Mathematics Commons^™

An Algebraic-Combinatorial Proof Of A Bézout-Type Inequality For Mixed Volumes Of Three-Dimensional Zonoids, Gennadiy Averkov, Ivan Soprunov

Mathematics and Statistics Faculty Publications

We present a new algebraic-combinatorial approach to proving a Bézout-type inequality for zonoids in dimension three, which has recently been established by Fradelizi, Madiman, Meyer, and Zvavitch. Our approach hints at connections between inequalities for mixed volumes of zonoids and real algebra and matroid theory.

Mathematical Melodies: The Exploration Of Music Using Fourier Signal Analysis, Courtney Francois

Honors Theses

Upon initial inspection, mathematics and music appear to be distinct disciplines lacking any connections to one another. However, many complex intersections lie beneath the surface. This paper seeks to explore these connections through the analysis of the Fourier series and the Fourier transformation of musical sound signals. Orthogonal functions of various frequencies are used to approximate and recover sound signals. Following the examination of the basis of Fourier signal analysis, MATLAB is utilized to visualize the connectedness of mathematics and music through sound signals from varied musical instruments and by performing Fourier signal analysis to the sound signals. Then, the …

Graph Codes, Jacquelyn Franqui

Theses, Dissertations and Culminating Projects

The concept of graph codes, introduced in recent work by Alon, applies coding theory to graphs by defining codewords as graphs and measuring distances between them through structural differences. In ordinary coding theory, the distance between two words is the number of positions in which the two words differ. In graph codes, each word is a graph and the distance between two graphs is measured by structural properties of their difference. For a fixed graph H, an H-code is a collection F of graphs on vertex set [n] = {1, 2, . . . , n} such that the symmetric …

A Multi-Scale Compartmental Model For Glucose Regulation And Diabetes Treatment, Andrew M. Watts

Honors Theses

Glucose is a fundamental energy source for cellular function, and its regulation is critical for maintaining metabolic stability in the human body. Glucose homeostasis is governed by a network of biochemical processes involving multiple organ systems that coordinate glucose production, storage, and uptake. Disruptions in this regulation contribute to metabolic disorders such as diabetes mellitus, underscoring the need for mathematical models that provide a mechanistic understanding of systemic glucose dynamics. Herein, we report a multi-time scale discrete-time dynamical systems model using compartmental difference equations to describe glucose concentrations across key physiological compartments. By quantitatively modeling glucose transport and metabolism, this …

Bibliography Of Christianity And Mathematics Update, Calvin Jongsma

Faculty Work Comprehensive List

This was a banquet talk given at the Twenty-fourth Biennial Conference of the Association of Christians in the Mathematical Sciences held at Dordt University on May 28-June 1, 2024.

It provides an update on the progress being made in the author’s project of producing a second edition of Bibliography of Christianity and Mathematics. This work is now being developed as a Zotero database with a slightly broader focus on Religious Faith and the Mathematical Sciences and with a much expanded list of books, articles, and blog posts on the topic. The author hopes to make the database public sometime …

Setting Up Students For Success: Analysis Of Effectiveness For Mathematics Placement, Jeff Carvell, Jason N.E. Ho, Dave Klanderman, Sarah Klanderman

Faculty Work Comprehensive List

How do we effectively and equitably place students into math classes in a way that provides them the best chance of success? As many higher education institutions veer away from placement based on standardized testing, many departments are seeking placement alternatives that will properly support students. Additionally, math placement determines not only a student’s mathematics courses but also influences their progress in related fields, including physics, chemistry, engineering, and more. This paper will describe three different existing placement systems at each of our liberal arts institutions as well as the affordances and constraints of each approach. Further, we analyze data …

The Impact Of Corporate Profits On Gdi Estimates: Forecasting And Data Revisions, Peterson Haas

Honors Theses

The National Income and Product Accounts (NIPAs) produced by the U.S. Bureau of Economic Analysis (BEA) provide key measures of U.S. economic activity, including gross domestic product (GDP) and gross domestic income (GDI). Although conceptually equivalent, GDP and GDI often diverge due to differences in source data and revision timing. This study focuses on corporate profits—a small but volatile component of GDI that is frequently revised, especially during the BEA’s annual (A1) and benchmark (C1) revisions. I examine how revisions to corporate profits influence GDI revisions and whether they can improve real-time estimates of GDI. First, I document the size …

Knighted Pawn's Tour, Morgan Wilson

Honors Theses

The Knighted Pawn’s Tour is a variant of the traditional Knight’s Tour problem, whichitself is an instance of the Hamiltonian cycle problem. The deviation from the Knight’s Tour problem is that a pawn begins on any field on the second rank (row), and advances with legal moves that can include captures to the opposite end of the board to become a knight. These fields, used by the pawn on the path to knighthood, are subsequently forbidden for the knight’s return to the starting field. The knight must traverse the rest of the chessboard, visiting each remaining field exactly once …

Stochastic Analysis With Operational Calculus In Reliability, Hend Hamdan Al-Jahani

Theses and Dissertations

Our dissertation models several reliability systems subject to occasional random shocks of random magnitudes W1,W2,..occurring at times tau0, tau2,..In Model 1, the underlying system becomes inoperational if it wears out due to aging specified by a monotone increasing continuous function Delta identifying system's wear at any time t>=0 . The system is deemed inoperational if delta crosses a sustainability threshold at some moment T=(delta )^-1(D). The precise time T is difficult to identify making the realistic failure time randomly delayed and thus identified at some opportune observation epoch. The system can also fail due to damages by external shocks, …

Small Scale Magnetohydrodynamic Thruster, Samuel Rabaey

Celebrating Scholarship and Creativity Day (2018-)

This paper explores the performance of a self-constructed, small-scale magnetohydrodynamic (MHD) thruster using saltwater as the conductive fluid. The MHD drive generates propulsion through Lorentz force by applying an electric current across electrodes in the presence of an orthogonal magnetic field. Two experiments were conducted: one measuring static water displacement to determine force output, and another using fluid velocity in a closed loop to evaluate both force and efficiency at varying magnetic field strengths. Theoretical predictions based on MHD and fluid dynamics principles were compared with experimental results. While the measured outputs were consistently lower than theoretical approximations, likely due …

Countering Deficit Narratives Through A Blackcrit Lens By Examining Case Studies Of Black College Mathematics Students’ Classroom Experiences, Akhenaton Wilbourn

All Dissertations

This dissertation examines the lived experiences of 11 Black college mathematics students at their predominantly white institution (PWI) through the lens of Black Critical Theory (BlackCrit) to counter deficit narratives about the racial achievement gap (RAG) in mathematics education courses. Deficit narratives often attribute disparities between Black and white students’ mathematical performance to assumed deficiencies in Black students’ abilities rather than systemic inequities, historical marginalization, and ongoing anti-Blackness in educational settings (Cobb & Russell, 2015; Kress, 2021). Using multiple case studies, this study explores how anti-Blackness manifests in mathematics classrooms, how students navigate tensions between multiculturalism, neoliberal educational policies, and …

Comparative Study Of Non-Iterative Seqential Method For Biot's Poroelasticity Model, Jeff Frimpong Amponsah

Open Access Theses & Dissertations

Linear poroelasticity theory describes the interaction between the motion of fluids and deformation of porous media. The theory serves various applications in a wide range of science and engineering fields, such as soil mechanics, oil reservoir modeling, and bio-medical applications. Partial differential equations are used to model the complex interaction between fluid flow and solid deformation in porous media. Since analytical solutions to these equations are rarely available for realistic problems, we resort to numerical solutions. One major advantage is their ability to provide accurate approximations of the solutions. Various numerical methods have been proposed to solve Biot's poroelasticity system. …

A Numerical Study Of Self-Assembling Amphiphilic Systems, Joshua Albert Sackey

Open Access Theses & Dissertations

Mixing processes in ternary mixtures involve immiscible fluids such as oil and water, and a surface-active molecule called surfactant. These physical processes find applications in various fields, including enhanced oil recovery, drug delivery design systems, and the formulation of cleaning products. Even though this process has several applications, the mathematical models describing it and the numerical methods solving it are not well understood. The underlying mathematical model is a nonlinear initial-boundary value problem involving sixth-order derivatives and belongs to the class of sixth-order Cahn-Hilliard equations. Authors Sharma and Tierra recently proposed a numerical method to approximate its solutions in two …

Car Price Prediction Using Machine Learning: Analyzing The Dvm-Car Dataset, Yaman Abu Ghareebaih

Electronic Theses and Dissertations

The objective of this study is to predict car prices using machine learning models and the DVM-CAR dataset, which includes over 1.4 million images and car specifi- cations from 899 car models. Key factors such as mileage, engine power, and year of registration were analyzed for their correlation with car prices. Extensive data cleaning was performed, including filling missing values, identifying outliers, and normalizing numerical variables. Discrete variables like car make and body type were encoded using one-hot encoding. Linear relationships were analyzed with Multiple Logistic Regression, and Random Forest models were used for nonlinear patterns. Model performance was evaluated …

The Improved New Intersection Theorem Revisited, Lars Winther, Luigi Ferraro

School of Mathematical & Statistical Sciences Faculty Publications

We prove a generalized version of Evans and Griffith’s improved new intersection theorem: Let I be an ideal in a local ring R. If a finite free R-complex, concentrated in nonnegative degrees, has I-torsion homology in positive degrees, and the homology in degree 0 has an I-torsion minimal generator, then the length of the complex is at least dimR−dimR/I. This improves the bound htI obtained by Avramov, Iyengar, and Neeman in 2018.

Course Insight Portfolio: Math 1060 Calculus Of One Variable I, Julianne Barnhart, Rayna Elizabeth Maleki, Antsa Rakotondrafara

Publications

We presented this Course Insight Portfolio project as a final assignment for the class Teaching Undergraduate Math MATH 9700 in Summer 2025. It covers the Clemson class MATH 1060 Calculus of One Variable I and is a fruit of the collaborative work of Julianne Barnhart, Rayna Maleki, and Antsa Rakotondrafara.

Quotients, Equivalence Relations, And Normality In Non-Associative Algebra With Regards To Loops And Quasigroups, Matthew L. Mulholland

All NMU Master's Theses

This thesis will contain a detailed overview of relations, quotients, normality, loops, quasigroups, and related theorems and varieties. Nonassociative algebra is a relatively new area of mathematics, it came about in the past hundred years, and has started making progress in the past 60 years. In nonassociative algebra, varieties do not necessarily satisfy associativity. Several interesting problems with relations, quotients, and normality arise from the setting of nonassociative algebra. In the language of equivalence relations, quotients, and subsets what are the conditions of normality, or existence of a subalgebra in quasigroups and loops? A quasigroup, Q, is defined to be …

Stability Analysis Of Turbulent Fluid Flow, Adam D. Schroeder

Mathematics, Statistics, and Computer Science Honors Projects

Hydrodynamic stability refers to the study of when and how laminar flows transition to turbulence. This includes investigations of the mechanisms of transition, as well as the classification of known flow configurations as either stable or unstable and the identification of critical values of flow parameters at which this bifurcation occurs. In this thesis, we introduce the mathematical theory behind continuum mechanics and fluid dynamics as well as some tools from the study of dynamical systems. We apply these concepts to the linear stability analysis of zero pressure gradient flat plate flow via numerical simulations in OpenFOAM, discussing both the …

P-Adic Quantum Mechanics, Infinite Potential Wells, And Continuous-Time Quantum Walks, Nathaniel P. Mayes

Theses and Dissertations

In this thesis, we introduce a p-adic version of the infinite potential well in quantum mechanics (QM). This model describes the confinement of a particle in a p-adic ball. We rigorously solve the Cauchy problem for the Schrödinger equation and determine the stationary solutions. The p-adic balls are fractal objects. By dividing a p-adic ball into a finite number of sub-balls and using the wavefunctions of the infinite potential well, we construct a continuous-time quantum walk (CTQW) on a fully connected graph, where each vertex corresponds to a sub-ball in the partition of the original ball. …

The Herzog-Takayama Resolution Over A Skew Polynomial Ring, Linoy Utkina

Theses and Dissertations

Let k be a field, and let I be a monomial ideal in the polynomial ring R = k[x1,..., xn]. In her thesis, Taylor introduced a complex that yields a finite free resolution of R/I as an R-module. Building on Taylor’s work, Ferraro, Martin, and Moore extended this construction to monomial ideals in skew polynomial rings. Because the Taylor resolution is typically not minimal, subsequent research efforts went into identifying specific classes of ideals whose minimal free resolutions can be constructed more simply. In 1990, Eliahou and Kervaire devised an approach for handling minimal resolutions of …

A Dg-Algebra Structure With Divided Powers On The Generalized Taylor Resolution, Raul F, Alvarez

Theses and Dissertations

This thesis investigates the construction of a DG Γ-algebra structure on the Generalized Taylor Resolution (GTR) associated with monomial ideals. The classical Taylor resolution is known for providing a free but generally non-minimal resolution, leading to computational challenges and inefficiencies in algebraic analysis. In contrast, the GTR preserves essential algebraic structures while optimizing the resolution process, offering a more efficient and comprehensive framework for studying monomial ideals.

We introduce a novel DG Γ-structure that incorporates divided powers into the GTR, enhancing its multiplicative and homological properties. This structure preserves strict graded commutativity and is fully compatible with the differential graded …

Camassa-Holm Type Equations And Multi-Peakon Solutions, Yonghong Chen

Theses and Dissertations

This thesis investigates the multi-peakon solutions of a class of Camassa-Holm type equations with quadratic nonlinearities, specifically focusing on the differential equation mt +θmu+ amxu+bmux = 0, where m = u−uxx, and θ, a, b are arbitrary constants. We derive the nonlocal form of the equation and explore its peakon dynamics, including the well-known Camassa–Holm, Degasperis–Procesi, and Holm–Staley b-family equations. By employing a practical computational approach, we analyze the N-peakon solutions and present the corresponding dynamical systems, particularly focusing on the two-peakon case. The results will …

Congruences In Arithmetic Progression For Coefficients Of Gaussian Polynomials And Crank Statistics, Joselyne Aniceto

Theses and Dissertations

The study of partition congruences, inspired by Ramanujan’s discoveries for ��(��) over a century ago, remains a central topic in this field. This dissertation examines congruence properties in two restricted partition functions: ��(��,��), which counts partitions of �� into at most �� parts, and ��(��,��,��), which further limits the size of the largest part to be at most ��. Building on Kronholm’s 2007 result, now known as the Interval Theorem, and a recent result by Eichhorn, Engle, and Kronholm, we establish new infinite families of congruences for ��(��,��,��). This dissertation extends not only the recent results of Eichhorn, Engle, …

Koszul Cohomology Of Canonical Products, Alexander Scott Duncan

Graduate Theses and Dissertations

In this thesis, we give a complete classification of the Koszul cohomology groups K_p,₁(C, B, ω_C ⊗ B) on a smooth curve C of genus g ≥ 2 with B p-very ample. Such a classification in the case B = ω_C has been incomplete until [5]. The classification follows easily from our main result which precisely calculates K_p,1(C, B, B ω_C ⊗ B) in terms of h⁰(C, B). This result also handles the case B = ω_C. A straightforward …

Development Of Saddlepoint Methodologies For Sparse Sample Multiple Parameter Generalized Linear Models And Correlated Data Scenarios, Christopher Johnson

All Graduate Theses and Dissertations, Fall 2023 to Present

Parameter estimation using maximum likelihood techniques may be biased when sample sizes are small, event rates are low, or otherwise sparse counts exist in a parametric model. This in turn may lead researchers to draw invalid statistical conclusions when conventional methods are utilized. The saddlepoint approximation has potential to lessen the degree of bias in sparse data conditions through its use of moments beyond the mean and variance, which allows for more accurate approximations using a smaller number of observations. We propose two novel saddlepoint methods for use in practical analysis scenarios, as an alternative to maximum likelihood estimation. First, …

Constructing Binary Encoding Matrices From Joined Graphs, Joshua Avalos

Electronic Theses, Projects, and Dissertations

Codes and technology are part of our daily lives and allow the modern world to function, and for us to have conveniences in our lives such as smartphones that can be used to privately call people on the other side of the planet, and for secure access to the internet. In this thesis we will explore the construction of binary codes created by vertex-edge incidence matrices of planar graphs. The Hamming (7,4) code was an incredible code that allowed the detection and correction of errors after receiving them through a transmission. We will explore the possibility of the creation of …

Algebraic Properties Of Boolean Models, Harrison Fisher

All Theses

Boolean models are n-tuples of polynomial functions in n variables over the finite field of order 2. These models define finite dynamical systems which are used for modeling many different biological systems such as gene regulatory networks. These systems can be defined by updating every function synchronously, or by updating one function at a time asynchronously. In this project, we discuss a method for reverse engineering the model space of all Boolean models which fit a set of partial asynchronous data. This method is a generalization of a known method for synchronous data. In addition, we show that given the …

Functional Data Analysis Of Weekly Confirmed Covid-19 Cases Per Million In Relation To Unemployment Rates And Emergency Declaration Responses, Elaina Kay Mcgovern

Boise State University Theses and Dissertations

At the onset of the COVID-19 pandemic, U.S. states implemented policies that attempted to mitigate the spread and effects of the disease, such as a state of emergency declaration. This study explores the application of functional data analysis (FDA) as a means to investigate the impact of U.S. state-level emergency declarations on weekly confirmed COVID-19 cases per million during the first year of the pandemic. We focus on the duration and extent to which proactive states showed significantly different patterns of COVID-19 spread than those that implemented policies reactively. Additionally, we examine patterns in monthly state-level unemployment rates over the …

Leading Digits Of Some P-Adic Numbers, Jinha Park

Boise State University Theses and Dissertations

I investigated the leading digits of some sequences in the p-adic numbers Q_p, hoping to find some sequences following Benford's law, or following something completely different. We found that the sequence of partial sums Sum^N_{n=1}\frac{1}{n^s}, where s\in\N is fixed, shows uneven distribution of leading digits, except for s\equiv 0 (mod{p,/em>-1}), where the distribution of leading digits is eventually even. We were able to characterize the distribution of this partial sum for almost all s.