Abstract Algebra: An introduction with Applications, 2nd Edition

This is the second edition of the introduction to abstract algebra. In addition to introducing the main concepts of modern algebra, the book contains numerous applications, which are intended to illustrate the concepts and to convince the reader of the utility and relevance of algebra today. There is ample material here for a two semester course in abstract algebra.

Table of Contents

Chapter 1 Sets, relations and functions
Chapter 2 The integers
Chapter 3 Introduction to groups
Chapter 4 Quotient groups and homomorphisms
Chapter 5 Groups acting on sets
Chapter 6 Introduction to rings
Chapter 7 Division in commutative rings
Chapter 8 Vector spaces
Chapter 9 Introduction to modules
Chapter 10 The Structure of groups
Chapter 11 The Theory of elds
Chapter 12 Galois Theory
Chapter 13 Tensor products
Chapter 14 Further topics