Mathematics Commons^™

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, …

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 …

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 …

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.

On The Determinant Of Up On Mk(P,Χ), Xingyu Huang, Timothy J. Huber, Dongxi Ye

School of Mathematical & Statistical Sciences Faculty Publications

In this work, for p a prime, we compute the absolute value of the determinant of the UpUp-operator on the vector space Mk(p,χ)Mk(p,χ) of holomorphic modular forms of weight k and level Γ0(p)Γ0(p) with character χχ. As an implication, we confirm a number of conjectures of the second author.

Exploring Graphs And Chromatic Symmetric Functions, Olivia Payne

Undergraduate Research Conference

We consider graphs with a small number of vertices and analyze the coefficients of hook partitions of their chromatic symmetric function, which is a generalization of the chromatic polynomial of a graph. Some of these coefficients can hold information about the graphs themselves and, in this research, we find a combinatorial formula for coefficients of hook partitions. This research is motivated by Stanley's Tree Conjecture.

Numerical Analysis Of The Seir Model, Abigail R. Beckelhimer

Departmental Honors & Graduate Capstone Projects

Epidemiological models delineate the spread of diseases within a population. In this research project, the Susceptible-Exposed-Infected-Recovered (SEIR) Model was examined numerically for comparison between several methods. Approximations were obtained through Euler’s Method, Taylor’s Method, Runge-Kutta Methods, and Multi-step Methods. Hypothetical situations with parameter alterations were considered in order to better understand the effects the parameters have on the model. The goal of this project was to portray the usefulness of numerical approximations for predicting the behavior of the SEIR model and thus the course of a pandemic.

Counting Hamiltonian Cycles In Quartic Circulant Graphs, Allison Hilliard

Seaver College Research And Scholarly Achievement Symposium

We consider the problem of counting Hamiltonian cycles in circulant graphs $C_n^{1,k}$. Our method is to partition the set of Hamiltonian cycles according to their winding numbers. Then, we construct a weighted digraph that allows us to produce a generating function that counts the number of Hamiltonian cycles for each winding number. Summing these generating functions derives a formula for the total number of Hamiltonian cycles in a circulant graph with $n$ vertices.

Training Artificial Intelligence Agents To Play A Family Of Combinatorial Games, Megan Haeussler, Lina Mo, Sidney Wright

24th Annual A. Paul and Carol C. Schaap Celebration of Undergraduate Research and Creative Activity (2025)

This project explores the application of various artificial intelligence techniques in developing strategy for combinatorial games. A family of deterministic 2-player games is played on m-by-n grids, potentially with some cells removed. Players take turns placing pieces on the board until the board is filled, then sequences of pieces are scored based on length. AI agents are trained to play the game using methods including tabular reinforcement learning, evaluation of N-tuples of grid squares, and development of genetic training methods with artificial neural networks. These agents are trained against a variety of non-learning agents, then evaluated against both non-learning agents …

Applications Of Clustered Regularly Interspaced Short Palindromic Repeats In Food Security And Nutraceuticals, Rukayat Abiodun Oyegoke, Jahswill Toluwanimi Osifade, Adenike Temidayo Oladiji

Al-Bahir

The CRISPR/Cas9 system is a revolutionary genome-editing tool that enables precise and inheritable modifications, transforming plant genetic engineering. Previous literature has indicated that, in agriculture, CRISPR has improved crop yield, biofortification, and resistance to environmental stressors, fostering resilient and high-yielding crops essential for sustaining a growing global population. In nutraceuticals, CRISPR has enhanced the biosynthesis of bioactive compounds such as anthocyanins, flavonoids, and omega-3 fatty acids, improving the nutritional and therapeutic value of crops.

Despite its immense potential, CRISPR technology faces technical, ethical, and regulatory challenges, including off-target effects, accessibility concerns, and public acceptance. Addressing these issues is crucial for …

Control System Properties Of Discrete-Time Linear Switched Systems With Application To Epidemic Models, Yamen Mehialdin Bawabji

Thesis/ Dissertation Defenses

This thesis studies discrete-time linear switched systems and their application to epidemic models. It focuses on three key properties: stability, controllability, and stabilizability. Stability ensures systems return to equilibrium, controllability examines reaching desired states, and stabilizability determines if unstable systems can be controlled. Using mathematical tools and examples, the research shows how switching between disease transmission modes, like quarantine or vaccination, can help control outbreaks. The work highlights the importance of discrete-time models in epidemiology, as real-world data is often collected at discrete intervals, and provides a foundation for future research on more complex epidemic models.

Some Characterizations Of Weakly Pseudo Semi 2-Absorbing Submodules In Terms Of Some Types Of Modules, Omar H. Taha, Omar A. Abdullah, Ali Sh. Ajeel

Al-Bahir

The purpose of this paper is to investigate characterizations of weakly pseudo semi-2-absorbing submodules in terms of some types of modules. We provide characterizations for the class of multiplication modules with the help of some types of modules such as faithful, non-singular, Z-regular, and projective modules. Furthermore, we add some conditions to proof the residual of a weakly pseudo semi-2-absorbing submodule is a weakly pseudo semi-2-absorbing ideal.

Learning With Errors Parameter Analysis, Archana Parameswaran

Cybersecurity Undergraduate Research Showcase

We implement a systematic approach for generating, evaluating, and benchmarking Learning with Errors implementations in Sage Math by varying lattice dimensions, moduli, error standard deviations, and multiple error distributions to observe concrete security-efficiency tradeoffs. The security estimator maps parameter sets to concrete security levels and bits, while performance metrics measured computational efficiency and memory requirements. Results indicate that various distribution types do not significantly impact security, though binomial distributions require more computational overhead than discrete gaussian or uniform. Memory requirements increased when modulus q increased from 12289 to 65537. Larger dimensions have an exponentially growing requirement for memory, but this …

Data Science For Engineers, Heidi Moulton

Student Research Symposium

30% of USU undergraduate students participate in some sort of research, and for engineering students this often means generating large amounts of data.

Data Science for Engineers is a series of four modules that introduce students to data processing, visualization, and graphing in the Python programming language using Pandas DataFrames and Juypter Notebooks.

The modules are intended for students with a basic understanding of programming in Python, specifically those who have taken CS 1400 Introduction to Computer Science.

The Stem Gender Gap: Can It Be Closed?, Makenna Roberts

Student Research Symposium

Introduction

While many industries have achieved gender parity, women remain underrepresented in STEM fields, with participation stagnating between 32% and 35% from 2011 to 2021. Research suggests this gap is influenced by relative cognitive strengths and social/societal factors. This study analyzes two datasets: (1) SAT score report data from the National College Board and (2) employment data from the 2021 NCSES Survey of Recent College Graduates. Findings highlight disparities at the highest percentiles and lower workforce participation among female STEM graduates.

The Applicability Of A/B Testing In Clinical Trials, Carlie Prinster

Student Research Symposium

• A/B Testing is a study method that allows researchers to compare two different options in a variety of different contexts, most usually in a business context (i.e.: font color).

• A/B Testing is starting to used in biostatistical application, such as for clinical trial recruitment improvement.

• A study done by previous researchers aimed to apply A/B Testing to clinical trial recruitment improvement.

• My goal was to build a model that used the data from this study but implement a dependent structure.

Dedekind-Macneille And Related Completions: Subfitness, Regularity, And Booleanness, G. Bezhanishvili, F. Dashiell Jr., M. A. Moshier, Joanne Walters-Wayland

Mathematics, Physics, and Computer Science Faculty Articles and Research

Completions play an important rôle for studying structure by supplying elements that in some sense “ought to be.” Among these, the Dedekind-MacNeille completion is of particular importance. In 1968 Janowitz provided necessary and sufficient conditions for it to be subfit or Boolean. Another natural separation axiom connected to these is regularity. We explore similar characterizations of when closely related completions are subfit, regular, or Boolean. We are mainly interested in the Bruns-Lakser, ideal, and canonical completions, which (unlike the Dedekind-MacNeille completion) satisfy stronger forms of distributivity. The first two are widely used in pointfree topology, while the latter is of …

On Mach's Principle In General Relativistic Cosmological Models, Zach Zito

Student Research Symposium

General Relativity

1. Gravity is the mechanism by which matter influences inertia
2. This influence happens across a spacelike hypersurface
3. Geometrodynamic equations mathematically describe this influence