A Book of Abstract Algebra: Second Edition

Brief Description:
Originally published: 2nd ed. New York: McGraw-Hill, 1990.

Marc Notes:
Originally published: 2nd ed. New York: McGraw-Hill, 1990.;Includes bibliographical references and index.

Biographical Note:
Charles C. Pinter is Professor Emeritus of Mathematics at Bucknell University.

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

Publisher Marketing:
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.