A finite field is a mathematical structure that contains a finite number of elements and follows the rules of a field. The most common examples are integers mod p when p is a prime number. Finite fields have applications in various areas of mathematics and computer science, including number theory, cryptography, and coding theory.

This advanced course reexamines traditional concepts of discrete mathematics (relations, functions, logic, graphs, algebra, automata) in the context of computation and algorithms, necessitating a strong background in discrete math.