X-ray computed tomography is a noninvasive imaging modality capable of reconstructing exact density values of 3D objects. Computed tomography machines are deployed across the world to provide doctors with an image that reveals more detail than a standard x-ray image. We investigate algorithms based on exact computed tomography reconstruction formulas...
Following the work of Asai, Kaneko, and Ninomiya for Faber polynomials associated to the modular group, and Bannai, Kojima, and Miezaki's partial proof for the case of the Fricke group of level 2, we show that the zeros of certain modular functions for some low-level genus zero groups associated to...
In this dissertation, we begin by presenting the result of F. K. C. Rankin and Swinnerton-Dyer on the location of the zeros of the Eisenstein series for the full modular group in the standard fundamental domain. Their simple but beautiful argument shows that all zeros are located on the lower...
This thesis is an exploration of writing a music album from a singer-song writer perspective. It contains the process of writing lyrics and music, inspiration from other artists, as well as performance. It goes through the emotional ebbs and flows of creative writing, ground work for recording an album and...
String theory, one of the more popular approaches to quantizing gravity, is a highly complex
theory, involving high level mathematics and physics. But the basic ideas of string theory are not inaccessible, even to the undergraduate. This document acts as report to my thesis project, the writing of A Detailed...
The goal of this research project is to determine the fractal nature, if any, which
surface water waves exhibit when viewed on a microscopic scale. Due to the
relatively recent development of this area of mathematics, a brief introduction to the
study of fractal geometry, as well as several examples...
Microbial ecology has been transformed by metagenomics, the study of the genetic in-formation in entire communities of organisms. In the following we develop metagenomic tools arising from the classic Wasserstein metric as applied to questions regarding the diversity between microbial communities. We provide a novel proof of the characteriza-tion of...
A concept image is that collection of all images, pictures, symbols, definitions
and properties associated with any given mathematical concept. One of the
most important components in the mental representation of concepts in the concept
image of advanced mathematical thinkers is visualization. This component, in
turn, is indispensable in the...