Mathematics Commons^™

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.

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 …

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 …

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 …

The Locus Of Intersecting Tangents, James Austin Canard

Student Theses and Dissertations

Consider two tangent lines to a given function, whose horizontal distance between the tangent points is a constant h. As the tangent lines change on the function, the intersection of the two tangent lines trace out a curve. We study the relationship between this new curve, called the locus curve, and the original function. We begin by studying the effects of vertical scaling, vertical shifting, vertical sheering, horizontal scaling, and horizontal shifting. Then we use asymptotical methods to study the behavior of the locus as the tangent lines approach infinity. We use a similar method to observe the behavior as …

Trimming Five Generated Gorenstein Ideals, Luigi Ferraro, W. Frank Moore

School of Mathematical & Statistical Sciences Faculty Publications

Let (𝑅,𝔪,𝕜) be a regular local ring of dimension 3. Let I be a Gorenstein ideal of R of grade 3. It follows from a result of Buchsbaum and Eisenbud that there is a skew-symmetric matrix of odd size such that I is generated by the sub-maximal pfaffians of this matrix. Let J be the ideal obtained by multiplying some of the pfaffian generators of I by 𝔪; we say that J is a trimming of I. In a previous work, the first author and A. Hardesty constructed an explicit free resolution of 𝑅/𝐽 and computed a DG algebra …

Shaping Mathematics Identity: An Exploratory Study On Specifications Grading In Calculus I At A Hispanic-Serving Institution, Luis M. Fernandez, Kaitlyn Stephens Serbin, Cristina Villalobos, Shaghayegh Azadi Setayesh, Guillermo Garza

School of Mathematical & Statistical Sciences Faculty Publications

Calculus I courses play a pivotal role in shaping students' STEM pathways, making it essential to adopt pedagogies that foster both achievement and mathematics identity development, particularly among underserved groups such as Hispanic students. This study explores the impact of Specifications Grading, an alternative assessment method where students meet specific course learning objectives through multiple attempts, on students’ mathematics identity development. Through a comparative case study of two Calculus I students at a Hispanic-Serving Institution, one enrolled in a specification graded course and the other in a traditionally-graded course, we examine shifts in their self-perceptions of competence, interest, recognition in …

Data-Driven Survival Modeling For Breast Cancer Prognostics: A Comparative Study With Machine Learning And Traditional Survival Modeling Methods, Theophilus Gyedu Baidoo, Hansapani Rodrigo

School of Mathematical & Statistical Sciences Faculty Publications

Background This investigation delves into the potential application of data-driven survival modeling approaches for prognostic assessments of breast cancer survival. The primary objective is to evaluate and compare the ability of machine learning (ML) models and conventional survival analysis techniques, to identify consistent key predictors of breast cancer survival outcomes.

Methods This study employs data-driven survival modeling approaches to predict breast cancer survival, including survival-specific methods such as the Cox Proportional Hazards (CPH) model, Random Survival Forests (RSF), and Cox Proportional Deep Neural Networks (DeepSurv), as well as machine learning models like Random Forests (RF), XGBoost, Support Vector Machines (SVM) …

Analyticity And Supershift With Regular Sampling, Fabrizio Colombo, Irene Sabadini, Daniele C. Struppa, Alain Yger

Mathematics, Physics, and Computer Science Faculty Articles and Research

The notion of supershift (in itself a generalization of the notion of superoscillation arising in quantum mechanics) expresses the fact that the sampling of a function in an interval allows to compute the values of the function far from the interval. In this paper, we study the relation between supershift and real analyticity. We use a classical result due to Serge Bernstein to show that real analyticity for a complex-valued function implies a strong form of supershift. On the other hand, we use a parametric version of a result by Leonid Kantorovitch to show that the converse is not true. …

Reinventing Mathematics Learning: An Exploration Of Undergraduate Mathematics Learning Post-Pandemic, Morgan R. Balesano

Honors Scholar Theses

In response to the COVID-19 pandemic, beginning in March 2020 nearly all secondary and undergraduate mathematics students were forced to adapt to new methods of learning and testing. As a result, the current experience for these mathematics students has changed vastly, as have the opinions and preferences of these students in terms of their learning. This study aims to identify instruction and testing resources and methods that students prefer and those that students find less beneficial in their current, post-pandemic educational experience. The past few years have seen a focus on the direct impacts of online learning during the pandemic, …

Exploring Teacher Knowledge In Meeting The Expectations Of Integrated Content Language Development In Mathematics: A Descriptive Case Study, Carrissa Rozelaar-Miller

Doctoral Dissertations and Projects

The purpose of this descriptive case study was to discover how knowledge is applied to meet the expectations of integrated content and language development in mathematics for Title I elementary teachers at an urban school district in the central United States. Halliday’s theory on systemic functional linguistics guided the research as it relates to the function and purpose of language through meaning and social interaction in different genres. The central research question was: How do Title I elementary teachers apply specific integrated content and language development knowledge in mathematics? The participants consisted of 10 teachers with at least three years …

Existence And Nonexistence Of Positive Solutions For Fractional Boundary Value Problems With Lidstone-Inspired Fractional Conditions, Jeffrey Lyons, Jeffrey T. Neugebauer, Aaron G. Wingo

EKU Faculty and Staff Scholarship

This paper investigates the existence and nonexistence of positive solutions for a class of nonlinear Riemann–Liouville fractional boundary value problems of order 𝛼 +2⁢𝑛, where 𝛼 ∈(𝑚 −1,𝑚] with 𝑚 ≥3 and 𝑚,𝑛 ∈ℕ. The conjugate fractional boundary conditions are inspired by Lidstone conditions. The nonlinearity depends on a positive parameter on which we identify constraints that determine the existence or nonexistence of positive solutions. Our method involves constructing Green’s function by convolving the Green functions of a lower-order fractional boundary value problem and a conjugate boundary value problem and using properties of this Green function to apply the Guo–Krasnosel’skii …

The Universe Through The Lens Of Gravitational Waves, Bartosz Fornal

Mathematics Colloquium Series

Gravitational waves were predicted by Einstein’s theory of general relativity back in 1916, but it took 100 years of scientific and technological progress to measure them directly at the Laser Interferometer Gravitational-Wave Observatory (LIGO). Although the signals detected by LIGO originated from cataclysmic astrophysical events such as black hole and neutron star mergers, one expects the presence of a primordial gravitational wave background permeating space today emitted within one trillionth of a second after the Big Bang, some 13.8 billion years ago. Such a signal could have been produced by various particle physics phenomena in the early Universe, including phase …

Algebraic Topics For Future Middle School Teachers, Leonard Van Wyk

Department of Mathematics and Statistics - Faculty Scholarship

This text contains algebraic concepts relevant to the middle school mathematics curriculum. Topics include the basics of number theory, functions, linear systems, matrices, and polynomials.