Finite Fields, with Applications to Combinatorics

This book uses finite field theory as a hook to introduce the reader to a range of ideas from algebra and number theory. It constructs all finite fields from scratch and shows that they are unique up to isomorphism. As a payoff, several combinatorial applications of finite fields are given: Sidon sets and perfect difference sets, de Bruijn sequences and a magic trick, and the polynomial time algorithm for primality testing.

The book forms the basis for a one-term intensive course with…