Mathematics Commons^™

The Tones And Frequencies Of A Glockenspiel, Edward Czudak

Theses, Dissertations and Culminating Projects

In this thesis, I will analyze the tones and frequencies of a glockenspiel based on the results of Warburton’s 1954 article, “The Vibration Of Rectangular Plates,” [12]. I will be measuring and modeling the frequencies of a glockenspiel and connect them with the analytical and expected numerical solutions. The solutions will be based on the plate equation along with the boundary conditions of a rectangle free on all edges. I will look at the high modes of vibration for the bars and their corresponding overtones in the acoustic spectrum.

Volume 17, Christian O’Neill, Kyara Greene, Savva Sidorov, Laura Bisaillon, Luke Clemmer, Hannah Gordon, Kitt Benson, Taylor Blount, Rachel Danzitz, Nicholas Duellman, Chase Gionis, Hima Fernando, Seth Franzyshen, Onyx Gonzalez, Bryan Lin, Samantha Start, Ysabel Wells, Maggie Duncan

Incite: The Journal of Undergraduate Scholarship

Introduction Dr. Amorette Barber, Director, Office of Student Research

From the Editor Dr. Hannah Dudley-Shotwell

Cover Artist’s Statement Maggie Duncan

On Mentoring Dr. Yulia Uryadova

Ukrainian Resistance in the Face of Russification: Nestor Makhno and Anarchism

by Christian O’Neill

Life Vest by Kyara Greene

Isolation and 16S rRNA Identification of Bacteria from Fire Department Connection Pipe by Savva Sidorov

The Effectiveness of Planned Exercise in Reducing ADHD Symptoms in Children by Laura Bisaillon & Luke Clemmer

Linguistic Analysis on Confidence and Communication Strategies with Disparities Between Sign Fluency and Hearing Impairment by Hannah Gordon

Freedmen in Indian Territory by Kitt …

Analyzing The Evolution Of Science: Topological Cycles And Community Detection In Knowledge Networks, Frances C. Mcconnell

Mathematics, Statistics, and Computer Science Honors Projects

How scientific knowledge grows and organizes itself is a central question in the study of science. This thesis uses tools from topology and network science to detect and characterize knowledge gaps—places in a field’s literature where related concepts do not co-occur. We develop a metric to quantify the degree of interdisciplinarity of each gap, using the community structure of the underlying network as a proxy for subfields. Across a wide range of fields, gaps reliably span multiple subfields and evolve in recognizable temporal patterns, highlighting new insights into how scientific fields are structured and their stage of development.

From The Hopf Fibration To Instantons: Geometry In Gauge Theory, Emily D. Wessman

Undergraduate Honors Capstone Projects

This paper explores the relationship between topology, differential geometry, and gauge theory through the study of Yang-Mills theory and its solutions, known as instantons. Beginning with the Hopf fibration, we show how principal fiber bundles encode topological information and appear in physical contexts such as electromagnetism. In particular, we consider how the fibration of S³ over CP¹ ≅ S² represents the Dirac magnetic monopole, and how the Chern number associated with the bundle is exactly the winding number for the monopole.

We then develop the framework of gauge theory, focusing on connections on principal SU(2) bundles …

Fractsynth: Exploring Glitch Timbres With Chaos Theory, Aidan Roach

The Transdisciplinary STEAM+ Journal

In this paper, I explore how chaos theory can be used to design a new kind of synthesizer with the primary focus of producing glitchy, unpredictable sounds. Glitch music embraces abstract sound design, malfunctioning electronics, and randomness as the main compositional elements. However, most synthesizers rely on stable, repetitive oscillators that often sound too controlled. To challenge this, I developed FractSynth, a real-time synthesizer that uses chaotic attractors–including the Logistic Map, Henon Map, and Lorenz System–as modulation sources for frequency, amplitude, and tone. The software also features real-time Lyapunov Exponent Tracking, which gives users a direct visual of how …

Interactions Of Dance And Mathematics: A Closer Look At Mathematical Sequences As Scores For Choreography From A Choreographic Lens, Caroline Wolfe

The Transdisciplinary STEAM+ Journal

This paper investigates the embodiment of infinite mathematical sequences through concert contemporary dance, examining how choreography can serve both as an artistic and analytical tool for exploring numerical patterns. Grounded in interdisciplinary literature on mathematical visualization in choreography, the study centers on two original choreographic works presented and performed at Missouri State University: Golden Ratio Sequence (Spring 2025), which maps the Fibonacci sequence and the natural applications of the Golden Ratio onto a spiral floor pattern, and Tetrahedral Numbers (Fall 2024), which employs an accumulation score to embody three-dimensional number growth through layered movement motifs and body created tetrahedra. The …

Getting Your Master's, Is It Worth It?, Vy Le, Madyson Schreifels

Celebrating Scholarship and Creativity Day (2018-)

This project uses a differential equation model to evaluate whether earning a master’s degree is financially worthwhile. Using UC Berkeley’s Master of Computer Science program as a case study, we modeled student loan repayment and compared long-term earnings between bachelor’s and master’s degree holders. The model predicts monthly loan payments and estimates the break-even point where the higher salary from the master’s degree outweighs the total investment cost. Results suggest that the degree becomes financially beneficial after approximately 15 years.

Bibliography Of Religious Faith And The Mathematical Sciences, Calvin Jongsma

Faculty Work Comprehensive List

This Bibliography is offered as a helpful resource for anyone who wishes to thoughtfully explore the connections between religious faith and the mathematical sciences. Searching the database for a topic of interest will bring up items with that focus. An entry’s attached PDF (when publicly available) can be opened and read while in the database. Alternatively, each item contains a URL/web link to a location where one can either read the item or retrieve information about how to obtain a copy of it.

An Analysis Of A Family Of Root Finding Methods, Arabella Fuzak

Celebrating Scholarship and Creativity Day (2018-)

This thesis analyzes the behavior of a family of iterative root-finding methods, the Hansen-Patrick Family, which has a parameter, alpha, to create methods such as Newton’s methods, Halley’s method, and Euler’s method. By varying the parameter alpha, with both real and complex values, this project examines how the parameter can change convergence, divergence, and stability for different functions. This is shown by basin maps and Mandelbrot-like sets to visualize this behavior and classify points based on whether they converge to a root, diverge to infinity, or remain bounded without converging.

Redefining Certainty: Non-Euclidean Geometry And Theology Transformation Throughout The Intellectual Unrest Of The Early 1800s, Luke Bensinger

Honors Theses

To bridge the gap between mathematics and theology, it is necessary to explore their intersection and challenge the notion that these fields are incompatible. This study focuses on the 19th century, a period when non-Euclidean geometries emerged and disrupted mathematical certainty, while Protestant theologians such as Barton W. Stone and Alexander Campbell grappled with Calvinism and shifting theological perspectives. By analyzing mathematicians studying geometry, such as Gauss, Lobachevsky, and Riemann, this research examines how both disciplines balance change with enduring truths.

Lebesgue’S Theory Of Integration: An Introduction To Modern Integration Theory, Nathanael C. Krug

Senior Honors Theses

The depth and richness of integration theory far surpasses the introductory material presented in an elementary calculus classroom. The work of Bernhard Riemann and Henri Lebesgue demonstrates just a small sample of the richness of the field of analysis. In formulating and contrasting the Riemann and Lebesgue integrals, students can gain an enriched and well-rounded introduction to integration theory. This not only deepens understanding and love for previously learned material, but also enables further study within the fields of analysis and measure theory. An introductory primer to integration theory equips students with the tools needed to continue their exploration of …

Detection, Mapping, And Spraying Of Carolina Redroots In Cranberry Bogs Using Ai And Autonomous Drones, Duwon Ham, Bishal Neupane, Thien Ba Nguyen, Thanh Nguyen, Hieu D. Nguyen, Thierry Besancon

STEM Student Research Symposium Posters

Use artificial intelligent and autonomous drones to automatically detect Carolina Redroots in cranberry bogs, create density maps of the weed, and perform spot spraying.

Finiteness Of Torsion Loci And Normal Functions Arising From Cycles On Hadamard Products, Devin Akman

Arts & Sciences Graduate Student Theses and Dissertations

The unifying theme of this dissertation is normal functions. In the first chapter, we study an invariant of knot exteriors and similar manifolds called the A-polynomial through the lens of vanishing loci of normal functions. Using a special case of the Zilber-Pink conjecture, proven in the second chapter, we show that only finitely many irreducible Laurent polynomials of bounded overgenus appear as factors of A-polynomials. In the third chapter, we construct normal functions from hypergeometric variations of Hodge structure and compute their regulators. Finally, we determine under which conditions incomplete motivic cohomology cycles on families complete to cycles on their …

Complexity Of The Zero Set Of A Matrix Schubert Ideal, Cesar Julian Meza

Arts & Sciences Graduate Student Theses and Dissertations

T-varieties are normal varieties equipped with an action of an algebraic torus T. When the action is effective, the complexity of a T-variety X is dim(X)−dim(T). Matrix Schubert varieties, introduced by Fulton in 1992, are T-varieties consisting of n×n matrices satisfying certain constraints on the ranks of their submatrices. In this dissertation, we focus on the complexity of certain torus-fixed affine subvarieties of matrix Schubert varieties. Concretely, given a matrix Schubert variety X_w where w∈S_n, we study the complexity of Y_w obtained by the decomposition X_w = Y_w ×C^k with k as large as possible. Building on results by Escobar–Mészáros …

Rosenzweig's Elements And Universal History, Martin Zwick

Complex Systems Faculty Publications and Presentations

This paper uses Rosenzweig’s conception of the three elements of God, World, and Human from The Star of Redemption in a model of universal history. The model also has some relation to Rosenzweig’s geopolitical essay, Globus, which is very different from the meta-historical Star. Based on a systems-theoretic schema of events and processes, the model views human history in terms of three linked processes: a primary process labeled “World” – the origin and development of human society embedded in nature, a secondary process labeled “God” – the origin and development of the Axial religions and philosophies, and a …

Boolean Rank Via Monomial Ideals And Neural Ideals, Juliann Marie Geraci

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

This dissertation develops new connections between Boolean matrix factorization, combinatorial neural codes, and commutative algebra. The central goal is to understand how structural and algebraic invariants can be used to measure and bound complexity in discrete data. We begin by studying the Boolean matrix factorization (BMF) problem, which seeks to express a binary matrix as a product over the Boolean semiring with minimal inner dimension, known as the Boolean rank. By interpreting binary matrices as bipartite graphs, we relate Boolean rank to biclique covers and introduce algebraic techniques to study this quantity. We associate to a matrix its edge ideal …

Halo: High Autonomous Low-Swap Operations, Sloan Hatter, Blake Gisclair

Mathematics and System Engineering Student Publications

Orbital object detection is a vital aspect of space operations, particularly for identifying satellite components. Convolutional Neural Networks (CNNs) are typically used for such operations by running onboard models directly on satellite systems. However, a new neural network architecture, known as Vision Transformers (ViTs), have shown greater effectiveness due to their ability to capture global context. One main issue of deploying systems with such capabilities is resource allocation. One solution is to run models on a Low-SWaP system; however, this results in inefficient performance. To enable efficient ViT operations on Low-SWaP systems, the model must be scaled down through quantization, …

Stochastic Network Resilience Under Random Failures, Blake Gisclair

Mathematics and System Engineering Student Publications

This project investigates threshold-crossing probabilities in stochastic networks. Using probabilistic modeling and transform-based analytical methods, the work derives expressions that characterize when cumulative losses exceed prescribed limits with the goal of providing insight into the relationship between local random behavior and global network risk.

Determining Material Transport Method For Moon Colony Using Differential Equations, Scott Meeson, Anthonie Page, Matas Vaitkevicius

Mathematics and System Engineering Student Publications

NASA Artemis Missions: NASA’s Artemis program marks a fundamental shift from short-term lunar exploration to sustained, permanent colonization.

The Invisible Shield: Why Our Stomach Doesn’T Digest Itself, Kevon Findley

Mathematics and System Engineering Student Publications

The stomach contains highly acidic gastric fluid with a very low pH.  A thin mucus lining protects the stomach from self-digestion and keeps nearby epithelial cells near a pH 7.  A weakened mucus layer is associated with conditions such as Gastritis and Peptic Ulcer Disease.

How can the protective mucus barrier be maintained and be of stable thickness?