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In Love and Math, renowned mathematician Edward Frenkel reveals a side of math we’ve never seen, suffused with all the beauty and elegance of a work of art. In this heartfelt and passionate book, Frenkel shows that mathematics, far from occupying a specialist niche, goes to the heart of all matter, uniting us across cultures, time, and space.

Love and Math tells two intertwined stories: of the wonders of mathematics and of one young man’s journey learning and living it. Having braved a discriminatory educational system to become one of the twenty-first century’s leading mathematicians, Frenkel now works on one of the biggest ideas to come out of math in the last 50 years: the Langlands Program. Considered by many to be a Grand Unified Theory of mathematics, the Langlands Program enables researchers to translate findings from one field to another so that they can solve problems, such as Fermat’s last theorem, that had seemed intractable before.

At its core, Love and Math is a story about accessing a new way of thinking, which can enrich our lives and empower us to better understand the world and our place in it. It is an invitation to discover the magic hidden universe of mathematics.

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.

Our CLEP* test preps are perfect for adults returning to college (or attending for the first time), military service members, high-school graduates looking to earn college credit, or home-schooled students with knowledge that can translate into college credit.

There are many different ways to prepare for the CLEP*. What's best for you depends on how much time you have to study and how comfortable you are with the subject matter. Our test prep for CLEP* College Algebra and the free online tools that come with it, will allow you to create a personalized CLEP* study plan that can be customized to fit you: your schedule, your learning style, and your current level of knowledge.

Here's how it works:

Diagnostic exam at the REA Study Center focuses your study

Our online diagnostic exam pinpoints your strengths and shows you exactly where you need to focus your study. Armed with this information, you can personalize your prep and review where you need it the most.

Most complete subject review for CLEP* College Algebra

Our targeted review covers all the material you'll be expected to know for the exam and includes a glossary of must-know terms.

Two full-length practice exams

The online REA Study Center gives you two full-length practice tests and the most powerful scoring analysis and diagnostic tools available today. Instant score reports help you zero in on the CLEP* College Algebra topics that give you trouble now and show you how to arrive at the correct answer-so you'll be prepared on test day.

An introductory chapter traces concepts of abstract algebra from their historical roots. Succeeding chapters avoid the conventional format of definition-theorem-proof-corollary-example; instead, they take the form of a discussion with students, focusing on explanations and offering motivation. Each chapter rests upon a central theme, usually a specific application or use. The author provides elementary background as needed and discusses standard topics in their usual order. He introduces many advanced and peripheral subjects in the plentiful exercises, which are accompanied by ample instruction and commentary and offer a wide range of experiences to students at different levels of ability.

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

Instructors will find the latest edition pitched at a suitable level of difficulty and will appreciate its gradual increase in the level of sophistication as the student progresses through the book. Rather than inserting superficial applications at the expense of important mathematical concepts, the Beachy and Blair solid, well-organized treatment motivates the subject with concrete problems from areas that students have previously encountered, namely, the integers and polynomials over the real numbers.

Supplementary material for instructors and students available on the books Web site: www.math.niu.edu/~beachy/abstract_algebra/

This highly versatile text provides mathematical background used in a wide variety of disciplines, including mathematics and mathematics education, computer science, biology, chemistry, engineering, communications, and business.

Some of the major features and strengths of this textbook

More than 1,600 exercises, ranging from elementary to challenging, are included with hints/answers to all odd-numbered exercises.

Descriptions of proof techniques are accessible and lively.

Students benefit from the historical discussions throughout the textbook.

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.

Trying to tackle algebra but nothing's adding up? No problem! Factor in Algebra Demystified, Second Edition and multiply your chances of learning this important branch of mathematics.

Written in a step-by-step format, this practical guide covers fractions, variables, decimals, negative numbers, exponents, roots, and factoring. Techniques for solving linear and quadratic equations and applications are discussed in detail. Clear examples, concise explanations, and worked problems with complete solutions 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 how to:

Translate English sentences into mathematical symbols Write the negative of numbers and variables Factor expressions Use the distributive property to expand expressions Solve applied problemsSimple enough for a beginner, but challenging enough for an advanced student, Algebra Demystified, Second Edition helps you master this essential math subject. It's also the perfect resource for preparing you for higher level math classes and college placement tests.

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

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.

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.

Hidden symmetries were first discovered nearly two hundred years ago by French mathematician évariste Galois. They have been used extensively in the oldest and largest branch of mathematics--number theory--for such diverse applications as acoustics, radar, and codes and ciphers. They have also been employed in the study of Fibonacci numbers and to attack well-known problems such as Fermat's Last Theorem, Pythagorean Triples, and the ever-elusive Riemann Hypothesis. Mathematicians are still devising techniques for teasing out these mysterious patterns, and their uses are limited only by the imagination.

The first popular book to address representation theory and reciprocity laws, Fearless Symmetry focuses on how mathematicians solve equations and prove theorems. It discusses rules of math and why they are just as important as those in any games one might play. The book starts with basic properties of integers and permutations and reaches current research in number theory. Along the way, it takes delightful historical and philosophical digressions. Required reading for all math buffs, the book will appeal to anyone curious about popular mathematics and its myriad contributions to everyday life.

In this book the author solves the problem of maintaining the interest of students at both levels by offering a combinatorial approach to elementary number theory. In studying number theory from such a perspective, mathematics majors are spared repetition and provided with new insights, while other students benefit from the consequent simplicity of the proofs for many theorems.

Among the topics covered in this accessible, carefully designed introduction are multiplicativity-divisibility, including the fundamental theorem of arithmetic, combinatorial and computational number theory, congruences, arithmetic functions, primitive roots and prime numbers. Later chapters offer lucid treatments of quadratic congruences, additivity (including partition theory) and geometric number theory.

Of particular importance in this text is the author's emphasis on the value of numerical examples in number theory and the role of computers in obtaining such examples. Exercises provide opportunities for constructing numerical tables with or without a computer. Students can then derive conjectures from such numerical tables, after which relevant theorems will seem natural and well-motivated..

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 second edition adds a discussion of vector auto-regressive, structural vector auto-regressive, and structural vector error-correction models. To analyze the interactions between the investigated variables, further impulse response function and forecast error variance decompositions are introduced as well as forecasting. The author explains how these model types relate to each other.

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.

"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.

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.

In Chapter 1, the author discusses the essential ingredients of a mathematical system, and in the next four chapters covers the basic number systems, decompositions of integers, diophantine problems, and congruences. Chapters 6 through 9 examine groups, rings, domains, fields, polynomial rings, and quadratic domains.Chapters 10 through 13 cover modular systems, modules and vector spaces, linear transformations and matrices, and the elementary theory of matrices. The author, Professor of Mathematics at the University of Pittsburgh, includes many examples and, at the end of each chapter, a large number of problems of varying levels of difficulty.

Fortunately for you, there's Schaum's.

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. You also get hundreds of examples, solved problems, and practice exercises to test your skills.

This Schaum's Outline gives you

885 fully solved problems Complete review of all course fundamentalsFully 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!

Topics include: Fundamental Concepts; Polynomials; Rational Expressions; First-Degree Equations and Inequalities; Exponents, Roots, and Radicals; Second-Degree Equations and Inequalities; Systems of Equations and Inequalities; Relations and Functions; Exponential and Logarithmic Functions; and Sequences, Series, and the Binomial Theorem

Schaum's Outlines--Problem Solved.

Unlike many authors, however, Mr. Friedberg encourages students to think about the imaginative, playful qualities of numbers as they consider such subjects as primes and divisibility, quadratic forms and residue arithmetic and quadratic reciprocity and related theorems. Moreover, the author has included a number of unusual features to challenge and stimulate students: some of the original problems in Diophantus' Arithmetica, proofs of Fermat's Last Theorem for the exponents 3and 4, and two proofs of Wilson's Theorem.

Readers with a mathematical bent will enjoy and benefit from these entertaining and thought-provoking adventures in the fascinating realm of number theory. Mr. Friedberg is currently Professor of Physics at Barnard College, where he is Chairman of the Department of Physics and Astronomy.

-- 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!

"Seamless R and C++ integration with Rcpp" is simply a wonderful book. For anyone who uses C/C++ and R, it is an indispensable resource. The writing is outstanding. A huge bonus is the section on applications. This section covers the matrix packages Armadillo and Eigen and the GNU Scientific Library as well as RInside which enables you to use R inside C++. These applications are what most of us need to know to really do scientific programming with R and C++. I love this book. -- Robert McCulloch, University of Chicago Booth School of Business

Rcpp is now considered an essential package for anybody doing serious computational research using R. Dirk's book is an excellent companion and takes the reader from a gentle introduction to more advanced applications via numerous examples and efficiency enhancing gems. The book is packed with all you might have ever wanted to know about Rcpp, its cousins (RcppArmadillo, RcppEigen .etc.), modules, package development and sugar. Overall, this book is a must-have on your shelf. -- Sanjog Misra, UCLA Anderson School of Management

The Rcpp package represents a major leap forward for scientific computations with R. With very few lines of C++ code, one has R's data structures readily at hand for further computations in C++. Hence, high-level numerical programming can be made in C++ almost as easily as in R, but often with a substantial speed gain. Dirk is a crucial person in these developments, and his book takes the reader from the first fragile steps on to using the full Rcpp machinery. A very recommended book! -- Søren Højsgaard, Department of Mathematical Sciences, Aalborg University, Denmark

"Seamless R and C ++ Integration with Rcpp" provides the first comprehensive introduction to Rcpp. Rcpp has become the most widely-used language extension for R, and is deployed by over one-hundred different CRAN and BioConductor packages. Rcpp permits users to pass scalars, vectors, matrices, list or entire R objects back and forth between R and C++ with ease. This brings the depth of the R analysis framework together with the power, speed, and efficiency of C++.

Dirk Eddelbuettel has been a contributor to CRAN for over a decade and maintains around twenty packages. He is the Debian/Ubuntu maintainer for R and other quantitative software, edits the CRAN Task Views for Finance and High-Performance Computing, is a co-founder of the annual R/Finance conference, and an editor of the Journal of Statistical Software. He holds a Ph.D. in Mathematical Economics from EHESS (Paris), and works in Chicago as a Senior Quantitative Analyst.

Bellos has traveled all around the globe and has plunged into history to uncover fascinating stories of mathematical achievement, from the breakthroughs of Euclid, the greatest mathematician of all time, to the creations of the Zen master of origami, one of the hottest areas of mathematical work today. Taking us into the wilds of the Amazon, he tells the story of a tribe there who can count only to five and reports on the latest findings about the math instinct—including the revelation that ants can actually count how many steps they’ve taken. Journeying to the Bay of Bengal, he interviews a Hindu sage about the brilliant mathematical insights of the Buddha, while in Japan he visits the godfather of Sudoku and introduces the brainteasing delights of mathematical games.

Exploring the mysteries of randomness, he explains why it is impossible for our iPods to truly randomly select songs. In probing the many intrigues of that most beloved of numbers, pi, he visits with two brothers so obsessed with the elusive number that they built a supercomputer in their Manhattan apartment to study it. Throughout, the journey is enhanced with a wealth of intriguing illustrations, such as of the clever puzzles known as tangrams and the crochet creation of an American math professor who suddenly realized one day that she could knit a representation of higher dimensional space that no one had been able to visualize.

Whether writing about how algebra solved Swedish traffic problems, visiting the Mental Calculation World Cup to disclose the secrets of lightning calculation, or exploring the links between pineapples and beautiful teeth, Bellos is a wonderfully engaging guide who never fails to delight even as he edifies. Here’s Looking at Euclid is a rare gem that brings the beauty of math to life.

The book begins with a systematic study of real numbers, understood to be a set of objects satisfying certain definite axioms. The concepts of a mathematical structure and an isomorphism are introduced in Chapter 2, after a brief digression on set theory, and a proof of the uniqueness of the structure of real numbers is given as an illustration. Two other structures are then introduced, namely n-dimensional space and the field of complex numbers.

After a detailed treatment of metric spaces in Chapter 3, a general theory of limits is developed in Chapter 4. Chapter 5 treats some theorems on continuous numerical functions on the real line, and then considers the use of functional equations to introduce the logarithm and the trigonometric functions. Chapter 6 is on infinite series, dealing not only with numerical series but also with series whose terms are vectors and functions (including power series). Chapters 7 and 8 treat differential calculus proper, with Taylor's series leading to a natural extension of real analysis into the complex domain. Chapter 9 presents the general theory of Riemann integration, together with a number of its applications. Analytic functions are covered in Chapter 10, while Chapter 11 is devoted to improper integrals, and makes full use of the technique of analytic functions.

Each chapter includes a set of problems, with selected hints and answers at the end of the book. A wealth of examples and applications can be found throughout the text. Over 340 theorems are fully proved.

Covering all the mathematical techniques required to resolve geometric problems and design computer programs for computer graphic applications, each chapter explores a specific mathematical topic prior to moving forward into the more advanced areas of matrix transforms, 3D curves and surface patches. Problem-solving techniques using vector analysis and geometric algebra are also discussed.

All the key areas are covered including: Numbers, Algebra, Trigonometry, Coordinate geometry, Transforms, Vectors, Curves and surfaces, Barycentric coordinates, Analytic geometry.

Plus – and unusually in a student textbook – a chapter on geometric algebra is included.

The book begins with fundamentals, with a definition of complex numbers, their geometric representation, their algebra, powers and roots of complex numbers, set theory as applied to complex analysis, and complex functions and sequences. The notions of proper and improper complex numbers and of infinity are fully and clearly explained, as is stereographic projection. Individual chapters then cover limits and continuity, differentiation of analytic functions, polynomials and rational functions, Mobius transformations with their circle-preserving property, exponentials and logarithms, complex integrals and the Cauchy theorem , complex series and uniform convergence, power series, Laurent series and singular points, the residue theorem and its implications, harmonic functions (a subject too often slighted in first courses in complex analysis), partial fraction expansions, conformal mapping, and analytic continuation.

Elementary functions are given a more detailed treatment than is usual for a book at this level. Also, there is an extended discussion of the Schwarz-Christolfel transformation, which is particularly important for applications.

There is a great abundance of worked-out examples, and over three hundred problems (some with hints and answers), making this an excellent textbook for classroom use as well as for independent study. A noteworthy feature is the fact that the parentage of this volume makes it possible for the student to pursue various advanced topics in more detail in the three-volume original, without the problem of having to adjust to a new terminology and notation .

In this way, IntroductoryComplex Analysis serves as an introduction not only to the whole field of complex analysis, but also to the magnum opus of an important contemporary Russian mathematician.

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!

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.

". . .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.

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.

- 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