Book:Joseph A. Gallian/Contemporary Abstract Algebra/Ninth Edition

Subject Matter

 * Abstract Algebra
 * Group Theory
 * Ring Theory
 * Field Theory
 * Galois Theory

Contents

 * Preface


 * Part 1: Integers and Equivalence Relations
 * Chapter 0: Preliminaries


 * Part 2: Groups
 * Chapter 1: Introduction to Groups
 * Chapter 2: Groups
 * Chapter 3: Finite Groups, Subgroups
 * Chapter 4: Cyclic Groups
 * Chapter 5: Permutation Groups
 * Chapter 6: Isomorphisms
 * Chapter 7: Cosets and Lagrange's Theorem
 * Chapter 8: External Direct Products
 * Chapter 9: Normal Subgroups and Factor Groups
 * Chapter 10: Group Homomorphisms
 * Chapter 11: Fundamental Theorem of Finite Abelian Groups


 * Part 3: Rings
 * Chapter 12: Introduction to Rings
 * Chapter 13: Integral Domains
 * Chapter 14: Ideals and Factor Rings
 * Chapter 15: Ring Homomorphisms
 * Chapter 16: Polynomial Rings
 * Chapter 17: Factorization of Polynomials
 * Chapter 18: Divisibility in Integral Domains


 * Part 4: Fields
 * Chapter 19: Vector Spaces
 * Chapter 20: Extension Fields
 * Chapter 21: Algebraic Extensions
 * Chapter 22: Finite Fields
 * Chapter 23: Geometric Constructions


 * Part 5: Special Topics
 * Chapter 24: Sylow Theorems
 * Chapter 25: Finite Simple Groups
 * Chapter 26: Generators and Relations
 * Chapter 27: Symmetry Groups
 * Chapter 28: Frieze Groups and Crystallographic Groups
 * Chapter 29: Symmetry and Counting
 * Chapter 30: Cayley Digraphs of Groups
 * Chapter 31: Introduction to Algebraic Coding Theory
 * Chapter 32: An Introduction to Galois Theory
 * Chapter 33: Cyclotomic Extensions


 * Selected Answers


 * Index of Mathmaticians


 * Index of Terms