A Book of Abstract Algebra

Description

Title Page Copyright Page Dedication Contents Preface 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 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 Induction Answers to Selected Exercises Index