Mathematics Commons^™

On Finite Groups With Essential Dimension 2 Over ℚ, Michael Huggins

Theses and Dissertations

We determine all finite subgroups of Aut(X) which have essential dimension 2 over ℚ, where X is a minimal Del Pezzo surface of degree at least 5. Additionally, finite groups with essential dimension 2 whose order is divisible only by the prime numbers 2 and 3 are classified with the exception of the groups dic ₁₂ , C₁₂, and Dih₂₄, whose essential dimensions remain unknown, but may possibly be equal to 2.

Generalized Sierpiński Numbers And New Irreducibility Criteria On Legendre Polynomials, Robert Scottfield Groth

Theses and Dissertations

A Sierpiński number is an odd positive integer k such that k·2n +1 is composite for all n ∈ Z+. Similarly, a Riesel number is an odd positive integer k such that k · 2n − 1 is composite for all n ∈ Z+, and a Brier number is a number that is both Sierpiński and Riesel. In this dissertation, we consider a generalization of a Sierpiński number and establish their existence by showing, for every fixed A ≥ 2, there are infinitely many odd positive integers k such that the k · an + 1 is composite for every …

Supershift Properties For Nonanalytic Signals, Fabrizio Colombo, Irene Sabadini, Daniele Carlo Struppa, Alain Yger

Mathematics, Physics, and Computer Science Faculty Articles and Research

The phenomenon of superoscillations is of great interest in microscopy, antenna design, and material sciences. This phenomenon has been generalized and has given rise to the concept of supershift, which is a far reaching extension that applies to functions that may present discontinuous derivatives. From this perspective, this is a notion that might have significant applications. This paper will provide an up to date report on the complex connections between the concept of supershift and that of analyticity.

An Investigation Into Continued Fraction Expansions Of √ N, Sara R. Ladik, Abdulkadir Hassen

STEM Student Research Symposium Posters

A continued fraction represents a number using an integer part and a sequence of positive integers in the denominators, with all numerators equal to one. This research examines the infinite continued fraction expansions of square roots of non-perfect squares. We observed and proved patterns in these expansions.

Stability Analysis & Analytic Solutions To Unforced Kinematic Property Equations, James Turbett

STEM Student Research Symposium Posters

We present analytic solutions and a stability analysis for a system of nonlinear coupled differential equations that describe the time evolution of kinematic properties of geophysical fluids. Solution curves in phase space are interestingly hyperbolic, elliptical, or parabolic in nature, depending on the initial conditions we input and have interesting geometrical properties.

Fixed-Size Ledger Of Fungible Tokens, Sky P. Waterpeace, Nick Ivanov

STEM Student Research Symposium Posters

Hypotheses:

1. Using a fixed number of fixed-size tokens, the storage of transaction history can be outsourced to the owners of the tokens or to the network.

2. With distributed transaction histories, disjunctive (targeted) proof becomes possible.

Enabling Localized Execution Of Smart Contracts Via Distributed Event Beacons, Rakesh Vasa, Sky P. Waterpeace, Nick Ivanov

STEM Student Research Symposium Posters

Modern smart contracts save their state transitions on a distributed ledger, such as blockchain [3, 4] or a particularly configured cloud [1]. These approaches necessitate storage and synchronization of large amounts of distributed data, leading to scalability deficiencies in decentralized permissionless smart contract platforms. In this poster, we introduce a novel concept of local execution of smart contracts which only required synchronizing the transaction data between the members of the private channel, without the need to storing state transitions on the distributed storage. To achieve this, we design a distributed storage-free decentralized beacon network that allows to perform provenance signatures …

An Analysis On The Time Effectiveness Of Speeding While Driving A Vehicle, Joy Skaggs

ATU Scholars Symposium

Speeding is responsible for roughly a third of all crashes, often coming at a deadly cost. The National Highway Traffic Safety Administration reports many negative consequences, such as a greater likelihood of loss of vehicle control, reduced protection equipment effectiveness, increased stopping distance, crash severity, and fuel consumption (National Highway Traffic Safety Administration, n.d.). Yet despite these costs, drivers continue to speed. In fact, in our fast paced world, speeding is so normalized that it’s uncommon to encounter a driver following the speed limit. Hawaiian psychology professor Leon James explains it best: people have twisted their definitions of speeding to …

The Dialogue Dilemma: The Role Of Patient-Clinician Communication For Low-Income People Who Smoke And Manage Multiple Conditions, Monique T. Cano, Michael R. Lindstrom, Ricardo F. Muñoz

School of Mathematical & Statistical Sciences Faculty Publications

Introduction: Adults from low-income backgrounds who smoke face significant health disparities related to tobacco use, often at disproportionately high rates. These individuals are more likely to endure multiple mental and physical (MP) health conditions, which can negatively influence their self-rated health (SRH). The quality and effectiveness of patient-clinician communication (PCC) can influence how patients perceive their own health. Understanding how PCC influences SRH among low-income adults who smoke and suffer from multiple MP conditions is essential for clinical care as multimorbidity is on the rise. This study examines how PCC may influence the health perceptions of low-income adults who smoke …

Quantization For A Condensation System, Shivam Dubey, Mrinal Kanti Roychowdhury, Saurabh Verma

School of Mathematical & Statistical Sciences Faculty Publications

For a given r∈(0,+∞), the quantization dimension of order r, if it exists, denoted by Dr(μ), represents the rate at which the nth quantization error of order r approaches zero as the number of elements n in an optimal set of n-means for μ tends to infinity. If Dr(μ) does not exist, we define D−−r(μ) and ¯¯¯Dr(μ) as the lower and the upper quantization dimensions of μ of order r, respectively. In this paper, we investigate the quantization dimension of the condensation measure μ associated with a condensation system ({Sj}Nj=1, (pj)Nj=0,ν). We provide two examples: one where ν is an …

Construction Of Stock Portfolios By Machine Learning Methods, Alfan Gehad Abulehia

Thesis/ Dissertation Defenses

We review the theoretical foundations and empirical workings of Long Short-Term Memory Networks (LSTM) and Random Forest for stock market prediction. To be precise, our work initiates with a deep-dive exploration in the mathematics of these algorithms which covers topics like gradient descent, automatic differentiation, and a bit on recurrent neural networks as well.
An application creates stock portfolios through LSTM and Random Forest rules- based strategies, using either technical or fundamental indicators as input variables. The process involves predicting returns and ranking stocks accordingly to build portfolios with a certain level of diversification and annual rebalancing over a defined …

Does Better Firm Performance Imply Better Management And Esg Scores?, Shawn Lisann

Research Symposium

No abstract provided.

Prime Theta-Curves From Torus Knots, Sam Nieman, Jack Calcut

Research Symposium

Classical knot theory is the placement problem for a circle in Euclidean 3-space or in the 3-sphere. That problem has been generalized in numerous ways. Knotted graph theory replaces the circle with a graph. Knotting of certain graphs has been well-studied. That includes the theta-graph consisting of two vertices connected by three edges---a copy of the letter theta. A theta-curve is an embedding of the theta-graph in 3-space or in the 3-sphere. Connected sum of knots yields the notion of a prime knot. Similarly, one may sum two theta-curves at a vertex and one may sum a theta-curve and a …

Study Habits And Review Sessions, Lillian Gottstine

Fisher Showcase 2025

Seeing the outcomes of using and teaching different studying habits in a review session to see the effects on student preparedness for unit exams.

Some Inequalities Of A Matrix And Its Modulus In Powers Acting On Unit Vectors, Fuzhen Zhang

Mathematics Colloquium Series

Given a square matrix, one can associate it with a variety of numerical values and properties—such as the trace, determinant, eigenvalues, and singular values (at the undergraduate level), and the numerical range (and numerical radius), matrix norms, and majorization inequalities involving eigenvalues and singular values (at the graduate level). These studies all serve a common goal: to describe and understand the matrix as thoroughly as possible. In this talk, we present several inequalities involving a matrix A and its operator modulus ∣A∣, particularly in the context of their powers acting on the unit sphere (i.e., unit vectors)

2025 Acssc Program, Acssc Planning Committee

Annual Celebration for Student Scholarship and Creativity

No abstract provided.

Basketball Jump Shot Correction Using Computer Vision, Matthew Moran

Mathematics & Computer Science Student Scholarship

Matthew Moran ’25, Computer Science major

Faculty mentor: Dr. Martin Hellwig, Mathematics and Computer Science

Basketball has evolved significantly over the years, with players continuously striving to improve their shooting accuracy and efficiency. As the game becomes more data-driven, advancements in artificial intelligence and computer vision have provided new methods for analyzing and correcting shooting mechanics that allow players to improve their game. Using deep learning, this research aims to fill a gap in these advancements, which is looking at the position of the shooters fingers relative to the ball. Doing so can improve stability and overall shooting performance.

Designing A Statistical Plan For Measuring Self-Efficacy Using A 2k Factorial Design​, Rachel A. Hart, Eugene H. Thompson

Mathematics, Computer Science & Statistics Presentations

This study focuses on designing a statistical plan that measures the effects of self-efficacy using a 2k factorial design. Specifically, we simulated data on physical, mental, spiritual, and social health, so we could focus on their interaction with self-efficacy. By using ANOVA to see the main and interaction effects, we can see the impact of individual autonomy on health. Our findings show the need for experimental data on the demographic of interest, peri-and post-menopausal women.

Analyzing The Sentiment Of Feminist And Non-Feminist Works, Jasmine Borie, Megan G. Falschlehner

Mathematics, Computer Science & Statistics Presentations

This presentation focuses on a group of texts that advocate for a change in the current belief system. These texts are the Feminist Manifesto, Sojourner Truth: Ain’t I a Woman?, and Civilization and Its Discontents. These first two texts advocate for women’s rights, while Freud’s book is focused on civilization’s decline and how our understanding of community can affect this. Through our presentation, we want to examine the differences in sentiment and language between the feminist texts and Freud’s texts to pinpoint whether or not sentiment changes when advocating for different beliefs.

Analyzing Cie Texts Through History Using R, Rachel A. Hart, Aaron Ditto

Mathematics, Computer Science & Statistics Presentations

In this presentation, we analyzed three separate CIE texts from different time periods. First, “The Allegory of the Cave” from 380 BC, then “The Declaration of Independence” from 1776, and lastly “The Lottery” from 1948. We compared them using tidy text techniques like sentiment lexicons, creating word clouds, and bigram analysis to see if the types of words and sentiments used have changed over time in these short texts.

A Statistical Comparison Of Selected Old Testament And New Testament Books, Branden F. Stahl, Kevin Guan, Adam Denn

Mathematics, Computer Science & Statistics Presentations

The purpose of this project was to discover similarities between sentiments in Old Testament and New Testament books of the Bible, track emotional valence and find the most common words and sentiments in the books. Text analysis was performed on Genesis, Exodus, Matthew and Luke. Word clouds were also created for these texts.

Using Text Mining In R To Explore How Three Cie Related Texts Answer One Of Ursinus College’S Quest Curriculum Questions: “How Should We Live Together?”, Elizabeth Dill

Mathematics, Computer Science & Statistics Presentations

This presentation explores the application of text mining techniques using R programming to analyze literary text. In the process of this project, I performed data cleaning, tokenization, sentiment analysis, and frequency analysis on selected literary works. This study illustrates how R enables the transformation of unstructured textual data into meaningful insights through visualizations and statistical summaries. My presentation highlights both the technical process and the interpretive results, demonstrating how computational methods can be used to explore traditional literary analysis.

A Text Mining And Sentiment Analysis Of Valuable Cie Texts Using R, Eric Sugarman, Ethan Turber-Ortiz, Hannah Quinn

Mathematics, Computer Science & Statistics Presentations

The purpose of this project was to perform a sentiment analysis of three texts used in Ursinus College's Common Intellectual Experience (CIE) course: Between the World and Me by Ta-Nehisi Coates, The New Jim Crow by Michelle Alexander and Discourse on Method by Rene Descartes. Word count and word cloud analysis were also performed on the texts as well as term frequency and bigram analysis.

The Significance Of Symmetry: Exploring T-Numbers And Their Role In Virus Survival And Behavior, Jenna Franco, Taylor Ligozio

Mathematics & Computer Science Student Scholarship

Jenna Franco ’25, Biology major

Taylor Ligozio ’25, Biology major

Faculty mentor: Dr. Su Jeong Kang, Mathematics and Computer Science

We studied the symmetry of different structures in common viruses and their T-numbers. We related these T-numbers with characteristics of the virus. Next we researched how the T-number of each virus was optimal for its survival and reproduction in its environment. We can use this information to infer or predict the behavior of viruses in the future based on their T-numbers.

Volume 16, Maggie Duncan, Madeline Little, Alicia Hoffman, Megan Livesay, Gabrielle Quaresma, Serenity Allen, Laina Pfountz, Ainslie Allred, Sabrina Robles, Nicholas J. Duellman, Trinity L. Deguzman, Melissa H. Savage, Margaret Dudley, Jocelyn Escobar, Olivia Hildreth, Olivia Hopkins, Benjamin Gettier, Lee Kassay, Jade Riddle, Ashley Seiders

Incite: The Journal of Undergraduate Scholarship

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

From the Editor Dr. Hannah Dudley-Shotwell

Artist’s Statement Maggie Duncan

On Mentoring Dr. Lee Millar Bidwell

The Hujum Campaign in Uzbekistan and its Consequences by Madeline Little

Wet Cupping Compared to Dry Needling for Treatment of Patients with Low Back Pain: A Critically Appraised Topic by Alicia Hoffman and Megan Livesay

Optimization of eDNA Air Sampling Via 3D Printed Fan by Gabrielle Quaresma

Beyond the Classroom: A Qualitative Study of Teacher Attrition and Retention by Serenity Allen and Laina Pfountz

The Treatment of Subacromial Impingement Syndrome with Platelet-Rich plasma Injections Verses …

Gerrymandering And How To Find It: A Mathematical Approach, Nicholas Small

Mathematics & Computer Science Student Scholarship

Nicholas Small ’25, Mathematics and Computer Science major

Faculty mentor: Dr. Liam Donohoe, Mathematics and Computer Science

Gerrymandering is a phenomenon that has plagued American politics for over 200 years. This process, which involves redrawing congressional and legislative district boundaries to favor one group over another, has become a fact of life in the past few decades. This project explores the history of gerrymandering and some of the algorithms proposed to combat it. The two main strategies of Gerrymandering are packing—or limiting the other group’s influence by making them the extreme majority in a few districts—and cracking—or splitting up a …

Existence Of Maximal And Minimal Weak Solutions And Dinite Difference Approximations For Elliptic Systems With Nonlinear Boundary Conditions, S. Bandyopadhyay, T. Lewis, Nsoki Mavinga

Mathematics & Statistics Faculty Works

We establish the existence of maximal and minimal weak solutions between ordered pairs of weak sub- and super-solutions for a coupled system of elliptic equations with quasimonotone nonlinearities on the boundary. We also formulate a finite difference method to approximate the solutions and establish the existence of maximal and minimal approximations between ordered pairs of discrete sub- and super-solutions. Monotone iterations are formulated for constructing the maximal and minimal solutions when the nonlinearity is monotone. Numerical simulations are used to explore existence, nonexistence, uniqueness and non-uniqueness properties of positive solutions. When the nonlinearities do not satisfy the monotonicity condition, we …

Quadratic Stochastic Processes: Algebraic Structures And Their Applications, Taimun Qaisar

Thesis/ Dissertation Defenses

This research focuses on the algebraic structures of the Quadratic Stochastic Processes (QSPs). In this work, we first study 𝜉^(𝑎)- Quadratic Stochastic Operators (QSOs) linked to the partition ℙ₃. We simultaneously discuss the dynamics of the obtained QSOs. Moreover, the algebraic structure of the associated genetic algebra is studied. Further, we build Quadratic Stochastic Processes (QSPs) using the given Markov processes. Consequently, we obtain an ordinary differential equation for the resultant Quadratic Stochastic Processes (QSPs). Besides, we apply the solution of this ordinary differential equation to the option pricing problem. Thereafter, we construct Quadratic Stochastic Processes …

Combinatorial Rigidity And Flexibility Of Simplicial 2-Complexes With Few Vertices, Serge A. Lawrence, Abdulkarim M. Magomedov, Olga I. Chelyapina, Valentina M. Rudenko

Theory & Applications of Graphs

We study the problem of reconstruction of a simplicial 2-complex from its 1- skeleton together with the prescribed quantities of 2-simplices at each 1-simplex, under the restriction that these quantities are bounded above by 2. It is a known fact that a 2-complex is uniquely reconstructible, or “combinatorially rigid”, if it has 5 or fewer vertices. In this paper “combinatorially flexible” 2-complexes (that is, non-uniquely reconstructible from their 1-skeletons) with 6 vertices are characterized in terms of necessary 2-subcomplexes.

Ai Meets Economics: Can Deep Learning Surpass Machine Learning And Traditional Statistical Models In Inflation Time Series Forecasting?, Ezekiel N.N. Nortey, Edmund F. Agyemang, Enoch Sakyi-Yeboah, Obu-Amoah Ampomah, Louis Agyekum

School of Mathematical & Statistical Sciences Faculty Publications

This study examined the forecasting ability of deep learning (DL) and machine learning (ML) models against benchmark traditional statistical models for the monthly inflation rates in the USA. The study compared various DL and ML models like transformers, linear regression, gradient boosting (GB), extreme gradient boosting (XGBoost), and adaptive boosting (AdaBoost) with traditional baseline time-series models like autoregressive integrated moving averages (ARIMA) and exponential smoothing (ETS) with Holt-Winters seasonal method utilizing data sourced from the Federal Reserve Bank of St. Louis. The study consistently showed that all DL and ML models outperformed the traditional approaches. In particular, the Transformer (RMSE …