Book of Abstract Algebra

Book of Abstract Algebra

Paperback Dover Books on Mathematics

By (author) Charles C. Pinter

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  • Publisher: Dover Publications Inc.
  • Format: Paperback | 400 pages
  • Dimensions: 136mm x 214mm x 16mm | 340g
  • Publication date: 26 March 2010
  • Publication City/Country: New York
  • ISBN 10: 0486474178
  • ISBN 13: 9780486474175
  • Edition: 2, Revised
  • Edition statement: 2nd Revised edition
  • Sales rank: 35,892

Product description

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.

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Table of contents

Chapter 1       Why Abstract AlgebraChapter 2       OperationsChapter 3       The Definition of GroupsChapter 4       Elementary Properties of GroupsChapter 5       SubgroupsChapter 6       FunctionsChapter 7       Groups of PermutationsChapter 8       Permutations of a Finite SetChapter 9       IsomorphismChapter 10     Order of Group ElementsChapter 11     Cyclic GroupsChapter 12     Partitions and Equivalence RelationsChapter 13     Counting CosetsChapter 14     HomomorphismChapter 15     Quotient GroupsChapter 16     The Fundamental Homomorphism TheoremChapter 17     Rings: Definitions and Elementary PropertiesChapter 18     Ideals and HomomorphismChapter 19     Quotient RingsChapter 20     Integral DomainsChapter 21     The IntegersChapter 22     Factoring into PrimesChapter 23     Elements of Number Theiory (Optional)Chapter 24     Rings of PolynomialsChapter 25     Factoring PolynomialsChapter 26     Substitution in PolynomialsChapter 27     Extensions of FieldsChapter 28     Vector SpacesChapter 29     Degrees of Field ExtensionsChapter 30     Ruler and CompassChapter 31     Galois Theory: PreambleChapter 32     Galois Theory: The Heart of the MatterChapter 33     Solving Equations by RadicalsAppendix A    Review of Set TheoryAppendix B    Review of the IntegersAppendix C    Review of Mathematical Integers                       Answers to Selected Exercises                        Index