A Book of Abstract Algebra: Second Edition

✍ Scribed by Charles C. Pinter

• Publisher: Dover Publications
• Year: 2015
• Tongue: English
• Leaves: 397
• Series: Dover Books on Mathematics
• Edition: 2
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

CONTENTS
PREFACE
CHAPTERS
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: HOMOMORPHISMS
CHAPTER 15: QUOTIENT GROUPS
CHAPTER 16: THE FUNDAMENTAL HOMOMORPHISM
THEOREM
CHAPTER 17: RINGS: DEFINITIONS AND
ELEMENTARY PROPERTIES
CHAPTER 18: IDEALS AND HOMOMORPHISMS
CHAPTER 19: QUOTIENT RINGS
CHAPTER 20: INTEGRAL DOMAINS
CHAPTER 21: THE INTEGERS
CHAPTER 22: FACTORING INTO PRIMES
CHAPTER 23: ELEMENTS OF NUMBER THEORY (OPTIONAL)
CHAPTER 24: RINGS OF POLYNOMIALS
CHAPTER 25: FACTORING POLYNOMIALS
CHAPTER 26: SUBSTITUTI ON 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
APPENDIX A: REVIEW OF SET THEORY
APPENDIX B: REVIEW OF THE INTEGERS
APPENDIX C: REVIEW OF MATHEMATICAL INDUCTION
ANSWERS TO SELECTED EXERCISES
CHAPTER 2
CHAPTER 3
CHAPTER 4
CHAPTER 5
CHAPTER 6
CHAPTER 7,8
CHAPTER 9
CHAPTER 10
CHAPTER 11
CHAPTER 12,13
CHAPTER 14
CHAPTER 15,16
CHAPTER 17
CHAPTER 18, 19, 20
CHAPTER 21, 22
CHAPTER 23
CHAPTER 24
CHAPTER 25, 26
CHAPTER 27
CHAPTER 28
CHAPTER 29
CHAPTER 30, 31
CHAPTER 32, 33
INDEX

✦ Subjects

Mathematics; Abstract Algebra