomial theorem, and may include generating functions, Catalan numbers, and Stirling numbers. This course is offered every other year.
Math 431 (Numerical Analysis): Theory and applications of numerical techniques. Topics will include error analysis, solution of non-linear equations and systems of equations, interpolation, approximation, numerical integration and differentiation and numerical solution of initial-value problems. This course is offered every other year.
Math 480 (Connections in Advanced Mathematics): Study of connections and relationships among various disciplines within mathematics. Specific content varies. Topics may include, but are not limited to, the following: historical development of mathematics and various philosophies of mathematics, cultural similarities and differences in viewpoints and developments in mathematics, cross-discipline approaches that combine subdisciplines such as probability techniques in number theory and random graph theory, field theory and geometric constructions, and algebraic topology. This course is offered every other year.
Math 498-499 (Capstone): Students reflect on the field of mathematics via an integrative project developed in concert with a faculty mentor. Students analyze mathematical ideas related to their projects and integrate this knowledge with ideas learned in the mathematics curriculum. This course sequence is offered every year.
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Pre-Calculus, Gr. 9-12
Pre-calculus is the bridge between Algebra II and Calculus, and is a great way to get acquainted with ideas like function and rate of change. Analyze angles and geometric shapes to find absolute values. Discover new ways to record solutions with interval notation, and plug trig identities into your equations.
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famous problems of squaring the circle, doubling the cube and trisecting an angle captured the imagination of both professional and amateur mathematicians for over two thousand years. Despite the enormous effort and ingenious attempts by these men and women, the problems would not yield to purely geometrical methods. It was only the development. of abstract algebra in the nineteenth century which enabled mathematicians to arrive at the surprising conclusion that these constructions are not possible. In this book we develop enough abstract algebra to prove that these constructions are impossible. Our approach introduces all the relevant concepts about fields in a way which is more concrete than usual and which avoids the use of quotient structures (and even of the Euclidean algorithm for finding the greatest common divisor of two polynomials). Having the geometrical questions as a specific goal provides motivation for the introduction of the algebraic concepts and we have found that students respond very favourably. We have used this text to teach second-year students at La Trobe University over a period of many years, each time refining the material in the light of student performance.
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Investigate a mathematical model that compares the cost of education to potential earnings. Compute the amount to be repaid each year for the life of the loan, compare the answer to starting salaries and discuss other factors to be considered.
Explore the concept of slope as a rate of change by measuring liquid levels in bottles of various shapes and creating a scatterplot of the data. Calculate the rate of change between two points on a curve by determining the slope of the line joints.
Explore general patterns of polynomial and rational functions. Construct boxes of various dimensions, collect height and volume data and create a scatterplot in order to determine the height of the box with the maximum volume.
Explore modern specifications and construction of boxing rings. Apply various methods for finding the area of circles, rectangles, trapezoids and complex area coverings, and compare and contrast areas and overlaps for attack and defense in the ring.
Investigate how ciphers can conceal and protect information and how they have been used. Decode an encrypted message using trial-and-error substitution and put a simple message into a complex cipher using a decoder ring.
Recognize patterns that are different from lines. Use real-world scenarios to explore basic connections between graphs, tables and symbolic representations for lines, parabolas, inverse models and exponential models.
Explore the mathematics of architecture by investigating the unusual shapes of some of the rooms in the White House, such as the Blue Room's elliptical shape. Use a graph to plot, draw and determine the equation of an ellipse.
Collect data from a variety of experiments, and determine what type of model best fits the data. Explore a variety of relationships using pennies, pressure, temperature, light and pendulums to determine algebraic equations.
Develop a mathematical model for a plant which hypothetically grows in steps. Make a table showing the length of the plant's stem at the end of a number of steps, graph the values in the table and write a formula representing the pattern of growth.
Investigate the nature of communications with the Rovers, including the use of Mars Orbiters as relay stations. Calculate transmission times and problems associated with sending and receiving messages with the probes.
Explore the relationship among the amount of weight that can be supported by a spaghetti bridge, the thickness and the length of the bridge to determine the algebraic equation that best represents a pattern modeled by the three variables.
Explore linear patterns, write a pattern in symbolic form and solve linear equations using algebra tiles, symbolic manipulation and the graphing calculator. Calculate a budget to save for a yo-yo, and create patterns with pennies.
Investigate quadratic functions using geometric toothpick designs. Match the symbolic form of the function to the appropriate graph, analyze the various transformations and determine the equation for the functions.
Solve problems involving the plotting of two lines that intersect on a coordinate system. Follow the kids on the video as they use information from a "secret government Web site" to search for the location of aliens living under the city.
Identify, describe and extend geometric and numeric patterns into growing and shrinking patterns, then represent and record patterns using tools such as tables and graphs. Follow the kids on the video as they use patterns to open a door in the cave.
Use number sense to identify and extend a pattern, and explore the pattern known as triangular numbers. Follow the kids on the video as they attempt to repeat a pattern of numbers and sequenced flashing lights.
Interpret multiple representations to name equivalent fractions, and represent fractions and mixed numbers using physical models. Follow the kids on the video as they use their knowledge of models and fractions to solve the mystery of the aliens.
books & links
Each month, PBS Teachers delivers a new selection of books and web sites recommended for teachers and students across grade levels and subjects. Explore our archive of more than 2,500 recommended resources.
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This site contains six research projects that investigate topics in geometry and number theory. Each provides the...
see more
This site contains six research projects that investigate topics in geometry and number theory. Each provides the objectives, prerequisites, a summary, the project itself, and reference. The nontrivial and open-ended projects are designed to inspire students to make conjectures and research mathematics. The emphasis of each project is on obtaining results. Proofs are suggested and provided in the solutions, but students are not expected to be able to prove all the results obtainedGrowing out of classes in computer music at Dartmouth College this is web version of a book that is intended as a...
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Growing out of classes in computer music at Dartmouth College this is web version of a book that is intended as a "user-friendly" introduction to music and computers. AN excellent introduction to what is sound.
If the spaces and structures that result from facilities planning are to provide a safe, engaging, efficient, and...
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If the spaces and structures that result from facilities planning are to provide a safe, engaging, efficient, and cost-effective environment for students and faculty for many years, they must be planned by and for the community that is to use them. Those who understand the nature of observation, investigation, problem-solving, and communication that is at the heart of the scientific way of knowing must have leadership roles in this process. This handbook is intended for use by colleges and universities that are thinking about, or in the process of planning for, new or renovated spaces for their undergraduate programs in science and mathematics, but the steps for the processes illustrated would also be useful to those who plan for K12 science facilities. Structures for Science includes materials, expanded and edited for publication, used at PKAL Facilities Workshops. The handbook also includes material developed specifically for this PKAL report about the planning and design process.
The Beamer package is a LaTeX class for creating presentations that are held using a projector, but it can also be used to...
see more
The Beamer package is a LaTeX class for creating presentations that are held using a projector, but it can also be used to create transparency slides. The Beamer is perfect for creating a presentation with a large amount of mathematical formulas. It is freely available for download.
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Brief Calculus: Applied Approach - rev edition
Summary: This accessible introduction to Calculus is designed to demonstrate how calculus applies to various fields of study. The text is packed with real data and real-life applications to business, economics, social and life sciences. Applications using real data enhances student motivation. Many of these applications include source lines, to show how mathematics is used in the real world.
NEW! Conceptual probl...show moreems ask students to put the concepts and results into their own words. These problems are marked with an icon to make them easier to assign.
More opportunities for the use of graphing calculator, including screen shots and instructions, and the use of icons that clearly identify each opportunity for the use of spreadsheets or graphing calculator.
Work problems appear throughout the text, giving the student the chance to immediately reinforce the concept or skill they have just learned.
Chapter Reviews contain a variety of features to help synthesize the ideas of the chapter, including: Objectives Check, Important Terms and Concepts, True-False Items, Fill in the Blanks and Review Exercises.
Chapter 1. Functions and Their Graphs. Chapter 2. Classes of Functions. Chapter 3. The Limit of a Function. Chapter 4. The Derivative of a Function. Chapter 5. Applications: Graphing Functions; Optimization. Chapter 6. The Integral of a Function and Applications. Chapter 7. Other Applications and Extensions of the Integral. Chapter 8. Calculus of Functions of Two or More Variables. Appendix: Graphing Utilities. Appendix 1. The Viewing Rectangle. Appendix 2. Using a Graphing Utility to Graph Equations. Appendix 3. Square Screens. Appendix 4. Using a Graphing Utility To Locate Intercepts and Check for Symmetry. Appendix 5. Using a Graphing Utility to Solve Equations. Answers to Odd-Numbers Problems. Photo Credits. Index.
Hardcover Very Good 0471707619 Very good condition, clean, no writings.
$5.78
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Discrete Mathemetics
9780618415380
0618415386
Summary: Discrete Mathematics combines a balance of theory and applications with mathematical rigor and an accessible writing style. The author uses a range of examples to teach core concepts, while corresponding exercises allow students to apply what they learn. Throughout the text, engaging anecdotes and topics of interest inform as well as motivate learners. The text is ideal for one- or two-semester courses and for studen...ts who are typically mathematics, mathematics education, or computer science majors. Part I teaches student how to write proofs; Part II focuses on computation and problem solving. The second half of the book may also be suitable for introductory courses in combinatorics and graph theory.
Ferland is the author of Discrete Mathemetics, published 2008 under ISBN 9780618415380 and 0618415386. Three hundred ninety five Discrete Mathemetics textbooks are available for sale on ValoreBooks.com, twenty one used from the cheapest price of $138.07, or buy new starting at $199.95.[read more]
Ships From:Houston, TXShipping:Standard, ExpeditedComments:100% BRAND NEW ORIGINAL US HARDCOVDER STUDENT 1st edition / Mint condition / Never been read / IS... [more]100% BRAND NEW ORIGINAL US HARDCOVDER STUDENT 1st edition / Mint condition / Never been read / ISBN-10: 0618415386. Shipped out in one business day with free tracking18415380-4-0-3 Orders ship the same or next business day. Expedited shipping within U.S. [more]
May include moderately worn cover, writing, markings or slight discoloration. SKU:97806184153
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Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especially second order with constant coefficients; Undetermined coefficients and variation of parameters; Sinusoidal and exponential signals: oscillations, damping, resonance; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear systems: eigenvalues and eigenvectors; and Non-linear autonomous systems: critical point analysis and phase plane diagrams.
Reviewer:YajurTheJ -
-
April 2, 2012 Subject:
A Word of Thanks!
I found the video lectures extremely useful in understanding about differential equations. These videos helps me improving my DE skills to a much higher level, studied along with rest of the material in MIT OCW. Great thing!!!
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Learning Outcomes
Mathematics is a deductive science that requires rigorous proof of discovered facts about numbers and shapes. It employs the axiomatic method of inquiry in its method and modes of presentation of its discoveries and creations. Along with other academic departments at Principia College, the Mathematics Department has identified various learning outcomes each mathematics student, minor, and especially major needs to demonstrate in his or her work and habits of learning. The nine learning outcomes for mathematics are based on the following objective for mathematics minors and majors.
Learning Outcomes Objective: To coordinate with Principia's mission to serve the Cause of Christian Science, the Mathematics Department at Principia College continues to encourage majors and non-majors in mathematics to strive to become careful, compassionate, creative, tolerant, logical, analytical, and critical thinkers and problem solvers. Since Christian Science is also a deductive science, students of mathematics should be guided through their courses of study to demonstrate to a significant degree the usage, understanding, and assimilation of the following learning outcomes. These outcomes are intended to promote the proper practice of deductive reasoning necessary for both mathematics and Christian Science.
Learning Outcomes for Mathematics:
1. Problem Solving
Our students should accurately assess problems and think about them creatively, conceptually, critically, insightfully, analytically, and metaphysically. They should choose appropriate processes and heuristics and apply them skillfully and confidently to gain the solution.
2. Reasoning and Proof
Our students should understand as well as create proofs using both direct and indirect deductive methods. They should also be able to use induction to analyze patterns and formulate conjectures about them.
3. Abstraction and Generalization
Our students should identify the character and underlying properties of mathematical objects.
4. Modeling and Representation
Our students should analyze contextual constructs and create appropriate mathematical models which reflect the fundamental features of the constructs.
5. Effective Communication
Our students should convey and receive information and ideas accurately, consistently, and efficiently in oral, visual, and written form, formally and informally across a diversity of audiences. Good communication necessitates honesty and effectual listening.
6. Intellectual Integrity
Our students should embody intellectual integrity in discovering and presenting solutions to problems and answering questions.
7. Connections
Our students should recognize and create connections between mathematics and other disciplines and within mathematics itself.
8. History and Development of Mathematics
Our students should demonstrate knowledge of the historical and cultural context of mathematics as it has evolved over the centuries.
9. Facility with Computer Tools and Algorithmic Thinking
Our students should use computerized tools such as programming languages, calculators, and software such as Mathematica to explore mathematical concepts visually, verbally, symbolically, and numerically, thereby getting insight into the underlying mathematics.
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Available online
More options
Contributors
Contents/Summary
Bibliography
Includes bibliographical references (p. [513]-530) and index.
Contents
Triangulations in Mathematics.- Configurations, Triangulations, Subdivisions, and Flips.- Life in Two Dimensions.- A Tool Box.- Regular Triangulations and Secondary Polytopes.- Some Interesting Configurations.- Some Interesting Triangulations.- Algorithmic Issues.- Further Topics.
(source: Nielsen Book Data)
Publisher's Summary
Triangulations appear in many different parts of mathematics and computer science since they are the natural way to decompose a region of space into smaller, easy-to-handle pieces. From volume computations and meshing to algebra and topology, there are many natural situations in which one has a ?xed set of points that can be used as vertices for the triangulation. Typically one wants to ?nd an optimal triangulation of those points or to explore the set of their all triangulations. The given points may represent the "sites" for a Delaunay triangulation computation, d thetest pointsfora surfacereconstruction, ora set ofmonomials, representedaslattice pointsinZ , inanalgebra- geometric meaning. A central theme of this book is to use the rich geometric structure of the space of triangulations of a given set of points to solve computational problems (e.g., counting the number of triangulations or ?nding optimal triangulations with respect to various criteria), and for setting up connections to novel applications in algebra, computer science, combinatorics, and optimization. Thus at the heart of the book is a comprehensive treatment of the theory of regular subdivisions, secondary polytopes, ?ips, chambers, and their interactions. Again, we ?rmly believe that understandingthe fundamentsof geometry and combinatoricspays up for algorithmsand applications. (source: Nielsen Book Data)
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Extending Frontiers of Mathematics - 06 edition
ISBN13:978-1597570428 ISBN10: 1597570427 This edition has also been released as: ISBN13: 978-0470412220 ISBN10: 0470412224
Summary: In the real world of research mathematics, mathematicians do not know in advance if their assertions are true or false. Extending the Frontiers of Mathematics: Inquiries into proof and argumentation requires students to develop a mature process that will serve them throughout their professional careers, either inside or outside of mathematics. Its inquiry-based approach to the foundations of mathematics promotes exploring proofs and other advanced mathematical ideas through these fe...show moreatures: - Puzzles and patterns introduce the pedagogy. These precursors to proofs generate creativity and imagination that the author builds on later - Prove and extend or disprove and salvage, a consistent format of the text, provides a framework for approaching problems and creating mathematical proofs - Mathematical challenges are presented which build upon each other, motivate analytical skills, and foster interesting discussion ...show less
Edition/Copyright:06 Cover: Publisher:Key College Publishing Year Published: 2006
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I've bought some books and I guess they're written in a way that presumes a previous background or assignment in some mathematics course - these books just spit the content directly in your face. This kind of book is not suited for me (for a first reading in the subject): I'm not in a maths course, and they wouldn't be even if I were in a maths course because I like to learn the content, It's history and why study it. I've found one book on this class and I'd like to mention it as an example:
A book of abstract algebra, Charles Pinter;
The chapter titled Why abstract algebra? is very useful, it contains a light historical background and also some motivation for it. After this chapter the book starts to provide a normal introductory abstract algebra course.
I am looking specifically for books with this spirit, there are a lot of history books about specific fields of mathematics, for example:
A history of abstract algebra, Kleiner;
Number theory and its history, Oystein Ore.
They are nice books and they can provide some motivation for study, but my impression is that they are more a history book than a textbook that could be used in a undergraduate course of mathematics. You can suggest books in any mathematical subject you wish, but they have to attain to that criteria.
It is a very tricky thing to do correctly. "Hindsight" history of mathematics is not history. The original stuff is often quite hard, even unrecognizable without close study.
–
André NicolasNov 19 '13 at 4:06
There's always Lawvere & Schanuel's "Conceptual Mathematics", which is an introduction to category theory aimed at undergraduates. It very much takes the approach of starting simple and motivating each next step.
To a lesser degree, Goldblatt's "Topoi" also attempts to motivate many of the ideas of topos theory, but he does so a bit more rapidly than the book above. This one is less for undergraduates, but is approachable with some determination. I can say I found the author's motivating comments helpful enough to make the material approachable at a time I had no more than a vague knowledge of set theory, so that's something.
Journey through Genius: The Great Theorems of Mathematics by William Dunham.
This book contains within its pages the reason I became a Pure Mathematician. There is one chapter dedicated entirely to $\sum \frac{1}{k^2}=\frac{\pi^2}{6}$ and the ingenuity it took to figure that out. In high school our teacher tolds us the sum converged, but said it wasn't known to what. I found this book in my search for the answer and there it was, an entire chapter just on this one problem.
Every chapter is a gem of mathematics explained within the historical context of its discoverers and its times. I am not sure this is a book for a course, but if you need a reason to be excited or motivated about pure mathematics I strongly recommend it.
Willard's "General Topology" has an extensive section devoted to historical notes, providing a background to each topic he goes through.
Goldblatt's "Lectures on the Hyperreals" has a section on historical background in the first chapter.
Unfortunately there doesn't seem to be an English translation, but Jürgen Elstrodt's "Maß- und Integrationstheorie" provides plenty of historical motivation as well as several short biographies of key mathematicians detailing how they helped to develop the field.
Generally speaking, maths books tend to steer clear of history (and quite often any sort of context whatsoever). To compensate I tend to browse Wikipedia (and specialised wiki's like nlab when available) to get some sense of background and how what I'm learning fits into the bigger picture. It's not enough on its own, but it helps to supplement the more streamlined textbooks.
I haven't read too much literature about mathematics, but I read one very good book, called Mathematics: from the birth of numbers by Jan Gullberg, which I found very interesting. It covers everything from numbers to partial differential equations, while assuming no significant understanding of the topics. It also includes a few pages of history of the subject at the beginning of each chapter.
On wavelets, I liked "Analysis and Probability / Wavelets, Signals, Fractals" by P. Jorgersen. It comes with a lengthy "Getting started" and within it, a Glossary that explains -in a no linear way!- the interplay between mathematics (& probability), engineering and physics in the development of the subject over the last decades. The book is at graduate/advanced level tough.
And of course the classic "Ten lectures on wavelets" by Daubechies, Chapter 1; more suitable as text book imho.
I know most people on this forum already did Cal. But, I thought I might throw it out.
James Stewart's Calculus textbook is awesome. It separates historical/theoretical and sometimes mixes them. Would recommend. (Anyhow it worked for me.)
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--This text refers to an out of print or unavailable edition of this title.
From the Back CoverMost Helpful Customer Reviews
This book was an excellent read, and provided some great information. However, as a math text, I feel like it should have provided a bit more examples, and perhaps even a solutions manual.
I understand that the books main focus was on the abstract discussions of mathematics, but I feel like that should merit the writer to put a bit more examples to drive home the theorems before copious amounts of problems are assigned at the end of each chapter. A ton of these problems are classical, and need to be understood, in light of this, why isn't there a solutions manual to better explain these problems?
I greatly appreciated the voices of the writers keeping themselves grounded in pragmatic language. Too often will mathematicians get lofty in their dictions and fuddle the material they claim to understand all too well. This book did a great job discussing simple concepts simply, meanwhile working the more difficult ones with more space.
I'm using this in an undergraduate introduction to proofs class with a focus on analysis. As a freshman, it seems a bit overwhelming at times - I wouldn't recommend it to most freshmen or even sophomores. I do feel like this does a more than adequate job preparing me for more advanced math, and goes far above and beyond similar "proofs and problem solving" style books.
I ran into the first edition of this book ten years ago when taking courses at George Mason University, and really loved it. I still love it. It covers proofs from all basic "pieces" of mathematics and gives the reader a good feel for the "proofology," both in technique and fundamental nomenclature and results, that a student is expected to know when taking the first analysis and abstract algebra courses. It's not perfect though. I haven't bought the second edition, but in the first edition, Example 2.21, p.27 says: "An integer is even if and only if it is the sum of two odd integers." Obviously, it is easy to show the sum of two odd integers is even by forming the sum (2k+1) + (2l+1) = 2(k+l+1), which is twice an integer and thus even. But, if an integer is even, it can be the sum of two odd integers OR two even integers, so the statement is not complete. If small stuff like that doesn't bother you, this book is for you.
The author gives solutions or hints for one-third to one half the problems depending on the chapter, which is more than enough for self-study. I would disregard the whiny one star review that is posted for this book; it is typical of someone who wants to be spoonfed mathematics.
My main problem with this text is the level of understanding it assumes on behalf of the reader. Many reviewers say "great reference" or something of the sort. But this book is a *foundational* text. It's not a book for mathematicians or a mathematically mature reader -- they should already own the techniques presented here. A book of this kind should be suitable for self study and this book fails in that department. Given the amount of math it assumes, I would imagine those at that level are already fairly assimilated to proofs and the like. Hence my critique that the level and function is confused. Note also that this book is *expensive*.
If you want a book on problem solving, go with Zeitz or Engel, or something of "olympiad" character. If you want a book to learn proof techniques, Vellman or Eccles is good; Solow for true beginners.
I originally purchased this book as a text for a math course and quite enjoyed the selections that we worked through in it. It has been about a year since I took that course and I still find myself going back for references in the book. It is a must have for someone who is interested in proofs or will be doing them on a semi-regular basis.
Most of the chapters on discrete mathematics are very well-written with concise and fully explained proofs, although can't say the same about the chapters on continuous mathematics. Has enough english explanations to merit a couch read, but not enough for a full self-study I'd like to think. Chapter on induction is so-so. Exercises are similar enough to examples that most can be done (although certain exercises with (!) require an unrealistic amount of prior knowledge/experience). All in all, this is a great book if you're just transitioning from Calculus into proof-based mathematics and have a professor who is somewhat lenient about the exercises assigned.
I used this for a junior level intro to proofs/discrete math course. My course covered chapters 1-10, so that is all this review is referring to. I thought it was a pretty good text. It assumes very little mathematical knowledge, though more "mathematical maturity" would be useful. I thought the authors explain the material well and the exercises definitely advance your understanding of the material. Like any other math course, you must actually do the exercises to truly understand the material. My one complaint is that I wish the "Hints for Selected Exercises" was more informative. I estimate that they provide hints for roughly 40% of the problems and some of those are pretty terse (and there are no solutions).
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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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2012 1118466160Rattan's Introductory Mathematics for Engineering Applications is designed is to improve student retention, motivation and success through application-driven, just-in-time engineering math instruction. It is intended to be taught by engineering faculty, not math faculty, so the emphasis is on using math to solve engineering problems, not on derivations and theory.
The book is a product of four NSF grants to develop and disseminate a new approach to engineering mathematics education. The authors have developed a course that does just this, and have recruited faculty at more than two dozen institutions to pilot aspects of this course in their own curricula. This approach covers only the salient math topics actually used in core engineering courses, including physics, statics, dynamics, electric circuits and computer programming. More importantly, the course replaces traditional math prerequisites for the above core courses, so that students can advance in the engineering curriculum without first completing the required calculus sequence. The result has shifted the traditional emphasis on math prerequisite requirements to an emphasis on engineering motivation for math, and has had an overwhelming impact on engineering student retention
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Mathematics Applied to Electronics - 6th edition
Summary: For undergraduate college-level courses in Mathematics for Electronics, Tech Math (Algebra and Trigonometry) for Electronics, Computer, Automation, and Electromechanics.
This text provides an introduction to mathematics applied to electronics, computers, electromechanics, and automation. Organized to be compatible with electric circuit books currently in use, its content balances a formal proof-orientation against the need for expediency in developing a br...show moreoad, general mathematics ability.
Features
NEW--Companion website at multiple choice and true/false review quizzes for each chapter.
Tests the students comprehension and e-mails the score back to the instructor.
Natural Numbers and Number Systems. Signed Numbers. Numerical Expressions and Equations. Order of Operations. Symbols of Grouping. Double Meaning of + and -. Absolute Value of a Signed Number. Combining Signed Numbers. Relational Operators. Multiplying with Signed Numbers. Dividing with Signed Numbers.
International System of Units. Selected Physical Quantities. Forming Decimal Multiples and Submultiples of the SI Units. Unit Analysis and Conversion between Systems. Applying Unit Analysis to Energy Cost. Units and Exponents.
Multiplying Monomials. Multiplying a Monomial and a Binomial. Multiplying a Monomial and a Polynomial. Subtracting Polynomials. Additional Work with Polynomials. Division of Monomials. Dividing a Polynomial by a Monomial. Factoring Polynomials with a Common Monomial Factor. Evaluating Algebraic Expressions.
Voltage Division in a Series Circuit. Conductance of the Parallel Circuit. Equivalent Resistance of the Parallel Circuit. Current Division in the Parallel Circuit. Solving Parallel Circuit Problems. Using Network Theorems to Form Equivalent Circuits.
11. Special Products, Factoring, and Equations.
Mentally Multiplying Two Binomials. Product of the Sum and Difference of Two Numbers. Square of a Binomial. Factoring the Difference of Two Squares. Factoring a Perfect Trinomial Square. Factoring By Grouping. Combining Several Types of Factoring. Literal Equations.
21. Applications of Logarithmic and Exponential Equations to Electronic Concepts.
The Decibel. System Calculations. RC and RL Transient Behavior. Preferred Number Series.
22. Angles and Triangles.
Points, Lines, and Angles. Special Angles. Triangles. Right Triangles and the Pythagorean Theorem. Similar Triangles; Trigonometric Functions. Using the Trigonometric Functions to Solve Right Triangles. Inverse Trigonometric Functions. Solving Right Triangles When Two Sides Are Known.
23. Circular Functions.
Angles of Any Magnitude. Circular Functions. Graphs of the Circular Functions. Inverse Circular Functions. The Law of Sines and the Law of Cosines. Polar Coordinates. Converting between Rectangular and Polar Coordinates
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Algebra Skills
Subject:SSS
Course Number:115
Credits:3 Credits
Available Online:No
The goal of this course is to strengthen basic math skills in preparation for future math courses. The course begins by reviewing operations with signed numbers, fractions, and radicals. The course builds to simplifying algebraic expressions and solving and graphing linear equations, both equalities and inequalities. This face-to-face course will utilize just-in-time individualized learning, cooperative learning, and computer technology to enhance the student experience.
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Stewart's clear, direct writing style in SINGLE VARIABLE CALCULUS, VOLUME 2, 5th Edition guides you through key ideas, theorems, and problem-solving steps. Every concept is supported by thoughtfully worked examples and carefully chosen exercises. Many of the detailed examples display solutions that are presented graphically, analytically, or numerically to provide further insight into mathematical concepts. Margin notes expand on and clarify the steps of the solution.
Table of Contents
Functions And Models
Four Ways to Represent a Function
Mathematical Models: A Catalog of Essential Functions
New Functions from Old Functions
Graphing Calculators and Computers
Review
Principles of Problem Solving
Limits
The Tangent and Velocity Problems
The Limit of a Function
Calculating Limits Using the Limit Laws
The Precise Definition of a Limit
Continuity
Review
Problems Plus
Derivatives
Derivatives and Rates of Change
Writing Project: Early Methods for Finding Tangents
The Derivative as a Function
Differentiation Formulas
Applied Project: Building a Better Roller Coaster
Derivatives of Trigonometric Functions
The Chain Rule
Applied Project: Where Should a Pilot Start Descent? Implicit Differentiation
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A resource written specifically for the Principles of Mathematics 10 (MPM2D) course. Principles of Mathematics 10 will help students learn the mathematics skills and concepts they need to succeed in school and beyond.
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Year 9 Workbook: Year 9
Browse related Subjects
...Read More Pack, including Homework Sheets and Assessment Tests, Maths Frameworking offers a comprehensive and engaging route to Framework success
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'What this book is: This "textbook" (+videos+WeBWorKs) is suitable for a sophomore level linear algebra course taught in...
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'What this book is: This "textbook" (+videos+WeBWorKs) is suitable for a sophomore level linear algebra course taught in about twenty-five lectures. It is designed both for engineering and science majors, but has enough abstraction to be useful for potential math majors. Our goal in writing it was to produce students who can perform computations with linear systems and also understand the concepts behind these computations. For more details, see the Table of Contents or the Preface.Homework: This book is designed to be used in conjunction with online homework exercises written in the WeBWorK system. These exercises help the students read the lecture notes and learn basic computational skills. There are also in-depth conceptual problems at the end of each lecture, designed for written assignments. See the homework page for more information about homework or to obtain access to the online homework exercises.'
' The general layout of content in the units proceeds, wherever possible from the concrete representation of the...
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' The general layout of content in the units proceeds, wherever possible from the concrete representation of the concepts to their abstract forms.Unit 1 begins with a treatment of systems of linear equations and their solutions. This is followed by a section that introduces vectors and matrices and dwells quite a lot on operations on these and the theory and properties of determinants. The relatively more abstract concept of vector spaces is treated next. The theory and properties of Linear transformations closes this unit.Unit 2 introduces the notions of eigenvalues and eigenvectors. The diagonalisation property is demonstrated and proved.Each unit has a maximum of four activities, one of which focuses on mathematics education, pedagogics and didactics. This helps students not only to focus on mathematical content, but also to focus on their goal as teachers of mathematics in the secondary school.'
'This module introduces the learner to a particular mathematical approach to analysing real life activity that focuses on...
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'This module introduces the learner to a particular mathematical approach to analysing real life activity that focuses on making specific decisions in constrained situations. The approach, called linear programming, is presented here with an emphasis on appreciation of the style of thinking and interpretation of mathematical statements generated, rather than on computational competency per se, which is left to appropriate and readily available ICT software package routines.The module begins with Unit One that consists of 2 main Activities. Activity 1, formulation of a linear programming problem, is on a mathematical description of the problematic situation under consideration, and Activity 2, the geometrical approach considers a visual description of a plausable solution to the problem situation. Unit 1 therefore should move the learner towards an appreciation of real-life activity situations that can be modelled as linear programming problems.With 3 main activities, Unit 2 considers computational algorithms for finding plausible optimal solutions to the linear programming problem situations of the type formulated in Unit 1. Activity 3 examines conditions for optimality of a solution, which is really about recognising when one is moving towards and arrives at a candidate and best solution. Activity 4 discusses the centre piece of computational algebraic methods of attack, the famed Simplex algorithm. This module focuses on the logic of the algorithm and the useful associated qualitative properties of duality, degeneracy, and efficiency. The final Activity touches on the problem of stability of obtained optimal solutions in relation to variations in specific input or output factors in the constraints and objective functions. This so called post optimality or sensitivity analysis is presented here only at the level of appreciation of the analytic strategies employed.'
'" The Free High School Science Textbook (FHSST) project is our contribution towards furthering Science Education in South...
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'" The Free High School Science Textbook (FHSST) project is our contribution towards furthering Science Education in South Africa.As young South Africans who believe in building up our country, we want to use our skills as scientists to help our next generation by providing free science and mathematics textbooks for Grades 10-12 to all South African learners.Science education is about more than Physics, Chemistry and Mathematics... It's about learning to think and to solve problems which are valuable skills that can be applied through all spheres of life. Teaching these skills to our next generation will help them when it is their turn to make a difference to our country.״'
'The number theory module consists of two units. It pre-supposes the teacher trainee is conversant with Basic mathematics....
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'The number theory module consists of two units. It pre-supposes the teacher trainee is conversant with Basic mathematics. The first unit deals with properties of integers and linear diophantine equations. It progresses from properties of integers through divisibility with remainder, prime numbers and their distribution, Euclid's proof of infinitely many primes and Euclid's algorithm and its application in solving linear diophantine equations. The unit is concluded with Pythagorean triplets and Fermat's last theorem for the vitas powers and the proof of Wiles.The second unit assumes unit one as a prerequisite for the trainees. It introduces the field of integers( mod p), squares and quadratic residues, Alar's criterion, Legendre symbol, Gauss lemma and quadratic reciprocity law, Euclid's algorithm and unique factorisation of Gaussian integers, arithmetic of quadratic fields and application of diophantine equations, and is concluded with Fermat's last theorem for cubes, Pell's equation and units in real quadratic fields.'
'First Learning Activity: Types and Causes of ErrorsThe first learning activity aims at making the learner appreciate the...
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'First Learning Activity: Types and Causes of ErrorsThe first learning activity aims at making the learner appreciate the need for numerical methods. It is also felt that this is the right moment to define the concept of a mathematical error, point out the sources and types of errors and mention some practical ways of reducing their cumulative effect on the numerical solution.Second Learning Activity: InterpolationThe second learning activity deals with the concept of interpolation. Both linear and higher order polynomial interpolation methods, based on Lagrange, Newton's divided differences and finite difference interpolation techniques are presented.Third Learning Activity: Numerical IntegrationThe third learning activity looks at the problem of numerical integration. The discussion is limited to Newton-Cotes formulae. Specific attention is given to the Trapezoidal and Simpson's rules and the application of Richardson's extrapolation technique on both the Trapezoidal and Simpson's rules in deriving Romberg integration schemes.Fourth Learning Activity: Roots of functionsThe fourth and final learning activity presents the root finding problem associated with solving the nonlinear equation and solving the coupled system of two nonlinear equations.'
'This book entitled Numerical Methods with Applications is written primarily for engineering undergraduates taking a course...
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'This book entitled Numerical Methods with Applications is written primarily for engineering undergraduates taking a course in Numerical Methods. The textbook offers a unique treatise to numerical methods which is based on a holistic approach and short chapters. This book is a product of many years of work on educational projects funded since 2002 by the NSF. Features: 1) Examples of real-life applications are available from seven different engineering majors. 2) Each chapter is followed by multiple-choice questions. 3) Supplemental material such as primers on differential and integral calculus, and ordinary differential equations are available on the web.'
This textbook contains exposition, exercises, answers to the odd-numbered problems, and an index. Solutions for the...
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This textbook contains exposition, exercises, answers to the odd-numbered problems, and an index. Solutions for the exercises are notincluded in this file. The textbook has a "You Try It" problem in the margin near each example in the textbook. The online and CD versions of the Prealgebra textbook also have additional interactive "You Try It" problems for each example. Click on the "You Try It" link in the green rectangle next to each example to try a problem similar to the example. Solutions are included, and you can access up to five similar problems in this manner.
'In American universities two distinct types of courses are often called "Advanced Calculus": one, largely for...
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'In American universities two distinct types of courses are often called "Advanced Calculus": one, largely for engineers, emphasizes advanced computational techniques in calculus; the other, a more "theoretical" course, usually taken by majors in mathematics and physical sciences (and often called elementary analysis or intermediate analysis), concentrates on conceptual development and proofs. This ProblemText is a book of the latter type. It is not a place to look for post-calculus material on Fourier series, Laplace transforms, and the like. It is intended for students of mathematics and others who have completed (or nearly completed) a standard introductory calculus sequence and who wish to understand where all those rules and formulas come from. Many advanced calculus texts contain more topics than this ProblemText. When students are encouraged to develop much of the subject matter for themselves, it is not possible to "cover" material at the same breathtaking pace that can be achieved by a truly determined lecturer. But, while no attempt has been made to make the book encyclopedic, I do think it nevertheless provides an integrated overview of Calculus and, for those who continue, a solid foundation for a first year graduate course in Real Analysis. As the title of the present document, ProblemText in Advanced Calculus, is intended to suggest, it is as much an extended problem set as a textbook. The proofs of most of the major results are either exercises or problems. The distinction here is that solutions to exercises are written out in a separate chapter in the ProblemText while solutions to problems are not given. I hope that this arrangement will provide flexibility for instructors who wish to use it as a text. For those who prefer a (modified) Moore-style development, where students work out and present most of the material, there is a quite large collection of problems for them to hone their skills on. For instructors who prefer a lecture format, it should be easy to base a coherent series of lectures on the presentation of solutions to thoughtfully chosen problems.'
'Reasonable Decimal Arithmetic (RDA) is to be a complete bundle for a realistic ARITHMETIC course as could reasonably be...
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'Reasonable Decimal Arithmetic (RDA) is to be a complete bundle for a realistic ARITHMETIC course as could reasonably be taught in a Developmental program, that is with a reasonable number of students succeeding in the course but also, and much more important, in following courses. The bundle is being developed for a course meeting 80 minutes twice a week during a fifteen course semester. It will consist of 18 chapters each with daily homework and quiz, as well as three Reviews and three Exams. '
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include a full semester or equivalent of frequent and regular assignments that provide practice in mathematical modeling and mathematical techniques. Problems providing modeling practice
are phrased with limited use of mathematical notation and symbols;
require a formulation step on the part of the student;
require college-level mathematical techniques leading from the formulation to the conclusion;
have a conclusion that involves discovery or interpretation.
2. Courses approved for the Mathematical Modeling requirement must demonstrate and provide a system for consistency in instruction and in assessment of student achievement.
3. Courses approved for the mathematical modeling requirement should engage students with mathematical concepts and techniques that prepare them for a variety of possible future courses and degrees.
4. A course used to satisfy the Mathematical Modeling Foundations requirement may not double-count toward the Breadth of Inquiry Natural and Mathematical Sciences requirement.
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Technical Calculus with Analytic Geometry - 4th edition
Summary: This text is written for today's technology student, with an accessible, intuitive approach and an emphasis on applications of calculus to technology. The text's presentation of concepts is clear and concise, with examples worked in great detail, enhanced by marginal annotations, and supported with step-by-step procedures whenever possible. Another powerful enhancement is the use of a functional second color to help explain steps. Differential and integral calculus a...show morere introduced in the first five chapters, while more advanced topics, such as differential equations and LaPlace transforms, are covered in later chapters. This organization allows the text to be used in a variety of technology programs. ...show less
The Cartesian Coordinate System. The Slope. The Straight Line. Curve Sketching. Discussion of Curves with Graphing Utilities. The Conics. The Circle. The Parabola. The Ellipse. The Hyperbola. Translation of Axes; Standard Equations of the Conics. Review Exercises.
Antiderivatives. The Area Problem. The Fundamental Theorem of Calculus. The Integral: Notation and General Definition. Basic Integration Formulas. Area Between Curves. Improper Integrals. The Constant of Integration. Numerical Integration. Review Exercises9296.56
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Mathematica!
> Kaplow
Match Results - Algebra I Vocabulary. Logic. One area of mathematics that has its roots deep in philosophy is the study of logic.
Logic is the study of formal reasoning based upon statements or propositions. (Price, Rath, Leschensky, 1992) Logic evolved out of a need to fully understand the details associated with the study of mathematics.
Business Calculus. Spring 2009 course descriptionspring 2009 syllabusinstructions for the TI-83/84course reviewstudy tips Calculus is usually a major change for math students.
This is appropriate, because calculus is the study of change: slope, velocity, growth rate, and other ways that we describe how one quantity changes with respect to another. Calculus is also perceived as difficult, and historically for the scientific community it was. It took about 300 years of concentrated effort to develop calculus as a usable and well-founded discipline!
A famous stage actress was once asked if she had ever suffered from stage-fright, and if so how she had gotten over it. She laughed at the interviewer's naive assumption that, since she was an accomplished actress now, she must not feel that kind of anxiety.
Understanding Mathematics. Peter Alfeld, --- Department of Mathematics, --- College of Science --- University of Utah a study guide by Peter Alfeld.
I wrote this page for students at the University of Utah. You may find it useful whoever you are, and you are welcome to use it, but I'm going to assume that you are such a student (probably an undergraduate), and I'll sometimes pretend I'm talking to you while you are taking a class from me. Let's start by me asking you some questions.
If you are interested in some suggestions, comments, and elaborations, click on the Comments.
Graphing Calculator.
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books.google.com - Respected for its detailed guidance in using technology, CONTEMPORARY PRECALCULUS: A GRAPHING APPROACH, Fifth Edition, is written from the ground up to be used with graphing technology--particularly graphing calculators. The text has also long been recognized for its careful, thorough explanations and... Precalculus: A Graphing Approach
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This manipulative allows you to construct factor tree(s) of prime factors for one or two numbers, and then from the prime...
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This manipulative allows you to construct factor tree(s) of prime factors for one or two numbers, and then from the prime factorization of two number, you are asked to identify the Least Common Multiple (LCM) and the Greatest Common Factor (GCF) of the two given numbers using a Venn Diagram.
OpenAlgebra.com is a free online algebra study guide and problem solver designed to supplement any algebra course. There are...
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OpenAlgebra.com is a free online algebra study guide and problem solver designed to supplement any algebra course. There are hundreds of solved problems, video solutions, sample test questions, worksheets, and interactives.
This site is a selection of mathlets designed for "geometry classes to review basic algebra skills in such a way that they...
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This site is a selection of mathlets designed for "geometry classes to review basic algebra skills in such a way that they can check their answers and/or get hints as to how to proceed. The idea behind these "procedure-based" dynamic worksheets is to provide students the opportunity to review and practice algebra skills with problems they create, while at the same time providing a means for students to check their answers and to get a hint if needed. The hints will walk the student through the problem in a step by step manner.״
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text, extensively class-tested over a decade at UC Berkeley and UC San Diego, explains the fundamentals of algorithms in a story line that makes the material enjoyable and easy to digest. Emphasis is placed on understanding the crisp mathematical idea behind each algorithm, in a manner that is intuitive and rigorous without being unduly formal.
Features include: The use of boxes to strengthen the narrative: pieces that provide historical context, descriptions of how the algorithms are used in practice, and excursions for the mathematically sophisticated.
Carefully chosen advanced topics that can be skipped in a standard one-semester course, but can be covered in an advanced algorithms course or in a more leisurely two-semester sequence.
An accessible treatment of linear programming introduces students to one of the greatest achievements in algorithms. An optional chapter on the quantum algorithm for factoring provides a unique peephole into this exciting topic. In addition to the text, DasGupta also offers a Solutions Manual, which is available on the Online Learning Center.
"Algorithms is an outstanding undergraduate text, equally informed by the historical roots and contemporary applications of its subject. Like a captivating novel, it is a joy to read." Tim Roughgarden Stanford University
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I used this book for CSE 101 Design and Analysis of Algorithms at UCSD. It's OK, but the level of detail of algorithms was too low for me to use just this book. I sometimes had to reference Wikipedia and other publications to achieve complete understanding.
I occasionally teach algorithms at CU Boulder to our undergraduates. This book accomplishes what it set out to do: provide a comprehensible (but not comprehensive) treatment of a core piece of Computer Science at an affordable cost.
That we get one of the greatest researchers in the area (Papadimitriou) alongside two other distinguished authors is just icing on the cake.
The first printing had numerous errors, though the online version of the book had already corrected many of them. I haven't used the book since then, but will in the Fall, and I'd expect with the vigor already invested by the authors, the book will be in even better shape.
One of the most appealing characteristics of this book is the small size. Textbooks in algorithms are similar to those of other fields in that they have continued to increase in girth over the years. At 320 pages, this book is a relative midget. However, that does not in any way mean that it is weak in content, there is plenty of material for a one-semester course in algorithms. The chapters are:
*) Prologue - a bit of history and the big-O notation *) Algorithms with numbers - basic and modular arithmetic, primality testing and cryptography *) Divide-and-conquer algorithms - multiplication, recurrence relations, mergesort, matrix multiplication and the Fast Fourier Transform (FFT). *) Decomposition of graphs - the fundamental definition of directed and undirected graphs and performing depth-first searches. *) Paths in graphs- basic algorithms used in graph searches *) Greedy algorithms - some fundamental greedy algorithms and their basic level of performance *) Dynamic programming - shortest paths, knapsack optimization and independent sets in trees *) Linear programming and reductions - the definition of linear programming and some of the standard problems that it can be used to solve *) NP-complete problems - definition of NP-complete, some examples and reduction strategies used to show NP equivalence *) Coping with NP-completeness - intelligent search, approximation and random algorithms *) Quantum algorithms - a brief foray into a possible revolution in computing. Explanations of how data may be stored and processed at the quantum level.
The explanations are brief yet thorough enough for advanced computer science students, the algorithms are presented in a generic pseudocode.Read more ›
This is one of the best introductory text on algorithms I've ever read. The concepts are presented clearly, the writing style is lucid, and whole book is very easy to follow. It emphasizes the ideas and insightful hints behind every algorithms, rather than the overly rigorous mathmatic proofs often found in other books. The book also includes a lot of exercises, as a complementary to the content. The side bars also provide a lot of interesting information.
As a CS undergrad at UC San Diego, the author used rough drafts of this book to teach the algorithms course I took as a student. Although we also used the Cormen("The Bible") Algorithms book for casual reference, this text is by far better to explain the concepts behind the algorithms. I must say that the author presents the course with this text far clearer and superior than the usual dry mathematicians and the contents of the material reflects his expertise in lecturing and writing. The lucid writing makes it a joy to actually read an algorithms book, and the exercises are definitely worth investigating. This book simply makes algorithms fun!
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MERLOT Search - category=2545&sort.property=overallRating
A search of MERLOT materialsCopyright 1997-2014 MERLOT. All rights reserved.Sun, 21 Dec 2014 16:08:26 PSTSun, 21 Dec 2014 16:08:26 PSTMERLOT Search - category=2545&sort.property=overallRating
4434MathPages
This site contains several hundred articles concerned with mathematics and physics. General topics include Number Theory, Combinatorics, Geometry, Algebra, Calculus & Differential Equations, Probability & Statistics, Set Theory & Foundations, Reflections on Relativity, History, and Physics. The articles under each general heading are highly varied, many are quite advanced, and there is no apparent organizational scheme. For example, under Calculus & Differential Equations there is a proof that pi is irrational, a examination of the Limit Paradox, a discussion of Ptolemy's Orbit, and an historical review of the cycloid among many other articles. Visitors can browse by topics or search by keyword. (Anyone with information on the identity of the site author please contact the MERLOT submitter.)Mi tarea
This is an exceptional site for locating all types of content material in creating modules. The are links to the following disciplines: Sciences, History, Art and Culture, Humanities, and general resources. On several of the links, one can find audio files, e.g., Christmas carols. While this site is designed for native speakers in middle school or a secondary level, it is quite appropriate for Spanish language students having an intermediate language proficiency or higher in secondary or college courses.Applied Discrete Structures
Applied Discrete Structures by Al Doerr and Ken Levasseur is a free open content textbook in discrete mathematics. Originally published in 1984 & 1989 by Pearson, the book has been updated to include references to Mathematica and Sage, the open source computer algebra system. Contents:Front Matter: Contents and IntroductionChapter 1: Set Theory I Chapter 2: Combinatorics Chapter 3: Logic Chapter 4: More on Sets Chapter 5: Introduction to Matrix Algebra Chapter 6: Relations and Graphs Chapter 7: Functions Chapter 8: Recursion and Recurrence Relations Chapter 9: Graph Theory Chapter 10: Trees Chapter 11: Algebraic Systems Chapter 12: More Matrix Algebra Chapter 13: Boolean Algebra Chapter 14: Monoids and Automata Chapter 15: Group Theory and Applications Chapter 16: An Introduction to Rings and Fields Solutions to Odd-Numbered Exercises Combinatorial Math: How to Count Without Counting
A collection of JavaScript for computing permutations and combinations counting with or without repetitions.Diamond Theory
Symmetry properties of the 4x4 array. The invariance of symmetry displayed in the author's Diamond 16 Puzzle (online) suggests insights into finite geometry, group theory, and combinatorics.Mudd Math Fun Facts
This archive is designed as a resource for enriching your courses with mathematical Fun Facts! It is designed to pique the interest of students in different areas of mathematics. The fun facts were originally conceived as five minute warm ups at the beginning of lectures so that non mathematics majors would not think math was just calculus. Presentation suggestions are also given.Polyforms
Background and description of polyform sets as a new puzzle genre.The Diamond 16 Puzzle
In solving this puzzle, you permute rows, columns, and quadrants in a 4x4 array of 2-color tiles to make a variety of symmetric designs. A link to underlying theory is provided.
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Summit Argo StatisticsPrealgebra focuses primarily on arithmetic. The most fundamental skills are reading and writing of whole numbers. From there, basic arithmetic operations of addition, subtraction, multiplication and division are defined for the whole numbersHow things work is an area of knowledge that we will apply throughout our lives, whether our main pursuits are gardening, construction, culinary arts, quantum physics, or performing arts. A solid grounding in physical science helps us understand a variety of physical aspects of the world we live...
...Unfortunately there is no short-cutting in math, as a solid foundation is always needed before advancing on. I learned this first hand while studying for two years of Calculus and beyond to get my Computer Science degree. I recently returned from living for two years in Ecuador and Colombia teaching English.
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Overview
Funded by a National Science Foundation grant, Discovering Higher Mathematics emphasizes four main themes that are essential components of higher mathematics: experimentation, conjecture, proof, and generalization. The text is intended for use in bridge or transition courses designed to prepare students for the abstraction of higher mathematics. Students in these courses have normally completed the calculus sequence and are planning to take advanced mathematics courses such as algebra, analysis and topology. The transition course is taken to prepare students for these courses by introducing them to the processes of conjecture and proof concepts which are typically not emphasized in calculus, but are critical components of advanced courses.
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Meet the Author
Alan Levine is a graduate of the State University of New York at Stony Brook with a degree in Operations Research and Applied Math. Since 1983 he has taught at Franklin and Marshall College. He is the co-author, with George Rosenstein, of Discovering Calculus
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Carefully focused on reading and writing proofs, this introduction to the analysis of functions of a single real variable helps readers in the transition from computationally oriented to abstract mathematics. It features clear expositions and examples, helpful practice problems, many drawings that illustrate key ideas, and hints/answers for selected problems. Logic and Proof. Sets and Functions. The Real Numbers. Sequences. Limits and Continuity. Differentiation. Integration. Infinite Series. Sequences and Series of Functions. For anyone interested in Real Analysis or Advanced CalculusBestprice4youalways via United States
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Topology is generally considered to be one of the three linchpins of modern abstract mathematics (along with analysis and...
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This course is a seminar in topology. The main mathematical goal is to learn about the fundamental group, homology and...
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This course is a seminar in topology. The main mathematical goal is to learn about the fundamental group, homology and cohomology. The main non-mathematical goal is to obtain experience giving math talks.
This is a free online course offered by the Saylor Foundation.'"Everything is numbers." This phrase was uttered by the lead...
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This is a free online course offered by the Saylor Foundation.'"Everything is numbers." This phrase was uttered by the lead character, Dr. Charlie Epps, on the hit television show "NUMB3RS." If everything has a mathematical underpinning, then it follows that everything is somehow mathematically connected, even if it is only in some odd, "six degrees of separation (or Kevin Bacon)" kind of way.Geometry is the study of space (for now, mainly two-dimensional, with some three-dimensional thrown in) and the relationships of objects contained inside. It is one of the more relatable math courses, because it often answers that age-old question, "When am I ever going to use this in real life?" Look around you right now. Do you see any triangles? Can you spot any circles? Do you see any books that look like they are twice the size of other books? Does your wall have paint on it?In geometry, you will explore the objects that make up our universe. Most people never give a second thought to how things are constructed, but there are geometric rules at play. Most people never think twice about a rocket launch, but if that rocket is not launched at an exact angle, it will miss its target. A football field has to be measured out to be a rectangle; if you used another shape, such as a trapezoid, that would give an unfair advantage to one team, because that one team would have more space to work with.In this course, you will study the relationships between lines and angles. Have you ever looked at a street map? Believe it or not, there is a lot of geometry on a map, as you will see from this course. You will learn to calculate how much space an object covers, which is useful if you ever have to, say, buy some paint. You will learn to determine how much space is inside of a three-dimensional object, which is useful for those times you are trying to fit four suitcases, three kids, two adults, and a dog into the back of your vehicle.These are just some of the topics you will be learning. As you will quickly see, everything is not just numbers; it is also relationships. Even nature itself knows this. What did the little acorn say when it grew up? "Gee, I'm a tree!"'
This free online textbook/course "looks at various aspects of shape and space. It uses a lot of mathematical vocabulary, so...
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This free online textbook/course "looks at various aspects of shape and space. It uses a lot of mathematical vocabulary, so you should make sure that you are clear about the precise meaning of words such as circumference, parallel, similar and cross-section. You may find it helpful to note down the meaning of each new word in your Learning Journal, perhaps illustrating it with a diagram. This module contains some interactive geometry activities which use the Java based software, Geogebra.״
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Reviews
Useful and practical introduction to Matlab. Assignments do take a significant amount of time, though, and depending on how fast you work, the 1 unit designation can be deceiving. Quizzes are also annoying in that any wrong answers (even simple mistakes) require a completely new retake after 2 days.
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Summary: This text is for a one-term course in intermediate algebra, for students who have had a previous elementary algebra course. A five- step problem-solving process is introduced, and interesting applications are used to motivate students. Coverage progresses from graphs, functions, and linear equations to sequences, series, and the binomial theorem. New to this edition are sections on connecting concepts, study tips, and exercises designed to foster intuitive problem so...show morelving. Bittinger teaches at Indiana University; Ellenbogen at Community College of Vermont.171.03 +$3.99 s/h
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Elementary Linear Algebra
9780132296540
ISBN:
0132296543
Edition: 9 Pub Date: 2007 Publisher: Prentice Hall
Summary: This text presents the basic ideas of linear algebra in a manner that offers students a fine balance between abstraction/theory and computational skills. The emphasis is on not just teaching how to read a proof but also on how to write a proof.
Kolman, Bernard is the author of Elementary Linear Algebra, published 2007 under ISBN 9780132296540 and 0132296543. Four hundred fourteen Elementary Linear Algebra t...extbooks are available for sale on ValoreBooks.com, eighty five used from the cheapest price of $115.94, or buy new starting at $152 days. Hassle free 14 day return policy. Contact Customer Service for questions.[less]
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MATH FOR ELEMENTARY SCHOOL TEACHERS II
Second of two courses designed for prospective elementary teachers. Emphasizes probability, data analysis, and geometry. Explorations focus on representations of data and two and three-dimensional shapes, their properties, measurements, constructions, and transformations. Prerequisite: MATH 209 with a minimum grade of 'C-."
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Developed from the author's popular text, A Concise Introduction to the Theory of Numbers, this book provides a comprehensive initiation to all the major branches of number theory. Beginning with the rudiments of the subject, the author proceeds to more advanced topics, including elements of cryptography and primality testing, an account of number fields in the classical vein including properties of their units, ideals and ideal classes, aspects of analytic number theory including studies of the Riemann zeta-function, the prime-number theorem and primes in arithmetical progressions, a description of the Hardy-Littlewood and sieve methods from respectively additive and multiplicative number theory and an exposition of the arithmetic of elliptic curves. The book includes many worked examples, exercises and further reading. Its wider coverage and versatility make this book suitable for courses extending from the elementary to beginning graduate studies"-- Provided by publisher.
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1130 - Mathematics for Liberal Arts
Survey of modern mathematics and applications, historical perspective, and calculator/computer applications with emphasis on the liberal arts. Topics include: sets, probability and statistics, systems of numeration, modern algebraic structures and modern geometries.
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Designed and centered around Maple's ability to perform symbolic computations, plot, animate, and permit readers to investigate various nonlinear models, this book is an invaluable reference for anyone looking to enhance their understanding of nonlinear physics.
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A text for a course introducing the basic concepts and applied mathematical methods of nonlinear science at a level ranging from junior or early graduate. Requires one semester of ordinary differential equations and an intermediate course in classical mechanics for the earlier chapters; some familiarity with partial derivatives and exposure to the wave, diffusion, and Schr<:o>dinger equations are needed for the later material. Makes extensive use of the symbolic, numeric, and plotting capabilities of the Maple V Release 4 software. Includes a 3.5<"> disk for Windows
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ECE 3250 Mathematics of Signal and System Analysis
Course description
Course aims to deepen students' working knowledge of mathematical tools relevant to ECE applications. While the course emphasizes fundamentals, it also provides an ECE context for the topics it covers, which include foundational material about sets and functions; linear algebra; inner products and orthogonal representations; basic ideas from multivariable calculus; and elementary convex analysis.
Outcome 1: Deepen their understanding of fundamental concepts from real analysis and linear algebra to which they have been exposed in their calculus and differential equation courses by putting them to work in an engineering context.
Outcome 2: Achieve a sophisticated understanding of fundamental signals and systems concepts, a few of which they have been exposed to on an elementary level in ECE 2200, by learning the mathematics behind them.
Outcome 3: Attain an appreciation of the central role that advanced mathematics plays in modeling, analysis, and design of engineering systems.
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High School Calculus in the United States and in Japan
by Thomas W. Judson November 2001
In Japan, as in the United States, calculus is a gateway course that students must pass to study science or engineering. Japanese educators often voice complaints similar to those that we made about students' learning of calculus in the 1970s and 1980s. They believe that many students learn methods and templates for working entrance-examination problems without learning the concepts of calculus. University professors report that the mathematical preparation of students is declining and that even though Japanese middle school students excelled in mathematics in TIMSS-R, these same students expressed a strong dislike for the subject.
Japan has a national curriculum that is tightly controlled by the Ministry of Education and Science. In Japan, grades K–12 are divided into elementary school, middle school, and high school; students must pass rigorous entrance examinations to enter good high schools and universities. After entering high school, students choose either a mathematics and science track or a humanities and social science track. Students in the science track take suugaku 3 (calculus) during their last year of high school; most of them take a more rigorous calculus course at the university.
The course curricula for AP Calculus BC and suugaku 3 are very similar. The most noticeable differences are that Japanese students study only geometric series and do not study differential equations. The epsilon-delta definition of limit does not appear in either curriculum.
In the spring and summer of 2000, Professor Toshiyuki Nishimori of Hokkaido University and I studied United States and Japanese students' understanding of the concepts of calculus and their ability to solve traditional calculus problems. We selected two above-average high schools for our study, one in Portland, Oregon, and one in Sapporo, Japan. Our investigation involved 18 students in Portland and 26 students in Japan. Of the 16 Portland students who took the BC examination, six students scored a 5. We tested 75 calculus students in Sapporo; however, we concentrated our study on 26 students in the A class. The other two classes, the B and C groups, were composed of students of lower ability. Each student took two written examinations. The two groups of students that we studied were not random samples of high school calculus students from Japan and the United States, but we believe that they are representative of above-average students. We interviewed each student about his or her background, goals, and abilities and carefully discussed the examination problems with them.
Since we did not expect Japanese students to be familiar with calculators, we prohibited their use on the examinations. However, the students in Portland had made significant use of calculators in their course and might have been at a disadvantage if they did not have access to calculators. For that reason, we attempted to choose problems that were calculator independent. However, some problems on the second examinations required a certain amount of algebraic calculation.
We used problems from popular calculus-reform textbooks on the first examination. These problems required a sound understanding of calculus but little or no algebraic computation. For example, in one problem from the Harvard Calculus Project, a vase was to be filled with water at a constant rate. We asked students to graph the depth of the water against time and to indicate the points at which concavity changed. We also asked students where the depth grew most quickly and most slowly and to estimate the ratio between the two growth rates at these depths.
We found no significant difference between the two groups on the first examination. The Portland students performed as expected on calculus-reform-type problems; however, the Sapporo A students did equally well. Indeed, the Sapporo A group performed better than we had expected. We were somewhat surprised, since the Japanese students had no previous experience with such problems. The performance of Japanese students on the first examination may suggest that bright students can perform well on conceptual problems if they have sufficient training and experience in working such problems as those on the university entrance examinations.
The problems on the second examination were more traditional and required good algebra skills. For example, we told students that the function f(x) = x3+ ax2 + bx assumes the local minimum value—(2 )/9 at x = 1/—and asked them to determine a and b. We then asked them to find the local maximum value of f(x) and to compute the volume generated by revolving the region bounded by the x-axis and the curve y = f(x) about the x-axis. The Sapporo A students scored much higher than the Portland students did on the second examination. In fact, the Portland group performed at approximately the same level as the Sapporo C group and significantly below the Sapporo B group. Several Japanese students said in interviews that they found that certain problems on the second examination were routine, yet no American student was able to completely solve these problems. The Portland students had particular difficulty with algebraic expressions that contained radicals. Several students reported that they worked slowly to avoid making mistakes, possibly because they were accustomed to using calculators instead of doing hand computations.
Students from both countries were intelligent and highly motivated, and they excelled in mathematics; however, differences were evident in their performances, especially in algebraic calculation. One of the best Portland students correctly began to solve a problem on the second examination but gave up when he was confronted with algebraic calculations that involved radicals. On his examination paper he wrote, "Need calculator again."
Perhaps the largest difference between the two groups lies in the different high school cultures. Japanese students work hard to prepare for the university entrance examinations and are generally discouraged from holding part-time jobs. In contrast, students in the United States often hold part-time jobs in high school, and many are involved in such extracurricular activities as sports or clubs.
Thomas Judson is a visiting assistant professor at the University of Puget Sound in Tacoma, Washington. He is interested in mathematics education and has spent parts of the last eight summers visiting Japan to learn Japanese and study mathematics education there.
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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Welcome!
Welcome to the Department of Mathematics and Statistics. We offer a wide variety of undergraduate and graduate degree programs designed for students with diverse career or higher educational goals. Our faculty members maintain active research programs in the fields of combinatorics, algebra, analysis, applied mathematics and applied statistics. In a nod toward the unity of mathematics, we offer the following question—whose answer requires several of the above fields, as well as geometry:
A collection of small waves are travelling through shallow water and happen to collide. What happens next?
The first half of the above sentence is governed by the famous KdV equations. (Jerry Bona, UIC, spoke at our colloquium about these waves not long ago.)
The second half of the above sentence is governed by cells in the totally positive part of the Grassmannian and plabic graphs. (Dr. Lauve can tell you more about this aspect of the theory of totally positive matrices.)
See our Faculty Research page for a list of local people to ask for more details, or consult the original sources
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Algebra: Chapter 0 is a self-contained introduction to the main topics of algebra, suitable for a first sequence on the subject at the beginning graduate or upper undergraduate level. The primary distinguishing feature of the book, compared to standard textbooks in algebra, is the early introduction of categories, used as a unifying theme in the presentation of the main topics. A second feature consists of an emphasis on homological algebra: basic notions on complexes are presented as soon as modules have been introduced, and an extensive last chapter on homological algebra can form the basis for a follow-up introductory course on the subject. Approximately 1,000 exercises both provide adequate practice to consolidate the understanding of the main body of the text and offer the opportunity to explore many other topics, including applications to number theory and algebraic geometry. This will allow instructors to adapt the textbook to their specific choice of topics and provide the independent reader with a richer exposure to algebra. Many exercises include substantial hints, and navigation of the topics is facilitated by an extensive index and by hundreds of cross-references.
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More About the Author
Paolo Aluffi was born in Italy, and studied mathematics in Torino under the direction of Alberto Collino, and then at Brown University, obtaining a Ph.D. with a dissertation in algebraic geometry under the supervision of William Fulton. He has held postdoctoral positions at the University of Chicago and Oklahoma State University, and joined the department of mathematics at Florida State University in 1991. He is currently professor of mathematics at FSU. Paolo Aluffi has visited many universities and mathematics institutes for extended periods of time. Among these are the Max-Planck-Institut in Bonn, Germany; Harvard University; the Institut des Mathématiques in Luminy, France; the Mittag-Leffler Institut in Stockholm, Sweden; the Mathematical Sciences Research Institute in Berkeley, California; and the California Institute of Technology.
Beside `Algebra: Chapter 0', he has published more than 40 research papers in algebraic geometry. He has also published a book of mathematics for the `general public' in Italian, `Fare Matematica'.
Most Helpful Customer Reviews
This is a well organized and clearly written book. Professor Aluffi must be an excellent teacher. He guides the reader through the material and shows the beauty of the subject. His use of category theory- particularly universal properties- reveals the underlying unity of seemingly disparate notions.The chapters on Field Theory and Homological Algebra are superb. He always provides useful comments to place topics in context. I hope Professor Aluffi will write more texts.
I should first mention that I, along with about twenty of my fellow first-year mathematics graduate students, scoured this book from beginning to end. We completed nearly every exercise, and discovered a number of errata (there is quite a large list available on the author's website, but this book shines in spite of it all).
I've experienced Fraleigh, Artin, Dummit and Foote, and Aluffi's texts on abstract algebra. While each has it's place, I have to say that Aluffi is my favorite. His writing style is phenomenal (and humorously pretentious at times). This text is not intended to be a reference, but instead read from start to finish, and Aluffi monopolizes this to its full effect. The content is spot on for the intended audience. His exercises cover important, relevant topics to important fields I and my fellow graduate students intend to pursue. These include, but are not limited to: algebraic geometry, commutative algebra, homological algebra, and Lie theory.
This book is the best I have encountered for transitioning from an elementary understanding of abstract algebra to a mature perspective, backed by the might of category theory. That being said, I can see how the book may go more smoothly if one has had some initial exposure to algebra before Aluffi. This text does an excellent job synthesizing my understanding, but the organization could be confusing for a beginner.
My only real disappointment with the book is in the final chapter on homological algebra. By the last two or three sections, the content is almost prohibitively confusing. It could be the case that there are errata that have confused me (indeed, the listed errata on his website sharply fall in this chapter, and I believe it's because most students don't get this far).Read more ›
I attended a course in abstract algebra using Fraleigh's book. Then I sorta just stumbled across this one (which I should add covers a lot more than Fraleigh). With experience from Fraleigh's book (which is good) I can say this one is absolutely brilliant. It is well organized, covers a lot of ground in a (not too) leisurly pace, and the exercises are interesting. The best part about this book, however, is the way it seamlessly and naturally uses and demystifies category theory -- a subject I thought I'd not be able to understand for years -- to unify a great deal of the topic that is undergraduate/graduate algebra.
This is a very good book overall, the author is a great expositor. Most of the book is very elegant in a way that does not sacrifice readability, and he will not hesitate to help parse when it does. My personal opinion is that it is outclassed by Mac Lane and Birkhoff's "Algebra", but I still wouldn't have many qualms about recommending the text to someone with suitable maturity wanting to learn the subject.
My only real quibbling with the book is how its main feature - the integration of category theory - is handled. I certainly agree that its use is beneficial in this context, but I think delaying the introduction of functors until the second-to-last chapter is a weakness if categories are going to come up as much as they do. He tosses them aside early for a more intuitive "working definition" of universals, which is understandable at first as it could easily be a bit much to take in at the time, but I assume that's the same reason adjoints are glossed over the way they are when introduced very shortly after functors. I think it would be helpful to just once when proving something is an adjunction prove the naturality part as well as the bijection part, because not doing so somewhat gives the idea that the naturality condition is simply auxiliary. In general, chapter VIII is a weak point in an otherwise very good book, in many ways it just seems like a preview of the following chapter with less substance than anywhere else in the book.
I'll also add as a very minor complaint: the determinant is poorly motivated upon it's introduction.Read more ›
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X and the City: Modeling Aspects of Urban Life [NOOK Book] ...
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This Book by an asteroid? Every math problem and equation in this book tells a story and examples are explained throughout in an informal and witty style. The level of mathematics ranges from precalculus through calculus to some differential equations, and any reader with knowledge of elementary calculus will be able to follow the materials with ease. There are also some more challenging problems sprinkled in for the more advanced reader. Filled with interesting and unusual observations about how cities work, X and the City shows how mathematics undergirds and plays an important part in the metropolitan landscape.
Editorial Reviews
Choice
For mathematics professionals, especially those engaged in teaching, this book does contain some novel examples that illustrate topics such as probability and analysis.
Mathematical Reviews Clippings
- Sandra L. Arlinghaus
Read this book and come away with a fresh view of how cities work. Enjoy it for the connections between mathematics and the real world. Share it with your friends, family, and maybe even a municipal planning commissioner or two!
From the Publisher
"[Adam's] writing is fun and accessible. . . . College or even advanced high school mathematics instructors will find plenty of great examples here to supplement the standard calculus problem sets."—Library Journal
"For mathematics professionals, especially those engaged in teaching, this book does contain some novel examples that illustrate topics such as probability and analysis."—Choice
"Read this book and come away with a fresh view of how cities work. Enjoy it for the connections between mathematics and the real world. Share it with your friends, family, and maybe even a municipal planning commissioner or two!"—Sandra L. Arlinghaus, Mathematical Reviews Clippings
"It goes without saying that the exposition is very friendly and lucid: this makes the vast majority of material accessible to a general audience interested in mathematical modeling and real life applications. This excellent book may well complement standard texts on engineering mathematics, mathematical modeling, applied mathematics, differential equations; it is a delightful and entertaining reading itself. Thank you, Vickie Kearn, the editor of A Mathematical Nature Walk, for suggesting the idea of this book to Professor Adam—your idea has been delightfully implemented!"—Svitlana P. Rogovchenko, Zentralblatt MATH
"[Y]ou'll find this book quite extensive in how many different areas you can apply mathematics in the city and just how revealing even a simple model can be. . . . A Mathematical Nature Walk opened my eyes to nature and now Adam has done the same for cities."—David S. Mazel, MAA Reviews
"The author has an entertaining style, interweaving clever stories with the process of mathematical modeling. This book is not designed as a textbook, although it could certainly be used as an interesting source of real-world problems and examples for advanced high school mathematics courses."—Theresa Jorgensen, Mathematics Teacher
Library Journal
Adam (mathematics, Old Dominion Univ.; Guesstimation: Solving the World's Problems on the Back of a Cocktail Napkin) intends to complement his previous titles on the mathematics of natural systems with a new book about mathematical models of human-made systems. In 25 brief chapters, he introduces readers to exercises related to traffic flow, population growth, changing demographics, and probability. His writing is fun and accessible, but, aside from the short introductions to each section, it focuses on discovering and unpacking mathematical problems in everyday situations. The book assumes a familiarity with basic calculus and is designed to help students practice application-based problem-solving skills. Well known to engineers, economists, and others in the field, the ability to look at a situation, determine how to represent it in mathematical terms, and set up a solvable equation is all too frequently forgotten in most pure calculus courses; even experienced calculus users often struggle with setting up problems. VERDICT College or even advanced high school mathematics instructors will find plenty of great examples here to supplement the standard calculus problem sets.—J.J.S. Boyce, formerly with Louis Riel and Pembina Trails Sch. Divisions, Winnipeg
Related Subjects
Meet the Author
AdamJohn A.: John A. Adam is professor of mathematics at Old Dominion University. He is the author of "A Mathematical Nature Walk" and "Mathematics in Nature", and coauthor of "Guesstimation: Solving the World's Problems on the Back of a Cocktail Napkin" (all
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Learning a Subject
What to learn and how to learn
There is something special about each course. Your grades will improve when you discover exactly what you need to learn and how to learn it.
What to learn
For each course or each chapter, you need:
Contents: Be very clear about what this chapter or course covers and what problems are solved. At the end of each chapter, try to list all you have learned and put them into an order you understand.
General theories (theorems, formulas, etc.);
Related exercises, problems.
Methods: Special methods exist to prove theorems and solve problems. You should study those methods. Then you will be much better with problem solving. Each chapter or each course normally has several typical methods that you are expected to learn and apply to problems. If you are aware and pay attention to those "tricks," learning and problem solving will become much easier.
Special examples and problems: Sometimes there are special examples and problems that require special tricks to solve. Pay attention. Those problems have more of a chance to be the candidates for test problems.
Summaries of each chapter and the course: You should have a summary for each chapter and a summary for the course at the end. Then it is much easier for you to understand and retrieve the material. Only well-organized knowledge can be remembered for a long time.
How to get it:
The academic success skills given in the following pages should help you to achieve the goals of learning.
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There is a very good reason to teach long division: algebra. I need my
precalculus students to be able to do polynomial long division. This will also
be important when they use partial fraction decomposition for integration in
calculus. If my students understand arithmetic long division, then it's not
very hard to teach polynomial long division. If they do not understand
arithmetic long division, it's very difficult for them to learn polynomial long
division
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You are here
Assessment Practices in Undergraduate Mathematics.
Publisher:
Mathematical Association of America
Number of Pages:
292
Price:
36.95
ISBN:
978-0-88385-161-6
How can I review a bag of assorted jellybeans? On one hand, they're all essentially the same -- a sugary crust enclosing an ellipsoidal blob of gel. On the other hand, they're different in the details of color, size, and most importantly, taste. So the statement "I like jellybeans" is only a broad generalization; some flavors, sizes and colors I like a lot, some are okay, and there might even be a few kinds I dislike. My review can only give you my overall feeling, and I can provide a few specific examples for illustrative purposes (personally, I love the sky-blue mints, but I can't stand red-hot cinnamons). Assessment Practices in Undergraduate Mathematics is a tasty collection of seventy-odd different jellybeans... oops, I mean, articles. Some are tastier than others, but as a whole, the collection is a worthwhile treat.
Assessment techniques offered in this book range from several-minute classroom exercises and examples of alternative assignments and cooperative exercises, to examples of how departments may evaluate their course placement, major, service to other departments, and teaching. This nearly overwhelming variety of information is organized into something sensible through the use of two clever editorial fiats described below.
The articles are brief and uniformly formatted. A five-line summary precedes no more than five pages covering background and purpose, method, findings, use of findings, and success factors. Enough information is given about the context of the assessment that you can decide how well you could transfer the techniques to your specific academic situation. Generalizable results are not the point of these articles, but useful, transferable skills and methods are. This makes the book ideal for browsing. When you have no specific assessments needs in mind, you can page randomly and very quickly decide if the article describes something personally meaningful to you, how it was done, and what the results were. If you are particularly intrigued by particular article, points of contact for the authors are included in an index.
The book has two extremely useful tables of contents. The breadth of coverage of the book is somewhat daunting, but makes it a very useful reference when you have a specific assessment need. Perhaps you're on the committee that writes the report for regional accreditation, and you need to know about assessing the major. Or your department has recently embarked on a reform initiative, and you're wondering what worked. Or you're simply looking for an alternative to a formal end-of-term teacher evaluation form as a way to examine the quality of your teaching. All of these assessment techniques are in the book, but best of all, you can find them. The table of contents covers 17 topics, broken into 4 parts: assessing the major, the individual classroom, the department, and teaching. If these 17 topic labels don't cover what you're looking for, check the list of articles arranged by topic a few pages further on. Multi-topic articles are cross-listed, and therefore easier to find. Also, new topics are included, ones that cross-cut the 4 parts of the table of contents (e.g., "Exams," "Portfolios," "Cooperative Learning").
I could conclude this book review by providing an analysis of several of the articles, but I feel that wouldn't really do justice to the variety of topics and usefulness of presentation in Assessment Practices in Undergraduate Mathematics. Instead, I'll recount four examples of how I used it last semester (Fall 1999).
Part II, Assessment of the Individual Classroom included a topic category called Projects and Writing to Learn Mathematics, which helped me because I just switched institutions, and my new department uses projects and writing much more extensively than my old one.
Another article in Part II dealt with using e-mail to provide feedback for students' problem solving in a way that balanced individualized attention with the efficiency of semiautomation. I found this article quite dense with ideas, perhaps even too telegraphic, but the author noted it was an excerpt from a longer work. I haven't yet contacted him, but I might if I find my thoughts wandering back to his methods and results.
Student understanding is one of my research interests, so I read the article by Kathy Heid that discussed using interviews to understand student understanding. The assessment she suggests has strong shades of educational research; the boundary between assessment and research is fuzzy, and practicing the kind of thoughtful, explorative assessment she suggests would be excellent training for doing mathematics education research.
I ran across a "gem" on page 270 while browsing through Part IV, Assessing Teaching. It shows a way to get feedback from your students about how well they understand the material. Instead of asking "Does anyone still not get this?" during a lecture, say "Raise your hand if you understand this part." It's a gem because it is so simple and easy, but it's something I would have never thought of myself.
Gideon L. Weinstein (ag7084@usma.edu) is an assistant professor of mathematics at the US Military Academy in West Point, NY. He shares his joy of calculus with future Army officers by morning and tries to write mathematics education articles by afternoon. His academic interests include mathematical sophistication, motivation, technology, and assessment.
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This course follows on from FE & RM Part I. We will consider portfolio optimization, risk management and some advanced examples of derivatives pricing that draw from structured credit, real options and energy derivatives. We will also cast a critical eye on how financial models are used in practice.
This course will introduce you to the fundamentals of probability theory and random processes. The theory of probability was originally developed in the 17th century by two great French mathematicians, Blaise Pascal and Pierre de Fermat, to understand gambling.
Calculus is about the very large, the very small, and how things change. The surprise is that something seemingly so abstract ends up explaining the real world. Calculus plays a starring role in the biological, physical, and social sciences. By focusing outside of the classroom, we will see examples of calculus appearing in daily life.
In this course, you will study basic algebraic operations and concepts, as well as the structure and use of algebra. This includes solving algebraic equations, factoring algebraic expressions, working with rational expressions, and graphing linear equations.
Algebra is the foundation of modern mathematics. In this course we draw from materials by the amazing Salman Khan, of Khan Academy, to show you how to work with variables to write expressions, equations, inequalities, and functions.
Geometry is the study of shapes, size, and relative position and helps us to measure and understand the world around us. In this course you will learn about points and lines in the plane, properties of angles and shapes.
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Other Formats
Product Description
In What's Math Got to Do with It? Jo Boaler, a professor of mathematics education at Stanford University, outlines specific strategies and solutions for addressing the problem of math and science deterioration among students in the United States. If you want to help your child learn these important disciplines, read the advice given to parents in this one of a kind book.
Publisher's Description
A recent assessment of mathematics performance around the world ranked the United States twenty-eighth out of forty countries in the study. When the level of spending was taken into account, we sank to the very bottom of the list. We are falling rapidly behind the rest of the developed world when it comes to math education-and the consequences are dire.
In this straightforward and inspiring book, Jo Boaler, a professor of mathematics education at Stanford for nine years, outlines concrete solutions that can change things for the better, including classroom approaches, essential strategies for students, and advice for parents. This is a must-read for anyone who is interested in the mathematical and scientific future of our country.
Author Bio
Jo Boaler is a Professor of Mathematics Education at Stanford University. She was formerly the Marie Curie Professor of Mathematics Education at the University of Sussex in England and a classroom teacher in London and California. She is a regular contributor to national television and radio in the United States and the U.K., and her research has appeared in newspapers around the world, including The Wall Street Journal and The Times(London). She lives in Palo Alto, California.
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Reviews
Just a continuation of 121A. With Neu, the class is fast, confusing, and I didn't really learn anything. One redeeming thing is that Neu gives homework help during office hours. Other than that, he's the worst teacher I have had in my educational career.
Reviewed on
Jun 6, 2011
Is this helpful?
YesNo
I took this class with John Neu. The textbook was notes he wrote for the class. First things first, if you take this with Neu (or 121A) (I cannot speak for other professors) you will HAVE to go to office hours. The homework takes forever without it, and sometimes he expects you to know little tricks or other things that I often did not know. He treats office hours as another class hour (basically is seeing how the almost the entire class shows up). He picks a homework problem, picks someone to work on the whiteboard, and walks you all through it. Very helpful. In my experiences, office hours were usually on mondays and wednesdays in the afternoon, though it can change (this semester they were originally monday and thursday but he changed it so we could have more time between office hours and the homework being due thursday). The class was devoted to solving PDE's. It is not theory intensive, I found it to be very practical. Physical problems with physical explanations. I thought the class was really useful, Neu picks examples based on physics so you can see actual applications. You'll see a lot of the material covered in physics classes, I found it helpful to see it in a class devoted to math first. Overall, useful class but hard.
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New YorkComputer science--Mathematics.LovászLászlóLovász, László, 1948-1948c2003Undergraduate texts in mathematics200350494481Discrete mathematics : elementary and beyond2003en290Informatique--Mathématiques."This book is aimed at undergraduate mathematics and computer science students interested in developing a feeling for what mathematics is all about, where mathematics can be helpful, and what kinds of questions mathematicians work on. The authors discuss a number of selected results and methods of discrete mathematics, mostly from the areas of combinatorics and graph theory, with a little number theory, probability, and combinatorial geometry. Wherever possible, the authors use proofs and problem solving to help students understand the solutions to problems. In addition, there are numerous examples, figures, and exercises spread throughout the book."--Jacket.acid-free paper97803879558410387955844Combinatória.Mathématiques.SpringerPelikánJ.Pelikán, J. (József)Mathematics.VsztergombiK.Vsztergombi, K. (Katalin)Combinatieleer.Computer science--Mathematics.97803879558580387955852nyuDiskrete Mathematik.
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Math Processor (MP) helps you solve different types of mathematical and statistical problems. It allows you to work on large data sets in an easy and fast environment. It has some plotting capabilities as well. Do not be mistaken by the small size or simple interface of Math Processor. Just read the help file of MP to see how you can solve complex mathematical and statistical problems with ease and speed.
MP provides a simple interpreted language called Math Processor Command Language (MPCL) to get commands from the user. This simple language can be a very good start for someone desiring to learn computer programming. Please refer to the product help to learn more about MPCL.
MP provides simplicity and robustness in a single package. On one hand, students of Grade-6 can get help for their homework and learn mathematics in a helpful environment. On the other hand, senior students will have sufficient power at their disposal to solve complex problems related to math, statistics and other allied fields.
You are welcome to send feature requests. Your suggestions will be given full consideration. You may also send comments regarding anything you want to say about Math Processor. On top of all, please never let a Bug you find go un-reported.
Kashif Imran
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the proof of the nontrisectibility of an arbitrary angle as a final goal, the author develops, in an easy conversational style, the basics of rings, fields, and vector spaces. Originally developed as a text for an introduction to algebra course for future high-school teachers at California State University, Northridge, the focus of this book is on exposition, on conveying mathematical insight to an audience that is as yet unaccustomed to abstraction. Familiarity with the material is developed by exposing the students to a large number of examples, and the text is peppered liberally with questions intended to encourage the students to think through the material themselves.
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Math Study Skills-Workbook - 4th edition
Summary: Help your students become more effective at studying and learning mathematics with the MATH STUDY SKILLS WORKBOOK, Fourth Edition. Typically used as an a course supplement, the Nolting strategy helps students identify their strengths, weaknesses, and personal learning styles and then presents an easy-to-follow system to help them become more successful at math
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2004eared toward helping students visualize and apply mathematics, Elementary and Intermediate Algebra: Graphs and Models, Second Edition is designed for a two-semester course. The authors make use of illustrations, graphs, and graphing technology to enhance students' mathematical skills. This is accomplished through Interactive Discoveries, Algebraic-Graphical Side-by-Sides, and the incorporation of real-data applications. In addition, students are taught problem-solving skills using the Bittinger hallmark five-step problem-solving process coupled with new Connecting the Concepts and Aha! exercises. And, as you have come to expect with any Bittinger text, we bring you a complete supplements package that now includes an Annotated Instructor's Edition and MyMathLab, Addison-Wesley's on-line course solution.
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Synopses & Reviews
Please note that used books may not include additional media (study guides, CDs, DVDs, solutions manuals, etc.) as described in the publisher comments.
Publisher Comments:
Need to Learn MATLAB? Problem SOLVED!
Get started using MATLAB right away with help from this hands-on guide. MATLAB Demystified offers an effective and enlightening method for learning how to get the most out this powerful computational mathematics tool.
Using an easy-to-follow format, this book explains the basics of MATLAB up front. You'll find out how to plot functions, solve algebraic equations, and compute integrals. You'll also learn how to solve differential equations, generate numerical solutions of ODEs, and work with special functions. Packed with hundreds of sample equations and explained solutions, and featuring end-of-chapter quizzes and a final exam, this book will teach you MATLAB essentials in no time at all.
This self-teaching guide offers:
The quickest way to get up and running on MATLAB
Hundreds of worked examples with solutions
Coverage of MATLAB 7
A quiz at the end of each chapter to reinforce learning and pinpoint weaknesses
A final exam at the end of the book
A time-saving approach to performing better on homework or on the job
Simple enough for a beginner, but challenging enough for an advanced user, MATLAB Demystified is your shortcut to computational precision.
Synopsis:
"Synopsis"
by Libri,
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Enter your mobile number or email address below and we'll send you a link to download the free Kindle Reading App. Then you can start reading Kindle books on your smartphone, tablet, or computer - no Kindle device required.
This is a practical anthology of some of the best elementary problems in different branches of mathematics. Arranged by subject, the problems highlight the most common problem-solving techniques encountered in undergraduate mathematics. This book teaches the important principles and broad strategies for coping with the experience of solving problems. It has been found very helpful for students preparing for the Putnam exam.
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Most Helpful Customer Reviews
I would like to suggest that the audience for this book is somewhat broader than just the "all-star" math students. I will indeed use this book to help students preparing to take the Putnam exam this fall - it is the best book I have seen for this purpose. But in just the first two chapters, Larson presents strategies such as working backwards, modifying the problem, mathematical induction, and the pigeonhole principle, in a way which all math majors can benefit from. A graduating senior reported that once he started participating in math contests, his performance in ALL of his math classes improved. Problem solving unifies mathematical understanding. This student took the Putnam last fall (which, if you've got this far without knowing, is a six-hour national undergraduate mathematics competition taken by 3000 students in the US and Canada each year, approximately half of whom score zero) just to see what he could do, to gauge his improvement in mathematics. There isn't much more of a compliment a student could give me, intentional or otherwise. That can't all be attributed to this book, but it is that good. The presentation is unique; the organization - by strategy, rather than by year or whatever you see in other problem books - is illuminating by itself, and has improved my pedagogy; and he just makes hard problems look easy. Any student past the level of Linear Algebra who is up for a challenge will benefit from this book.
An excellent resource for anyone interested in mathematical problem solving at the undergraduate level. Comes with many interesting problems taken from various mathematics contests. Additionally, the writing is clear and user-friendly. The only thing lacking is a companion workbook/solution guide. If you know anyone taking the AIME, USAMO, IMO, or Putnam exam, do them a favor and buy them this book! It's well worth it!
This book would be especially helpful for someone planning to compete in the Putnam Exam. Lots of example covering many topics in upper undergraduate maths and of course the classic "folklore" techniques, strategies, and tools of problem solving(e.g., pigeonhole, invariants, coloring proofs, etc.). This is more of an advanced book as compared to others aimed at Olympiad contestants. Nonetheless, it is an invaluable source for anyone interested in non-routine mathematics.
Finally, a book that develops problem solving techniques in a structured way for the Putnam. However, the techniques can be generally applicable to solve problems in many different areas. The power of using "first principles" to solve problems that at first sight seem almost impossible is brought out clearly. (Example, show that any sequence of consecutive integers is divisible by n!. Where does even start to solve such problems? The book shows you how.) You can read the book from the beginning to end, but a better way is to read it at random. Read the first chapter, though. It does a marvellous job of enumerating the different types of techniques. Enjoy this book. You'll be amazed at how simple ideas can lead to difficult problems.
I have been teaching for the Math Olympiad for seven years and this book is one of my favorite resources. It covers a lot of great techniques for problem solving, specially the first chapter. The first chapter is a great introduction to problem solving. The chapters covers several techniques which the author calls heuristics, which are the basics. This chapter is kind of like learning the basic moves of a new dance. To do learn any other aspects of the dance, you need to master the basics and this book really honed in on the basics. Mastering the first chapter is, in my opinion, a crucial step in preparing for mathematical competitions, like the Mathematical Olympiad or the Putnam.
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Applied Combinatorics - 5th edition
Summary: Updated with new material, this Fifth Edition of the most widely used book in combinatorial problems explains how to reason and model combinatorically. It also stresses the systematic analysis of different possibilities, exploration of the logical structure of a problem, and ingenuity. Combinatorical reasoning underlies all analysis of computer systems. It plays a similar role in discrete operations research problems and in finite probability. This book seeks to develo...show morep proficiency in basic discrete math problem solving in the way that a calculus text develops proficiency in basic analysis problem solving50 +$3.99 s/h
Good
Peninsula FOL Palos Verdes Estates, CA
2006-11-29 Hardcover Very Good Phone number written on front end paper. Yellow highlighting on pages 57 and 182. Pages are clean and binding is tight. nm All proceeds benefit local libraries
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Summary: Strategies and Guidelines for
Using a
Computer Algebra System
in the Classroom
by
G. Donald Allen1
Jim Herod2
Mark Holmes3
Vince Ervin4
Robert Lopez5
Joe Marlin6
Doug Meade7
David Sanchez1
Introduction
More and more faculties of mathematics have chosen to use a Computer Alge-
bras System CAS, such as Maple8, Mathematica9, or MATLAB10, in the class-
room, substantially the calculus classroom. All but a handful genuinely understand
what di culties they will encounter. The main problem is to formulate answers to
the questions
What part of the course objectives are assisted by the use of technology?
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DeMYSTiFieD is your solution for tricky subjects like trigonometry
If you think a Cartesian coordinate is something from science fiction or a hyperbolic tangent is an extreme exaggeration, you need Trigonometry DeMYSTiFieD , Second Edition, to unravel this topic's fundamental concepts and theories at your own pace.
This practical guide eases ? whether you need a supplement to your textbook... more...
Most math and science study guides are a reflection of the college professors who write them-dry, difficult, and pretentious.
The Humongous Book of Trigonometry Problems is the exception. Author Mike Kelley has taken what appears to be a typical trigonometry workbook, chock full of solved problems-more than 750!-and made notes in the margins... more...
This encyclopedia contains trigonometric identity proofs for some three hundred identities. The book is presented in the form of mathematical games for the reader's enjoyment and includes a concordance of trigonometric identities, enabling easy reference. Trig or Treat is a must-have for:. • every student of trigonometry, to find the proofs... more...
Tough Test Questions? Missed Lectures? Not Enough Time?
Fortunately, there's Schaum's. This all-in-one-package includes more than 600 fully solved problems, examples, and practice exercises to sharpen your problem-solving skills. Plus, you will have access to 20 detailed videos featuring Math instructors who explain how to solve the most commonly
| 677.169 | 1 |
Shipping prices may be approximate. Please verify cost before checkout.
About the book:
"Kline is a first-class teacher and an able writer. . . . This is an enlarging and a brilliant book." Scientific American "Dr. Morris Kline has succeeded brilliantly in explaining the nature of much that is basic in math, and how it is used in science." San Francisco ChronicleSince the major branches of mathematics grew and expanded in conjunction with science, the most effective way to appreciate and understand mathematics is in terms of the study of nature. Unfortunately, the relationship of mathematics to the study of nature is neglected in dry, technique-oriented textbooks, and it has remained for Professor Morris Kline to describe the simultaneous growth of mathematics and the physical sciences in this remarkable book.In a manner that reflects both erudition and enthusiasm, the author provides a stimulating account of the development of basic mathematics from arithmetic, algebra, geometry, and trigonometry, to calculus, differential equations, and the non-Euclidean geometries. At the same time, Dr. Kline shows how mathematics is used in optics, astronomy, motion under the law of gravitation, acoustics, electromagnetism, and other phenomena. Historical and biographical materials are also included, while mathematical notation has been kept to a minimum. This is an excellent presentation of mathematical ideas from the time of the Greeks to the modern era. It will be of great interest to the mathematically inclined high school and college student, as well as to any reader who wants to understand perhaps for the first time the true greatness of mathematical achievements. Usually ships within 1 - 2 business days, Brand New. Delivery is usually 5 - 8 working days from order, International is by Royal Mail Airmail Used - Good, Usually ships in 1-2 business days, Book has some visible wear on the binding, cover, pages. Biggest little used bookstore in the world.
Softcover, ISBN 0486241041 Publisher: Dover Publications, 1981 Revised ed.. Softcover. Used - Good Good . Book has some visible wear on the binding, cover, pages. Biggest little used bookstore in the world. Revised ed.
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Many people do not realize how much algebra you actually do in calculus. I
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Introduction to Algebra - 2nd edition
ISBN13:978-0198527930 ISBN10: 0198527934 This edition has also been released as: ISBN13: 978-0198569138 ISBN10: 0198569130
Summary: Developed to meet the needs of modern students, this Second Edition of the classic algebra text by Peter Cameron covers all the abstract algebra an undergraduate student is likely to need. Starting with an introductory overview of numbers, sets and functions, matrices, polynomials, and modular arithmetic, the text then introduces the most important algebraic structures: groups, rings and fields, and their properties. This is followed by coverage of vector spaces and ...show moremodules with applications to abelian groups and canonical forms before returning to the construction of the number systems, including the existence of transcendental numbers. The final chapters take the reader further into the theory of groups, rings and fields, coding theory, and Galois theory. With over 300 exercises, and web-based solutions, this is an ideal introductory text for Year 1 and 2 undergraduate students in mathematics47.73
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Combinatorics and Graph useful pointers to further reading at the post-graduate level
Definitions are followed by representative examples
contains numerous exercises, figures, and exposition
More streamlined than most similar texts
This book covers a wide variety of topics in combinatorics and graph theory. It includes results and problems that cross subdisciplines, emphasizing relationships between different areas of mathematics. In addition, recent results appear in the text, illustrating the fact that mathematics is a living discipline.
The second edition includes many new topics and features:
• New sections in graph theory on distance, Eulerian trails, and Hamiltonian paths.
• New material on partitions, multinomial coefficients, and the pigeonhole principle.
• Expanded coverage of Pólya Theory to include de Bruijn's method for counting arrangements when a second symmetry group acts on the set of allowed colors.
• Topics in combinatorial geometry, including Erdos and Szekeres' development of Ramsey Theory in a problem about convex polygons determined by sets of points.
• Expanded coverage of stable marriage problems, and new sections on marriage problems for infinite sets, both countable and uncountable.
• Numerous new exercises throughout the book.
About the First Edition:
". . . this is what a textbook should be! The book is comprehensive without being overwhelming, the proofs are elegant, clear and short, and the examples are well picked."
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Why Do I Need To Know Algebra?
The Contra Costa Office of Education and Chevron Corporation know how important it is that our students understand the link between what they learn in the classroom and how they will use that knowledge as they move into higher education and into their careers.
Many students believe algebra doesn't apply to real life. They echo the common refrain, "Why do I need to know Algebra?" But as adults we know that math applies to many careers, not just those in math and science. In this resource, students will see the wide variety of careers that use Algebra. From racecar engineer to human resource manager, students will have the opportunity to hear directly from these professionals how they use math in their day-to-day work life.
The DVD and supporting materials are designed to help students understand how classroom math connects to the real world. The DVD contains interviews with people working in a variety of careers. Students can hear directly from adults in the workplace about their day-to-day work life and how their training in math contributes to their ability to do their job. Students will have the opportunity to practice math problems as they learn about these careers.
Who Should Use This Program?
"Why Do I Need To Know Algebra?" is designed for use with middle or junior high students. It is also suitable for use in after school programs and career exploration classes.
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Summary: This text is for a one-term course in intermediate algebra, for students who have had a previous elementary algebra course. A five- step problem-solving process is introduced, and interesting applications are used to motivate students. Coverage progresses from graphs, functions, and linear equations to sequences, series, and the binomial theorem. New to this edition are sections on connecting concepts, study tips, and exercises designed to foster intuitive problem so...show morelving. Bittinger teaches at Indiana University; Ellenbogen at Community College of Vermont57182 Like New copy, without any marks or highlights. has shelf wear on covers. This is Student US Edition. Same day shipping with free tracking number. Expedited shipping avail...show moreable. A+ Customer Service! ...show less
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Comprehensive but concise, this workbook is less rigorous than most calculus texts. Topics include functions, derivatives, differentiation of algebraic functions, partial differentiation, indeterminate forms,...
$ 14.79
This in-depth introduction to classical topics in higher algebra provides rigorous, detailed proofs for its explorations of some of mathematics' most significant concepts, including matrices, invariants, and...
This classic text is one of the most useful and practical expositions of Fourier's series, and spherical, cylindrical, and ellipsoidal harmonics. Includes 190 problems, approximately half with answers. 1893...
$ 51.99
This landmark dissertation (1961) provides a systematic introduction to systems of modal logic and stands as the first presentation of what have become central ideas in philosophy of language and metaphysics,...
$ 52.99
The key to good primary teaching of numeracy and mathematics is confidence in mathematical knowledge and its relevance to the real world. In particular, effective implementation of the National Numeracy Strategy...
$ 38.79
This text focuses on the basics of algebraic theory, giving detailed explanations of integral functions, permutations, and groups, and Lagrange and Galois theory. Many numerical examples with complete solutions....
$ 32.79
Elementary transformations and bilinear and quadratic forms; canonical reduction of equivalent matrices; subgroups of the group of equivalent transformations; and rational and classical canonical forms. 1952...
$ 36.29
More than 1,200 common series appear here. Collected, summed, and grouped for easy reference, they constitute an immensely useful handbook for mathematicians, physicists, computer technicians, engineers, and...
$ 36.29
On July 17, 2012, the centenary of Henri Poincaré's death was commemorated; his name being associated with so many fields of knowledge that he was considered as the Last Universalist. In Pure and Applied Mathematics,...
$ 60.29
The book Making Mathematics Practical (published by World Scientific in 2011) proposes a new paradigm in teaching problem solving in secondary school mathematics classrooms. It is a report of the research project...
$ 20.29
Ideal for self-instruction as well as for classroom use, this text improves understanding and problem-solving skills in analysis, analytic geometry, and higher algebra. Over 1,200 problems, with hints and complete...
$ 21.79
A problem-oriented text for evaluating statistical procedures through decision and game theory. First-year graduates in statistics, computer experts and others will find this highly respected work best introduction...
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Among other subjects explored are the Clements-Lindström extension of the Kruskal-Katona theorem to multisets and the Greene-Kleitmen result concerning k-saturated chain partitions of general partially ordered...
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Here is a clear, well-organized coverage of the most standard theorems, including isomorphism theorems, transformations and subgroups, direct sums, abelian groups, and more. This undergraduate-level text features...
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Geared toward students of mathematical programming, this user-friendly text offers a thorough introduction to the part of optimization theory that lies between approximation theory and mathematical programming....
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Mathematics for Economists
Browse related Subjects
Mathematics for Economists, a new text for advanced undergraduate and beginning graduate students in economics, is a thoroughly modern treatment of the mathematics that underlies economic theory.Mathematics for Economists, a new text for advanced undergraduate and beginning graduate students in economics, is a thoroughly modern treatment of the mathematics that underlies economic theory.Read Less
Very good. Hardcover. Has minor wear and/or markings. SKU: 97803939573343957334
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All Mathematic Titles
This book teaches readers how to solve mathematical problems in science and engineering with the aid of numerical methods and programming. It features an example-oriented approach with all examples accompanied by complete program codes.
Designed for an undergraduate course or for independent study, this textbook presents sophisticated mathematical ideas in an elementary and friendly fashion. It features techniques to solve proofs as well as exercises of varying difficulty.
Taking off from Euclid's famous assertion to the contrary, this book leads the reader on a clear path - a royal road - through the elements of modern algebraic geometry from algebraic curves to the present shape of the field to Grothendieck's theory of schemes.
The book is a primer of the theory of Ordinary Differential Equations. Each chapter is completed by a broad set of exercises; the reader will also find a set of solutions of selected exercises. The bo ...
This book starts with concrete topics and applications based on everyday experiences that naturally lead students to algebraic questions and concepts. The down-to-earth presentation is accessible to an audience with no previous knowledge of the subject.
With a fresh geometric approach that incorporates more than 250 illustrations, this textbook sets itself apart from all others in advanced calculus. Besides the classical capstones--the change of variables formula, implicit and inverse function theorems, the integral theorems of Gauss and Stokes--the text treats other important topics in differential analysis, such as Morse's lemma and the Poincaré lemma. The ideas behind most topics can be understood with just two or three variables. This is a textbook for undergraduates and graduate students in mathematics, the physical sciences, and economics. There is enough material for a year-long course on advanced calculus and for a variety of semester courses--including topics in geometry. The measured pace of the book, with its extensive examples and illustrations, make it especially suitable for independent study.
Presenting advanced concepts of digital imaging, this volume enables researchers to process and analyze color images and video with algorithms. Comprising of contributions from global leaders in the field, this reference offers up-to-date information on data processing of video and color images.
This book explains schemes in algebraic geometry from a beginner's level up to advanced topics such as smoothness and ample invertible sheaves. Includes examples and exercises that illustrate each section.
The technical difficulties of algebraic number theory often make this subject appear difficult to beginners. This undergraduate textbook provides a welcome solution to these problems as it provides an ...
This book offers a unified treatment of the various algebraic approaches of geometric spaces. It details the algebraic ingredients necessary to develop all the major aspects of the theory of algebraic curves.
This volume's historical focus, with fully worked solutions to all the famous problems in classical geometry, demonstrates the profound influence of axiomatic geometry, over more than three millennia, on the evolution of mathematics as an academic discipline.
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Summary: As in previous editions, the focus in ALGEBRA: INTRODUCTORY & INTERMEDIATE remains on the Aufmann Interactive Method (AIM). Users are encouraged to be active participants in the classroom and in their own studies as they work through the How To examples and the paired Examples and You Try It problems. The role of ''active participant'' is crucial to success. Presenting students with worked examples, and then providing them with the opportunity to immediately work similar problems, he...show morelps them build their confidence and eventually master the concepts1439046956 BRAND NEW! [ 5th U.S. Edition, Paperback / softback | ISBN: 9781439046951 | Same as picture shown ] SUPERFAST Delivery-sent out same day with notification of tracking number. Same book as s...show moreold by your college bookstore. Order Now! ...show less
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2010-02-16
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Introduction to graph theory
Browse related Subjects
...Read More introduction to the subject for non-mathematicians. The opening chapters provide a basic foundation course, containing definitions and examples, connectedness, Eulerian and Hamiltonian paths and cycles, and trees, with a range of applications. This is followed by two chapters on planar graphs and colouring, with special reference to the four-colour theorem. The next chapter deals with transversal theory and connectivity, with applications to network flows. A final chapter on matroid theory ties together material from earlier chapters, and an appendix discusses algorithms and their
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Find a Gladwyne MathIn algebra 2, students build upon the foundation of algebra 1, and become ready to tackle higher level of mathematical problems. topics as systems of equations, inequalities, and functions, exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matri...
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Apologies if this has been covered. Went back to college two years ago and im not as familiar with the general algebraic operations, rules of indices, etc that seem to be universal in maths courses. Im studying daly but it still doesnt come naturally and its slowing me down. How can I get up to speed so this is semi-second nature?
Thanks.
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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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A great many students have participated annually in the Annual High School Mathematics Examinations (AHSME) sponsored by the Mathematical Association of America (MAA) and four other national organizations in the mathematical sciences (Society of Actuaries, Mu Alpha Theta, the National Council of Teachers of Mathematics, and the Casualty Actuarial Society). In 1960, 150,000 students participated from about 5,200 high schools. In 1980, 416,000 students participated from over 6,800 high schools.
Since 1950, when the first of these examinations was given, American high school students have tested their skills and ingenuity on such problems as:
The rails on a railroad are 30 feet long. As the train passes over the point where the rails are joined, there is an audible click. The speed of the train in miles per hour is approximately the number of clicks heard in how many seconds?
Table of Contents
About the Author
Charles T. Salkind, for many years a teacher of mathematics at Brooklyn Polytechnic Institute, was one of the founders of the Annual High School Mathematics Examination which began in 1950 as an activity of the Metropolitan New York Section of the MAA. In 1957 the examination became a national competition sponsored by the MAA and the Society of Actuaries. Professor Salkind became the chairman of the MAA Committee on High School Contests in 1961 and served in that capacity until his death in 1968.
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This educational software allows students to manipulate the data in the models to see how changes can affect the entire system. Students can also explore mathematical concepts such as connectivity, ce... More: lessons, discussions, ratings, reviews,...
This set of problems is similar to the ones on pages 1 and 2, but this time, instead of looking for a particular structure within the graph, the question is whether or not the vertices (nodes) of the
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Practice solving linear equations with these fifty problems in elementary algebra. The student selects a single variable linear equation, solves for the variable, and checks the answer by viewing the step-by-step solution. Problems start with low difficulty and gradually increase to challenging. Most appropriate for 6th to 8th grade students.
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BasicBasic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole.
Key topics and features of Basic Algebra:
*Linear algebra and group theory build on each other continually
*Chapters on modern algebra treat groups, rings, fields, modules, and Galois groups, with emphasis on methods of computation throughout
*Three prominent themes recur and blend together at times: the analogy between integers and polynomials in one variable over a field, the interplay between linear algebra and group theory, and the relationship between number theory and geometry
*Many examples and hundreds of problems are included, along with a separate 90-page section giving hints or complete solutions for most of the problems
*The exposition proceeds from the particular to the general, often providing examples well before a theory that incorporates them; includes blocks of problems that introduce additional topics and applications for further study
*Applications to science and engineering (e.g., the fast Fourier transform, the theory of error-correcting codes, the use of the Jordan canonical form in solving linear systems of ordinary differential equations, and constructions of interest in mathematical physics) appear in sequences of problems
Basic Algebra presents the subject matter in a forward-looking way that takes into account its historical development. It is suitable as a text in a two-semester advanced undergraduate or first-year graduate sequence in algebra, possibly supplemented by some material from Advanced Algebra at the graduate level. It requires of the reader only familiarity with matrix algebra, an understanding of the geometry and reduction of linear equations, and an acquaintance with proofs.
Table of contents
Preliminaries about the Integers, Polynomials, and Matrices.- Vector Spaces over ?, ?, and ?.- Inner-Product Spaces.- Groups and Group Actions.- Theory of a Single Linear Transformation.- Multilinear Algebra.- Advanced Group Theory.- Commutative Rings and Their Modules.- Fields and Galois Theory.- Modules over Noncommutative Rings.
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Number central theme of this graduate-level number theory textbook is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers. This theme, in particular, is the central motivation for the modern theory of arithmetic algebraic geometry. In this text, this is considered through three aspects.
The first is the local aspect: one can do analysis in p-adic fields, and here the author starts by looking at solutions in finite fields, then proceeds to lift these solutions to local solutions using Hensel lifting. The second is the global aspect: the use of number fields, and in particular of class groups and unit groups. This classical subject is here illustrated through a wide range of examples. The third aspect deals with specific classes of equations, and in particular the general and Diophantine study of elliptic curves, including 2 and 3-descent and the Heegner point method. These subjects form the first two parts, forming Volume I.
The study of Bernoulli numbers, the gamma function, and zeta and L-functions, and of p-adic analogues is treated at length in the third part of the book, including many interesting and original applications.
Much more sophisticated techniques have been brought to bear on the subject of Diophantine equations, and for this reason, the author has included five chapters on these techniques forming the fourth part, which together with the third part forms Volume II. These chapters were written by Yann Bugeaud, Guillaume Hanrot, Maurice Mignotte, Sylvain Duquesne, Samir Siksek, and the author, and contain material on the use of Galois representations, points on higher-genus curves, the superfermat equation, Mihailescu's proof of Catalan's Conjecture, and applications of linear forms in logarithms.
The book contains 530 exercises of varying difficulty from immediate consequences of the main text to research problems, and contain many important additional results.
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About this course
This distance learning course provides the information you will need to prepare for the AQA A-Level in Maths with Statistics. In this home study course, you will focus on four core topics of algebra, geometry, trigonometry and calculus, which make up two-thirds of the A-Level qualification. The remaining third is focused on the study of statistics, including estimation, probability and distributions. The course is optimized for students studying at home and includes full tutor support via email.
A-Level Maths with Statistics is a valuable complement to other A-Level courses with a statistical element, such as biology, sociology or psychology, and for those wishing to study these subjects at a higher level. A-Level Maths with Statistics is also applicable to many jobs and careers and is a well-respected qualification that can be used for career progression and further training whilst in employment.
Entry requirements
English reading and writing skills, and maths to at least GCSE grade C or equivalent are required. You will need to have general skills and knowledge base associated with a GCSE course or equivalent standard.
This specification is designed to:
develop the student's understanding of mathematics and mathematical processes in a way that promotes confidence and fosters enjoyment
develop abilities to reason logically and to recognise incorrect reasoning, to generalise and to construct mathematical proofs
extend their range of mathematical skills and techniques and use them in more difficult unstructured problems
use mathematics as an effective means of communication
acquire the skills needed to use technology such as calculators and computers effectively, to recognise when such use may be inappropriate and to be aware of limitations
develop an awareness of the relevance of mathematics to other fields of study, to the world of work and to society in general
On this course you will study six units:
AS Level
Unit 1 MPC1 Core 1
Unit 2 MPC2 Core 2
Unit 3 MS1B Statistics 1B
A2 Level
Unit 4 MPC3 Core 3
Unit 5 MPC4 Core 4
Unit 6 MS2B Statistics 2
Each unit has 1 written paper of 1 hour 30 minutes.
Course Content
AS Level
Unit 1 MPC1 Core 1
Co-ordinate Geometry
Quadratic functions
Differentiation
Integration
Unit 2 MPC2 Core 2
Algebra and Functions
Sequences and Series
Trigonometry
Exponentials and logarithms
Differentiation
Integration
Unit 3 MS1B Statistics 1B
Statistical Measures
Probability
Discrete Random Variables
Normal Distribution
Estimation
A2 Level
Unit 4 MPC3 Core 3
Algebra and Functions
Trigonometry
Exponentials and Logarithms
Differentiation
Integration
Numerical Methods
Unit 5 MPC4 Core 4
Algebra and Functions
Coordinate Geometry in the (x, y) plane
Sequences and Series
Trigonometry
Exponentials and Logarithms
Differentiation and Integration
Vectors
Unit 6 MS2B Statistics 2
Poisson distribution
Continuous random variables
The t-distribution
Hypothesis Testing
Chi-squared tests
AS +A2 = A Level in Maths with Statistics. Both AS and A2 level courses and examinations must be successfully completed to gain a full A Level.
AQA Specification 6360
The course comes to you as a paper-based pack 24 months online distance learning course in A-Level Government and Politics offers a comprehensive guide through the AQA Government and Politics specification, allowing you to study for your A-Level at home using any kind of device. This fascinating and in-depth course covers many topics of contemporary relevance, including participation, political parties and pressure groups. In this course, you will study the governmental structures of both the UK and the USA, encouraging you to consider the connections and differences between political systems. This home studyonline course hopes to develop a critical understanding of political processes and the ability to evaluate political systems, allowing and encouraging students to become engaged in the political process as informed and active citizens. It is suitable for anyone who wants to gain a greater understanding of modern politics, as well as being an ideal complement to many other popular A-Levels, such as Economics and HistoryThis distance learning course in A-Level English Language and Literature is based on the AQA English Language and Literature A specification and treats English Language and Literature as a combined discipline. In this home study course, students will study four units. These are: Integrated Analysis and Text Production; Analysing Speech and Its Representation; Comparative Analysis and Text Adaptation; and Comparative Analysis through Independent Study. This course allows students to study non-fiction writing as part of their A-Level studies and to choose from a list of set texts in order to prepare individual coursework on a theme of their choice.
Prepared by expert tutors at UK Distance Learning and Publishing, this home study course is suitable for those with a general interest in English literature and language or for those who wish to progress to the study of English language and literature at university level. Interested students should already possess a GCSE in English, or an equivalent qualification
As green issues continue to gain in importance, now is the perfect time to learn more about the environment with this compelling home study course from UK Distance Learning & Publishing. Based on the AQA Environmental Studies A-Level specification, this distance learning course covers such key topics as: the living environment; the physical environment; energy resources and environmental pollution; and biological resources and sustainability.
This home study course is ideal for students wishing to study Environmental Studies at a higher level, or for those seeking careers in ecology, conservation or marine biology. It is also relevant to those studying for general interest. As we all become increasingly aware of the impact we have on the Earth, this distance learning A-Level course will help you to learn more about the fascinating issues involved in the preservation of our planet.
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What does quilting have to do with electric circuit theory? The answer is just one of the fascinating ways that best-selling popular math writer Paul Nahin illustrates the deep interplay of math and physics in the world around us in his latest book of challenging mathematical puzzles, Mrs. Perkins's Electric Quilt . With his trademark combination present title "Nanostructure and Nanoculture" has been compilated for under-graduate and post-graduate students of all Indian Universities. The focus of this book is the convergence of smart materials design and powerful new surface characterization techniques, which together are transforming the field of Heterogeneous catalysts-tool... more...
This title adopts the view that physics is the primary driving force behind a number of developments in mathematics. Previously, science and mathematics were part of natural philosophy and many mathematical theories arose as a result of trying to understand natural phenomena. This situation changed at the beginning of last century as science and mathematics...Vector analysis provides the language that is needed for a precise quantitative statement of the general laws and relationships governing such branches of physics as electromagnetism and fluid dynamics. more...
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Most college students are hesitant to take calculus because they consider it one of the most difficult subjects. However, those who take up engineering, chemistry, physics, and mathematics have to take this subject if they want to graduate from their course.
Just like any other subjects, there are some techniques that will help students cope easily with its demands. Here are some tips on how to learn calculus the easy way.
First, acquire basic knowledge and skills needed to understand the basic principles. For Calculus, a strong foundation in arithmetic is important. Master the four basic operations on whole numbers, fractions, and irrational numbers.
Second, study in advance by reading and understanding basic concepts and principles. Read the topics in your book and try solving some of the problems given. Some textbooks provide answer keys for some items. Trying to solve the items and checking your answer using the answer key is one way on how to learn calculus fast and easy. If your answer is different from the answer in your book, go over your computation again and discover where you have gone wrong. If you cannot find the right answer, you can ask for some explanations from your teacher when you have your class.
Third, pay close attention to the discussion and take down notes for future reference. Solving problems in calculus involves a step-by-step process and oftentimes, when you can follow the steps, you will have better chances of arriving at the correct answer. If a certain explanation is not clear to you always ask questions. Your teacher will appreciate you for asking rather than for pretending that you understand the lesson even if you don't.
Fourth, do your homework on the day it is assigned so that the principles and procedure of solving the problems are still fresh on your mind. Once you have already forgotten the steps, you will lose your interest to do your homework because you do not know how to do it. Not passing your assignment will surely affect your rating.
Fifth, always study long before a test is scheduled. Unlike other subjects, getting familiar with the procedure in solving problems in calculus is important if you want to learn and master calculus.
Last, practice, practice, and practice. Remember that the problems that you will encounter in calculus vary at all times. By spending time to practice, you will encounter different kinds of problem and you will know how to solve each. During the test, you will be able to answer the test surely and quickly. Consistent and persistent studying will bear good fruit as indicated by the improvement in your scores and marks in school.
How to learn calculus is not as daunting as many students claim. As long as you are persistent and consistent in studying and as long as you spend time daily to do some learning activities, you will be able to do well in calculus and be counted among the few students who find calculus easy and interesting.
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More About
This Textbook
Overview
Student Edition, Volume 1
Algebra: Concepts & Applications, is a comprehensive Algebra 1 program that is available in full and two-volume editions. Algebra: Concepts & Applications uses a clean lesson design with many detailed examples and straightforward narration that make Algebra 1 topics inviting and Algebra 1 content understandable.
Volume 1 contains Chapters 1-8 of Algebra: Concepts & Applications plus an initial section called Chapter A. Chapter A includes a pretest, lessons on prerequisite concepts, and a posttest.
Designed for students who are challenged by high school mathematics, the 2007 edition has many new features and support components.
Foldables are added to the beginning of the chapters for a unique way to enhance students study skills.
Concept Summaries highlight definitions, formulas, and other important ideas.
Homework Help with Extra Practice directs students to appropriate lesson examples to use as references for completing the exercises and to locate the appropriate additional practice pages.
Updated and new website links include: Self-Check Quizzes, Extra Examples, and Vocabulary Review
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2009Building upon the sequence of topics of the popular 5th Edition, Linear Algebra with Applications, Alternate Seventh Edition provides instructors with an alternative presentation of course material. In this edition earlier chapters cover systems of linear equations, matrices, and determinates. The vector space Rn is introduced in chapter 4, leading directly into general vector spaces and linear transformations. This order of topics is ideal for those preparing to use linear equations and matrices in their own fields. New exercises and modern, real-world applications allow students to test themselves on relevant key material and a MATLAB manual, included as an appendix, provides 29 sections of
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31Elementary and Intermediate Algebra
Elementary and Intermediate Algebra
Outlines and Highlights for Elementary and Intermediate Algebra by Gustafson, R David and Tussy, Alan S , Isbn : 9780495188742
Summary
Become fluent in "the language of algebra" with ELEMENTARY AND INTERMEDIATE ALGEBRA, Third Edition. This textbook will improve your ability to read, write, and communicate mathematical ideas. Tussy and Gustafson make learning easy with their five-step problem-solving approach: analyze the problem, form an equation, solve the equation, state the result, and check the solution. This edition also includes iLrn Testing and Tutorial; Personal Tutor with SMARTHINKING live online tutoring; the Interactive Video Skillbuilder CD-ROM with MathCue; a Book Companion Web Site featuring online graphing calculator resources; and The Learning Equation, powered by iLrn.
Table of Contents
An Introduction to Algebra
The Language of Algebra
Fractions
The Real Numbers
Adding Real Numbers
Subtracting Real Numbers
Multiplying and Dividing Real Numbers
Exponents and Order of Operations
Algebraic Expressions
Accent on Teamwork
Key Concept
Chapter Review
Chapter Test
Equations, Inequalities, and Problem Solving
Solving Equations
Problem Solving
Simplifying Algebraic Expressions
More about Solving Equations
Formulas
More about Problem Solving
Solving Inequalities
Accent on Teamwork
Key Concept
Chapter Review
Chapter Test
Cumulative Review Exercises
Linear Equations and Inequalities in two Variables
Graphing Using the Rectangular Coordinate System
Graphing Linear Equations
More about Graphing Linear Equations
The Slope of a Line
Slope?
Intercept Form
Point?
Slope Form
Graphing Linear Inequalities
Accent on Teamwork
Key Concept
Chapter Review
Chapter Test
Exponents and Polynomials
Rules for Exponents
Zero and Negative Exponents
Scientific Notation
Polynomials
Adding and Subtracting Polynomials
Multiplying Polynomials
Special Products
Division of Polynomials
Accent on Teamwork
Key Concept
Chapter Review
Chapter Test
Cumulative Review Exercises
Factoring and Quadratic Equations
The Greatest Common Factor
Factoring by Grouping
Factoring Trinomials of the Form x^2+bx+c
Factoring Trinomials of the form ax^2+bx+c
Factoring Perfect Square Trinomials and the Differences of Two Squares
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NOOK for PC
NOOK for Mac
NOOK for Web
More About
This Book
Overview
This is the perfect introduction for those who have a lingering fear of math. If you think that math is difficult, confusing, dull or just plain scary, then The Math Handbook is your ideal companion.
Covering all the basics including fractions, equations, primes, squares and square roots, geometry and fractals, Dr. Richard Elwes will lead you gently towards a greater understanding of this fascinating subject. Even apparently daunting concepts are explained simply, with the assistance of useful diagrams, and with a refreshing lack of jargon.
So whether you're an adult or a student, whether you like Sudoku but hate doing sums, or whether you've always been daunted by numbers at work, school or in everyday life, you won't find a better way of overcoming your nervousness about numbers and learning to enjoy making the most of mathematics.
Related Subjects
Meet the Author
Dr. Richard Elwes is a writer, teacher and researcher in Mathematics and a visiting fellow at the University of Leeds. He contributes to New Scientist and Plus Magazine and publishes research on model theory. Dr. Elwes is a committed popularizer of mathematics which he regularly promotes at public lectures and on
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More options
Contributors
Contents/Summary
Mathematical Problem Solving-- Scheme of Work and Assessment of the Mathematics Practical-- Detailed Lesson Plans-- Scaffolding Suggestions, Solutions to the Problems and Assessment Notes.
(source: Nielsen Book Data)
Publisher's Summary
This book is the first of its kind, as it includes both mathematics content and pedagogy. It is a professional instructional manual on how mathematical problem solving curriculum can be implemented in the classrooms. The book develops from the theoretical work of Polya and Schoenfeld, and explicates how these can be translated to the actual implementation in schools. It represents the work of a group of researchers from the Singapore National Institute of Education, after experimenting with it in the Singapore school classrooms. This book includes a set of scheme of work, lesson plans and a choice of mathematics problems that teachers can actually use in teaching problem solving. Certain pedagogical considerations are developed and suggested in this book. In addition, the book includes an assessment framework on how mathematical problem solving can be assessed. (source: Nielsen Book Data)
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This book will quickly, efficiently--and above all, effectively--help you prepare to succeed on the AP Calculus exam. Right from the start, the text helps you identify the course topics you most need practice on, allowing you to focus your study efforts on areas in need of improvement while also reviewing your general calculus knowledge. PREPARING... more...
Project management is becoming a key requirement for the modern manager.
The aim of this book is to provide a readable and practical introduction to the
subject, including what a project is; how a project can be chosen, planned,
organized, and managed; how to create and manage a project team; how to manage
the financial aspects of a project; and... more...
Take it step-by-step for pre-calculus success!
The quickest route to learning a subject is through a solid grounding in the basics. So what you won?t find in Easy Pre-calculus Step-by-Step is a lot of endless drills. Instead, you get a clear explanation that breaks down complex concepts into easy-to-understand steps, followed by highly focused... more...
Each year, hundreds of thousands of people who did not finish high school study to take the battery of GED examinations. A GED diploma opens up a new level of career, education, and compensation opportunities for them. This crash course helps them get up to speed quickly on the five major subject areas they will be tested on, and gives them test-taking... more...
Level B: Grades 3-4 Children of the elementary school age think differently than do older children, adolescents, or adults. They are more holistic in their interaction with the world. The hm Program presents study skills appropriate for young children, teaching them to listen, observe, and visualize with greater awareness. Each student workbook teaches... more...
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Course Communities
So far, we have identified resources for one-variable calculus, multivariable calculus, a first course in ordinary differential equations, and a probability course, as well as for a pseudocourse containing resources for developmental mathematics.
Check out and rate the resources, make comments, start discussions, and recommend additional resources.
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Intermediate Algebra
Browse related Subjects
...Read More are carefully coordinated to ensure that students are better able to make connections between mathematical concepts and understand the content. The new Student Support Edition continues the Larson tradition of guided learning by incorporating a comprehensive range of student success materials throughout the text. Additionally, instructors and students alike can track progress with HM Assess, a new online diagnostic assessment and remediation tool from Houghton Mifflin
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Synopsis
Getting into the nation's most competitive universities requires more than a good SAT score, it requires a perfect score. Perfect 800: SAT Math gives advanced students the tools needed to master the SAT math test.
Covering areas including arithmetic concepts; algebra; geometry; and additional topics such as probability and weighted average, the book offers exposure to a wide range of degrees of difficulty in a holistic approach that allows students to experience the "real thing," including the impact of time constraints on their performance. By emphasizing critical thinking and analytic skills over memorization and trial and error, this book ensures optimal usage of time and maximizes the pace of progress as students prepare for the all-important test. This book includes access to an online simulated test and an in-depth analysis tool that provides students with an assessment of their results and a list of recommendations for an improved performance. This unique book is a great companion to Perfect 800: SAT Verbal.
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More About
This Textbook
Overview
The invention of ideals by Dedekind in the 1870s was well ahead of its time, and proved to be the genesis of what today we would call algebraic number theory. His memoir "Sur la Theorie des Nombres Entiers Algebriques" first appeared in installments in the Bulletin des sciences mathematiques in 1877. This book is a translation of that work by John Stillwell, who adds a detailed introduction giving historical background and who outlines the mathematical obstructions that Dedekind was striving to overcome. Dedekind's memoir offers a candid account of the development of an elegant theory and provides blow by blow comments regarding the many difficulties encountered en route. This book is a must for all number theorists.
Editorial Reviews
From the Publisher
"The book has historical interest in providing a very clear glimpse of the origins of modern algebra and algebraic number theory, but it also has considerable mathematical interest. It is truly astonishing that a text written one hundred and twenty years ago, well before modern algebraic terminology and concepts were introduced and accepted, can provide a plausible introduction to algebraic number theory for a student today." Mathematical Reviews Clippings 98h
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Galileo, Gauss, and the Green Monster Dan Kalman and Daniel J. Teague Using ideas of Galileo and Gauss but avoiding calculus, students create a model that predicts whether a fly ball will clear the famous left-field wall at Fenway Park.
Geometric Reasoning about a Circle Problem- FREE PREVIEW! Gloriana González and Anna F. DeJarnette An open-ended problem about a circle illustrates how problem-based instruction can enable students to develop reasoning and sense-making skills.
Building Sinusoids Mara G. Landers A measurement-based activity can help students struggling to understand trigonometric functions.
Examples of worksheets and student solutions for Building Sinusoids
Students as Mathematics Consultants Jennifer L. Jensen Five problems—relating to gas mileage, the national debt, store sales, shipping costs, and fish population—require students to use functions to connect mathematics to the real world.
Tangent Lines without Calculus A problem that can help high school students develop the concept of instantaneous velocity and connect it with the slope of a tangent line to the graph of position versus time. It also gives a method for determining the tangent line to the graph of a polynomial function at any point without using calculus. It encourages problem solving and multiple solutions.
Creating and Exploring Simple Models Students manipulate data algebraically and statistically to
create models applied to a falling ball. They also borrow tools from arithmetic
progressions to examine the relationship between the velocity and the distance
the ball falls. A supplemental option is to use a Computer Based Laboratory
(CBL) for this activity. Students use graphing calculators to manipulate the
sequences (in the statistics editor). Students can plot their data and
superimpose their model on the calculator.
Illuminations Lesson: Varying Motion This lesson helps students clarify the relationship between
the shape of a graph and the movement of an object. Students explore their own
movement and plot it onto a displacement-vs.-time graph. From this original
graph, students create a velocity-vs.-time graph, and from there create an
acceleration-vs.-time graph. The movement and how to interpret each type
of graph are emphasized through the lesson, which serves as an excellent
introduction to building blocks of calculus.
Move the boat around the water by changing the magnitude and
direction of the boat's speed (blue vector) or the magnitude and direction of
the water current (red vector). Try to land the boat on the island — but be
careful not to hit the walls!
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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Trigonometry - 6th edition
Summary: This easy-to-understand trigonometry text makes learning trigonometry an engaging, simple process. The book contains many examples that parallel most problems in the problem sets. There are many application problems that show how the concepts can be applied to the world around you, and review problems in every problem set after Chapter 1, which make review part of your daily schedule. If you have been away from mathematics for awhile, study skills listed at the beginning of the first...show more six chapters give you a path to success in the course. Finally, the authors have included some historical notes in case you are interested in the story behind the mathematics you are learning. This text will leave you with a well-rounded understanding of the subject and help you feel better prepared for future mathematics54112.77 +$3.99 s/h
Good
HPB-Wisconsin Wauwatosa, WI
2007131.97 +$3.99 s/h
Good
Goodwill Indust. of San Diego San DIego, CA
2007 Hardcover Good
$133.56 +$3.99 s/h
Good
HPB-Dallas Dallas, TX
2007 Hardcover Good 005149.50150.36 +$3.99 s/h
Good
HPB-California Concord, CA
2007 Hardcover Good 6158.97 +$3.99 s/h
Good
Last Page Books-Dallas218
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More About
This Textbook
Overview
This spectacularly clear introduction to abstract algebra is is designed to make the study of all required topics and the reading and writing of proofs both accessible and enjoyable for readers encountering the subject for the first time. Number Theory. Groups. Commutative Rings. Modules. Algebras. Principal Idea Domains. Group Theory II. Polynomials In Several Variables. For anyone interested in learning abstract algebra.
Editorial Reviews
Booknews
The new edition of a textbook that introduces three related topics: number theory (division algorithm, unique factorization into primes, and congruences), group theory (permutations, Lagrange's theory, homomorphisms, and quotient groups), and commutative ring theory (domains, fields, polynomial and quotient rings, and finite fields). A final chapter combines the three topics to solve such problems as angle trisection, squaring the circle, and the construction of regular -gons. Annotation c. Book News, Inc., Portland, OR (booknews.com)
Related Subjects
Read an Excerpt but thePrefacebut the
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Synopsis
Helpful for college, high school, and homeschooled students, this book is for those who struggle with math in science. Scientific notation, algebra, geometry, trigonometry, and vector concepts are addressed as used in the sciences, with examples and exercises. Readers will gain proficiency with using math as the language of science.
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