My thesis for the Robert D. Clark Honors College and the Mathematics Department at the University of Oregon, which passed with distinction
Abstract: "This thesis establishes an orthogonal basis that accurately represents the structure of polynomials on any three-dimensional tripod. I define, restrict, and describe the contents of an inner product space for a corresponding orthogonal tripod. Then I explicitly construct a basis of the inner product space and study its transformation to an orthogonal basis, using many different algorithmic methods of increasing efficiency. Ultimately, my thesis extends the forefront of mathematical research in the numerical field and helps create a structure with which mathematicians can manipulate currently unmanageable monster polynomials that live in the three-dimensional world."