Book of Abstract Algebra

Book of Abstract Algebra

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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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Product details

  • Paperback | 400 pages
  • 136 x 216 x 23mm | 408g
  • New York, United States
  • English
  • Revised
  • 2nd Revised edition
  • Illustrations, unspecified
  • 0486474178
  • 9780486474175
  • 80,017

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
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About Charles C. Pinter

Charles C. Pinter is Professor Emeritus of Mathematics at Bucknell University.
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383 ratings
4.32 out of 5 stars
5 47% (181)
4 39% (151)
3 12% (45)
2 1% (5)
1 0% (1)
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