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1 Burnside - Bldg. 2 Mathematics- Abstract Algebra
1 Hawthorne Mathematics- General

A Book of Abstract Algebra

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A Book of Abstract Algebra Cover

 

Synopses & Reviews

Publisher Comments:

Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. Intended for undergraduate courses in abstract algebra, it is suitable for junior- and senior-level math majors and future math teachers. This second edition features additional exercises to improve student familiarity with applications.

An introductory chapter traces concepts of abstract algebra from their historical roots. Succeeding chapters avoid the conventional format of definition-theorem-proof-corollary-example; instead, they take the form of a discussion with students, focusing on explanations and offering motivation. Each chapter rests upon a central theme, usually a specific application or use. The author provides elementary background as needed and discusses standard topics in their usual order. He introduces many advanced and peripheral subjects in the plentiful exercises, which are accompanied by ample instruction and commentary and offer a wide range of experiences to students at different levels of ability.

Synopsis:

Accessible but rigorous, this outstanding text encompasses all of elementary abstract algebra's standard topics. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. 1990 edition.

Synopsis:

Accessible but rigorous, this outstanding text encompasses all of elementary abstract algebra's standard topics. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. 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
 
                       Index

Product Details

ISBN:
9780486474175
Author:
Pinter, Charles
Publisher:
Dover Publications
Author:
Pinter, Charles C.
Author:
Mathematics
Subject:
Algebra - Abstract
Subject:
Algebra
Subject:
Abstract algebra
Subject:
Undergraduate abstract algebra
Subject:
Mathematics-Abstract Algebra
Copyright:
Edition Description:
Second Edition, Unabridged
Series:
Dover Books on Mathematics
Publication Date:
20100131
Binding:
TRADE PAPER
Language:
English
Pages:
400
Dimensions:
8.5 x 5.38 in 0.96 lb

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Science and Mathematics » Mathematics » Algebra » Abstract Algebra
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A Book of Abstract Algebra New Trade Paper
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Product details 400 pages Dover Publications - English 9780486474175 Reviews:
"Synopsis" by ,
Accessible but rigorous, this outstanding text encompasses all of elementary abstract algebra's standard topics. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. 1990 edition.
"Synopsis" by ,
Accessible but rigorous, this outstanding text encompasses all of elementary abstract algebra's standard topics. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. 1990 edition.
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