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A Book of Abstract Algebra; Second Edition



Pub. Date:
Dover Publications
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What version or edition is this?

This is the 2nd edition with a publication date of 1/14/2010.

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Customer Reviews

Fantastic introduction to abstract algebra.  March 17, 2011

This introductory textbook on abstract algebra is simply superb. The author provides lots of exercises and some worked out solutions. The book offers a very step-by-step, each idea carefully explained approach to the subject. Each chapter ends with multiple exercises which show applications as well as theory. I'm happy with this purchase. I needed this textbook fast and sure enough I received it in a very timely manner, which I appreciated.

A Book of Abstract Algebra; Second Edition: 4 out of 5 stars based on 1 user reviews.


Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra.

A Book of Abstract Algebra's easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications.

1990 edition.

Table of Contents

Chapter 1       Why Abstract Algebra
Chapter 2       Operations
Chapter 3       The Definition of Groups
Chapter 4       Elementary Properties of Groups
Chapter 5       Subgroups
Chapter 6       Functions
Chapter 7       Groups of Permutations
Chapter 8       Permutations of a Finite Set
Chapter 9       Isomorphism
Chapter 10     Order of Group Elements
Chapter 11     Cyclic Groups
Chapter 12     Partitions and Equivalence Relations
Chapter 13     Counting Cosets
Chapter 14     Homomorphism
Chapter 15     Quotient Groups
Chapter 16     The Fundamental Homomorphism Theorem
Chapter 17     Rings: Definitions and Elementary Properties
Chapter 18     Ideals and Homomorphism
Chapter 19     Quotient Rings
Chapter 20     Integral Domains
Chapter 21     The Integers
Chapter 22     Factoring into Primes
Chapter 23     Elements of Number Theiory (Optional)
Chapter 24     Rings of Polynomials
Chapter 25     Factoring Polynomials
Chapter 26     Substitution in Polynomials
Chapter 27     Extensions of Fields
Chapter 28     Vector Spaces
Chapter 29     Degrees of Field Extensions
Chapter 30     Ruler and Compass
Chapter 31     Galois Theory: Preamble
Chapter 32     Galois Theory: The Heart of the Matter
Chapter 33     Solving Equations by Radicals
Appendix A    Review of Set Theory
Appendix B    Review of the Integers
Appendix C    Review of Mathematical Integers
                       Answers to Selected Exercises

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