Computation in Finite Fields Treatment of finite fields in undergraduate and graduate algebra courses ranges from the very brief (proofs of existence and uniqueness), to the theoretical (algebraic number theory), to the explicit (coding theory, cryptography, and designs). For the benefit of those us lacking exposure to the latter, I will talk about explicit, pencil-and-paper computations in finite fields. The goal is for us to be able to compute with finite fields as readily as we compute with, say, the rationals. Topics, depending on audience interest: * Determination of irreducible polynomials * Multiplication * Reciprocation * Automorphisms * Shanks' discrete log algorithm John Kerl Graduate Student Colloquium January 25, 2006