The Senior Thesis Program

Department of Mathematics
Harvey Mudd College

Nate Eldredge

Harvey Mudd College Mathematics 2003

A strange picture of me
Primary research interests: Representation Theory, Spectral Analysis, Combinatorics, Computational Algebra

Other mathematical interests: Real Analysis, Topology, Graph Theory

Starting in the fall of 2003, I will be a graduate student in the Department of Mathematics at the University of California, San Diego in beautiful La Jolla.

Senior Thesis

An Eigenspace Approach to Isotypic Projections for Data on Binary Trees

Advisor: Michael Orrison
Second Reader: Shahriar Shahriari

Abstract
The classical Fourier transform is, in essence, a way to take data and extract components (in the form of complex exponentials) which are invariant under cyclic shifts. We consider a case in which the components must instead be invariant under automorphisms of a binary tree. We present a technique by which a slightly relaxed form of the generalized Fourier transform in this case can eventually be computed using only simple tools from linear algebra, which has possible advantages in computational efficiency.

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