Tristan Brand

Harvey Mudd College Mathematics 2005

Thesis Proposal: Problem Statement - An FFT Algorithm on the Symmetric Group
Thesis: An FFT for the Symmetric Group
Poster: Presentation Days Poster Prof. Michael Orrison
Second Reader: Prof. Ghassan Sarkis

An FFT Algorithm on the Symmetric Group

A discrete Fourier transform, or DFT, is an isomorphism from a group algebra to a direct sum of matrix algebras. An algorithm that efficiently applies a DFT is called a fast Fourier transform, or FFT. The concept of a DFT will be introduced and examined from both a general and algebraic perspective. We will then present and analyze a specific FFT for the symmetric group.