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Everything you need to pass the exam and get the college credit you deserve.

CLEP* is the most popular credit-by-examination program in the country, accepted by more than 2,900 colleges and universities. For over 15 years, REA has helped students pass the CLEP* exam and earn college credit while reducing their tuition costs.

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Two full-length practice exams

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This well-known and highly regarded text makes the subject accessible to undergraduates with little mathematical experience. Written mainly for students in physics, engineering, economics, and other fields outside mathematics, the book gives the theory of matrices and applications to systems of linear equations, as well as many related topics such as determinants, eigenvalues, and differential equations.

Table of Contents:

l. The Algebra of Matrices

2. Linear Equations

3. Vector Spaces

4. Determinants

5. Linear Transformations

6. Eigenvalues and Eigenvectors

7. Inner Product Spaces

8. Applications to Differential Equations

For the second edition, the authors added several exercises in each chapter and a brand new section in Chapter 7. The exercises, which are both true-false and multiple-choice, will enable the student to test his grasp of the definitions and theorems in the chapter. The new section in Chapter 7 illustrates the geometric content of Sylvester's Theorem by means of conic sections and quadric surfaces. 6 line drawings. lndex. Two prefaces. Answer section.

The third edition contains major improvements and revisions throughout the book. More than 300 new exercises have been added since the previous edition. Many new examples have been added to illustrate the key ideas of linear algebra. New topics covered in the book include product spaces, quotient spaces, and dual spaces. Beautiful new formatting creates pages with an unusually pleasant appearance in both print and electronic versions.

No prerequisites are assumed other than the usual demand for suitable mathematical maturity. Thus the text starts by discussing vector spaces, linear independence, span, basis, and dimension. The book then deals with linear maps, eigenvalues, and eigenvectors. Inner-product spaces are introduced, leading to the finite-dimensional spectral theorem and its consequences. Generalized eigenvectors are then used to provide insight into the structure of a linear operator.

After a brief overview, the approach begins with elementary toposes and advances to internal category theory, topologies and sheaves, geometric morphisms, and logical aspects of topos theory. Additional topics include natural number objects, theorems of Deligne and Barr, cohomology, and set theory. Each chapter concludes with a series of exercises, and an appendix and indexes supplement the text.

". . .recommended for the teacher and researcher as well as for graduate students. In fact, [it] has a place on every mathematician's bookshelf." -American Mathematical Monthly

Linear Algebra and Its Applications, Second Edition presents linear algebra as the theory and practice of linear spaces and linear maps with a unique focus on the analytical aspects as well as the numerous applications of the subject. In addition to thorough coverage of linear equations, matrices, vector spaces, game theory, and numerical analysis, the Second Edition features student-friendly additions that enhance the book's accessibility, including expanded topical coverage in the early chapters, additional exercises, and solutions to selected problems.

Beginning chapters are devoted to the abstract structure of finite dimensional vector spaces, and subsequent chapters address convexity and the duality theorem as well as describe the basics of normed linear spaces and linear maps between normed spaces.

Further updates and revisions have been included to reflect the most up-to-date coverage of the topic, including: The QR algorithm for finding the eigenvalues of a self-adjoint matrix

The Householder algorithm for turning self-adjoint matrices into tridiagonal form The compactness of the unit ball as a criterion of finite dimensionality of a normed linear space Additionally, eight new appendices have been added and cover topics such as: the Fast Fourier Transform; the spectral radius theorem; the Lorentz group; the compactness criterion for finite dimensionality; the characterization of commentators; proof of Liapunov's stability criterion; the construction of the Jordan Canonical form of matrices; and Carl Pearcy's elegant proof of Halmos' conjecture about the numerical range of matrices.

Clear, concise, and superbly organized, Linear Algebra and Its Applications, Second Edition serves as an excellent text for advanced undergraduate- and graduate-level courses in linear algebra. Its comprehensive treatment of the subject also makes it an ideal reference or self-study for industry professionals.

Alpha Teach Yourself Algebra I in 24 Hours provides readers with a structured, self-paced, straight-forward tutorial on algebra. It's the perfect textbook companion for students struggling with algebra, a solid primer for those looking to get a head start on an upcoming class, and a welcome refresher for parents tasked with helping out with homework. The book provides 24 one-hour lessons, with each chapter designed to build on the previous one.

? Covers classifying number sets, expressions, polynomials, factoring, radicals, exponents and logarithms, and much more

? Each chapter ends with a quiz so readers can identify where they may need more help

"The author has an impressive knack for presenting the important and interesting ideas of algebra in just the right way, and he never gets bogged down in the dry formalism which pervades some parts of algebra." MATHEMATICAL REVIEWS

This book is intended as a basic text for a one-year course in algebra at the graduate level, or as a useful reference for mathematicians and professionals who use higher-level algebra. It successfully addresses the basic concepts of algebra. For the revised third edition, the author has added exercises and made numerous corrections to the text.

The focus throughout is rooted in the mathematical fundamentals, but the text also investigates a number of interesting applications, including a section on computer graphics, a chapter on numerical methods, and many exercises and examples using MATLAB. Meanwhile, many visuals and problems (a complete solutions manual is available to instructors) are included to enhance and reinforce understanding throughout the book.

Brief yet precise and rigorous, this work is an ideal choice for a one-semester course in linear algebra targeted primarily at math or physics majors. It is a valuable tool for any professor who teaches the subject.

Georgi E. Shilov, Professor of Mathematics at the Moscow State University, covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and unitary spaces, finite-dimensional algebras and their representations, with an appendix on categories of finite-dimensional spaces.

The author begins with elementary material and goes easily into the advanced areas, covering all the standard topics of an advanced undergraduate or beginning graduate course. The material is presented in a consistently clear style. Problems are included, with a full section of hints and answers in the back.

Keeping in mind the unity of algebra, geometry and analysis in his approach, and writing practically for the student who needs to learn techniques, Professor Shilov has produced one of the best expositions on the subject. Because it contains an abundance of problems and examples, the book will be useful for self-study as well as for the classroom.

Written by two pioneers of the concept of math anxiety and how to overcome it, Arithmetic and Algebra Again has helped tens of thousands of people conquer their irrational fear of math.

This revised and expanded second edition of the perennial bestseller:

Features the latest techniques for breaking through common anxieties about numbers Takes a real-world approach that lets mathphobes learn the math they need as they need it Covers all key math areas--from whole numbers and fractions to basic algebra Features a section on practical math for banking, mortgages, interest, and statistics and probability Includes a new section on the graphing calculator, a chapter on the metric system, a section on word problems, and all updated exercisesmethods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and

methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.

As a result, the book represents a blend of new methods in general computational analysis,

and specific, but also generic, techniques for study of systems theory ant its particular

branches, such as optimal filtering and information compression.

- Best operator approximation,

- Non-Lagrange interpolation,

- Generic Karhunen-Loeve transform

- Generalised low-rank matrix approximation

- Optimal data compression

- Optimal nonlinear filtering

“This volume is ground-breaking in terms of mathematical texts in that it does not teach from a detached perspective, but instead, looks to show students that competent mathematicians bring an intuitive understanding to the subject rather than just a master of applications.”

– Electric Review

A comprehensive introduction, Linear Algebra: Ideas and Applications, Fourth Edition provides a discussion of the theory and applications of linear algebra that blends abstract and computational concepts. With a focus on the development of mathematical intuition, the book emphasizes the need to understand both the applications of a particular technique and the mathematical ideas underlying the technique.

The book introduces each new concept in the context of an explicit numerical example, which allows the abstract concepts to grow organically out of the necessity to solve specific problems. The intuitive discussions are consistently followed by rigorous statements of results and proofs.

Linear Algebra: Ideas and Applications, Fourth Edition also features:

Two new and independent sections on the rapidly developing subject of wavelets A thoroughly updated section on electrical circuit theory Illuminating applications of linear algebra with self-study questions for additional study End-of-chapter summaries and sections with true-false questions to aid readers with further comprehension of the presented material Numerous computer exercises throughout using MATLAB® codeLinear Algebra: Ideas and Applications, Fourth Edition is an excellent undergraduate-level textbook for one or two semester courses for students majoring in mathematics, science, computer science, and engineering. With an emphasis on intuition development, the book is also an ideal self-study reference.

Part I begins with linear algebraic foundations, follows with the modern component-free definition of tensors, and concludes with applications to physics through the use of tensor products. Part II introduces group theory, including abstract groups and Lie groups and their associated Lie algebras, then intertwines this material with that of Part I by introducing representation theory. Examples and exercises are provided in each chapter for good practice in applying the presented material and techniques.

Prerequisites for this text include the standard lower-division mathematics and physics courses, though extensive references are provided for the motivated student who has not yet had these. Advanced undergraduate and beginning graduate students in physics and applied mathematics will find this textbook to be a clear, concise, and engaging introduction to tensors and groups.

Reviews of the First Edition

“[P]hysicist Nadir Jeevanjee has produced a masterly book that will help other physicists understand those subjects [tensors and groups] as mathematicians understand them... From the first pages, Jeevanjee shows amazing skill in finding fresh, compelling words to bring forward the insight that animates the modern mathematical view...[W]ith compelling force and clarity, he provides many carefully worked-out examples and well-chosen specific problems... Jeevanjee’s clear and forceful writing presents familiar cases with a freshness that will draw in and reassure even a fearful student. [This] is a masterpiece of exposition and explanation that would win credit for even a seasoned author.”

—Physics Today

"Jeevanjee’s [text] is a valuable piece of work on several counts, including its express pedagogical service rendered to fledgling physicists and the fact that it does indeed give pure mathematicians a way to come to terms with what physicists are saying with the same words we use, but with an ostensibly different meaning. The book is very easy to read, very user-friendly, full of examples...and exercises, and will do the job the author wants it to do with style.”

—MAA Reviews

This revised and enlarged third edition reflects the latest developements in the field and convey a greater experience with results previously formulated. For example, the theory of skew-orthogoanl and bi-orthogonal polynomials, parallel to that of the widely known and used orthogonal polynomials, is explained here for the first time.

Presentation of many new results in one place for the first time.First time coverage of skew-orthogonal and bi-orthogonal polynomials and their use in the evaluation of some multiple integrals. Fredholm determinants and Painlevé equations.The three Gaussian ensembles (unitary, orthogonal, and symplectic); their n-point correlations, spacing probabilities.Fredholm determinants and inverse scattering theory.Probability densities of random determinants.This popular study guide shows students easy ways to solve what they struggle with most in algebra: word problems. How to Solve Word Problems in Algebra, Second Edition, is ideal for anyone who wants to master these skills. Completely updated, with contemporary language and examples, features solution methods that are easy to learn and remember, plus a self-test.

As part of a collection, the book differs from other publications in this field by not being a mere selection of questions or a set of tips and tricks that applies to specific problems. It starts from the most basic theoretical principles, without being either too general or too axiomatic. Examples and problems are discussed only if they are helpful as applications of the theory. Propositions are proved in detail and subsequently applied to Olympic problems or to other problems at the Olympic level.

The book also explores some of the hardest problems presented at National and International Mathematics Olympiads, as well as many essential theorems related to the content. An extensive Appendix offering hints on or full solutions for all difficult problems rounds out the book.

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.

Practice makes perfect—and helps deepen your understanding of algebra by solving problems

1,001 Algebra I Practice Problems For Dummies, with free access to online practice problems, takes you beyond the instruction and guidance offered in Algebra I For Dummies, giving you 1,001 opportunities to practice solving problems from the major topics in algebra. You start with some basic operations, move on to algebraic properties, polynomials, and quadratic equations, and finish up with graphing. Every practice question includes not only a solution but a step-by-step explanation. From the book, go online and find:

One year free subscription to all 1,001 practice problems On-the-go access any way you want it—from your computer, smart phone, or tablet Multiple choice questions on all you math course topics Personalized reports that track your progress and help show you where you need to study the most Customized practice sets for self-directed study Practice problems categorized as easy, medium, or hardWhether you're studying algebra at the high school or college level, the practice problems in 1,001 Algebra I Practice Problems For Dummies give you a chance to practice and reinforce the skill s you learn in the classroom and help you refine your understanding of algebra.

Note to readers: 1,001 Algebra I Practice Problems For Dummies, which only includes problems to solve, is a great companion to Algebra I For Dummies, 2nd Edition which offers complete instruction on all topics in a typical Algebra I course.

Linear Sentences in One Variable

Segments, Lines, and Inequalities

Linear Sentences in Two Variables

Linear Equations in Three Variables

Polynomial Arithmetic

Factoring Polynomials

Rational Expressions

Relations and Functions

Polynomial Functions

Radicals and Complex Numbers

Quadratics in One Variable

Conic Sections

Quadratic Systems

Exponential and Logarithmic Functions

Sequences and Series

Additional Topics

Word Problems

Review Questions

Resource Center

Glossary

Fortunately, there's Schaum's. This all-in-one-package includes more than 1,900 fully solved problems, examples, and practice exercises to sharpen your problem-solving skills. Plus, you will have access to 30 detailed videos featuring Math instructors who explain how to solve the most commonly tested problems--it's just like having your own virtual tutor! You'll find everything you need to build confidence, skills, and knowledge for the highest score possible.

More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. Helpful tables and illustrations increase your understanding of the subject at hand.

This Schaum's Outline gives you

1,940 fully solved problems Hundreds of additional practice problems with answers Coverage of all course conceptsFully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time--and get your best test scores!

Schaum's Outlines--Problem Solved.

Ready to learn math fundamentals but can't seem to get your brain to function? No problem! Add Pre-Algebra Demystified, Second Edition, to the equation and you'll solve your dilemma in no time.

Written in a step-by-step format, this practical guide begins by covering whole numbers, integers, fractions, decimals, and percents. You'll move on to expressions, equations, measurement, and graphing. Operations with monomials and polynomials are also discussed. Detailed examples, concise explanations, and worked problems make it easy to understand the material, and end-of-chapter quizzes and a final exam help reinforce learning.

It's a no-brainer! You'll learn:

Addition, subtraction, multiplication, and division of whole numbers, integers, fractions, decimals, and algebraic expressions Techniques for solving equations and problems Measures of length, weight, capacity, and time Methods for plotting points and graphing linesSimple enough for a beginner, but challenging enough for an advanced student, Pre-Algebra Demystified, Second Edition, helps you master this essential mathematics subject. It's also the perfect way to review the topic if all you need is a quick refresh.

"This is a classic but still useful introduction to modern linear algebra. It is primarily about linear transformations … It's also extremely well-written and logical, with short and elegant proofs. … The exercises are very good, and are a mixture of proof questions and concrete examples. The book ends with a few applications to analysis … and a brief summary of what is needed to extend this theory to Hilbert spaces." — Allen Stenger, MAA Reviews, maa.org, May, 2016.

"The theory is systematically developed by the axiomatic method that has, since von Neumann, dominated the general approach to linear functional analysis and that achieves here a high degree of lucidity and clarity. The presentation is never awkward or dry, as it sometimes is in other 'modern' textbooks; it is as unconventional as one has come to expect from the author. The book contains about 350 well-placed and instructive problems, which cover a considerable part of the subject. All in all this is an excellent work, of equally high value for both student and teacher." — Zentralblatt für Mathematik.

The author presents the first extended treatment of MM algorithms, which are ideal for high-dimensional optimization problems in data mining, imaging, and genomics; derives numerous algorithms from a broad diversity of application areas, with a particular emphasis on statistics, biology, and data mining; and summarizes a large amount of literature that has not reached book form before.

In this charming volume, a noted English mathematician uses humor and anecdote to illuminate the concepts underlying "new math": groups, sets, subsets, topology, Boolean algebra, and more. According to Professor Stewart, an understanding of these concepts offers the best route to grasping the true nature of mathematics, in particular the power, beauty, and utility of pure mathematics. No advanced mathematical background is needed (a smattering of algebra, geometry, and trigonometry is helpful) to follow the author's lucid and thought-provoking discussions of such topics as functions, symmetry, axiomatics, counting, topology, hyperspace, linear algebra, real analysis, probability, computers, applications of modern mathematics, and much more.

By the time readers have finished this book, they'll have a much clearer grasp of how modern mathematicians look at figures, functions, and formulas and how a firm grasp of the ideas underlying "new math" leads toward a genuine comprehension of the nature of mathematics itself.

Practice Makes Perfect: Algebra II presents thorough coverage of skills, such as handling decimals and fractions, functions, and linear and quadratic equations, as well as an introducing you to probability and trigonometry. Inside you will find the help you need for boosting your skills, preparing for an exam or re-introducing yourself to the subject. More than 500 exercises and answers covering all aspects of algebra will get you on your way to mastering algebra!

Algebra II builds on your Algebra I skills to prepare you for trigonometry, calculus, and a of myriad STEM topics. Working through practice problems helps students better ingest and retain lesson content, creating a solid foundation to build on for future success.

Algebra II Workbook For Dummies, 2nd Edition helps you learn Algebra II by doing Algebra II. Author and math professor Mary Jane Sterling walks you through the entire course, showing you how to approach and solve the problems you encounter in class. You'll begin by refreshing your Algebra I skills, because you'll need a strong foundation to build upon. From there, you'll work through practice problems to clarify concepts and improve understanding and retention.

Revisit quadratic equations, inequalities, radicals, and basic graphs Master quadratic, exponential, and logarithmic functions Tackle conic sections, as well as linear and nonlinear systems Grasp the concepts of matrices, sequences, and imaginary numbersAlgebra II Workbook For Dummies, 2nd Edition includes sections on graphing and special sequences to familiarize you with the key concepts that will follow you to trigonometry and beyond. Don't waste any time getting started. Algebra II Workbook For Dummies, 2nd Edition is your complete guide to success.

Along the way, you'll go beyond solving hundreds of repetitive problems, and actually use what you learn to make real-life decisions. Does it make sense to buy two years of insurance on a car that depreciates as soon as you drive it off the lot? Can you really afford an XBox 360 and a new iPhone? Learn how to put algebra to work for you, and nail your class exams along the way.

Your time is way too valuable to waste struggling with new concepts. Using the latest research in cognitive science and learning theory to craft a multi-sensory learning experience, Head First Algebra uses a visually rich format specifically designed to take advantage of the way your brain really works.

"The main object of this book is to dispel the fear of mathematics," declares author W. W. Sawyer, adding that "Many people regard mathematicians as a race apart, possessed of almost supernatural powers. While this is very flattering for successful mathematicians, it is very bad for those who, for one reason or another, are attempting to learn the subject." Now retired, Sawyer won international renown for his innovative teaching methods, which he used at colleges in England and Scotland as well as Africa, New Zealand, and North America. His insights into the pleasures and practicalities of mathematics will appeal to readers of all backgrounds.

Key features:

* Introductory chapters present the main ideas and topics in graph theory—walks, paths and cycles, radius, diameter, eccentricity, cuts and connectivity, trees

* Subsequent chapters examine specialized topics and applications

* Numerous examples and illustrations

* Comprehensive index and bibliography, with suggested literature for more advanced material

New to the second edition:

* New chapters on labeling and communications networks and small-worlds

* Expanded beginner’s material in the early chapters, including more examples, exercises, hints and solutions to key problems

* Many additional changes, improvements, and corrections throughout resulting from classroom use and feedback

Striking a balance between a theoretical and practical approach with a distinctly applied flavor, this gentle introduction to graph theory consists of carefully chosen topics to develop graph-theoretic reasoning for a mixed audience. Familiarity with the basic concepts of set theory, along with some background in matrices and algebra, and a little mathematical maturity are the only prerequisites.

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From a review of the first edition:

"Altogether the book gives a comprehensive introduction to graphs, their theory and their application...The use of the text is optimized when the exercises are solved. The obtained skills improve understanding of graph theory as well... It is very useful that the solutions of these exercises are collected in an appendix."

—Simulation News Europe

Tips for simplifying tricky basic math and pre-algebra operations

Whether you're a student preparing to take algebra or a parent who wants or needs to brush up on basic math, this fun, friendly guide has the tools you need to get in gear. From positive, negative, and whole numbers to fractions, decimals, and percents, you'll build necessary math skills to tackle more advanced topics, such as imaginary numbers, variables, and algebraic equations.

Explanations and practical examples that mirror today's teaching methods Relevant cultural vernacular and references Standard For Dummiesmaterials that match the current standard and designBasic Math & Pre-Algebra For Dummies takes the intimidation out of tricky operations and helps you get ready for algebra!

Basic Math & Pre-Algebra Workbook For Dummies is your ticket to finally getting a handle on math! Designed to help you strengthen your weak spots and pinpoint problem areas, this book provides hundreds of practice problems to help you get over the hump. Each section includes a brief review of key concepts and full explanations for every practice problem, so you'll always know exactly where you went wrong. The companion website gives you access to quizzes for each chapter, so you can test your understanding and identify your sticking points before moving on to the next topic. You'll brush up on the rules of basic operations, and then learn what to do when the numbers just won't behave—negative numbers, inequalities, algebraic expressions, scientific notation, and other tricky situations will become second nature as you refresh what you know and learn what you missed.

Each math class you take builds on the ones that came before; if you got lost somewhere around fractions, you'll have a difficult time keeping up in Algebra, Geometry, Trigonometry, and Calculus—so don't fall behind! This book provides plenty of practice and patient guidance to help you slay the math monster once and for all. Make sense of fractions, decimals, and percentages Learn how to handle inequalities, exponents, square roots, and absolute values Simplify expressions and solve simple algebraic equations Find your way around a triangle, circle, trapezoid, and more

Once you get comfortable with the rules and operations, math takes on a whole new dimension. Curiosity replaces anxiety, and problems start feeling like puzzles rather than hurdles. All it takes is practice. Basic Math & Pre-Algebra Workbook For Dummies is your ultimate math coach, with hundreds of guided practice practice problems to help you break through the math barrier.

Your hands-on guide to real-world applications of linear algebra

Does linear algebra leave you feeling lost? No worries —this easy-to-follow guide explains the how and the why of solving linear algebra problems in plain English. From matrices to vector spaces to linear transformations, you'll understand the key concepts and see how they relate to everything from genetics to nutrition to spotted owl extinction. Line up the basics — discover several different approaches to organizing numbers and equations, and solve systems of equations algebraically or with matrices Relate vectors and linear transformations — link vectors and matrices with linear combinations and seek solutions of homogeneous systems Evaluate determinants — see how to perform the determinant function on different sizes of matrices and take advantage of Cramer's rule Hone your skills with vector spaces — determine the properties of vector spaces and their subspaces and see linear transformation in action Tackle eigenvalues and eigenvectors — define and solve for eigenvalues and eigenvectors and understand how they interact with specific matrices

Open the book and find: Theoretical and practical ways of solving linear algebra problems Definitions of terms throughout and in the glossary New ways of looking at operations How linear algebra ties together vectors, matrices, determinants, and linear transformations Ten common mathematical representations of Greek letters Real-world applications of matrices and determinants

Key features of Number Theory: Structures, Examples, and Problems:

* A rigorous exposition starts with the natural numbers and the basics.

* Important concepts are presented with an example, which may also emphasize an application. The exposition moves systematically and intuitively to uncover deeper properties.

* Topics include divisibility, unique factorization, modular arithmetic and the Chinese Remainder Theorem, Diophantine equations, quadratic residues, binomial coefficients, Fermat and Mersenne primes and other special numbers, and special sequences. Sections on mathematical induction and the pigeonhole principle, as well as a discussion of other number systems are covered.

* Unique exercises reinforce and motivate the reader, with selected solutions to some of the problems.

* Glossary, bibliography, and comprehensive index round out the text.

Written by distinguished research mathematicians and renowned teachers, this text is a clear, accessible introduction to the subject and a source of fascinating problems and puzzles, from advanced high school students to undergraduates, their instructors, and general readers at all levels.

- Teaches general principles that can be applied to a wide variety of problems.

- Avoids the mindless and excessive routine computations that characterize conventional textbooks.

- Treats algebra as a logically coherent discipline, not as a disjointed collection of techniques.

- Restores proofs to their proper place to remove doubt, convey insight, and encourage precise logical thinking.

- Omits digressions, excessive formalities, and repetitive exercises.

- Covers all the algebra needed to take a calculus course.

- Includes solutions to all problems.

Contents

1. A Few Basics

2. Exponents

3. Polynomials

4. Factoring

5. Linear & Quadratic Equations

6. Inequalities & Absolute Values

7. Coordinates in a Plane

8. Functions & Graphs

9. Straight Lines

10. Circles

11. Parabolas

12. Types of Functions

13. Logarithms

14. Dividing Polynomials

15. Systems of Linear Equations

16. Geometric Progressions & Series

17. Arithmetic Progressions

18. Permutation & Combinations

19. The Binomial Theorem

20. Mathematical Induction

21. Solutions

Whether you're brushing up on pre-Algebra concepts or on your way toward mastering algebraic fractions, factoring, and functions, CliffsQuickReview Algebra I can help. This guide introduces each topic, defines key terms, and carefully walks you through each sample problem step-by-step. In no time, you'll be ready to tackle other concepts in this book such as

Equations, ratios, and proportionInequalities, graphing, and absolute valueCoordinate GeometryRoots and radicalsQuadratic equationsCliffsQuickReview Algebra I acts as a supplement to your textbook and to classroom lectures. Use this reference in any way that fits your personal style for study and review—you decide what works best with your needs. Here are just a few ways you can search for topics:

Use the free Pocket Guide full of essential informationGet a glimpse of what you'll gain from a chapter by reading through the Chapter Check-In at the beginning of each chapterUse the Chapter Checkout at the end of each chapter to gauge your grasp of the important information you need to knowTest your knowledge more completely in the CQR Review and look for additional sources of information in the CQR Resource CenterUse the glossary to find key terms fast.With titles available for all the most popular high school and college courses, CliffsQuickReview guides are a comprehensive resource that can help you get the best possible grades.

Basic Math & Pre-Algebra Workbook For Dummies is your ticket to finally getting a handle on math! Designed to help you strengthen your weak spots and pinpoint problem areas, this book provides hundreds of practice problems to help you get over the hump. Each section includes a brief review of key concepts and full explanations for every practice problem, so you'll always know exactly where you went wrong. The companion website gives you access to quizzes for each chapter, so you can test your understanding and identify your sticking points before moving on to the next topic. You'll brush up on the rules of basic operations, and then learn what to do when the numbers just won't behave—negative numbers, inequalities, algebraic expressions, scientific notation, and other tricky situations will become second nature as you refresh what you know and learn what you missed.

Each math class you take builds on the ones that came before; if you got lost somewhere around fractions, you'll have a difficult time keeping up in Algebra, Geometry, Trigonometry, and Calculus—so don't fall behind! This book provides plenty of practice and patient guidance to help you slay the math monster once and for all. Make sense of fractions, decimals, and percentages Learn how to handle inequalities, exponents, square roots, and absolute values Simplify expressions and solve simple algebraic equations Find your way around a triangle, circle, trapezoid, and more

Once you get comfortable with the rules and operations, math takes on a whole new dimension. Curiosity replaces anxiety, and problems start feeling like puzzles rather than hurdles. All it takes is practice. Basic Math & Pre-Algebra Workbook For Dummies is your ultimate math coach, with hundreds of guided practice practice problems to help you break through the math barrier.

And if this e-book leaves you wanting even more! more! more! there's The Math Dude's Quick and Dirty Guide to Algebra, with even more math number games, explanations, and—dare we say it—fun.

-- A natural transition from basic math to algebra, with a review of relevant concepts and operations.

-- An introduction to linear equations and functions, including graphing and inequalities.

-- Explanations of how to solve absolute-value equations and radical equations.

-- Instructions on how to perform operations on polynomials, and factoring.

-- An exploration of how to work with quadratic equations and quadratic functions; and rational expressions, equations, and functions.

-- Special sidebars pointing out the reasoning behind the techniques, which is an essential part of Common Core instruction.

-- Separate workbook section of extra Algebra practice problems-like getting two books in one!

The book presents programming concepts such as variables, assignments, input/output, and selection statements as well as MATLAB built-in functions side-by-side, giving students the ability to program efficiently and exploit the power of MATLAB to solve problems. In-depth coverage is given to input/output, a topic that is fundamental to many engineering applications. A systematic, step-by-step approach that builds on concepts is used throughout the book, facilitating easier learning. There are also sections on ‘common pitfalls’ and ‘programming guidelines’ that direct students towards best practice.

This book will be an invaluable resource for engineers, engineering novices, and students learning to program and model in MATLAB.

Presents programming concepts and MATLAB built-in functions side-by-side, giving students the ability to program efficiently and exploit the power of MATLAB to solve problemsIn depth coverage of file input/output, a topic essential for many engineering applicationsSystematic, step-by-step approach, building on concepts throughout the book, facilitating easier learningSections on ‘common pitfalls’ and ‘programming guidelines’ direct students towards best practiceNew to this edition:

More engineering applications help the reader learn Matlab in the context of solving technical problemsNew and revised end of chapter problemsStronger coverage of loops and vectorizing in a new chapter, chapter 5Updated to reflect current features and functions of the current release of Matlab