A Book of Abstract Algebra; Second Edition:
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Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra.
A Book of Abstract Algebra's easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications.
1990 edition.
Charles C. Pinter is Professor Emeritus of Mathematics at Bucknell University.
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
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