Elementary Abstract Algebra. Examples and Applications

Аннотация

This book is designed to make "Abstract Algebra" as down-to-earth as possible. Before getting into the deep theoretical stuff, we first take a look at algebraic systems beyond the real numbers that are widely used in practical applications of mathematics. These include the complex numbers, integers mod n, polynomials, symmetries, and permutations. We then use these examples to motivate and illustrate the beautifully general ideas of the theory of groups, rings, and fields. Along the way, we give applications to signal processing, cryptography and coding theory, as well as making connections with other branches of mathematics such as geometry and number theory.