Physical Sciences and Mathematics Commons^™

How To Explain Allen-Manandhar’S Method To Beginner Mathematicians : A Convergence Analysis Of A Hybrid Method For Variable-Coefficient Boundary Value Problems, Rebecca Scariano

Honors Theses

In this project, analogies are employed to make complex math concepts approachable to beginners who may only have a basic understanding of calculus and linear algebra. Serving as the focal point of this project, Allen-Manandhar’s method solves an equation, known as an ordinary differential equation (ODE). The mentioned equation with its coefficients is comparable to a pie recipe with ingredients. With the outcome to a recipe seen as its solution, the solution to our pie recipe is a perfectly baked pie, as in without error. The chosen method for baking a pie then classifies as its baking approach that when …

2-Adic Valuations Of Square Spiral Sequences, Minh Nguyen

Honors Theses

The study of p-adic valuations is connected to the problem of factorization of integers, an essential question in number theory and computer science. Given a nonzero integer n and prime number p, the p-adic valuation of n, which is commonly denoted as νp(n), is the greatest non-negative integer ν such that p ν | n. In this paper, we analyze the properties of the 2-adic valuations of some integer sequences constructed from Ulam square spirals. Most sequences considered were diagonal sequences of the form 4n 2 + bn + c from the Ulam spiral with center value of 1. Other …

A Logistic Regression Analysis Of First-Time College Students’ Completion Rates At The University Of Southern Mississippi, Jesse Homer Robinson

Honors Theses

The demand for employees with a college degree is steadily on the rise in a plethora of competitive job markets throughout the United States. This increase in demand has aided in the increasing college enrollment rates throughout the country. However, unlike enrollment trends, the rate of college completion has not had the same fortunate rise.

The goal of this study is to research and compare differences among those first-time college students who completed college within four years, six years, or did not complete. The primary source for data in this study was the Office of Institutional Research at USM. Both …

Applications Of The Sierpiński Triangle To Musical Composition, Samuel C. Dent

Honors Theses

The present paper builds on the idea of composing music via fractals, specifically the Sierpiński Triangle and the Sierpiński Pedal Triangle. The resulting methods are intended to produce not just a series of random notes, but a series that we think pleases the ear. One method utilizes the iterative process of generating the Sierpiński Triangle and Sierpiński Pedal Triangle via matrix operations by applying this process to a geometric configuration of note names. This technique designs the largest components of the musical work first, then creates subsequent layers where each layer adds more detail.

2-Domination And Annihilation Numbers, Sean C. Patterson

Honors Theses

Using information provided by Ryan Pepper and Ermelinda DeLaVina in their paper On the 2-Domination number and Annihilation Number, I developed a new bound on the 2- domination number of trees. An original bound, γ₂(G) ≤ (n+n₁)/ 2 , had been shown by many other authors. Our goal was to generate a tighter bound in some cases and work towards generating a more general bound on the 2-domination number for all graphs. Throughout the span of this project I generated and proved the bound γ₂(T ) ≤ …

Modeling The Diffusion Of Heat Energy Within Composites Of Homogeneous Materials Using The Uncertainty Principle, Elyse M. Garon

Honors Theses

The purpose of this project is to model the diffusion of heat energy in one space dimension, such as within a rod, in the case where the heat flow is through a medium consisting of two or more homogeneous materials. The challenge of creating such a mathematical model is that the diffusivity will be represented using a piecewise constant function, because the diffusivity changes based on the material. The resulting model cannot be solved using analytical methods, and is impractical to solve using existing numerical methods, thus necessitating a novel approach.

The approach presented in this thesis is to represent …

Application Of Linear Sequences To Cryptography, Amanda C. Yeates

Honors Theses

Cryptography is the study of a centuries–old technique of secretly transferring information between parties. Linear recurrences were the chosen method of encryption and decryption in the thesis. The Fibonacci sequence, with its Zeckendorf representation, allows for the flexibility of encoding any number desired based on a particular encoding technique used in the film Sherlock Holmes: A Game of Shadows. The main goal is to find other linear recurrences that possess characteristics similar to the Fibonacci sequence to use as suitable substitutes for encoding. Different sequences were analyzed based on a number of criteria. In order for a sequence to be …

A Comparison Of Van Hiele Levels And Final Exam Grades Of Students At The University Of Southern Mississippi, Cononiah Watson

Honors Theses

This research analyzed students final exam scores in a college mathematics class with geometric components and their van Hiele levels upon entering the class. After the class was completed, each student’s final exam grade was calculated. The researcher used a Spearman correlation to compare the two; the result was a correlation coefficient of 0.742. The researcher then reported that the results of the van Hiele test are a major component in predicting a student’s success in such a class.

Row Reduction Of Macaulay Matrices, Lorrin Debenport

Honors Theses

A computer can use a matrix to represent a system of non-linear multivariate polynomial equations. The fastest known ways to transform this system into a form with desirable computational properties rely on transforming its matrix into upper-triangular form [8, 9]. The matrix for such a system will have mostly zero entries, which we call sparse [7]. We propose to analyze several methods of performing row-reduction, the process by which matrices are reduced into upper-triangular form [2].

What is special about row-reducing matrices in this context? When row-reducing a matrix, swapping rows or columns is typically acceptable. However, if the order …

A Criterion For Identifying Stressors In Non-Linear Equations Using Gröbner Bases, Elisabeth Marie Palchak

Honors Theses

No abstract provided.