Mathematics Commons^™

Modeling Literary Connections: Exploring Transregional Resistance In Dalit Poetry, Antara Bhattacharyay

Mathematics, Statistics, and Computer Science Honors Projects

Structuring socio-political identities, the caste system (a graded form of hierarchy) remains entrenched in contemporary Indian society. Dalits, marginalized by the caste system, have expressed their resistance through literature, envisioning substantive equality and social change. In this thesis, I draw on digital humanities methods to examine regional variation in translated Dalit poetry from Bengali, Hindi/Urdu, Marathi, and Tamil languages. I utilize topic modeling—a machine learning algorithm that detects latent semantic structures in a text—as a point of departure for poetry analysis. I observe how topic modeling enables newer readings of the poems, revealing regionally resonant and broader Dalit themes.

How Much Should Consumers With Mild To Moderate Hearing Loss Spend On Hearing Devices?, Vinaya Manchaiah, Steve Taddei, Abram Bailey, De Wet Swanepoel, Hansapani Rodrigo, Andrew Sabin

School of Mathematical & Statistical Sciences Faculty Publications

Background: This study examined the relationship between hearing device price and sound quality. Method: A novel consumer-centric metric of sound quality (“SoundScore”) was used to assess hearing devices’ audio performance. Each hearing device is tested with two fittings. The “Initial Fit” is designed to approximate the most likely fitting for an individual with a mild-to-moderate sloping sensorineural hearing loss. The “Tuned Fit” includes adjusting parameters optimized to hit prescriptive fitting targets (NAL NL2) on an acoustic manikin. Each fitting is evaluated across five dimensions. Both fittings are combined using a weighted average to create a single number from 0 to …

Studies In Algebraic Cycles: Hodge Theory Of Degenerations, Regulators, And Cluster Varieties, Ricardo Jaime Acuna

Arts & Sciences Graduate Student Theses and Dissertations

This dissertation brings together results in Hodge theory and the theory of cluster varieties. The second chapter, based on a paper written in collaboration with Devin Akman and Matt Kerr, uses admissible normal functions to establish the first finiteness result for zero-dimensional components of the Hodge locus. The third chapter, based on joint work with Matt Kerr, shows that weak polar- ized relations constrain possible adjacencies of mixed Hodge structures across boundary strata in geometric compactifications. The fourth chapter gives a geometric construction of a 6-dimensional cluster variety with a disconnected mutation graph, as discovered by Yan Zhou. These three …

Some Interpolation Problems In The Projective Plane, Lilah Estes

Mathematical Sciences Undergraduate Honors Theses

Given some set of r general points in the projective plane, we want to better understand: what is the smallest degree of any polynomial passing through the points m times? How many linearly independent equations of this degree pass through the points m times? The investigation of these questions, particularly for the case of m=3 and r< 16, motivates the development of several results. We translate Terracini's inductive argument, a tool for evaluating the expectedness of certain sets of double points, into a version which can be used for triple points, and prove that the argument holds. We compute the minimal graded free resolutions for the ideals corresponding to up to 15 points, for m up to 6, and we conjecture a connection between the expectedness of these ideals and what their resolutions look like. Further, we prove that this conjecture holds when m=1, and we either fully or partially prove that these ideals are …

On The Hexgame, Corwin Jones

Mathematical Sciences Technical Reports (MSTR)

The SOMA Cube has been studied by mathematicians for a number of decades, but so far methods for solving three-dimensional space-filling puzzles like the SOMA cube remain numerical; we do not have a means to predict the number of solutions to SOMA-like puzzles. We present a two-dimensional puzzle that shares certain features of the SOMA Cube, with the hope that it will be a more convenient object of study for future research into space-filling/space-covering puzzles.

The Spectral Asymptotics Of Toeplitz Operators On Hilbert Spaces Of Analytic Functions, Trevor Camper

All Dissertations

Many physical systems, whether they are ocean waves or particles moving through space, can be described using the mathematical language of “partial differ- ential equations.” In many circumstances, it is useful to study how these equations amplify an input to the equation, in which case the amplification factor is called an “eigenvalue.” The usefulness of these amplification factors is that they can be used to describe properties of the physical system. In this dissertation, I have studied this amplification factor for a related set of equations called “Toeplitz operators.” In par- ticular, I have studied eigenvalues using statistical techniques. The …

Analysis And Mathematical Recomposition Of The Art Of The Fugue, Joshua Cellar

Theses, Dissertations and Culminating Projects

The Art of the Fugue is a collection of 18 fugues and cannons written by Johann Sebastian Bach in the 1700s. Each piece starts with a single theme which is transformed, developed and mixed in fascinating mathematical combinations resulting in a distinctive musical style. In this paper, we use the method introduced in [7] to analyze 14 pieces from The Art of the Fugue. We focus on the variation of motifs from one piece to another as well as the complexities of mathematical transformations present throughout the entire collection. We also demonstrate how using maps of transformations and the rules …

Logic's Modern British Up-Enders, Defenders, And Extenders: Whately's Revitalization Of Logic, Calvin Jongsma

Faculty Work Comprehensive List

Logic developed dramatically during the last half of the nineteenth century. The baseline for these transformations in Great Britain was the revival of logic by Richard Whately around 1825. Whately successfully defended syllogistic logic as the science of valid reasoning against potent seventeenth and eighteenth-century detractors—Bacon, Locke, Reid, Campbell, Stewart, and others. In so doing, he made logic an intellectually respectable field of investigation for the next generation of logicians to explore and extend. This included John Stuart Mill (inductive logic), Augustus De Morgan (logic of relations), and George Boole (algebraic logic; propositional logic).

Culture And Context: How Frames Of Teaching And Of Learning Mathematics Form And Change For Graduate Student Instructors, Johan Benedict A. Cristobal

Department of Mathematics: Dissertations, Theses, and Student Research

Why do instructors teach the way that they do? This question is key in understanding how and why asset-based or deficit-based practices are enacted in the classroom. In consequence, this question also gives insight into how the environment where students learn is shaped. Mathematics education research, in particular, has been concerned with how instructors respond to students’ contributions in the classroom and how these ways of responding can (dis)empower students.

One way to answer this question is to understand how instructors frame their own teaching and their students’ learning. Frames are mental constructs which help individuals filter details, interpret information, …

Modules Of Finite Projective Dimension And Singularities, Nawaj Kc

Dissertations and Doctoral Documents, University of Nebraska-Lincoln, 2023–

In the first part of this thesis, we study liftings of modules of finite projective dimension. We introduce a notion of “Serre liftable” modules and deduce applications to multiplicity conjectures in local algebra. In the second part, we introduce and study a module of mixed K\"ahler differentials for finite algebras over ramified discrete valuation rings of mixed characteristic. We state and prove a Jacobian criterion for computing the singular loci of such algebras.

Advisors: Jack Jeffries and Mark Walker

Using Permutation Groups To Identify Family Of Capacity Achieving Codes, Daniel Joseph Welchons

Dissertations and Doctoral Documents, University of Nebraska-Lincoln, 2023–

When communicating over a noisy channel, the probability of message interference sets a maximum possible transmission rate known as the channel capacity. Any family of codes which have rates converging to the channel capacity and arbitrarily low probability of decoding failure is called capacity achieving. Such codes have been known to exist since the birth of information theory but are difficult to find explicitly. It has recently been shown that the permutation groups of a family of codes can be used to show that the family is capacity achieving on the q-ary erasure channel.

This this thesis seeks to …

Using Permutation Groups To Identify Families Of Capacity Achieving Codes, Daniel Welchons

Department of Mathematics: Dissertations, Theses, and Student Research

When communicating over a noisy channel, the probability of message interference sets a maximum possible transmission rate known as the channel capacity. Any family of codes which have rates converging to the channel capacity and arbitrarily low probability of decoding failure is called capacity achieving. Such codes have been known to exist since the birth of information theory, but are difficult to find explicitly. It has recently been shown that the permutation groups of a family of codes can be used to show that the family is capacity achieving on the q-ary erasure channel.

This thesis seeks to apply the …

Ritt’S Theorem And The Chebyshev Polynomials, Eric Neuhaus

Honors Theses

We explore polynomial composition through Ritt’s Theorem and mondromy groups. J.F. Ritt asked the question of when a polynomial can be written as the composition of two other polynomials of smaller, nontrivial degree. Ritt’s Theorem provides a method for determining whether or not a polynomial is composite by observing the actions of its associated monodromy group, a group of permutations acting upon the roots of a given polynomial. In this work, we study the monodromy groups of the Chebyshev polynomials of the first and second kinds to uncover their compositional properties.

Inversion Numbers Of Oriented Graphs, Sam Harris

Theses, Dissertations and Culminating Projects

This thesis investigates recent results and conjectures regarding inversion numbers of oriented graphs. We define the inversion number of an oriented graph G as the minimum size of a decycling family of subsets of vertices of G. We focus on three areas: the maximum inversion number of a graph on n vertices, the inversion numbers of dijoins of two oriented graphs, and computational algorithms for deciding the inversion number. The main contribution of this thesis is a proposed construction of a graph with higher inversion number than that of any other currently known construction. We also provide explicit, rather than …

Effects Of The Gravity Gradient On The Path Of 1i/‘Oumuamua, Hannah R. Richardson

Poster Presentations

In October 2017, the asteroid 1I/’Oumuamua first passed into viewing range [1]. The asteroid is notable for being the first interstellar object to enter the solar system. 1I/’Oumuamua was also unusual in its geometry; it is thought to have an aspect ratio of 6:1 and a length of approximately 400 m [2] [3]. The asteroid was observed to experience a non-Keplerian acceleration estimated to be on the order of 1×10−6 m s-2 Several theories have been proposed for the cause of this acceleration, all of which are non-gravitational in nature: volatile outgassing, photon pressure, and solar winds [1][4]. However, none …

Culture And Context: How Frames Of Teaching And Of Learning Mathematics Form And Change For Graduate Student Instructors, Johan Benedict Arroyo Cristobal

Dissertations and Doctoral Documents, University of Nebraska-Lincoln, 2023–

Why do instructors teach the way that they do? This question is key in understanding how and why asset-based or deficit-based practices are enacted in the classroom. In consequence, this question also gives insight into how the environment where students learn is shaped. Mathematics education research, in particular, has been concerned with how instructors respond to students’ contributions in the classroom and how these ways of responding can (dis)empower students.

One way to answer this question is to understand how instructors frame their own teaching and their students’ learning. Frames are mental constructs which help individuals filter details, interpret information, …

2-Segal Sets And Pseudomonoids In The Bicategory Of Spans, Sophia E. Marx, Rajan Amit Mehta

Mathematics Sciences: Faculty Publications

In this survey article, we give an introduction to the notion of a 2-Segal set and prove that 2-Segal sets are equivalent to pseudomonoids in the bicategory of spans. The proof utilizes graphical techniques for 2-Segal sets and spans that should be useful in more general settings.
There are procedures for obtaining an associative algebra from a 2-Segal set (satisfying finiteness conditions). We describe these procedures and give several examples of algebras arising from 2-Segal sets.
Wherever possible, we avoid higher category theory so as to make the paper accessible to a wide audience.

Improving Research Software Engineering In Mathematics, Abram Miller

Honors Theses

Research Software Engineering is critical to modern mathematical research, enabling the creation, maintenance, and dissemination of computational tools that bridge theory and practice. However, the field faces systemic challenges, including insufficient funding, lack of institutional recognition, and gaps in training and infrastructure. This thesis investigates these challenges through two approaches: (1) a comparative survey study focused on mathematicians and (2) hands-on contributions to an open-source research software project.

The Improving Research Software Engineering in Mathematics survey, conducted from September 2024 to January 2025, adapts the survey framework developed by Carver et al. in A survey of the state of the …

Computer Vision In Soccer: Yolov11 Analytics Engine For Quantifying Game Strategy, Connor S. Maurer

Data Science Undergraduate Honors Theses

Single-shot object detection capabilities significantly reduce computational overhead for real-time computer vision in sports analytics at 60 FPS. YOLO11’s lightweight CNN gives promising accuracy while meeting the low-latency demand of dynamic soccer matches. As data-driven approaches take over the sport of soccer, efficient player tracking systems become critical for informing coach’s strategies. I prototype the ETL (Extract, Transform, Load) process of data collected from a single- shot detection program and evaluate its viability for estimating player fatigue. YOLO11 detects players, the ball, and other characteristics, with the output transformed by homography to estimate the positions in the real world. These …

Two-Player Trick-Taking Games On Bipartite Tournaments., Allan Bagley

College of Arts & Sciences Senior Theses

We consider a two-person game played on a bipartite tournament with equal size parts. The game is modeled after trick-taking card games like bridge or euchre. The two players, South and North, each receive one of the parts as their hand, and the arcs from a vertex in one hand beat the corresponding vertices in the other hand. The game is played over rounds called tricks where the number of tricks is equal to the number of vertices in each player’s hand. At the beginning of the game, one player is designated as the leader, and they play the first …

A Study Of Knots And Quandles, Zhaoqi Wu

Math and Computer Science Honors Theses

We explore the mathematical theory of knots through the lens of algebraic structures known as kei and quandles. We begin by introducing classical knot invariants and then study the fundamental kei of a knot as a tool for distinguishing knot types. We generalize this approach using various kinds of quandles, including Alexander and dihedral quandles, and investigate their associated polynomial invariants. We also examine the connection between quandles and group theory, as well as their algebraic representations in quandle rings. Moreover, we analyze idempotent elements in quandle rings over finite fields, providing both general results and specific examples.

Geometric Algebra For Field Theory In Curved Spacetime, Kevin Rhine

All Graduate Reports and Creative Projects, Fall 2023 to Present

Physics seeks to understand the universe by uncovering the fundamental laws that govern matter, energy, space, and time. At its heart lies the challenge of unification: finding a mathematical framework that consistently describes these interactions across all scales, from the subatomic to the cosmological.

This thesis explores geometric algebra, a mathematical language that unifies algebra and geometry, as a tool for advancing this understanding. By extending this framework to curved spacetimes, where gravity influences the structure of space and time, we investigate its ability to describe physical phenomena such as electromagnetism and general relativity. A notable contribution includes the geometric …

Yield Prediction Of Pv Solar Energy Systems And Its Application In The Energy Grid For Operational Efficiency, Pablo Bustamante

Open Access Theses & Dissertations

The generation of power from photovoltaic (PV) solar panels is influenced by a multitude of factors. These include the tilt and orientation of the solar panels, the latitude of their location, and the prevailing climate and weather conditions. Additionally, shading at specific locations, particularly if the panels are not part of a solar facility, can significantly impact their efficiency. The quality and efficiency of the panels themselves, along with the preventive maintenance of both the solar panels and associated components such as inverters and trackers, are also critical. Finally, the overall system design and installation play a vital role in …

Multiscale Integration Of Receptor-Ligand Dynamics Into Discrete And Continuous Tumor Growth Models With Application To Tyrosine Kinase Inhibitor Treatment, Romasa Qasim

Open Access Theses & Dissertations

The epidermal growth factor (EGF) receptor cascade plays a crucial role in the survival and proliferation of tumor cells. Tyrosine kinase inhibitors (TKIs) are a class of drugs that inhibit epidermal growth factor receptors (EGFRs), thereby preventing the downstream signal transduction. Despite their importance, models that link spatial receptor dynamics to tumor growth remain scarce. Further, TKIs act through selective mechanisms, inhibiting active, inactive, or all receptor states, which poses a challenge to traditional modeling approaches.

We propose to numerically study two mathematical models incorporating receptor-dynamics into cancer models to describe the impact of EGFR overexpression and TKIs. The first …

Efficient Fully Bayesian Approach To Brain Activity Mapping With Complex-Valued Fmri Data, Zhengxin Wang, Daniel B. Rowe, Xinyi Li, D. Andrew Brown

Mathematical and Statistical Science Faculty Research and Publications

Functional magnetic resonance imaging (fMRI) enables indirect detection of brain activity changes via the blood-oxygen-level-dependent (BOLD) signal. Conventional analysis methods mainly rely on the real-valued magnitude of these signals. In contrast, research suggests that analyzing both real and imaginary components of the complex-valued fMRI (cv-fMRI) signal provides a more holistic approach that can increase power to detect neuronal activation. We propose a fully Bayesian model for brain activity mapping with cv-fMRI data. Our model accommodates temporal and spatial dynamics. Additionally, we propose a computationally efficient sampling algorithm, which enhances processing speed through image partitioning. Our approach is shown to be …

Maximal Independent Set Algorithms Within Procedural Planar Maps: A Large-Scale Evaluation, Chaucer Ihrig

Honors College Theses

Analysis of a childhood game has led us to the problem of maximum independent sets in planar graphs. We wrote a graph creation utility using R to generate a random planar map and its dual graph. This utility then finds a graph’s maximal independent set using a variety of six algorithms. We investigate statistical connections between graph structure, colorability, and the maximal independent sets found using these algorithms over an incredibly large and procedurally generated dataset. We find one can always win the coloring game if the resultant graph is two-colorable. The algorithms perform statistically and practically significantly better on …

Math Course Placement Models At Csbsju Using Data Analysis, Josephine Jackson

Celebrating Scholarship and Creativity Day (2018-)

Many majors at the College of Saint Benedict and Saint John’s University (CSBSJU) require students to complete a course in calculus or statistics, however incoming students have various levels of preparation for these courses. This research investigates strategies for predicting student success in these courses and potential recommendations for remediation courses, e.g., pre-calculus or pre-statistics. The research uses data analysis to make this determination based on their previous math coursework and other data incoming students provide. Trends for success in math classes at CSBSJU have previously been based on outdated and inequitable methods. This project identifies correlations between prior coursework …

Decision Space Decomposition For Multiobjective Programs, Emma Soriano

All Dissertations

Being inspired by the parametric decomposition theorem for multiobjective optimization problems (MOPs) of Cuenca and Miguel (2017), and by the block- coordinate descent for single objective optimization problems, we present a decom- position theorem for computing the set of minimal elements of a partially ordered set. This set is decomposed into subsets whose minimal elements are used to retrieve the overall minimal elements. We apply this approach to strictly convex MOPs de- composing their decision space into lines. The line decomposition benefits from the fact that a multiobjective line search problem is equivalent to solving a collection of single objective …

Reuben Hersh's What Is Mathematics, Really? (Book Review), Calvin Jongsma

Faculty Work Comprehensive List

Reuben Hersh’s 1997 book What is Mathematics, Really? popularized a trend in the philosophy of mathematics that was gaining some traction at the time it was written. This essay examines Hersh’s work within the broader historical context of 19th- and 20th-century developments in mathematics and philosophy of mathematics. It also focuses on Hersh’s antagonism toward the influence of religion on (philosophy of) mathematics, concluding by briefly considering two positions taken by Christian mathematicians associated with ACMS in defense of such a connection.

Equity Vs. Excellence: Dichotomy Or Duo?, Nadjia I. Logans

Honors Program: Senior Projects (Public)

In this thesis, I investigate recent changes in mathematics education and how these developments connect to the principles of equity and excellence. I place a special focus on “active learning” methods. My methodology primarily consisted of interviews with educators, along with analyzing literature from math education researchers. I first define and explain the motivations behind active learning instruction methods. Next, I explore not only how instructors define equity and excellence but how educators perceive the role of the two principles within education. Finally, I challenge the pervasive media portrayal of equity and excellence as being mutually exclusive. Instead, I find …