Description
Book SynopsisContemporary Abstract Algebra, Tenth Edition
For more than three 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.
The author presents the concepts and methodologies of contemporary abstract algebra as used by working mathematicians, computer scientists, physicists, and chemists. Students will learn how to do computations and to 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. Applications are included to illustrate the utility of the abstract concepts.
Examples and exercises are the heart of the book. Examples elucidate the definitions, theorems, and proof techniques; exercises facilitate understanding, provide insight, and develop the ability to do proofs. The
Trade Review
"It has now been 35 years since Gallian's classic textbook Contemporary Abstract Algebra was first published. The book is deservedly popular with instructors of abstract algebra courses. It is written at an appropriate level for junior and senior undergraduates, has lucid coverage of all of the standard topics and several nonstandard ones (Frieze Groups and Crystallographic Groups, Coding Theory, Greek Geometric Construction Problems, etc), is example-driven, and contains thousands of exercises at various levels of difficulty. Moreover, every chapter begins with an interesting quote or two (by as diverse a group of people as Einstein, Miguel de Cervantes, Ralph Waldo Emerson, Bob Dylan, etc) and most conclude with a mini- biography of a mathematician whose work relates to the chapter's content. This is an interesting book that is a pleasure to read.
According to the Preface, changes made for the tenth edition include:
1. Approximately 200 new exercises
2. Many new examples
3. New quotes
4. A freshening of the discussion portions"
- Benjamin Linowitz, Oberlin College, Published in MAA
Table of Contents1 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
