Physical Sciences and Mathematics Commons^™

Developing Prediction Models For Kidney Stone Disease, Joseph Palko

Honors Theses

Kidney stone disease has become more prevalent through the years, leading to high treatment cost and associated health risks. In this study, we explore a large medical database and machine learning methods to extract features and construct models for diagnosing kidney stone disease.

Data of 46,250 patients and 58,976 hospital admissions were extracted and analyzed, including patients’ demographic information, diagnoses, vital signs, and laboratory measurements of the blood and urine. We compared the kidney stone (KDS) patients to patients with abdominal and back pain (ABP), patients diagnosed with nephritis, nephrosis, renal sclerosis, chronic kidney disease, or acute and unspecified renal …

Choice Of Choice: Paradoxical Results Surrounding Of The Axiom Of Choice, Connor Hurley

Honors Theses

When people think of mathematics they think "right or wrong," "empirically correct" or "empirically incorrect." Formalized logically valid arguments are one important step to achieving this definitive answer; however, what about the underlying assumptions to the argument? In the early 20th century, mathematicians set out to formalize these assumptions, which in mathematics are known as axioms. The most common of these axiomatic systems was the Zermelo-Fraenkel axioms. The standard axioms in this system were accepted by mathematicians as obvious, and deemed by some to be sufficiently powerful to prove all the intuitive theorems already known to mathematicians. However, this system …

Elliptic Curve Cryptology, Francis Rocco

Honors Theses

In today's digital age of conducting large portions of daily life over the Internet, privacy in communication is challenged extremely frequently and confidential information has become a valuable commodity. Even with the use of commonly employed encryption practices, private information is often revealed to attackers. This issue motivates the discussion of cryptology, the study of confidential transmissions over insecure channels, which is divided into two branches of cryptography and cryptanalysis. In this paper, we will first develop a foundation to understand cryptography and send confidential transmissions among mutual parties. Next, we will provide an expository analysis of elliptic curves and …

Primality Proving Based On Eisenstein Integers, Miaoqing Jia

Honors Theses

According to the Berrizbeitia theorem, a highly efficient method for certifying the primality of an integer N ≡ 1 (mod 3) can be created based on pseudocubes in the ordinary integers Z. In 2010, Williams and Wooding moved this method into the Eisenstein integers Z[ω] and defined a new term, Eisenstein pseudocubes. By using a precomputed table of Eisenstein pseudocubes, they created a new algorithm in this context to prove primality of integers N ≡ 1 (mod 3) in a shorter period of time. We will look at the Eisenstein pseudocubes and analyze how this new algorithm works with the …

Partial Differential Equations, Nathaniel James Onnen

Honors Theses

This paper will discuss methods for solving many different partial differential equations, as well as real world applications in physics. We are interested in finding solutions to the wave and heat equations in one dimension, the wave equation in two dimensions, as well as a solution to Schrodinger’s equation. In order to do this, we will study different methods including Fourier series, Bessel functions, and Hermite polynomials. I will use these methods to derive solutions for the mentioned problems, as well as to produce visualizations for many of them.

Elections With Three Candidates Four Candidates And Beyond: Counting Ties In The Borda Count With Permutahedra And Ehrhart Quasi-Polynomials, Adam Margulies

Honors Theses

In voting theory, the Borda count’s tendency to produce a tie in an election varies as a function of n, the number of voters, and m, the number of candidates. To better understand this tendency, we embed all possible rankings of candidates in a hyperplane sitting in m-dimensional space, to form an (m - 1)-dimensional polytope: the m-permutahedron. The number of possible ties may then be determined computationally using a special class of polynomials with modular coefficients. However, due to the growing complexity of the system, this method has not yet been extended past the case of m = 3. …