Elementary Abstract Algebra: Examples and Applications

This textbook introduces the basic notions of group theory by a thorough treatment of important examples, including complex numbers, modular arithmetic, symmetries, and permutations. Also included are applications to communications, cryptography, and coding theory.

This book is our best effort at making "Abstract Algebra" as down-to earth as possible. We use concrete mathematical structures such as the complex numbers, integers mod n, symmetries, and permutations to introduce some of the beautifully general ideas of group theory. Along the way, we give applications to signal processing, cryptography and coding theory, and we draw connections with other branches of mathematics such as geometry and number theory.