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The book consists of four chapters. Chapter 1 introduces algebras and coalgebras over a field K; Chapter 2 treats bialgebras; Chapter 3 discusses Hopf algebras and Chapter 4 consists of three applications of Hopf algebras. Each chapter begins with a short overview and ends with a collection of exercises which are designed to review and reinforce the material. Exercises range from straightforward applications of the theory to problems that are devised to challenge the reader. Questions for further study are provided after selected exercises. Most proofs are given in detail, though a few proofs are omitted since they are beyond the scope of this book.

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.

Let Basic Math and Pre-Algebra Workbook For Dummies, 2nd Edition take the guessing out of math and help you discover your problem solving potential.

Barron's popular "Painless Series " of study guides for middle school and high school students offer a lighthearted, often humorous approach to their subjects, transforming details that might once have seemed boring or difficult into a series of interesting and mentally challenging ideas. Most titles in the series feature many fun-to-solve "Brain Tickler" problems with answers at the end of each chapter.

If you are absolutely confused by absolute value equations, or you think parabolas are short moral stories, College Algebra DeMYSTiFied, Second Edition is your solution to mastering the topic's concepts and theories at your own pace. This thoroughly revised and updated guide eases you into the subject, beginning with the math fundamentals then introducing you to this advanced form of algebra. As you progress, you will learn how to simplify rational expressions, divide complex numbers, and solve quadratic equations. You will understand the difference between odd and even functions and no longer be confused by the multiplicity of zeros. Detailed examples make it easy to understand the material, and end-of-chapter quizzes and a final exam help reinforce key ideas.

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

The x-y coordinate plane Lines and intercepts The FOIL method Functions Nonlinear equations Graphs of functions Exponents and logarithmsSimple enough for a beginner, but challenging enough for an advanced student, College Algebra DeMYSTiFieD, Second Edition is your shortcut to a working knowledge of this engaging subject.

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/

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

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 exercisesTrying 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.

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.

The Essentials For Dummies Series

Dummies is proud to present our new series, The Essentials For Dummies. Now students who are prepping for exams, preparing to study new material, or who just need a refresher can have a concise, easy-to-understand review guide that covers an entire course by concentrating solely on the most important concepts. From algebra and chemistry to grammar and Spanish, our expert authors focus on the skills students most need to succeed in a subject.

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.

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.

This naive approach to Lie theory is originally due to von Neumann, and it is now possible to streamline it by using standard results of undergraduate mathematics. To compensate for the limitations of the naive approach, end of chapter discussions introduce important results beyond those proved in the book, as part of an informal sketch of Lie theory and its history.

John Stillwell is Professor of Mathematics at the University of San Francisco. He is the author of several highly regarded books published by Springer, including The Four Pillars of Geometry (2005), Elements of Number Theory (2003), Mathematics and Its History (Second Edition, 2002), Numbers and Geometry (1998) and Elements of Algebra (1994).

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.

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!

-- 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!

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.

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.

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.

In the first three chapters the authors briefly review the great explosions that will form the subject matter of the book--namely, supernovae and gamma-ray bursters. They describe the very early universe, after the Big Bang, and then how "the lights came on all over the universe as the very first stars began to shine." The importance of stellar mass in governing not only the lifetime of a star (the most massive stars live relatively short lives) but also the way in which a star ends its days is also explained.

Chapter 4 describes the explosion of certain massive stars, outlining the various stages at the end of these stars' lives, which result in the cataclysmic explosions known as supernovae. In Chapter 5 the authors introduce the more exotic and spectacular forms of stellar explosion known as gamma-ray bursters. Chapter 6 studies the markers used for cosmic surveys and Hubble's contributions to the field. The penultimate chapter looks at the very distant, highly luminous sources known as quasars and the evolution of our universe from the earliest times. The final chapter shows how observations of distant supernovae have revealed that the expansion of the universe is in fact accelerating--one of the most exciting and remarkable discoveries in recent years. It was this discovery that lead to the idea that 70% of the universe is made up of mysterious dark energy.

Scott Page gives a concise primer on how diversity happens, how it is maintained, and how it affects complex systems. He explains how diversity underpins system level robustness, allowing for multiple responses to external shocks and internal adaptations; how it provides the seeds for large events by creating outliers that fuel tipping points; and how it drives novelty and innovation. Page looks at the different kinds of diversity--variations within and across types, and distinct community compositions and interaction structures--and covers the evolution of diversity within complex systems and the factors that determine the amount of maintained diversity within a system.

Provides a concise and accessible introduction Shows how diversity underpins robustness and fuels tipping points Covers all types of diversity The essential primer on diversity in complex adaptive systemsImportant Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

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.

"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.

The book's first five chapters give an exposition of the theory of infinity-categories that emphasizes their role as a generalization of ordinary categories. Many of the fundamental ideas from classical category theory are generalized to the infinity-categorical setting, such as limits and colimits, adjoint functors, ind-objects and pro-objects, locally accessible and presentable categories, Grothendieck fibrations, presheaves, and Yoneda's lemma. A sixth chapter presents an infinity-categorical version of the theory of Grothendieck topoi, introducing the notion of an infinity-topos, an infinity-category that resembles the infinity-category of topological spaces in the sense that it satisfies certain axioms that codify some of the basic principles of algebraic topology. A seventh and final chapter presents applications that illustrate connections between the theory of higher topoi and ideas from classical topology.

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.

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.

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.

The early chapters provide students with background by investigating the basic properties of groups, rings, fields, and modules. Later chapters examine the relations between groups and sets, the fundamental theorem of Galois theory, and the results and methods of abstract algebra in terms of algebraic number theory, algebraic geometry, noncommutative algebra, and homological algebra, including categories and functors. An extensive supplement to the text delves much further into homological algebra than most introductory texts, offering applications-oriented results. Solutions to all problems appear in the text.

The quickest route to learning a subject is through a solid grounding in the basics. So what you won’t find in Easy Algebra 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 exercises that are linked to core skills--enabling learners to grasp when and how to apply those techniques.

This book features: Large step-by-step charts breaking down each step within a process and showing clear connections between topics and annotations to clarify difficulties Stay-in-step panels show how to cope with variations to the core steps Step-it-up exercises link practice to the core steps already presented Missteps and stumbles highlight common errors to avoidYou can master algebra as long as you take it Step-by-Step!

"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.

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.

“The text is geared to the needs of the beginning graduate student, covering with complete, well-written proofs the usual major branches of groups, rings, fields, and modules...[n]one of the material one expects in a book like this is missing, and the level of detail is appropriate for its intended audience.” (Alberto Delgado, MathSciNet)

“This text promotes the conceptual understanding of algebra as a whole, and that with great methodological mastery. Although the presentation is predominantly abstract...it nevertheless features a careful selection of important examples, together with a remarkably detailed and strategically skillful elaboration of the more sophisticated, abstract theories.” (Werner Kleinert, Zentralblatt)

For the new edition, the author has completely rewritten the text, reorganized many of the sections, and even cut or shortened material which is no longer essential. He has added a chapter on Ext and Tor, as well as a bit of topology.

It starts by introducing, in a completely self-contained way, all mathematical tools needed to use symmetry ideas in physics. Thereafter, these tools are put into action and by using symmetry constraints, the fundamental equations of Quantum Mechanics, Quantum Field Theory, Electromagnetism, and Classical Mechanics are derived.

As a result, the reader is able to understand the basic assumptions behind, and the connections between the modern theories of physics. The book concludes with first applications of the previously derived equations.

The volume consists of three sections: introductory issues, types of relationships, and relationship processes. In the first section, there is an exploration of the functions and benefits of close relationships, the diversity of methodologies used to study them, and the changing social context in which close relationships are embedded. A second section examines the various types of close relationships, including family bonds and friendships. The third section focuses on key relationship processes, including attachment, intimacy, sexuality, and conflict.

This book is designed to be an essential resource for senior undergraduate and postgraduate students, researchers, and practitioners, and will be suitable as a resource in advanced courses dealing with the social psychology of close relationships.

Solving Word Problems is one of the biggest hurdle that kids face in Algebra. A bit of imagination is required to understand and solve these type of problems along with the calculations.

This book breaks simple word problems using graphics thus helping the kids to visualize and understand the word problems. It develops the imaginative thinking required to solve these problems from an early level. This will help the kids to solve difficult problems as they will learn to imagine, analyze and break the problem into small parts which gives a better understanding on how to solve these type of problems.