# Tristan Brand

Harvey Mudd College Mathematics 2005

Thesis Proposal: | Problem Statement - An FFT Algorithm on the Symmetric Group | |
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Thesis: | An FFT for the Symmetric Group | |

Poster: | Presentation Days Poster | Prof. Michael Orrison |

Second Reader: | Prof. Ghassan Sarkis | |

E-Mail: | tbrand@hmc.edu |

## 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.