The fifth edition of this classic reference work has been updated to give a reasonably accurate account of the present state of knowledge.

    Focused on groups, rings and fields, this text gives students a firm foundation for more specialized work by emphasizing an understanding of the nature of algebraic structures. KEY TOPICS: Sets and Relations; GROUPS AND SUBGROUPS; Introduction and Examples; Binary Operations; Isomorphic Binary Structures; Groups; Subgroups; Cyclic Groups; Generators and Cayley Digraphs; PERMUTATIONS, COSETS, AND DIRECT PRODUCTS; Groups of Permutations; Orbits, Cycles, and the Alternating Groups; Cosets and the Theorem of Lagrange; Direct Products and Finitely Generated Abelian Groups; Plane Isometries; HOMOMORPHISMS AND FACTOR GROUPS; Homomorphisms; Factor Groups; Factor-Group Computations and Simple Groups; Group Action on a Set; Applications of G-Sets to Counting; RINGS AND FIELDS; Rings and Fields; Integral Domains; Fermat's and Euler's Theorems; The Field of Quotients of an Integral Domain; Rings of Polynomials; Factorization of Polynomials over a Field; Noncommutative Examples; Ordered Rings and Fields; IDEALS AND FACTOR RINGS; Homomorphisms and Factor Rings; Prime and Maximal Ideas; Gr�bner Bases for Ideals; EXTENSION FIELDS; Introduction to Extension Fields; Vector Spaces; Algebraic Extensions; Geometric Constructions; Finite Fields; ADVANCED GROUP THEORY; Isomorphism Theorems; Series of Groups; Sylow Theorems; Applications of the Sylow Theory; Free Abelian Groups; Free Groups; Group Presentations; GROUPS IN TOPOLOGY; Simplicial Complexes and Homology Groups; Computations of Homology Groups; More Homology Computations and Applications; Homological Algebra; Factorization; Unique Factorization Domains; Euclidean Domains; Gaussian Integers and Multiplicative Norms; AUTOMORPHISMS AND GALOIS THEORY; Automorphisms of Fields; The Isomorphism Extension Theorem; Splitting Fields; Separable Extensions; Totally Inseparable Extensions; Galois Theory; Illustrations of Galois Theory; Cyclotomic Extensions; Insolvability of the Quintic; Matrix Algebra MARKET: For all readers interested in abstract algebra.

    Pose the same question to students and many will use words like "boring", "useless", and even "humiliating". In  Becoming the Math Teacher You Wish You'd Had , author Tracy Zager helps teachers close this gap by making math class more like mathematics. Tracy has spent years working with highly skilled math teachers in a diverse range of settings and grades. You'll find this book jam-packed with new ideas from these vibrant classrooms.  How to Teach Student-Centered Mathematics: Zager outlines a problem-solving approach to mathematics for elementary and middle school educators looking for new ways to inspire student learningBig Ideas, Practical Application: This math book contains dozens of practical and accessible teaching techniques that focus on fundamental math concepts, including strategies that simulate connection of big ideas; rich tasks that encourage students to wonder, generalize, hypothesize, and persevere; and routines to teach students how to collaborateKey Topics for Elementary and Middle School Teachers:  Becoming the Math Teacher You Wish You'd Had  offers fresh perspectives on common challenges, from formative assessment to classroom management for elementary and middle school teachersAll teachers can move towards increasingly authentic and delightful mathematics teaching and learning. This important book helps develop instructional techniques that will make the math classes we teach so much better than the math classes we took.

    Practical Algebra is an easy andfun-to-use workout program that quickly puts you in command of allthe basic concepts and tools of algebra. With the aid of practical, real-life examples and applications, you'll learn: * The basic approach and application of algebra to problemsolving * The number system (in a much broader way than you have known itfrom arithmetic) * Monomials and polynomials; factoring algebraic expressions; howto handle algebraic fractions; exponents, roots, and radicals;linear and fractional equations * Functions and graphs; quadratic equations; inequalities; ratio, proportion, and variation; how to solve word problems, andmore Authors Peter Selby and Steve Slavin emphasize practical algebrathroughout by providing you with techniques for solving problems ina wide range of disciplines--from engineering, biology, chemistry, and the physical sciences, to psychology and even sociology andbusiness administration. Step by step, Practical Algebra shows youhow to solve algebraic problems in each of these areas, then allowsyou to tackle similar problems on your own, at your own pace.Self-tests are provided at the end of each chapter so you canmeasure your mastery.

    Kurt Giidel maintained, and offered detailed proof, that in any arithmetic system, even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. It is thus uncertain that the basic axioms of arithmetic will not give rise to contradictions. The repercussions of this discovery are still being felt and debated in 20th-century mathematics.The present volume reprints the first English translation of Giidel's far-reaching work. Not only does it make the argument more intelligible, but the introduction contributed by Professor R. B. Braithwaite (Cambridge University}, an excellent work of scholarship in its own right, illuminates it by paraphrasing the major part of the argument.This Dover edition thus makes widely available a superb edition of a classic work of original thought, one that will be of profound interest to mathematicians, logicians and anyone interested in the history of attempts to establish axioms that would provide a rigorous basis for all mathematics. Translated by B. Meltzer, University of Edinburgh. Preface. Introduction by R. B. Braithwaite.

    . . like a pendulum? These may not look like math questions, but they are-because they all have to do with patterns. And mathematics, at heart, is the study of patterns. That realization changed Eddie Woo's life-by turning the "dry" subject he dreaded in high school into a boundless quest for discovery. Now an award-winning math teacher, Woo sees patterns everywhere: in the "branches" of blood vessels and lightning, in the growth of a savings account and a sunflower, even in his morning cup of tea! Here are twenty-six bite-size chapters on the hidden mathematical marvels that encrypt our email, enchant our senses, and even keep us alive-from the sine waves we hear as "music" to the mysterious golden ratio. This book will change your mind about what math can be. We are all born mathematicians-and It's a Numberful World.

    In this book, William Cook takes readers on a mathematical excursion, picking up the salesman's trail in the 1800s when Irish mathematician W. R. Hamilton first defined the problem, and venturing to the furthest limits of today's state-of-the-art attempts to solve it. He also explores its many important applications, from genome sequencing and designing computer processors to arranging music and hunting for planets.In Pursuit of the Traveling Salesman travels to the very threshold of our understanding about the nature of complexity, and challenges you yourself to discover the solution to this captivating mathematical problem.

    Feynman gave his famous course on computation at the California Institute of Technology, he asked Tony Hey to adapt his lecture notes into a book. Although led by Feynman, the course also featured, as occasional guest speakers, some of the most brilliant men in science at that time, including Marvin Minsky, Charles Bennett, and John Hopfield. Although the lectures are now thirteen years old, most of the material is timeless and presents a “Feynmanesque” overview of many standard and some not-so-standard topics in computer science such as reversible logic gates and quantum computers.

    The book is unique among popular books on mathematics in combining an engaging, easy-to-read history of the subject with a comprehensive mathematical survey text. Intended, in the author's words, "for the benefit of those who never studied the subject, those who think they have forgotten what they once learned, or those with a sincere desire for more knowledge," it links mathematics to the humanities, linguistics, the natural sciences, and technology.Contains more than 1000 original technical illustrations, a multitude of reproductions from mathematical classics and other relevant works, and a generous sprinkling of humorous asides, ranging from limericks and tall stories to cartoons and decorative drawings.

    Stewart's Calculus is successful throughout the world because he explains the material in a way that makes sense to a wide variety of readers. His explanations make ideas come alive, and his problems challenge, to reveal the beauty of calculus. Stewart's examples stand out because they are not just models for problem solving or a means of demonstrating techniques--they also encourage readers to develp an analytic view of the subject. This edition includes new problems, examples, and projects. This version of Stewart's book introduced exponential and logarithmic functions in the first chapter and their limits and derivatives are found in Chapters 2 and 3.

    In the paper, Wigner observed that the mathematical structure of a physical theory often points the way to further advances in that theory and even to empirical predictions.

    Even when dealing with standard material, Stillwell manages to dramatize it and to make it worth rethinking. In short, his book is a splendid addition to the genre of works that build royal roads to mathematical culture for the many." (Mathematical Intelligencer)This second edition includes new chapters on Chinese and Indian number theory, on hypercomplex numbers, and on algebraic number theory. Many more exercises have been added, as well as commentary to the exercises explaining how they relate to the preceding section, and how they foreshadow later topics.

    The text begins with a discussion of the real number system as a complete ordered field. (Dedekind's construction is now treated in an appendix to Chapter I.) The topological background needed for the development of convergence, continuity, differentiation and integration is provided in Chapter 2. There is a new section on the gamma function, and many new and interesting exercises are included. This text is part of the Walter Rudin Student Series in Advanced Mathematics.

    of Wisconsin-Madison) and Wichern (Texas A&M U.) present the newest edition of this college text on the statistical methods for describing and analyzing multivariate data, designed for students who have taken two or more statistics courses. The fifth edition includes the addition of seve

    His Contemporary Abstract Algebra, 6/e, includes challenging topics in abstract algebra as well as numerous figures, tables, photographs, charts, biographies, computer exercises, and suggested readings that give the subject a current feel and makes the content interesting and relevant for students.