Abstracts

By: Amy Adkins (Morehead State University )

Presentation time and place: Saturday, 2:20 PM–2:40 PM in Student Union 109

Abstract: This presentation strives to highlight a collection of teaching strategies implemented in a College Algebra E-course to cultivate and encourage the learning of Mathematics. The presenter will share techniques employed in a Math 152E College Algebra course to facilitate learning for E-Course students. Several different strategies were developed such as digital content resources, Pearson deep links for assignments, flexible due dates, content worksheets, and working alongside the student tutor. Digital content resource folders for each section covered were provided on Blackboard. The folders contain resources provided by Pearson such as a link to the digital text section, a Power-point for each section, and 8-13 content videos. These resources benefited textual and visual learners. Additionally, Access Pearson Deep Links were developed within the assignment tab in Blackboard so that students could directly access assignments. This helped to integrate the Blackboard LMS and the Pearson digital homework. The direct deep links helped students stay organized and save time on accessing the homework. Flexible due dates on homework assignments helped to reduce math anxiety. Students in E-courses are challenged by mathematics, and it takes them a longer amount of time to master the concepts. Allowing students to improve upon their homework grades gave students motivation “HOPE” that they could improve their grade. Content Worksheets provide students with the opportunity to practice, review, and drill basic content knowledge. These worksheets also allow students to have practice showing their work. Often students want to work problems in their head but most of these types of students are not good at mental math. These worksheets provided a safe space for students to learn how to appropriately show mathematical computation in a logical and correct manner. I found that working alongside my student tutor often improved attendance on lab days. Improvement of attendance often means that students improve their ability to have success in the classroom. Once again this also allowed more students to get their questions answered and the tutor/student ratio was more conducive to success.

By: Ciana Applegate (Eastern Kentucky University)

Presentation time and place: Friday, 4:35 PM–4:55 PM in Student Union 104

Abstract: Throughout history women have been a foundational and integral part of the field of mathematics and statistics. However, while we have continued to see year to year increases in the number of women in STEM, women have typically been a marginalized group in the field. One way to continue to improve this statistic is to promote and encourage women to be in the field of STEM, and particularly in the field of Mathematics and Statistics. One way to do that is to continuously talk about and celebrate the impressive things that women have contributed to the field. This presentation will give a brief history of important and influential women in the field of Mathematics and Statistics. Individual female mathematicians and statisticians and their accomplishments and contributions to their fields will be presented. This talk will be geared towards undergraduate students.

By: Micheal Arnal-Brown (Murray State University )

Presentation time and place: Friday, 5:50 PM–6:10 PM in Griffin Hall 240

Abstract: A neighborhood-prime labeling is a bijective function \(f\) from \(V(G)\) to the set of positive integers up to \(|V(G)|\) such that for every non-pendent vertex \(v\), the greatest common divisor of the set of labels of the neighborhood of \(v\) is \(1\). We strengthen this definition by introducing a strong neighborhood-prime labeling for every vertex \(v\) in \(V(G)\), there exists a neighborhood-prime labeling \(f\) such that \(f(v)=1\). We will investigate which families of graphs are strongly neighborhood-prime and will extend this labeling to Gaussian integers.

By: Ferhan Atici (Western Kentucky Univeristy)

Presentation time and place: Saturday, 10:45 AM–11:05 AM in Griffin Hall 230

Abstract: In this paper, we introduce two sets of linear fractional order h-difference equations and derive their solutions. These solutions, referred to as trigonometric functions of fractional h-discrete calculus, are proven to have properties similar to Sine and Cosine functions on \(R\). The illustrated graphs confirm these similarities.

By: Mustafa Atici (Western Kentucky University)

Presentation time and place: Saturday, 10:45 AM–11:05 AM in Student Union 108

Abstract: Three combinatorial structures; extremal set, perfect hash family, and geodesic in graph theory can be summarized as follows. Extremal Set: This concept comes from extremal combinatorics, which studies the maximum or minimum size of a collection of finite objects under certain constraints. Extremal set theory focuses on families of sets and explores problems like the largest number of subsets that can satisfy specific intersection properties. Perfect Hash Family: A perfect hash family is a collection of hash functions with specific properties. It ensures that for any subset of a given size, there exists at least one hash function in the family that maps the elements of the subset to distinct values. These structures are widely used in computer science for efficient data storage, retrieval, and cryptographic applications. Geodesic in Graph Theory: In graph theory, geodesic is the shortest path between two vertices in a graph. The concept is central to understanding the structure and properties of graphs, such as geodetic numbers, which measure the minimum size of a set of vertices needed to cover all the shortest paths in the graph. Geodesics are also used to study distance-related properties and metrics in graphs. In this talk, we will show some interesting relationships among these structures.

By: Michael Baker (University of Kentucky)

Presentation time and place: Friday, 5:50 PM–6:10 PM in Student Union 108

Abstract: Photonic crystals are periodic layers of films which light passes through, changing the transmission spectra among other optical properties. These changes of transmission are useful for many applications such as transferring information and blocking out light at certain wavelengths for motor vehicles. Liu, Ukhtary, and Saito found in 2017 that for multilayer films consisting of two materials at a certain frequency of light, there were unexpected symmetries that preserved the transmission at that frequency. They wondered if the natural study of symmetry, group theory, could be used to study these symmetries. In this talk, we shall explore a group structure that these symmetries satisfy and use it to study the transmission spectra of these films.

By: Olivia Barga, Kelsey Hatton, Fatima Mbodji (Thomas More University)

Presentation time and place: Friday, 5:00 PM–5:20 PM in Griffin Hall 240

Abstract: Nearest Neighbor Nim (NNN) is a modified version of the game Nim. In Nim, 2 players take turns taking objects from a set number of “piles” and the last player to take an object wins. In NNN, the piles are in set positions, and players can only take from connected piles. This talk explores game winning strategies for NNN by partnering with programmers in creating programs that can accurately and efficiently solve games and aid in research.

By: Tyler Billingsley, Dr. Benjamin Braun, University of Kentucky, Dr. Christia Spears Brown, University of Kentucky, Dr. Carolyn Gentle-Genitty, Butler University, Julie Seitz, Youngstown State University (Rose-Hulman Institute of Technology)

Presentation time and place: Saturday, 9:55 AM–10:40 AM in Student Union 104

Abstract: In this meeting's Section NExT panel, we'll discuss a fundamental factor underlying everyone's experience with mathematics: mental health. Panelists will discuss their experiences supporting the mental health of themselves and others throughout their mathematical journeys. Bring any and all questions about how you can support yourself and your students inside class or out to engage in the candid, empathetic, inclusive discussion.

By: Axel Brandt (John Carroll University)

Presentation time and place: Saturday, 10:45 AM–11:30 AM in Student Union 104

Abstract: In a landscape of declining enrollments, participants in this 45-minute discussion will share strategies and ideas on how to better recruit and retain students.

By: Benjamin Braun (University of Kentucky)

Presentation time and place: Friday, 6:15 PM–6:35 PM in Student Union 109

Abstract: Student beliefs about the nature of mathematics and their mathematical practices, and students' sense of belonging in mathematics, all play an important role in mathematical learning and development. After surveying some of the ways that these factors influence students, I will discuss a new survey instrument, the College Mathematics Beliefs and Belonging scale, that was developed by an interdisciplinary team including mathematicians, psychologists, mathematics education researchers, and engineers. As part of our work, we have identified five independent types of belonging experienced by students; these findings expand our understanding of how students experience belonging and/or exclusion in mathematics settings.This talk is based on joint projects with Pooja Sidney, Cindy Jong, Derek Hanely, Matthew Kim, Kaitlyn Brown, Julianne Vega, Jack Schmidt, Julie Shirah, Chloe U. Wawrzyniak, and Johne Parker.

By: Katie Cerrone (The University of Akron)

Presentation time and place: Friday, 5:25 PM–5:45 PM in Student Union 109

Abstract: The University of Akron has finally jumped on the corequisite bandwagon. Our first attempt at implementation started in the fall of 2023 with our Technical Mathematics sequence. This presentation will discuss results on overall success in the course, examine how students are faring in subsequent courses, and give insight on how students are doing at the learning outcome level.

By: Jaki Chowdhury (Ohio Northern University)

Presentation time and place: Saturday, 10:20 AM–10:40 AM in Student Union 109

Abstract: We investigate the algebraic independence of some derivatives of certain multiplicative arithmetical functions over the field ℂ of complex numbers.

By: Adam Coffman (Purdue University Fort Wayne)

Presentation time and place: Friday, 6:15 PM–6:35 PM in Student Union 104

Abstract: The multiplicity of a root of a polynomial drops when you take a derivative. To understand how the same idea might work for other kinds of functions, we consider a differential inequality. Joint work with Yifei Pan and Yuan Zhang at Purdue Fort Wayne.

By: Megan Coon (Ashland University)

Presentation time and place: Saturday, 10:45 AM–11:05 AM in Griffin Hall 250

Abstract: This project explores an alternative password authentication method based on a 1995 scheme by Horng-Twu Liaw and Chin-Laung Lei. It maps password characters to unit circle angles, converting them into coordinate pairs via trigonometric functions for storage and authentication. The implementation in Python evaluates its security and efficiency against conventional hashing techniques and geometric-based approaches, assessing its viability as a novel authentication method.

By: Jeremiah Coughlon (Murray State University)

Presentation time and place: Saturday, 1:55 PM–2:15 PM in Griffin Hall 230

Abstract: Wavelets are short, scalable, wavelike functions which satisfy a set of conditions which imbue them with unique properties that have far-reaching implications. They are defined by an appropriate scaling function (a type of normalized refinement equation) and their ability to freely undergo translations and dilations across a given domain while simultaneously maintaining inner products of zero and nonzero norms. Wavelets can be utilized in techniques called wavelet transforms in which translated and dilated iterations of the functions map complex “high-energy” signals to a simpler “low-energy” set of coefficients at multiple levels of resolution. Due to their success in representing localized details in time-frequency domains, wavelet transforms have secured prominence in the field of signal processing, especially in image compression, seismology, and fingerprint analysis. In recent decades, the capabilities of wavelet transforms have also been applied in biological contexts, including the prediction of gene locations in DNA sequences and improving the accuracy of traditional data processing techniques used to identify protein features. In this discussion, we will present a brief introduction to wavelet theory, as well as some common wavelets used in the discrete wavelet transform. We will also explore how the signal compression and analysis techniques offered by the discrete wavelet transform may be applied in novel ways to DNA sequences from publicly available reference genomes provided by the NIH and NCBI.

By: Zijian Diao (Ohio University)

Presentation time and place: Friday, 5:25 PM–5:45 PM in Student Union 104

Abstract: In 1650, Mengoli posed the famous Basel problem: What is the sum of the reciprocals of the squares of all natural numbers? After baffling brilliant minds—including the Bernoulli family, Goldbach, Leibniz, and De Moivre—for nearly a century, this problem was first solved by Euler in 1735. Since then, numerous solutions have been discovered using a variety of methods from multiple branches of mathematics. In this talk, we present a new approach to the problem rooted in the study of quantum computing algorithms.

By: Evan Fisher (Ohio Northern University)

Presentation time and place: Friday, 5:25 PM–5:45 PM in Griffin Hall 240

Abstract: FEniCSx is an open-source collection of packages that are useful for solving partial differential equations (PDEs) with finite element method (FEM). This project explores the fundamentals of FEM and how they translate into FEniCSx code, with a focus on educating those without a strong FEM or computation background.

By: Darren Gerrity (Cleveland State Univerisity)

Presentation time and place: Saturday, 10:45 AM–11:05 AM in Griffin Hall 240

Abstract: Digital topology is a field that studies the shapes of digital images. The hull complex of a digital image is a topological space associated to the digital image that has the same shape as the digital image. This allows us to use well known results in algebraic topology to study our original digital image. In particular, the fundamental group of the hull complex of a digital image is isomorphic to the digital fundamental group of the digital image. By showing that the hull complex of a two-dimensional digital image is homotopy equivalent to a graph, we show that the digital fundamental group of a digital image is isomorphic to a free group.

By: Andrew Gibbons, Maddie Kauffman, Bailey Soard (Asbury University)

Presentation time and place: Friday, 5:25 PM–5:45 PM in Griffin Hall 250

Abstract: We took two approaches to the problem of predicting the medal count at the 2028 Olympics. While one member of the team quantified most of the data and trained an XGBoost AI model to make predictions, the other two members looked at the less quantifiable part of the data. Finally, at the end we came together to draw conclusions from both approaches in our final predictions.

By: Emma Gillespie, Robert Powers (University of Louisville)

Presentation time and place: Saturday, 11:10 AM–11:30 AM in Griffin Hall 240

Abstract: Binary rules model a voting situation where there are two competing alternatives and \(n\) voters. An important example of a binary rule is simple majority rule. Under simple majority rule, the winner is the alternative that receives the most votes. Simple majority rule is just one of many examples of binary rules that satisfy the conditions of neutrality and monotonicity. Neutrality and monotonicity are mathematical conditions that are well known properties in the area of social choice. In this talk, we will present some recent work on determining the number of binary rules that satisfy neutrality and monotonicity for n=4 votes. Spoiler alert: This number is really large.

By: Rick Gillman (Valparaiso University)

Presentation time and place: Saturday, 1:55 PM–2:15 PM in Student Union 109

Abstract: This whimsical talk reflects on the instructions given to me by my (first grade?) teacher about learning addition. While knowing that my interpretation was wrong, I spent many years confounding my peers. Now that I am retired, I have the time to think about the matter more carefully and maturely. I discovered that the instruction does, almost, work!

By: Ryan Gipson, Dr. Ashlee Matney (Campbellsville University)

Presentation time and place: Saturday, 9:55 AM–10:15 AM in Student Union 108

Abstract: This talk invites educators to explore the exciting possibility of hosting a math camp, providing a comprehensive guide from conception to implementation. We will cover essential topics such as planning, budgeting, outreach, hosting, and many lessons learned throughout the process. The focus is on creating an engaging, interactive, camp-like experience that connects high school students to higher mathematics. By sharing our motivations, goals, and insights from every phase—ranging from initial planning to final reflection—this session offers practical advice for launching your own math camp, enhancing student engagement, and fostering a deeper appreciation for mathematics.

By: Jonathan Gonzalez Martinez (University of Indianapolis)

Presentation time and place: Saturday, 10:20 AM–10:40 AM in Griffin Hall 240

Abstract: The auditory system enables humans to process and understand surrounding information through speech and music. Sound waves entering the ears contain frequency components that are transmitted to different brain regions. Previous studies have shown that convolutional neural networks (CNNs) outperform general linear models (GLMs) in predicting neural responses in the primary auditory cortex (A1), with the best 1Dx2-CNN model accounting for 47% of the variance, compared to 31% for the best GLM and 39% for the best single-CNN model. This research aims to build on these findings by developing a model that closely mimics the A1 unit response while explaining more of the variation in the A1 unit response. Data was obtained from Zenodo (Pennington and David, 2023), with recordings performed in both A1 and the secondary auditory field (PEG) on five ferrets. This study focuses specifically on A1 recordings, which include 22 sites and 849 units. To model the A1 neurons’ response to external stimuli, CNNs were employed, with inputs consisting of stimuli at a given time point along with the previous 20-time points (spanning 200 ms, with a time bin of 10 ms), forming a 21-time by 18-frequency matrix. The results demonstrate that CNNs outperform GLMs, with the two-convolutional layer model slightly outperforming the one-layer model. In both models, the predicted responses closely follow the trend of actual responses; however, they fail to fully capture some extremely high and low values.

By: James Guffey (None)

Presentation time and place: Friday, 4:10 PM–4:30 PM in Student Union 108

Abstract: The randomized response technique is a clever and simple method by which researchers can ask about sensitive behaviors or opinions without the respondent answering directly, thereby providing confidentiality for the participant’s true actions or feelings. Responses are gathered in such a way that the researcher cannot know which of two questions, one benign and one sensitive, is actually being answered. As a result, this approach intends to reduce evasive answer bias. We will describe a couple of such approaches and illustrate how basic probability rules can be used to estimate the probability of occurrence of the sensitive behavior. Undergraduates are encouraged to attend this talk.

By: Christopher Hogan (Eastern Kentucky University)

Presentation time and place: Friday, 5:50 PM–6:10 PM in Student Union 104

Abstract: We consider the dynamics of a boosted soliton evolving under the cubic NLS with an external potential. We show that for sufficiently large velocities, the soliton is effectively transmitted through the potential. This result extends work of Holmer, Marzuola, and Zworski, who considered the case of a delta potential with no bound states in their 2007 paper "Fast soliton scattering by delta impurities" and the work of Datchev and Holmer, who considered the case of the delta potential with a linear bound state in their 2009 paper "Fast soliton scattering by attractive delta impurities."

By: Joshua Holden (Rose-Hulman Institute of Technology)

Presentation time and place: Saturday, 9:55 AM–10:15 AM in Student Union 109

Abstract: This paper continues the ElectroNic ExeRcises for CiphEricaL Learning (ENERCELL) project by introducing Lithium, a simplified version of the Dilithium digital signature scheme which is currently being standardized by the National Institute of Standards and Technology. This scheme is “post-quantum” in the sense that while it does not require a quantum computer to run, it is expected to be secure against practical quantum computers, which could be developed in the near future. No previous knowledge of quantum or postquantum cryptography is necessary for this talk or to teach Lithium in your classes. Versions of the system will be presented which are suitable for linear algebra, abstract algebra, and/or cryptography classes. (I have taught a similar system in a cryptography summer course in the past.)

By: Chaucer Ihrig (Murray State University)

Presentation time and place: Saturday, 10:20 AM–10:40 AM in Griffin Hall 250

Abstract: 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 graph and find its maximal independent set using a variety of algorithms. We investigate statistical connections between graph structure and Maximum Independent Sets found using these algorithms over an incredibly large and simulated dataset.

By: Abby Jones (Northern Kentucky University)

Presentation time and place: Saturday, 11:10 AM–11:30 AM in Griffin Hall 250

Abstract: Regression models are used to assess relationships between variables in a variety of real-world applications. Generalized linear models provide the tools to examine potential predictors of important outcomes. For example, simple and multiple linear regression models are used for quantitative outcomes, while ordinal logistic regression models can be used for ordinal (ranked) outcomes. This talk will focus on application of these methods within the context of public health application.

By: Abhinam Joshi (Northern Kentucky University)

Presentation time and place: Saturday, 2:20 PM–2:40 PM in Griffin Hall 240

Abstract: In a wide range of fields (e.g. Healthcare, Social Sciences, etc.) two-sample comparisons is a common approach to assess the effectiveness of an intervention. Relying solely on observed differences from summary statistics is not sufficient to draw reliable conclusions. This presentation will cover key statistical methods, such as two-sample independent T-tests, paired T-tests, and repeated measures ANOVA, to compare group means and make informed decisions. These methods will be illustrated using examples from an analysis of educational data.

By: Dhanuja Kasturiratna, Nelum Hapuhinna (Northern Kentucky University)

Presentation time and place: Saturday, 9:55 AM–10:15 AM in Griffin Hall 230

Abstract: A transformation of a random sample of size n from a k-variate normal distribution with an unknown mean vector and unknown covariance matrix into a sample of size \(nk−k(k+3)/2\) from a uniform distribution over the interval \((0, 1)\) is given. This transformation is used in the procedure to construct an EDF (empirical distribution function) goodness-of-fit test for a k-variate normal distribution. Monte Carlo method is used to estimate the power of the test at alternative distributions.

By: Haseeb Kazi, Areeba Kazi (Trine University)

Presentation time and place: Saturday, 10:20 AM–10:40 AM in Student Union 108

Abstract: This presentation examines the integration of the American Psychological Association (APA) and the Association of American Educators’ (AAE) recommendations pertaining to the enhancement of best mathematics education and assessment practices for online and hybrid instruction. By placing an emphasis on a balanced approach between monitored (proctored) and non-monitored (open-book or take-home) assessments, this research explores strategies that aim to uphold academic integrity while fostering student engagement and equitable learning experiences. We identify interactive approaches, effective instructional designs, and assessment methods that promote conceptual understanding as well as inclusivity through a combination of the APA’s evidence-based learning principles along with the academic guidelines of the AAE. Key recommendations include leveraging digital tools for active learning, implementing scaffolded instruction, receiving immediate feedback, and addressing accessibility challenges in virtual environments. These findings can provide educators with practical insights that are able to help optimize online math education while upholding rigorous academic and ethical standards.

By: Daniel Kiteck, [No additional speakers] (Indiana Wesleyan University)

Presentation time and place: Friday, 5:00 PM–5:20 PM in Student Union 108

Abstract: This talk gives an overview of the history and current thoughts concerning the ontology of numbers. This includes considering the so-called problem of God and abstract objects where one could ask something like, "was there one God before God created the number one?"

By: Tiffany Kolba (Valparaiso University)

Presentation time and place: Saturday, 1:55 PM–2:15 PM in Student Union 104

Abstract: At Valparaiso University, we have transformed our foundational mathematics courses in two distinct ways. Firstly, we reduced our three existing developmental-level courses (intermediate algebra, college algebra, and trigonometry and functions) to 1 credit each and now allow them to be taken as co-requisites with other STEM courses on campus, instead of requiring them as pre-requisites. These changes reduce barriers for students and allow them to take courses in their major and for general education sooner. Secondly, we created a new extended Calculus I course sequence which has no pre/co-requisites. This two-semester version of Calculus I contains embedded algebra and trigonometry review and includes interdisciplinary labs that apply the course content to real-world examples. This talk will highlight the benefits and challenges of the transformed foundational mathematics courses, including a discussion of student performance and retention data.

By: Matthew Landrum (Valparaiso University)

Presentation time and place: Saturday, 9:55 AM–10:15 AM in Griffin Hall 240

Abstract: In the nearly three years since the Ukrainian-Russian war officially began, it has become increasingly clear that neither country can obtain a total military victory. That is, some type of negotiated, or arbitrated, outcome must be achieved. In this presentation, we explore what a solution obtained by the Nash Arbitration Method (NAM) might look like.

By: Yong Ju Lee (Ashland University)

Presentation time and place: Friday, 4:35 PM–4:55 PM in Student Union 108

Abstract: This paper proposes a generalized three-step estimation procedure for the consistent estimation of a nonparametric simultaneous equations model under conditional heteroscedasticity in the reduced form. First, the reduced form is transformed to ensure homoscedasticity in the error component. Next, a local polynomial regression of the transformed reduced form is performed to obtain residuals. In the third step, these residuals are used as a control function to estimate the unknown structural form. Following Su and Ullah (2008), local polynomial kernel estimation is applied in all stages, and marginal integration is adopted. The identification, consistency, and asymptotic normality of the proposed estimator are established. Simulation results demonstrate that the proposed estimator improves efficiency for small samples compared to the ordinary two-step estimator of Su and Ullah (2008), which does not account for heteroscedasticity in the reduced form. An empirical application reveals that financial development significantly impacts growth in low-income countries. Additionally, a sufficient condition for the efficiency gain of the proposed estimator is provided.

By: Grace McCullough (Ashland University)

Presentation time and place: Saturday, 11:10 AM–11:30 AM in Student Union 109

Abstract: As we look at NAEP student math test scores, we can see categories of students that consistently perform well and categories of students that consistently perform poorly. This achievement gap has been a growing problem for school districts in the United States. I will be discussing specific strategies that school districts, textbooks/ curriculum, and test proctors can implement to help bridge the achievement gap.

By: Carl Miller (NKU)

Presentation time and place: Friday, 5:50 PM–6:10 PM in Student Union 109

Abstract: The growth mindset seeks to allow students the opportunity to demonstrate content learning in a differentiated timeline from peers if needed. By examining standards individually and giving structured learning and practice which ultimately leads to exam exercises for assessment, students can be held personally accountable for their learning while offering opportunities to revisit topics which were too challenging initially. In this talk, the structure of an introductory course in Statistics for non-majors is discussed. Examples of standards, instructional and formative assessments ("learning"), along with summative assessment (scores on exams) will be discussed. Re-assessment for non-mastered standards is offered to students and descriptive results of improvement will be discussed.

By: Mark Miller (Marietta College)

Presentation time and place: Saturday, 2:20 PM–2:40 PM in Student Union 104

Abstract: In a typical first semester calculus course, functions in which the variable appears in both the base and the exponent, such as \(\psi(x) = x^{\sin(x)}\), are introduced midway through the semester within the context of logarithmic differentiation. Often they are scarcely – or never – heard from again in the course. In this note we consider an approach whereby \(\psi(x)\) serves as a frequent visitor – showing up on day one, and continuing throughout the semester. Using this approach, students are encouraged to build an understanding about the behavior of “strange functions” by drawing upon their precalculus (and para-calculus) understandings of “well-behaved functions”. Along the way, we must grapple with the notion that we can learn to manipulate the mechanics of \(\psi(x)\) without a firm understanding as to what the function actually means – thus seeing that \(\psi(x)\) raises issues that are both metaphysical and epistemological … hence the onomatopoeia (sigh!)

By: Aidan Mullins-Pearson (Indiana University Indianapolis)

Presentation time and place: Friday, 4:10 PM–4:30 PM in Griffin Hall 240

Abstract: Many real-world systems exhibit complex nonlinear dynamics which traditional analytical methods can fail to capture. We present a Monte Carlo algorithm which is rooted in the logic of set operations as applied to a closed group, here a power set (the set \(\wp(S)\) of all combinations of elements in \(S\)). At each step, this model either deletes subsets from the system or attempts to regenerate missing subsets through applying a set operation to two randomly chosen subsets from the ones remaining in the system. By varying the ratio of probabilities of attempted regeneration to deletion, we show that the algorithm gives rise to Ising-like behaviors including phase transitions and critical dynamics. Potential applications and directions for future research are also discussed.

By: Jeremiah Naughton, Jasmine Reid, Sarah Jameson (Asbury University)

Presentation time and place: Friday, 5:50 PM–6:10 PM in Griffin Hall 250

Abstract: We created a food web model after retrieving data through research that depicts an ecosystem of a Kentucky cornfield recently transformed from a forest. We looked into how different animal species and insects can impact corn production as well as how different monthly factors impact the species populations. We then were able to model how herbicides and pesticides, the reintroduction of rabbits and deer, and introduction of bats can affect the food web. To accomplish this, we created a program to represent populations’ effects on one another on a monthly update cycle considering reproduction, aging, predation and starvation. As a result of our model, we found deeper connections between populations that may not have been readily apparent on the surface.

By: Brittney Nelson (Murray State University)

Presentation time and place: Saturday, 9:55 AM–10:15 AM in Griffin Hall 250

Abstract: Capture-recapture models are essential tools for estimating population dynamics in ecological studies. A fundamental component of these models is the capture history matrix, which records individual detection over time and serves as the basis for estimating survival and capture probabilities. This presentation explores three statistical approaches to these estimations: the Cormack-Jolly-Seber (CJS) model, the Hidden Markov Model (HMM) for CJS, and the Bayesian CJS model. The CJS model provides a likelihood-based framework for estimation, and the HMM CJS incorporates latent states into the model to account for uncertainty in detection. The Bayesian CJS extends this same analysis by integrating prior knowledge and simulating capture histories using Markov Chain Monte Carlo (MCMC) methods. Applying these models to the capture data of the Arizona tiger salamander, I will compare the assumptions, estimation techniques, and results of these methods while also discussing their strengths and limitations in ecological research.

By: Alvaro Ortiz (University of Cincinnati)

Presentation time and place: Friday, 4:35 PM–4:55 PM in Student Union 109

Abstract: Integrating innovative methodologies is key to preparing students for the day-to-day challenges. This talk will explore how the power of artificial intelligence (AI) is redefining mathematics education. We will discuss how AI tools can personalize learning experiences and the opportunities and challenges of creating and bringing these tools to learning environments. Through real-life examples, we will reflect on how these technologies empower developers, teachers, and students.

By: Daniel Otero (Xavier University)

Presentation time and place: Saturday, 1:55 PM–2:15 PM in Student Union 108

Abstract: It is clear from the outset of Euclid’s Elements that there are issues with some of his deductive steps. The first proposition makes a famous ill-founded leap; and his fourth proposition depends on the ability to “superpose” one figure onto another, which he nowhere supported in his axioms. The history of mathematics is replete with attempts to revise Euclid. This talk presents yet another modest effort at this.

By: Horia Petrache (Indiana University Indianapolis)

Presentation time and place: Friday, 5:00 PM–5:20 PM in Student Union 104

Abstract: Circulant matrices are square matrices in which rows and columns are cyclic permutations of elements. They are often used in signal and image processing, cryptography, and more recently in quantum algorithms. One useful property is that the product of two circulant matrices gives another circulant matrix, a property that can be checked at elementary level. It can also be shown that if all elements under the diagonal are multiplied by a constant, the circulant remains invariant under matrix multiplication. Here we discuss the properties of 1-parameter circulants and then show a generalization to multiple parameters.

By: Simon Richard (Cleveland State University)

Presentation time and place: Saturday, 11:10 AM–11:30 AM in Griffin Hall 230

Abstract: Over the last half century, mathematicians and computer scientists have been working to develop computer systems that verify proofs, with the goal of improving confidence in and consistency across math literature. These systems have been growing in popularity, but they remain outside of mainstream mathematics and they have a steep learning curve. This presentation will explore how AI systems including large language models (like ChatGPT) might enable mathematicians without formal (computer-based) proof experience to convert their natural language proofs into formal proofs that can be verified by these systems.

By: David Roach (Murray State University)

Presentation time and place: Saturday, 10:20 AM–10:40 AM in Griffin Hall 230

Abstract: Wavelets are finitely supported functions that are used to approximate complex data structures such as images. Each wavelet is associated with the solution of a refinement equation and is completely determined by a set of coefficients that satisfy a nonlinear system of equations. These coefficient vectors can be thought of as hyper-surfaces in \(R^n\). In this talk, we will examine some projection models that describe the shape of these objects and animate their cross-sections as they pass through our dimension. This topic is accessible to both students and faculty.

By: Daniel Rodman (Taylor University)

Presentation time and place: Saturday, 11:10 AM–11:30 AM in Student Union 108

Abstract: In topology, bridge spheres are useful tools to study knots and links. In this talk we will define bridge spheres and construct new examples of unperturbed links with arbitrarily high bridge number. This talk will be accessible to students and non-topologists.

By: Jay Schiffman (Retired (Rowan University))

Presentation time and place: Friday, 6:15 PM–6:35 PM in Griffin Hall 240

Abstract: This presentation explores divisibility, periodicity and prime outputs in the modified Tribonacci sequence in addition to palatable number tricks associated with the sequence requiring only a knowledge of basic algebra to justify. In contrast to the companion Fibonacci sequence which embodies a rich history of productive research, the OEIS (The Online Encyclopedia of Integer Sequences) indicates the study of the Tribonacci sequence is ripe for discovery. For example, only fourteen prime entries were known as of 2000. With the aid of several technological platforms including the OEIS, MATHEMATICA 13.0.1 and the open-source calculator attributed to Dario Alpern, I recently secured additional prime outputs which I will share and was able to completely factor the initial four hundred twenty-seven terms as well as achieve at least a partial factorization for each of the initial five hundred terms. While every integer \(n\) enters the Fibonacci sequence no later than the \(n^2\) term, no power of three beyond the second serves as a factor of any term in our sequence. The Pisano period analogue for the Tribonacci sequence are messy at best in contrast to the Fibonacci sequence but illustrate the power of modular arithmetic. I recently found that not every prime enters the Tribonacci sequence as a factor of some term. Moreover, a total of eight primes less than one thousand never enter the sequence as a factor. This presentation is accessible to both undergraduate and graduate students who enjoy topics in number theory, discrete mathematics, and computer science as well as recreational mathematics enthusiasts.

By: Marc Schilder (Ohio Northern University)

Presentation time and place: Saturday, 2:20 PM–2:40 PM in Student Union 108

Abstract: How can we unfold an \(n\)-dimensional cube into \((n-1)\)-dimensional cubes? The number of nets (unfoldings) of an \(n\)-dimensional cube is an interesting combinatorial problem and has some interesting connections to graph theory.

By: Isabella Schultz, Madison Snider (Thomas More University)

Presentation time and place: Friday, 4:35 PM–4:55 PM in Griffin Hall 240

Abstract: Game Theory - Nim

By: Elizabeth Sipes (Murray State University)

Presentation time and place: Friday, 6:15 PM–6:35 PM in Student Union 108

Abstract: There exist multiple types of geometry, differing in the postulates they are based on, and therefore the theorems and proof that makeup said geometry. Hyperbolic geometry differs from others by allowing there to exist multiple lines through a single point not on a given line, that are parallel to the given line. Every geometry has the idea of distance and isometries, distance preserving maps. By considering special collection of isometries called discrete groups, we can construct interesting surfaces, such as the torus and genus-\(g\) surface. The connection between the surface and the discrete group can be understood through the fundamental polygon, a polygon whose images by the isometries properly cover the plane \(R^2\) or hyperbolic space \(D^2\). While there are a number of ways to construct a fundamental polygon, we numerically investigate the behavior of images of a line by the group of hyperbolic isometries to see if they can be used to construct a fundamental polygon.

By: Jacob Sizemore, Paul Robert Stackhouse (Asbury University)

Presentation time and place: Friday, 4:10 PM–4:30 PM in Griffin Hall 250

Abstract: Throughout the years, many different types of transportation have been used to maneuver around the land. The city of Baltimore, Maryland, has had some issues with the transportation infrastructure, mainly the collapse of the Francis Scott Key Bridge which provided a vital link to the industries and ports to the south. With the rebuilding of the bridge and recent infrastructure budgets and improvements, the city has started the process of reviewing and implementing a selection of projects, but each one has many benefits and deficits to the residents, commuters, business owners, and tourists that are in the region. Some of our solutions include fixing old infrastructure and reviewing the budget, improving the existing system with new modes and lines, and a redevelopment of US-40 in West Baltimore.

By: Hayden Smeal, Andrea Collett (Asbury University)

Presentation time and place: Friday, 4:35 PM–4:55 PM in Griffin Hall 250

Abstract: We are presenting a model to analyze changes in the ecosystem of a converted forest area. Our model observes how the populations of primary consumers, secondary consumers, tertiary consumers, and primary producers were impacted by three stages of converting a forest to a working farm. We will discuss the major issues that prevent sustainability in addition to potential solutions to these problems.

By: Byungjae Son (Ohio Northern University)

Presentation time and place: Saturday, 2:20 PM–2:40 PM in Griffin Hall 250

Abstract: This talk discusses the existence, multiplicity, and nonexistence of positive solutions to a steady state reaction diffusion model governed by logistic growth and exhibiting U-shaped density dependent dispersal on the boundary. A sub-supersolution method is used to obtain the results.

By: Ian Sugrue (Morehead State University)

Presentation time and place: Friday, 5:25 PM–5:45 PM in Student Union 108

Abstract: Driving in a foreign country can be stressful. If you want to visit a fixed number of cities in another country while minimizing the amount of driving you have to do, this can be modeled as an NP-hard binary quadratic problem known as the Maximum \(k\)-Cluster Problem. We will solve this problem using the binary quadratic solver BiqCrunch, and discuss the method BiqCrunch uses to get an exact solution.

By: Mahesh Sunkula (Purdue University)

Presentation time and place: Friday, 5:00 PM–5:20 PM in Student Union 109

Abstract: This talk will explore the structure and implementation of a flipped classroom for Calculus I (Fall 2024) and Calculus II (Spring 2025), focusing on how this approach reshaped student learning and classroom dynamics. I will discuss the key components of the flipped model, including pre-class preparation, in-class activities, and student engagement. By examining the impact of this structure on learning experiences, this session will offer insights for those interested in incorporating a flipped classroom approach in their own courses.

By: Charuka Wickramasinghe (Karmanos Cancer Institute, Wayne State University)

Presentation time and place: Saturday, 1:55 PM–2:15 PM in Griffin Hall 250

Abstract: Knowledge of drug penetration and exposure in the human central nervous system (CNS) is critical to the development of new drugs and the optimal use of current drugs for effective treatment of brain cancer. Compartment modeling in pharmacokinetics uses a mathematical approach to describe how drugs are distributed and eliminated in the body through a system of differential equations, incorporating drug- and system-specific parameters. Accurate parameter estimation is crucial for modeling drug behavior in the body and ensuring the effectiveness and safety of medications while inaccurate estimates can weaken pharmacokinetic predictions, slowing down drug development and clinical practices. This study employs a four-compartment brain model that it closely mimics the human brain functionally for the drug delivery to estimate critical drug-specific parameters. We present a detailed algorithm for parameter estimation based on the system of differential equations and validate our results through multiple steps. This analysis also yields key pharmacokinetic metrics, such as Cmax, Tmax, AUC, and half-life, all of which are vital for optimizing dosing strategies, predicting therapeutic outcomes, and reducing adverse effects. To make the model accessible to a broader audience for parameter estimation, we developed a user-friendly, web-based R/Shiny platform and used it for simulations in this work.

By: Tara Wilkinson (Northern Kentucky University)

Presentation time and place: Saturday, 1:55 PM–2:15 PM in Griffin Hall 240

Abstract: Categorical variables are important in medical studies, as they are often used to obtain ratings for concepts such as patient satisfaction, pain, and performance. Chi-square tests are used to evaluate association between categorical variables. This talk will provide an overview for a variety of chi-square tests using examples from medical and behavioral research. Specifically, the McNemar test, a type of chi-square test first introduced mid-20th century, can be used to detect change in a categorical variable measured at two times within a group. The McNemar test is limited to binary outcomes; when there are three or more categories, an extension called the McNemar-Bowker Test is available.

By: Amber Wu (Western Kentucky University)

Presentation time and place: Saturday, 2:20 PM–2:40 PM in Griffin Hall 230

Abstract: There is currently only an estimation method using the summation for cosine and sine known to produce the matrix-valued cosine and sine functions in discrete time. In this talk, we present two methods to calculate the matrix-valued cosine and sine functions in both discrete and continuous time. Firstly, we develop a formula using Jordan canonical form to calculate each term of a Jordan block of an nxn matrix valued cosine or sine of a matrix A. Secondly, we use differential and difference equations to develop an algorithm that calculates the nxn matrix valued cosine or sine of a matrix A through an imitation of the Putzer algorithm. Both methods depend on the calculation of the eigenvalues of the matrix A. To demonstrate the utility of our approach, we provide illustrative examples and provide a range of potential applications.

By: Michael Xue (Vroom Laboratory for Advanced Computing)

Presentation time and place: Saturday, 10:45 AM–11:05 AM in Student Union 109

Abstract: Mercury’s anomalous perihelion precession, unexplained by Newtonian mechanics, was resolved by Einstein in 1915 using general relativity. His derivation accurately accounted for the missing 43″ per century but omitted key steps, making it difficult to follow. This talk gives the full derivation, filling in missing details and clarifying the mathematical framework. Additionally, a printing error in Einstein’s original paper is identified and corrected.

By: Michael Yates, Caleb Bill, Aaron Hamby (Asbury University )

Presentation time and place: Friday, 5:00 PM–5:20 PM in Griffin Hall 250

Abstract: Juneau, Alaska faces significant challenges in managing tourism. While tourism generates substantial revenue that can support infrastructure and environmental initiatives, the daily influx of visitors leads to overcrowding and environmental degradation. To address this, we developed a sustainable tourism model for Juneau using a flowchart to represent the interconnected dynamics of the community. By defining five key sectors and analyzing their interactions, we identified critical variables that influence the balance between tourism, environmental health, and local well-being. This framework offers a practical approach to achieving long-term harmony between tourism and community needs.

By: Young Hwan You (Indiana University East)

Presentation time and place: Friday, 4:10 PM–4:30 PM in Student Union 109

Abstract: This study introduces an online framework for undergraduate mathematics research. It focuses on identifying accessible yet challenging research problems, recruiting passionate students, and forming virtual mentor-led teams. A preparatory phase, including online training and advanced concept study, bridges classroom learning and research. Weekly Zoom meetings and paper readings foster collaboration and critical thinking. Students develop academic writing skills through manuscript preparation, culminating in online conference presentations and journal publications. This comprehensive approach aims to enhance undergraduate research quality, increase STEM retention, and prepare students for advanced studies or research careers.

By: Shiheng Yuan, Aaron Raver, Reagan Labutis (Asbury University/West Jessamine HS)

Presentation time and place: Friday, 6:15 PM–6:35 PM in Griffin Hall 250

Abstract: This talk discusses a probability-based model to predict the medal counts for countries in the 2028 Los Angeles Olympics for Problem C of the 2025 COMAP contest. In the model, players are stratified by their experience in the Olympic games (first-time, second-time, third-time, fourth-time, etc.). Subsequently, the player demographic and the conditional probabilities for winning a medal are estimated for the 2028 Olympic cycle by studying historical data. With these two pieces of information, the predicted medal counts and the prediction intervals are obtained. The paper also analyzes factors such as the “hosting” and the “great coach” effect. To analyze the impact of hosting, Beta Graphs are constructed. Lastly, another statistical model is built to estimate the number of countries expected to earn their first medal in the 2028 Olympics.

By: Zachary Beard, Cat Lucier, and Ehren Dolan (University of Kentucky)

Abstract: Smooth projective varieties are rich objects of study in classical algebraic geometry. A divisor on such a space is an integral linear combination of codimension 1 subvarieties. For each divisor, we can define the section space of that divisor. Divisors and their section spaces can be used to define maps into projective space with certain divisors, called very ample divisors, giving embeddings. Tropically, we can replace smooth projective varieties with Bergman fans of matroids. In doing so, divisors become integral weightings of the rays of the fan, section spaces become lattice polytopes, and the embedding becomes a map of the Bergman fan into a simplicial fan corresponding to the divisor. We introduce this notion of an embedding and explore the tropical analogs of rank and linear series.

By: Samantha Bucholtz (Youngstown State University)

Abstract: This literature review examines the challenges students encounter in understanding functions within fundamental mathematics courses, with a particular focus on Trigonometry. A persistent deficit in function comprehension can hinder students' success in higher-level mathematics. This review synthesizes existing research on instructional strategies designed to improve students' grasp of functions, highlighting three different intervention methods aimed at enhancing conceptual understanding. By analyzing prior studies and pedagogical approaches, this work seeks to identify effective teaching practices that support student learning and retention. A strong foundation in functions is essential for mathematical success, whether students continue to advanced and rigorous courses like Abstract Algebra or Real Analysis or pursue other academic and professional paths. The insights from this review aim to inform educators and contribute to the development of improved instructional strategies for teaching functions in mathematics. These intervention methods will be tested in the upcoming academic year at Youngstown State University to evaluate their effectiveness in a real classroom setting.

By: Telmen Bayarbaatar, Kelvin Hernandez Salas, Ferenc Livak, and Aye Khant Khant Paing (Montgomery College)

Abstract: Classical Nim was solved by Charles Bouton in 1901. Since then, variations of Nim have been studied by combinatorial game theorists using the tools and theories developed by Conway et al. We present our analysis of a variation of Nim played on graphs, Nearest Neighbor Nim (NNNim). The main tool for our research was a calculator we programmed to compute the Minimum Excluded Value for NNNim games. We used this calculator to look for patterns in the values of NNNim games played on a three-vertex graph. We made a conjecture for rules governing these values and mathematically proved the rules held for all NNNim games played on this graph.

By: Natalie Dando (Youngstown State University)

Abstract: Google’s PageRank is the algorithm developed by Larry Page and Sergey Brin to sort search results by relevance based upon the link structure of the Internet. The mathematical backbone of PageRank is Perron's Theorem, and the Power Method is used to implement the algorithm. While Google uses PageRank to rank its webpages, the foundations of PageRank can be used to rank anything. This project uses the algorithm to rank professional tennis players. As a continuation of previous work, a script was developed to rank any list of professional tennis players between 1968-2023 relative to each other. Here, the mathematical background of the algorithm, how it was used to develop a model to rank tennis players, comparison of the model to existing tennis ranking systems, and testing of various models in predicting tennis match outcomes is discussed. The novelties of this model include career head-to-head interactions between players and implementation of several performance metrics within these matches.

Abstract: In the runner locating variation of the chaser and runner game on graphs, a chaser tries to determine the location of an invisible runner on a graph by probing a set of vertices on each turn. Each probed vertex returns the runner’s distance from that probe. If the runner is not located, then the runner can decide whether to stay or move to an adjacent vertex that was not just probed. We call a graph locatable if the chaser has a strategy that guarantees that the runner is located in a finite number of turns, and the minimum number of turns required for this strategy with k probes per turn is called the k-location number. We explore how the k-location number of specific bipartite graphs and snarks changes as k increases.