Contemporary Abstract Algebra, Eleventh Edition is intended for a course whose main purpose is to enable students to do computations and write proofs. This text stresses the importance of obtaining a solid introduction to the traditional topics, while at the same time presenting abstract algebra as a contemporary and very much active subject, which is currently being used by working physicists, chemists, and computer scientists.
For nearly four decades, this classic text has been widely appreciated by instructors and students alike. The book offers an enjoyable read and conveys and develops enthusiasm for the beauty of the topics presented. It is comprehensive, lively, and engaging.
Students will learn how to do computations and write proofs. A unique feature of the book are exercises that build the skill of generalizing, a skill that students should develop, but rarely do.
Examples elucidate the definitions, theorems, and proof techniques; exercises facilitate understanding, provide insight, and develop the ability to do proofs. The hallmark features of previous editions of the book are enhanced in this edition. These include:
A good mixture of approximately 1900 computational and theoretical exercises appearing in each chapter that synthesizes concepts from multiple chapters
Back-of-the-book skeleton solutions and hints to odd-numbered exercises
Over 300 worked-out examples ranging from routine computations to the more challenging
Links to interactive True/False questions with comments
Links to computer exercises that utilize interactive software available on the author's website, stressing guessing and making conjectures
Many applications from scientific and computing fields, as well as some from everyday life
Numerous historical notes and biographies that spotlight the people and events behind the mathematics
Motivational and humorous quotations
Hundreds of figures, photographs, and tables
Changes to the eleventh edition include new exercises, examples, biographies, and quotes, and an enrichment of the discussion portions. These changes accentuate and enhance the hallmark features that have made previous editions of the book a comprehensive, lively, and engaging introduction to the subject.
While many partial solutions and sketches for the odd-numbered exercises appear in the book, an Instructors Solutions Manual offers solutions for all the exercises. A Student's Solution Manual has comprehensive solutions for all odd-numbered exercises, many even-numbered exercises, and numerous alternative solutions as well.
1 Introduction to Groups
2 Groups
3 Finite Groups; Subgroups
4 Cyclic Groups
5 Permutation Groups
6 Ismorphisms
7 Cosets and Lagrange's Theorem
8 External Direct Products
9 Normal Subgroups and Factor Groups
10 Group Homomorphisms
11 Fundamental Theorem of Finite Abelian Groups
12 Introduction to Rings
13 Integral Domains
14 Ideals and Factor Rings
15 Ring Homomorphisms
16 Polynomial Rings
17 Factorization of Polynomials
18 Divisibilty in Integral Domains
19 Extension Fields
20 Algebraic Extensions
21 Finite Fields
22 Geometric Constructions
23 Sylow Theorems
24 Finite Simple Groups
25 Generators and Relations
26 Symmetry Groups
27 Symmetry and Counting
28 Cayley Digraphs of Groups
29 Introduction to Algebraic Coding Theory
30 An Introduction to Galois Theory
31 Cyclotomic Extensions
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