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...
The aim of this dissertation is to construct a virtual element method (VEM) for models in magneto-hydrodynamics (MHD), an area that studies the behavior and properties of electrically conducting fluids such as a plasma. MHD models are a coupling of the Maxwell’s equations for electromagnetics and models for fluid flow....
The author shows that a necessary and sufficient condition
for a convex polyhedron to be representable as a finite vector sum
of line segments is that each of its faces possesses central symmetry.
College Algebra is a prerequisite for calculus and is thus an important stepping stone in the careers of STEM-intending undergraduates. However, College Algebra has low pass rates across the United States, interrupting students’ pathways to success. To address this concern, a research-oriented university in the Northwest United States restructured its...
In this work, we provide a detailed analysis of a discrete time regime switching financial market model with jumps. We consider the model under two different scenarios: known and unknown initial regime. For each scenario we investigated conditions that guarantee the model's completeness. We find that the model under consideration...
The standard way of representing numbers on computers gives rise to errors
which increase as computations progress. Using p-adic valuations can reduce
error accumulation. Valuation theory tells us that p-adic and standard valuations
cannot be directly compared. The p-adic valuation can, however, be used in
an indirect way. This gives...
Machine learning models are powerful tools which may aid in the prediction of survival outcomes of cancer patients. This study evaluated eight classification models and eight regression models on their ability to predict survival outcomes on breast cancer and prostate cancer data sets from the SEER database. The most accurate...
Machine learning models are powerful tools which may aid in the prediction of survival outcomes of cancer patients. This study evaluated eight classification models and eight regression models on their ability to predict survival outcomes on breast cancer and prostate cancer data sets from the SEER database. The most accurate...
Microcomputers are being used in teaching and learning
mathematics. This paper examines ways that computers can be used
to enhance teaching in precalculus mathematics. The advantages of
computers discussed are: 1) instant access to graphs, 2) examples
that are not oversimplified to make computations manageable, 3)
encouragement of hypothesizing and...
In this paper we develop an upscaling technique for non-Darcy flow in porous media. Non-Darcy model of flow applies to flow in porous media when large velocities occur. The well-posedness results for theory of quasilinear elliptic partial differential equations. To discretize the model we used lowest order Raviart-Thomas mixed finite...