An easy-to-use, self-study guide to abstract algebra and its applications. 
Groups, rings, and fields are fast becoming vital in a wide range of applications utilizing mathematical models—in computer science, physics, chemistry, and engineering. This new edition of a proven text offers systematic, concise, easy-to-understand explanations for these basic structures of abstract algebra suitable for self-study. Revised and refined to be accessible even to readers with only rudimentary college algebra, the Second Edition carefully balances coverage of groups, rings, and fields and uses real-world problems to illustrate the theory. Concrete examples such as number theory, integers modulo n, and permutations are introduced at the outset, providing readers with a springboard to computations and subsequent abstract concepts. An ideal resource for scientists and engineers as well as students preparing for the algebra qualifying examinations, Introduction to Abstract Algebra, Second Edition presents an exciting array of features, including: <ul>
<li>Applications to cryptography, coding, geometrical constructions, and Polya counting techniques.</li> <li>Special topics such as symmetric polynomials, nilpotent groups, and finite-dimensional algebras.</li> <li>Nearly 500 solved examples along with hundreds of exercises.</li> <li>Biographies of 13 mathematicians plus historical notes.</li> <li>Review of the necessary background material.</li> </ul>

Introduction to Abstract Algebra

Science & Math

Nicholson, W. Keith

Mathematics

Wiley-Interscience

Praise for the first edition 
"This book is clearly written and presents a large number of examples illustrating the theory . . . there is no other book of comparable content available. Because of its detailed coverage of applications generally neglected in the literature, it is a desirable if not essential addition to undergraduate mathematics and computer science libraries." –CHOICE As a cornerstone of mathematical science, the importance of modern algebra and discrete structures to many areas of science and technology is apparent and growing–with extensive use in computing science, physics, chemistry, and data communications as well as in areas of mathematics such as combinatorics. Blending the theoretical with the practical in the instruction of modern algebra, Modern Algebra with Applications, Second Edition provides interesting and important applications of this subject–effectively holding your interest and creating a more seamless method of instruction. Incorporating the applications of modern algebra throughout its authoritative treatment of the subject, this book covers the full complement of group, ring, and field theory typically contained in a standard modern algebra course. Numerous examples are included in each chapter, and answers to odd-numbered exercises are appended in the back of the text. Chapter topics include: <ul>
<li>Boolean Algebras</li> <li>Polynomial and Euclidean Rings</li> <li>Groups</li> <li>Quotient Rings</li> <li>Quotient Groups</li> <li>Field Extensions</li> <li>Symmetry Groups in Three Dimensions</li> <li>Latin Squares</li> <li>Pólya―Burnside Method of Enumeration</li> <li>Geometrical Constructions</li> <li>Monoids and Machines</li> <li>Error-Correcting Codes</li> <li>Rings and Fields</li> </ul>
In addition to improvements in exposition, this fully updated Second Edition also contains new material on order of an element and cyclic groups, more details about the lattice of divisors of an integer, and new historical notes. Filled with in-depth insights and over 600 exercises of varying difficulty, Modern Algebra with Applications, Second Edition can help anyone appreciate and understand this subject.

Modern Algebra with Applications

Gilbert, William J.

John Wiley&Sons

This Third Edition of the acclaimed self-study text lets you learn abstract algebra at your own pace 
The Third Edition of Introduction to Abstract Algebra continues to provide an accessible introduction to the basic structures of abstract algebra: groups, rings, and fields.The text's unique approach helps readers advance to abstract theory by presenting concrete examples of induction, number theory, integers modulo n, and permutations before the abstract structures are defined. Readers can immediately begin to perform computations using abstract concepts that are developed in greater detail later in the text. As in the previous editions, the Third Edition offers many special features to help readers learn and apply their developing knowledge of abstract algebra: <ul>
<li>Historical notes and biographies of mathematicians provide context and perspective</li> <li>Some 500 worked examples help readers understand key concepts and their applications</li> <li>Almost 1,500 computational and theoretical exercises ranging from basic to complex challenge readers to apply their knowledge to solve problems. Many answers are provided in the text</li> <li>Applications to real-world problems in such areas as coding theory and combinatorics help readers grasp the topic's relevancy</li> <li>Special topics such as symmetric polynomials, nilpotent groups, semidirect products of groups, and the Wedderburn-Artin theorem for rings are included for more advanced study</li> </ul>
This Third Edition includes thoroughly revised chapters and much new material, including new sections covering free, semisimple, and projective modules; modules over principal ideal domains; as well as semidirect products and the Wedderburn-Artin theorem. Two new appendices have been added on Zorn's lemma and the proof of the recursion theorem. Numerous worked examples, exercises, and real-world applications make this text perfect for upper-level undergraduate and graduate courses. Moreover, with this book's self-contained chapters, students can learn at their own pace, and instructors can adapt the text to meet a variety of course objectives.

This book provides an introduction to the basic structures of abstract algebra: groups, rings and fields. In addition it contains several optional sections on special topics and applications.

PWS Pub. Co.

This successful text is an introduction to the basic ideas and techniques of linear algebra for first- or second-year students who have a working knowledge of high school algebra (calculus is not a prerequisite). The author maintains a balance among the computational skills, theory, and applications of linear algebra--while keeping the level suitable for beginning students--and offers a multitude of examples and exercises to help students master the material.

Linear Algebra With Applications

Linear Algebra With Applications: Partial Solutions Manual

Brooks/Cole Pub. Co.

Praise for the Third Edition ". . . an expository masterpiece of the highest didactic value that has gained additional attractivity through the various improvements . . ."―Zentralblatt MATH The Fourth Edition of Introduction to Abstract Algebra continues to provide an accessible approach to the basic structures of abstract algebra: groups, rings, and fields. The book's unique presentation helps readers advance to abstract theory by presenting concrete examples of induction, number theory, integers modulo n, and permutations before the abstract structures are defined. Readers can immediately begin to perform computations using abstract concepts that are developed in greater detail later in the text. The Fourth Edition features important concepts as well as specialized topics, including: <ul>
<li> The treatment of nilpotent groups, including the Frattini and Fitting subgroups </li> <li> Symmetric polynomials </li> <li> The proof of the fundamental theorem of algebra using symmetric polynomials </li> <li> The proof of Wedderburn's theorem on finite division rings </li> <li> The proof of the Wedderburn-Artin theorem </li> </ul>
Throughout the book, worked examples and real-world problems illustrate concepts and their applications, facilitating a complete understanding for readers regardless of their background in mathematics. A wealth of computational and theoretical exercises, ranging from basic to complex, allows readers to test their comprehension of the material. In addition, detailed historical notes and biographies of mathematicians provide context for and illuminate the discussion of key topics. A solutions manual is also available for readers who would like access to partial solutions to the book's exercises. Introduction to Abstract Algebra, Fourth Edition is an excellent book for courses on the topic at the upper-undergraduate and beginning-graduate levels. The book also serves as a valuable reference and self-study tool for practitioners in the fields of engineering, computer science, and applied mathematics.

wiley

An indispensable companion to the book hailed an "expository masterpiece of the highest didactic value" by Zentralblatt MATH 
This solutions manual helps readers test and reinforce the understanding of the principles and real-world applications of abstract algebra gained from their reading of the critically acclaimed Introduction to Abstract Algebra. Ideal for students, as well as engineers, computer scientists, and applied mathematicians interested in the subject, it provides a wealth of concrete examples of induction, number theory, integers modulo n, and permutations. Worked examples and real-world problems help ensure a complete understanding of the subject, regardless of a reader's background in mathematics.

Solutions Manual to accompany Introduction to Abstract Algebra, 4e

Praise for the Third Edition ". . . an expository masterpiece of the highest didactic value that has gained additional attractivity through the various improvements . . ."—Zentralblatt MATH The Fourth Edition of Introduction to Abstract Algebra continues to provide an accessible approach to the basic structures of abstract algebra: groups, rings, and fields. The book's unique presentation helps readers advance to abstract theory by presenting concrete examples of induction, number theory, integers modulo n, and permutations before the abstract structures are defined. Readers can immediately begin to perform computations using abstract concepts that are developed in greater detail later in the text. The Fourth Edition features important concepts as well as specialized topics, including:   The treatment of nilpotent groups, including the Frattini and Fitting subgroups   Symmetric polynomials   The proof of the fundamental theorem of algebra using symmetric polynomials   The proof of Wedderburn's theorem on finite division rings   The proof of the Wedderburn-Artin theorem   Throughout the book, worked examples and real-world problems illustrate concepts and their applications, facilitating a complete understanding for readers regardless of their background in mathematics. A wealth of computational and theoretical exercises, ranging from basic to complex, allows readers to test their comprehension of the material. In addition, detailed historical notes and biographies of mathematicians provide context for and illuminate the discussion of key topics. A solutions manual is also available for readers who would like access to partial solutions to the book's exercises. Introduction to Abstract Algebra, Fourth Edition is an excellent book for courses on the topic at the upper-undergraduate and beginning-graduate levels. The book also serves as a valuable reference and self-study tool for practitioners in the fields of engineering, computer science, and applied mathematics.

Introduction to Abstract Algebra, 4e Set

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Books by Nicholson, W. Keith

See the best price to sell, buy, or rent books by Nicholson, W. Keith. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Introduction to Abstract Algebra

Modern Algebra with Applications

Introduction to Abstract Algebra

Introduction to Abstract Algebra

Introduction to Abstract Algebra

Linear Algebra With Applications

Linear Algebra With Applications: Partial Solutions Manual

Introduction to Abstract Algebra

Solutions Manual to accompany Introduction to Abstract Algebra, 4e

Introduction to Abstract Algebra, 4e Set