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