1. Special
3. History

BRICKS AND BLOCKS OF ULTRA MATHEMATICIANS — Satish C. Bhatnagar <satish.bhatnagar@unlv.edu>

The humanistic approach to any aspect of mathematics adds a refreshing dimension. It is especially pertinent from the pedagogical angle. The session on the Unspoken History of Mathematics is a perfect platform to raise such questions and generate new lines of thinking. For the sake of simplicity, I have defined bricks and blocks of mathematics as a set in the complement of a set of hard core theorems, propositions, lemmas, corollaries, definitions, problems etc. In this paper, I explain bricks and blocks by taking the example of the most celebrated theorem, Fermat’s Last Theorem (FLT). After more than 350 years, its proof was ultimately put to rest in 1994 by Andrew Wiles (b.1953 - ). The nuts and bolts or bricks and blocks of FLT, with a focus on Wiles, are his wife and children, schools and colleges he attended, institutions he worked, his students, classmates, neighbors, friends, colleagues, supervisors, and any tangible factors. They are generally invisible, unheard, and unspoken!

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1. Special
3. Teaching Logic

Logic First: Making Logical Arguments and Writing Proofs as Separate Learning Tasks — Jennifer Aust <jaust@utsouthern.edu>

Mathematics majors with limited writing skills often struggle with the double hurdle of learning to formulate logical arguments and learning to write precisely and concisely to communicate mathematics effectively. I will introduce a pedagogical tool (which I call a Proof Outline) that provides a tabular format for logical arguments. The purpose of the tool is to separate the task of formulating the logical argument from the task of writing that argument in paragraph form, allowing students to make progress on logical reasoning and argument construction regardless of their skill level with mathematical writing. I will share examples that highlight the tool's purpose and lessons learned from using the tool in upper-level mathematics courses for several years.

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1. Special
3. Spoon!

3-D Grationality — Kevin Jaimes-Villagomez <mkx764@vols.utk.edu>

This project extends the concept of grationality from regular polygons to regular polyhedra. In two dimensions, grationality arises naturally from area scaling and geometric manipulations. In three dimensions, we introduce structural and arithmetic constraints, since only five regular polyhedra exist and volume scales differently than area. By defining a nice polyhedron as a regular polyhedron with natural-number side lengths, and calling an integer 𝑚 > 3 3D‑Grational when a polyhedron with 𝑚 vertices can be broken into 𝑚 smaller congruent copies, we analyze how these solids behave. These definitions and constraints highlight the fundamental differences between 2D and 3D behavior, reveal new geometric handicaps, and creates conjectures about which vertex counts can support grationality in three dimensions.

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1. Contributed

4-cycle-free induced subgraphs of grid graphs — Taiki Aiba <taiba3@gatech.edu>

The avoidance of induced forests, or induced acyclic subgraphs, in $d$-dimensional grid graphs, or lattice graphs, has been studied in Alon _et al._ (2001) and later in Caragiannis _et al._ (2002), finding upper and lower bounds with respect to the number of vertices in a single dimension $n$ and the dimension $d$. In this work, we study the avoidance of induced $C_4$-free subgraphs, a superset of induced forests, of $2$-dimensional grid graphs $G$ and characterize the maximal sets $S \subseteq V$ such that the induced subgraph $G_S$ of $G$ with vertex set $S$ is $C_4$-free. Additionally, we will give upper and lower bounds on the number of $C_4$-free induced subgraphs with slightly fewer vertices than contained in the maximum.

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1. Special
3. Practical AI

97D40 Transforming College Algebra Through ALEKS, Adaptive Learning, and Artificial Intelligence — Nelly Belinga <nbelinga@ung.edu>

College Algebra is a gateway course that presents significant challenges, such as varying student preparedness and math anxiety. This session explores the potential of ALEKS, an adaptive learning platform, integrated with artificial intelligence (AI), to enhance student engagement and learning outcomes. By examining classroom implementation and data-driven practices, this presentation demonstrates how ALEKS offers personalized learning paths, real-time diagnostic insights, and efficient remediation. It will also address AI's role in adaptive sequencing, feedback, and supporting equitable instruction. Participants will leave with actionable strategies for leveraging ALEKS to foster deeper mathematical understanding in College Algebra while aligning with desired learning outcomes.

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1. Special
3. Recreational

A (Nearly) Infinitesimally Quick Introduction to the Surreal Numbers — Jeff Clark <clarkjeffrey1961@gmail.com>

Almost all of our math classes make use of the real numbers as well as subsets (the rational numbers, the integers, the natural numbers) and occasionally supersets (the complex numbers). John Horton Conway, in his research on game theory, came up with the notion of Surreal Numbers, an ordered field that contains the real numbers and much more, including positive numbers smaller than every positive real numbers (positive infinitesimals) and numbers bigger than every positive real number (positive infinite numbers). This talk will introduce the main concepts behind the Surreal Numbers, including their connection to game theory and how the real numbers are themselves defined.

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1. Undergrad
3. Undergrad Papers

A Classification of Galois Groups for the Family x^10+ax^5+b — Aiden Benton <herobro0624@gmail.com>

Many polynomial equations cannot be solved by a simple formula like the quadratic formula, yet their roots still follow precise symmetry patterns. In this talk, we study the family *f(x) = x¹⁰ + ax⁵ + b* and ask: as the parameters \(a\) and \(b\) vary, what symmetry patterns can its ten complex roots exhibit? These patterns are described by the *Galois group*, which measures how the roots can be rearranged without changing the algebraic relationships they satisfy. Although ten roots could in principle exhibit many different symmetry behaviors, the special structure of this polynomial, particularly the presence of the x⁵ term, strongly limits what can occur. By combining theoretical arguments with computer algebra experiments in *Mathematica*, *GAP*, and *Pari/GP*, we show that only four symmetry types arise for irreducible polynomials in this family. Moreover, we determine concrete conditions on \(a\) and \(b\) that distinguish among these four possibilities. This classification highlights how the form of a polynomial shapes the symmetries of its solutions. This is joint research done in collaboration with C. Awtrey and F. Patane.

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1. Undergrad
3. Undergrad Posters

A Curious Sangaku Wooden Tablet Puzzle — Cassie Lane <cflane@student.king.edu>

We offer a solution and interpretation of a curious old Sangaku wooden tablet puzzle involving three mutually tangent circles C0, C1, and C2, together with an isosceles triangle T. Let C0 be the largest circle, and let d denote a diameter of C0. Along d lie both the center of C1 and the base of T. The endpoints of the base are denoted by A and B, where A ∈ C0 and B ∈ C1. The problem asks: Where is the center Q of the third circle C2, which is tangent to C0, C1, and the sides of T? Surprisingly, the point Q always lies on the line perpendicular to d at B, regardless of the position of B along d.

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1. Undergrad
3. Undergrad Posters

A Economic Exploration of Post-Pandemic America — Muhkayah Akbar <makbar1@wildcat.fvsu.edu>

In this study, we investigated the primary economic drivers of inflation in the United States from 2019-2025, and how can these forces be modeled to predict future inflation trends. This was important because the years following the Covid-19 pandemic brough a rapid rise in inflation, significantly impacting American households and businesses. This created a major challenge for policymakers, who needed to understand what was pushing prices up. This study aims to uncover these key drivers, providing insight to inform future economic decisions and better prepare for rising prices. To address this, we used a Vector Autoregression model, a statistical tool showing how economic factors influence each other over time. Our model included changes in consumer prices (CPI), money supply (M2SL), global supply chain pressures (GSCPI), unemployment changes, and personal savings. We ensured our data was stable for the model to work correctly and chose the best number of past periods to capture complex interactions. We then performed Granger Causality tests, to see if one variable could predict another; Impulse Response Function to show how variables react to unexpected shocks; and Forecast Error Variance Decomposition (FEVD), to find out which shocks were most responsible for future changes in each variable. Crucially, our model passed important checks for stability and reliability, ensuring our results are trustworthy. Our results showed that our model was robust and reliable. Granger Causality tests indicated that both M2SL (money supply) and the Global Supply Chain Pressure Index were significant predictors of the overall economy. However, changes in CPI did not significantly predict other variables. When analyzing shocks, a surprising increase in M2SL briefly lowered inflation and unemployment. Crucially, a GSCPI shock significantly pushed inflation higher, highlighting a strong link between supply chain issues and rising prices. The forecast analysis further changed due to its own past shocks from M2SL and especially GSCPI became increasingly important for understanding future inflation swings. Other variables like M2Sl and savings were largely divided by their own trends. These results suggest that global supply chain pressures played a major role in recent inflation, supporting a “supply-side” explanation for rising prices. While money supply does influence the economy, its direct impact on inflation can be complex and short lived. Our findings imply that strategies to strengthen supply chains could be as vital as central bank actions in controlling inflation. This deeper understanding helps improve forecasts and guides better economic policies moving forward.

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1. Contributed

A Few Data Sets for Data Science Exploration — Erin McNelis <emcnelis@email.wcu.edu>

Finding meaningful, realistic, but approachable data sets students can use to explore data science concepts is challenging. This talk will briefly review a few public data sets the presenter used in teaching an introductory data science course (aligned with Wickham, Cetinkaya-Rundel, and Grolemund's 2nd edition of [*R for Data Science*](https://r4ds.hadley.nz/) text) and the concepts the students explored with each.

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1. Contributed

A Flipped-Classroom Style Statistics Course — Jac Cole <jcole57@utsouthern.edu>

In Fall 2022, we switched our Statistics course from using graphing calculators to using Excel. This seemed to be going great until it became clear that the students had not spent enough time working with Excel when it came to the first test. That lead us to re-work our Statistics course into more of a flipped-style class. This gave students the opportunity to work on assignments and to build their skills and familiarity with Excel as they learned Statistics. This changed a bit of how content was presented and what the students did during class as how the tests were given. When we moved a section of the course on-line this semester, then this approach became the basis and skeleton of the course. We will talk about the changes we have made and what we have learned over the last few years.

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1. Undergrad
3. Undergrad Papers

A Graph on Bumpless Pipe Dreams — Prashreet Poudel <ppoudel1@catamount.wcu.edu>

Bumpless pipe dreams (BPDs) are combinatorial objects introduced in 2018 to study Schubert polynomials. Using results from the literature, we introduce a graph structure on the set of BPDs for a fixed permutation, where the edges are determined by certain local moves. We implemented these objects in SageMath and used our program to generate all 409,113 graphs for small permutations. We analyzed this data to form a conjecture on which permutations have acyclic graphs, which we proved using induction. In this talk, we give a pattern-avoidance condition that is necessary for a permutation’s BPD graph to be a tree.

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1. Special
3. Spoon!

A Magic Carpet Ride through Irrationality — Jeneva Clark <dr.jenevaclark@utk.edu>

Stanley Tennenbaum proved the irrationality of $\sqrt{2}$ using Carpets Theorem with square carpets, and others (myself, Conway, and Miller) have tried to generalize this proof by using triangular and pentagonal carpets. Although those families of proofs used simple tools, a.k.a. “spoons,” in this talk, I am going to try to “spoonify” this even more. I’ll prove the irrationality of $\sqrt{3}$ and $\sqrt{5}$ using only square-shaped carpets. This work extends the previous findings for grationality and opens up the possibility of more research into families of irrationality proofs.

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1. Special
3. History

A Mathematical History of Solitary Waves — Ryan Thompson <ryan.thompson@ung.edu>

In 1834, a Scottish engineer named John Scott Russell witnessed something he did not expect: a single wave rolling down a narrow canal without changing its shape. Intrigued, he chased it on horseback and later described it as a “wave of translation.” At a time when waves were thought to quickly spread out and disappear, Russell’s moving bump of water seemed almost impossible. His observation raised a lasting question: how can a wave travel long distances without breaking apart? Decades later, this mystery found a mathematical explanation. In the late nineteenth century, Diederik Korteweg and Gustav de Vries wrote down an equation for shallow water waves that allowed such stable traveling waves to exist. Their equation showed that two competing effects, one that tries to spread the wave out and one that tries to steepen it, can balance perfectly. The story did not end there. Over the twentieth century, mathematicians and physicists refined these ideas, searching for better ways to describe water waves and other wave phenomena. Important insights were provided by Gerald Whitham, who emphasized how simple wave patterns can slowly change as they move. The journey continues into the 1990s with a new chapter written by Roberto Camassa and Darryl Holm. Their Camassa–Holm equation predicts solitary waves with sharp crests, called “peakons,” revealing that even stranger wave shapes can arise from the same shallow water setting that inspired Russell’s canal experiment. This talk follows the path from a man on horseback chasing a wave to modern mathematical equations, illustrating how a simple physical curiosity grew into a rich theory of solitary waves and nonlinear equations.

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1. Contributed

A Review: The Mathematics of Climate Change Prediction and What It Reveals — Jeffrey Landgren <jeffrey.landgren@ung.edu>

For more than a century, scientists and mathematicians have sought to understand and predict environmental change. Accurate forecasting is essential for improving preparedness for hurricanes and droughts, as well as anticipating shifts in food availability. In this lecture, I examine the mathematical tools—including systems of differential equations and numerical methods—that researchers use to study hurricanes, sea ice extent, temperature patterns, and precipitation changes, and to assess the resilience of these systems in a rapidly changing climate.

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1. Special
3. Recreational

A Tale of Two Card Games: EvenQuads and Projective SET — Timothy Goldberg <timothy.goldberg@gmail.com>

The games Projective SET and EvenQuads are both inspired by the famous SET game, but in different directions. The SET game is a model for the affine finite geometry AG(n,3), and Projective SET is so-named because it is a model for the projective finite geometry, PG(n,3). On the other hand, EvenQuads is a model for the affine finite geometry AG(n,2). Despite their apparent differences, there is an interesting way to play Projective SET within EvenQuads, and hence a mathematical connection between properties of the two, which are of interest in algebraic coding theory. In this talk, I will introduce the two games, show how to play one game within the other, and describe some of the mathematics involved in each. Time permitting, I will discuss some connections to coding theory.

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1. Contributed

A UNIQUENESS THEOREM FOR INVERSE PROBLEMS IN QUASILINEAR ANISOTROPIC MEDIA ON RIEMANNIAN MANIFOLDS — Md Ibrahim Kholil <mikholil@nsu.edu>

We extend the study of inverse boundary value problems for quasilinear anisotropic conductivities from Euclidean domains to compact Riemannian manifolds with boundary. Given boundary voltage and current measurements, represented by the Dirichlet-to-Neumann (DN) map, we investigate whether the quasilinear anisotropic conductivity can be uniquely determined. Our main result establishes uniqueness for quasilinear anisotropic conductivities, where the conductivity tensor is given by a scalar function multiplied by a fixed Riemannian metric. Under natural geometric conditions, such as conformal flatness or boundary rigidity of the underlying manifold, we show that this scalar factor can be uniquely determined from the boundary measurements.

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1. Contributed

Acyclicity in Hypergraphs — Daniel Pragel <dpragel@ggc.edu>

An acyclic graph is defined to be a graph that contains no cycles. When extending the concept of acyclicity to hypergraphs, there are several nonequivalent definitions that, when reduced to graphs, are equivalent. We will look at some of these defintions.

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1. Undergrad
3. Undergrad Papers

Adjacency Graphs of Planar Tangles — Jadon Jones <jadon.jones@vikings.berry.edu>

A planar tangle is a planar closed simple smooth curve constructed from quarter circle arcs. These curves represent planar configurations of a fidget toy called a Tangle; which is constructed from connecting freely rotating quarter circular tubes. If you imagine that each pair of connected arcs are allowed to rotate in 3-space around the axis of connection, then there are two natural moves to create new planar tangles from known tangles. These moves induce a adjacency graphs on classes of move-equivalent tangles. This presentation develops properties such as maximum degree and bipartitionability of these graphs and develops an algorithm for generating the adjacency graph of a given class of move-equivalent tangles.

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1. Undergrad
3. Undergrad Papers

Almost Positively Curved Generalized Eschenburg Spaces — Joan West <jwest73@ut.utm.edu>

Manifolds that curve like a sphere are called positively curved, as opposed to those that curve like a saddle, which are called negatively curved. Manifolds with almost positive curvature are positively curved at almost every point in a probabilistic sense, and they are highly sought. The most recent discovery of a positively curved manifold was 2008, and no infinite family of almost positively curved manifolds has been discovered since 2002 until now. We construct infinitely many new examples of manifolds with positive curvature almost everywhere.

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1. Undergrad
3. Undergrad Papers

An Exploratory Approach to Detecting Structural Breaks in FAANG Stock Returns Using Mean Shift Clustering — Ryan Legg <rlegg@student.citadel.edu>

This paper takes a hands-on, exploratory look at whether Mean Shift clustering—a nonparametric method that does not force the data into any particular model—can highlight structural breaks or unusual behavior in FAANG stock returns from 2015 2025. By pairing daily log returns with a rolling volatility measure, we create a simple two-dimensional space that turns each trading day into a point whose location reflects its overall market conditions. The algorithm, developed in python, naturally identifies one large, stable region of data along with several much smaller groups of days that behave differently. To get a better sense of how typical this dominant regime is, a Q–Q plot is used to check how closely its return distribution resembles a normal one. Non dominant clusters are then compared with well-known periods of market stress. The goal of this paper is not to build a predictive tool, but to understand how a flexible, nonparametric clustering method can help reveal market shifts in an intuitive way.

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1. Undergrad
3. Undergrad Posters

An Introduction to the Theory of Determinants — Cooper Broughton <cbrough3@cbu.edu>

Before the emergence of the subfield of abstract algebra known as linear algebra, and even before the nowadays very familiar notion of a matrix, there was a robust theory dealing solely in abstraction with the objects known as determinants. Today we tend to think of these objects as a property of a matrix, just one way of describing the matrix and its behavior, but mathematicians used to place a lot of importance on determinants as an object of study in their own right. This poster's aim is to present the determinant and its definition in a way more in line with this older view of determinants, along with some motivation for the definition, and then to develop some properties of determinants - some that are familiar and others that are perhaps less so - using the language of the theory of determinants.

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1. Special
3. Recreational

Apollonius and the Hyperbolic Circle — andrew simoson <ajsimoso@king.edu>

Given distinct planar points $A$ and $B$ and a real number $k$, called the _index_, Apollonius long ago showed that the locus of all points $P$ for which $k$ is the ratio of the distances from $P$ to $A$ and from $P$ to $B$ is a circle. The puzzle we present is this one: Given a circle $\mathcal Q$ in the hyperbolic disk whose diameter $CD$ lies along the real axis, how may we recover $\mathcal Q$ as a circle of Apollonius? That is, what are $A$, $B$, and $k$? The beauty of this puzzle is that $B$ is the hyperbolic center of $\mathcal Q$.

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1. Undergrad
3. Undergrad Posters

Assembly and Testing of Lab-Scale Heat Exchanger for Thermal Energy Storage — Sidney Owens <sidneyowensjr0@gmail.com>

The increasing demand for efficient energy utilization has intensified research on thermal energy storage (TES) systems, where heat exchangers play a critical role in enhancing heat transfer performance. This study presents the assembly and testing of a lab-scale heat exchanger designed for thermal energy storage applications. The objective was to develop a compact, cost-effective experimental setup capable of evaluating thermal performance under controlled operating conditions. The heat exchanger was assembled using readily available materials and configured to facilitate efficient heat transfer between the heat transfer fluid and the storage medium. Instrumentation, including thermocouples and flow measurement devices, was integrated to monitor inlet and outlet temperatures, flow rates, and overall heat transfer characteristics. Experimental testing was conducted under varying flow rates and temperature conditions to assess thermal efficiency, heat transfer rate, and system stability. Results demonstrate that the assembled system effectively stores and releases thermal energy, with performance strongly influenced by flow rate and temperature gradient. The experimental findings validate the suitability of the lab-scale setup for studying heat exchanger behavior in TES systems and provide a foundation for further optimization and scaling. This work contributes to the development of efficient, small-scale thermal energy storage solutions for renewable energy and waste heat recovery applications.

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1. Undergrad
3. Undergrad Posters

Behind the numbers: A comparative study of enrollment vs. student success in the USG — Shari Pinckney <spinckn3@wildcat.fvsu.edu>

In this study, we examined whether rising enrollment in the University System of Georgia (USG) masks disparities in retention and graduation rates by ethnicity and Pell Grant recipient status. This topic is important because while Georgia’s public colleges and universities have experienced enrollment increases from 2020 to 2024, economic inequality, rising tuition costs, and shifts in public funding have the potential to obscure underlying gaps in student success. Addressing this concern is crucial to ensuring equitable educational pathways and informing policy decisions that impact Georgia’s students, particularly those from underrepresented and low-income backgrounds. We collected data from official USG enrollment reports spanning 2020–2024 across research, comprehensive, and state universities, as well as state colleges. We analyzed total enrollment, retention rates, and graduation rates in comparison to each ethnicity category and average Pell Grant percentages using Excel regression analysis. The general regression model used was Y = β0 + β1(%Black) + β2(%Hispanic) + β3(%White) + β4(%Asian) + β5(%Pell Grant) + ϵ, with Y representing the dependent variables of enrollment, retention, and graduation rates. Our results showed that although total enrollment increased, disparities persisted in retention and graduation rates for Pell Grant recipients and underrepresented ethnic groups. Specifically, while enrollment appeared inclusive, retention and graduation rates varied significantly, with Hispanic/Latino and Asian students showing relatively higher positive coefficients in retention and graduation regressions, while Pell Grant percentages and other underrepresented groups displayed lower impacts, suggesting challenges in sustained student success despite enrollment gains. These findings suggest that rising enrollment alone does not equate to equitable outcomes within the USG system. Economic inequality continues to influence higher education success, with Pell Grant recipients and some minority groups facing barriers in retention and graduation despite increasing enrollment figures. The implications of this study are significant for policymakers and educators seeking to address equity within Georgia’s higher education institutions are to provide data-driven insight that can support conversations around improving funding models, support systems, and institutional accountability to close the gaps in student success across diverse populations.

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1. Undergrad
3. Undergrad Posters

Beyond Pass/Fail: Developing a Mastery Continuum Rubric for College Algebra — Laila McCluskey <lmccluskey@una.edu>

Mastery-based assessment is often implemented using binary pass/fail decisions; however, this approach can be insufficient in gateway mathematics courses such as College Algebra, where student understanding develops along a continuum. This interactive undergraduate research poster presents preliminary results from a faculty-collaborative study to design a mastery-based rubric that captures meaningful levels of algebraic understanding. Faculty participants evaluated authentic student work and identified distinguishing features across emerging mastery levels, informing the development of a multi-category mastery continuum. Poster visitors will engage directly with anonymized student responses by placing them along the proposed mastery continuum and comparing their classifications with faculty-derived levels. This activity highlights challenges in binary mastery judgments and illustrates how continuum-based rubrics can better support feedback, grading consistency, and instructional decision-making in early collegiate mathematics.

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1. Undergrad
3. Undergrad Posters

Bioinformatic Characterization of Variants of COL11A2 Associated with Adolescent Idiopathic Scoliosis — Tate Purvis <tpurvis@una.edu>

Adolescent idiopathic scoliosis (AIS) is a type of scoliosis characterized not only by the curvature of the spine but also by the age at which it develops. AIS occurs in individuals between the ages of 10 and 18 years old and is defined as a lateral curvature of the spine with an angle exceeding 10 degrees. "Idiopathic" refers to scoliosis without a specific cause; however, the Scoliosis Research Society (2025) found that 30% of AIS patients have family members who have had scoliosis. Having AIS can lead to several physical symptoms, including a back or rib hump, uneven shoulders, and a torso lean due to the curvature of the spine. These symptoms can result in discomfort and even back pain, particularly in the lower back. Rebello et al. (2023) found the gene COL11A2 played a key role in vertebral development. While some COL11A2 variants have been classified, 96% of them have not. Classifying these variants can help to diagnose AIS at earlier stages and prevent further spinal curvature. Clinical submissions reported in the Ensembl database categorized pathogenic, benign and unclassified variants. YASARA modeling of the COL11A2 protein was used to examine the structural characteristics relative to regions with unclassified variants. SIFT, PolyPhen, Revel, CADD and MetaLR scores were normalized and plotted to compare known pathogenic and benign variants with selected R130W and R130Q unclassified variants. Molecular dynamics simulations were performed to model 20 nanoseconds of movement in an aqueous environment for the wild type COL11A2 as well as the two variants, R130W and R130Q. The results of these methods are mixed. The analysis of the in-silico predictor scores, as well as the chemical difference between arginine and tryptophan suggested that R130W may be pathogenic. Swaps between glutamine and arginine appear in 44.8% of pathogenic missense mutations in COL11A2. However, gene conservation analysis yielded low scores for position 130 when over 150 homologues and the molecular dynamics simulations for both R130W and R130Q demonstrated little divergence from the wild type COL11A2. This research will aid future studies into these mutations and other mutations of this gene, which will help to discover any existing links to adolescent idiopathic scoliosis and ultimately improve the ability of physicians to diagnose this condition before it becomes more severe. References: Denise Rebello, Elizabeth Wohler, Vida Erfani, Guozhuang Li, Alexya N Aguilera, Alberto Santiago-Cornier, Sen Zhao, Steven W Hwang, Robert D Steiner, Terry Jianguo Zhang, Christina A Gurnett, Cathleen Raggio, Nan Wu, Nara Sobreira, Philip F Giampietro, Brian Ciruna, COL11A2 as a candidate gene for vertebral malformations and congenital scoliosis, Human Molecular Genetics, Volume 32, Issue 19, 1 October 2023, Pages 2913–2928, https://doi.org/10.1093/hmg/ddad117 Scoliosis Research Society. (2025). Adolescent Idiopathic Scoliosis. Scoliosis Research Society, Springer Nature, [www.srs.org/Patients/Conditions/Scoliosis/Idiopathic-Scoliosis](http://www.srs.org/Patients/Conditions/Scoliosis/Idiopathic-Scoliosis).

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1. Contributed

Building a Cost-Effective Data Science Minor: A Faculty-Led Model for Expanding Opportunities in Mathematics — Yan Gong <ygong@lander.edu>

This workshop presents the successful design and launch of a Data Science Minor at Limestone University (2023-2025), developed by existing faculty without additional costs or new hires. The project demonstrates how mathematics faculty can lead data science initiatives that meet workforce demand, broaden student opportunities, and enhance institutional offerings within current academic structures and budgets. Participants will explore key steps in the program development process, including conducting market and peer-institution analyses, designing an interdisciplinary curriculum aligned with institutional mission, navigating approvals across campus offices, and selecting cost-effective digital learning systems. This session provides a replicable model for resource-conscious program innovation in higher education, particularly valuable for small colleges and liberal arts institutions.

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1. Contributed

Burnside's lemma and applications in competition problems — Taiki Aiba <taiba3@gatech.edu>

_Burnside's Lemma_, also referred to as the _Cauchy-Frobenius Theorem_, is a lemma found in group theory that takes advantage of symmetry in groups to enumerate mathematical objects. Although rooted in group theory, Burnside's Lemma is also a powerful enumerative combinatorial lemma that allows us to solve counting problems that would otherwise involve tedious casework. In this talk, we will briefly outline the statement and a standard proof of Burnside's Lemma, go over common problems where the lemma is commonly used, and provide unexpected solutions to problems found in mathematical competitions where the lemma was not intended to be used from the problem author's perspective.

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1. Undergrad
3. Undergrad Papers

Change Point Detection for Skew-t Structural Changes through Modified Energy Distance Approach — Ryan Avallone <rgavallon@coastal.edu>

In this report, we investigate a two-sample procedure for detecting distributional changes in stock returns using a modified energy statistic (EMIC) proposed by Njuki and Ning [2025]. The method compares two adjacent segments of a time series to assess whether they originate from the same underlying distribution. The finite sample properties of the proposed method are conducted to compare its powers and applications. Since the energy-based tests are sensitive to differences in location, scale, skewness, and tail behavior, the proposed approach on modified energy statistics provides a flexible nonparametric framework for identifying potential change-points in financial return data

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1. Contributed

Closed Neighborhood Balanced Colorings of Graphs — Brad Fox <foxb@apsu.edu>

For a graph *G*, a *neighborhood balanced coloring* is a coloring of the vertices using red and blue such that each vertex has an equal number of red and blue vertices in its neighborhood. We introduce a variation called a *closed neighborhood balanced coloring* in which each closed neighborhood (which includes the vertex itself) has an equal number of red and blue vertices. A graph is *closed neighborhood balanced colorable* (CNBC) if such a coloring exists. In this talk, we will discuss various families of CNBC graphs, focusing on trees and classes relating to graph products.

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1. Undergrad
3. Undergrad Papers

Color Trades on Generalized Theta and Wheel Graphs — Kaitlin Noles <knoles@una.edu>

Two proper edge-colorings of a graph _G_ are mate-colorings if and only if every vertex of _G_ is incident to the same set of colors under each edge-coloring while each edge receives a different color under each edge-coloring. The color-trade-spectrum (CTS) of a graph _G_ is the set of all _t_ for which there exist two mate-colorings of _G_ using _t_ colors. A generalized theta graph, denoted $$\theta_{n_1,n_2,...,n_k}$$, consists of _k_ paths having only the starting and ending vertices in common with lengths $$n_1,n_2,...,n_k\in\mathbb{N}$$. A generalized wheel graph, denoted $$W^{n}_{k}$$, consists of a central vertex and an _n_-cycle with a path of length _n_ between the central vertex and each vertex in the cycle. We determine the color-trade-spectra of generalized theta graphs and generalized wheel graphs.

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1. Special
3. Practical AI

Comparing the Student Success of Alternate Assessments to Traditional Exams in Undergraduate Mathematics — Lily Devlin <devlinlr@appstate.edu>

In this classroom action study, we compare an alternate assessment method to traditional exams in order to determine if there is a less stress-inducing way to assess students' understanding of the concepts in an undergraduate college algebra course. Grades on both alternate assessments and traditional exams, as well as the students’ perception of the assessment we're collected from three different sections of the course. This presentation will share the alternative assessment design, the methodology of the study, and the analysis of student data.

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1. Undergrad
3. Undergrad Posters

Computational Approaches using Machine Learning to Predict Functional Impact of SERPINA1 Missense Mutations — Lucas Hasting <lhasting@una.edu>

Bioinformatics is an important tool for genomics research, lowering the cost and reducing the time to wait for results. This research aims to use machine learning to predict the pathogenicity of variants of uncertain significant (VUS) for the Alpha-1 antitrypsin (AAT) protein associated with the *SERPINA1* gene. Data used was collected through the Ensembl database. Moreover, Python was used to clean the data and create/train the models used for prediction. The dataset contains 196 more benign observations than pathogenic, so we removed 196 benign observations for training. However, we used the full data set of 484 observations for testing to determine accuracy over all known missense swaps associated with SERPINA1. Next, four different models were used for prediction with all parameters found using the hold-out method (aside from the neural network) with a generalization gap of 0.015. The first model focuses on using a neural network built using PyTorch. This neural network is a multilayer perceptron (MLP) that will use known cases of missense swaps and their pathogenicity and their mutation accessor score to predict the pathogenicity of all VUS. This is done using linear affine transformations and then passing that information into a Rectified Linear Unit activation function through one hidden layer. The output layer also makes use of a linear affine transformation and then utilizes a sigmoid activation function to map into the open interval $(0,1)$ and translate that into a Bernoulli distribution to predict benign $(0)$ or pathogenic $(1)$. The model was optimized using the stochastic gradient descent algorithm, with a learning rate of 0.01, a momentum of 0.9, and a batch size of 32. The model was trained using backpropagation with 10000 epochs and a log-loss loss function. The second model utilized $K$-Nearest Neighbors (KNN) via scikit-learn with $K = 10$. The third model uses a maximum-depth decision tree which also uses the hold-out method. In this model, we used Gini impurity as a measure of information. Our last model uses a random forest with a max-depth of 4 and $n$-estimators with $n = 4$. We built these random forests using the bootstrap method which builds decision trees by taking out random subsets of our training data for each decision tree. These four models resulted in an accuracy of determining whether any given VUS was benign or pathogenic of $86\%, 85\%, 89\%,$ and $90\%$, respectively. These findings contribute to the understanding of how pathogenicity scores influence clinical significance of missense swaps related to *SERPINA1* and AAT which is associated with non-cystic fibrosis bronchiectasis while defining the importance of further investigation of these variants for improved diagnostics in clinical diagnosis.

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1. Undergrad
3. Undergrad Papers

Computational Modeling of Post-TAVR Cardiovascular Dynamics Using Reduced-Order Models — Daniel Olopade <daniel.olopade@bruins.belmont.edu>

Patients with aortic valve stenosis often have calcified valve leaflets that impede blood flow. Transcatheter aortic valve replacement (TAVR) offers patients a minimally invasive option to replace their aortic valve by guiding a catheter through their blood vessels to deploy a bioprosthetic valve. We developed a 0-D model of the left heart to investigate TAVR performance in a patient-specific context. To achieve this, we constructed a lumped-parameter representation of cardiovascular dynamics, incorporating flows, pressures, resistances, and compliances of the heart chambers and valves. These physiological elements were represented through a system of differential equations, which we solved numerically using Backward Euler. We simulated flow and pressure dynamics upstream and downstream of the aortic valve to better capture post-TAVR behavior. By tuning the model to post-TAVR clinical data found in the literature, we demonstrated its ability to capture patient-specific hemodynamics. This tuning allows for more accurate simulation of post-TAVR cardiac dynamics, providing cardiologists with a tool to optimize patient outcomes.

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1. Contributed

Conformal Deformations and the Positive Mass Theorem — Mohammad Tariquel Islam <mislam33@tennessee.edu>

The Positive Mass Theorem is a fundamental result in differential geometry and general relativity. It states that if a space looks flat far away and has nonnegative scalar curvature (a measure of how the space bends), then its total mass must be nonnegative. Moreover, the only way the mass can be zero is if the space is completely flat. A natural question is what happens to this total mass when we deform the geometry in a conformal way i.e, when we rescale distances by a smooth function. In joint work with Alex Freire, we study this question for asymptotically flat manifolds that have a noncompact boundary (such as a half-space). Using harmonic functions, we prove that a certain weighted combination of the masses of two conformally related metrics remains nonnegative under corresponding curvature conditions.

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1. Special
3. History

Connections Between Numerical Systems across North America: From Alaskan to Mayan Numerals — Elizabeth Baldwin <ebaldwin6@students.apsu.edu>

From two distinct areas at opposite ends of North America, Mayan and Katovik numerals share a great deal of similarities in both design and function. While Katovik numerals were only recently created in 1994, it served a purpose to its community that previously had difficulty in expressing how they had been doing math. The Mayans on the other hand had been able to calculate an accurate calendar and track cycles of the moon and the sun. Both of these systems are a form of body-counting, where they are a base 20 system, sub-base 5. These were meant to represent all of our fingers and our toes. The main difference between these two systems, is that the Mayan numerals are a near perfect system, where they changed how a place value worked in order to work with their records more accurately. Ultimately despite the difference in geography and involvement in the modern era, both of these cultures created reliable systems that help understand the world around us.

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1. Contributed

Counting Forests in Complete Graphs with Generating Functions — J.C. Price <jprice12@ggc.edu>

In this talk, we investigate the enumeration of spanning forests in complete graphs with a fixed set of vertices in each tree using exponential generating functions. We begin with a brief overview of generating functions and demonstrate how the Tree function (Lambert W function) can be applied to count these forests. This approach leads to an elegant and unified solution that may have broader implications.

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1. Contributed

Counting Trees and Forests in Graphs — Daniel Pinzon <dpinzon@ggc.edu>

A graph is a finite number of points(vertices) connected by edges. Graphs are used to model computer networks, business competitiveness, organic molecules, social media, logistics, computability, machine learning, etc. as well as being very useful in solving difficult theoretical problems in combinatorics and other mathematical fields. A spanning tree is a subgraph that contains all the vertices, but only some of the edges so that there are no cycles. This means that once you leave a vertex, you cannot return to that point unless you retrace your path. The Matrix-Tree Theorem states that if we represent the graph as an integer valued matrix, called a Laplacian, then its minor gives the number of spanning trees in the graph. This is useful not only in mathematics theories, but in questions about structure and reliability of the network. What is not very well known are questions such as: How many ways can you construct two disjoint subtrees (a 2-forest) where one vertex is in one tree and two others are in the other that together span all the vertices of the graph? There are many questions such as these that are unknown that can be answered by students as an undergraduate research project. We will explore what tools are needed to answer these questions using graph theory, linear algebra, abstract algebra, and mathematics software.

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1. Undergrad
3. Undergrad Posters

CycleQuest: The Mayan Challenge — Jasmine Prince <jasmine.prince@lander.edu>

This project stemmed from our research conducted into the Maya people and their mathematics. Particularly their method of calculations and the calendar that allowed them to predict events far into the past and future. To teach this incredibly impressive feat of ancient mathematics The work presented in this poster introduces an interactive virtual boardgame that models the 20- and 13-day cycles that the Maya used to keep track of their ritual calendar. The game’s core mechanics, the modular arithmetic engine, and implemented by the student developer into the visual wheel-based UI. This game requires players to calculate corresponding calendar days using Mayan modular arithmetic and cyclical counting systems to solve mathematical puzzles to align the other calendars to complete challenges and maintain their status. The game offers a culturally rich alternative to traditional math, transforming historical number systems into interactive tools that deepen understanding and honor ancient civilizations’ mathematical sophistication.

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1. Special
3. History

Degrees of Defiance: Underground Higher Education — Ryan Thomas <rthomas@csuniv.edu>

Throughout history, conquering powers have sought to suppress culture as a means of control. This talk will explore underground universities as sites of intellectual resistance, focusing on clandestine efforts in occupied Poland during the Second World War. Although higher education was directly targeted by Nazi policy, Polish scholars organized secret courses, exams, publications, and degree programs, often at great personal risk. Using education itself as an act of defiance, these faculty members and students contributed to sustaining national identity and many would go on to shape postwar intellectual life.

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1. Special
3. AI-Resistant

Designing AI-Resistant Mathematics Projects through Creativity, Personalization, and Mathematical Sensemaking in Liberal Arts Mathematics — Candice Quinn <cquinn@una.edu>

The rapid rise of generative artificial intelligence has intensified longstanding challenges in mathematics assessment, particularly for open-ended projects that can be easily outsourced to AI tools. Yet projects remain essential for fostering mathematical sensemaking, creativity, and positive mathematical identity, especially in liberal arts mathematics courses serving non-STEM majors. This session presents a sequence of AI-resistant mini-projects implemented in a Liberal Arts Mathematics (MA111) course. These projects are intentionally designed around personalization, invention, and reflective explanation, features that require authentic student thinking and cannot be meaningfully completed by AI alone. Examples include: (1) designing an original recursive number sequence inspired by Fibonacci-type patterns, (2) analyzing mathematical structure in a natural phenomenon of the student’s choosing, and (3) creating a personal number system with defined symbols, rules, and representations. The design framework integrates three core principles: 1. Personalization (student-chosen contexts and parameters), 2. Creation (students generate new mathematical objects or systems), and 3. Justification (written explanation of reasoning and meaning). Student artifacts and reflections indicate that these projects promote ownership, creativity, and deeper engagement with mathematical ideas while substantially reducing AI-generated submissions. Practical assignment prompts, scaffolding strategies, and grading approaches will be shared so participants can adapt AI-resistant project structures to their own courses.

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1. Contributed

Detecting Structural Changes in Longitudinal Bayesian Quantile Regression — Chao Gu <cgu@citadel.edu>

Detecting changes in relationships over time is a central problem in longitudinal data analysis. While classical change-point methods focus on mean regression, structural shifts may occur differently across the distribution of the response. We propose a CUSUM-based testing framework for detecting structural changes in Bayesian quantile regression models, allowing quantile-specific shifts to be identified. Our approach leverages Bayesian quantile regression with a plug-in estimator for the regression coefficients and constructs test statistics based on cumulative sums of quantile score processes. We establish theoretical guarantees for validity under parameter stability and consistency under single-change alternatives. Simulation studies demonstrate that the method maintains good size control and strong power, effectively detecting structural changes across the response distribution. The framework opens new possibilities for uncovering nuanced dynamics in longitudinal studies.

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1. Undergrad
3. Undergrad Papers

Determinants in a Number Triangle — Zih-Syun Fu <zfu@student.citadel.edu>

This presentation investigates a recursively defined number triangle that generalizes classical structures such as Pascal’s and Fibonacci’s triangles. The first diagonal is constant, while subsequent diagonals are generated using patterns related to Fibonacci and triangular numbers. A central result of this study is the discovery that all 5×5 matrices along the left side of the triangle have a determinant of 2. This matrix captures the recursive structure of the triangle and provides a systematic way to describe how entries depend on one another. Closed-form expressions for the third and fourth diagonals are derived to support and justify the matrix representation. This work demonstrates how matrix methods offer a new framework for understanding generalized number triangles and their connections to classical sequences.

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1. Special
3. Teaching Logic

Discussion: Teaching Logic and Reasoning - What Next? — Andrew Miller <andrew.miller@belmont.edu>

Following the talks in our session on teaching logic and reasoning, we will pause to reflect, discuss, and brainstorm where we might go next. Audience members and presenters are invited to stay and discuss how they might use ideas from today's talks in their own classes, how they might refine those ideas, and how we might explore other ideas for teaching reasoning to students in mathematics classes.

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1. Undergrad
3. Undergrad Papers

Distance k-Bondage Number of Common Graph Classes — Steven Rodriguez <steven2005rodriguez@gmail.com>

Given a simple finite graph $G=(V(G), E(G))$, a vertex subset $D\subseteq V(G)$ is a distance $k$-dominating set if every vertex $v\in V(G)-D$ lies within distance $k$ of some vertex in $D$. The distance $k$-domination number $\gamma_k(G)$ is the cardinality of a minimum distance $k$-dominating set. The distance k-bondage number $b_k(G)$ is the size of a minimum edge set B suchthat $\gamma_k(G-B)>\gamma_k(G)$. In this paper, we establish upper bounds on $b_k(G)$ in respect to degree sums and exact values of a k-distance bondage number for common graph classes. Our results generalize previous bounds by incorporating distance-based domination constraints. We also introduce a refined bound in respect to the number of internally disjoint paths. These findings contribute to the broader study of domination and bondage parameters in restricted graph classes and provide insights into combin atorial optimization.

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1. Undergrad
3. Undergrad Posters

D¨urer's Pentagon versus the Golden Triangle — Aleya Ebner <aaebner@student.king.edu>

In 1525, Albrecht D¨urer published a treatise on geometry, featuring, among many items, an algorithm for purportedly constructing a regular pentagon by starting with a regular hexagon, whose consecutive vertices, V0, V1, V2, V3, V4, V5, lie among a unit circle C with center O. Let r be the edge-lengths of the hexagonal sides. Here’s the algorithm. Let A be the point C lying on a ray from O through the midpoint of a segment V1V2. With V1 and V2 as two vertices of D¨urer’s pentagon, let a third vertex B be the intersection of ray V0A and a circle, center V2 and radius r. Angle̸ V 1V2B should be 108◦; but is it? We contrast this algorithm with that of Eudoxus during the time of Plato’s Academy, who used the golden triangle.

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1. Undergrad
3. Undergrad Posters

Enumeration of Transfer Systems on Rank 3 Lattices — Arad Ganir <arad.ganir@emory.edu>

Transfer systems are a combinatorial object that occurs naturally in the study of equivariant homotopy theory. Ormsby et. al (2025) showed bijections between (co)saturated transfer systems with numerous categorical constructions. This work explores various enumeration results on rank 3 lattices including explicit counts on lattices of certain structures and a scheme to enumerate (co)saturated transfer systems using matrices.

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1. Undergrad
3. Undergrad Posters

Estimating the Fractal Dimension of the Arctic — Christian Lee <cartwris+clee@fvsu.edu>

Measuring the geometry of natural landscapes is often straightforward, yet highly irregular terrains challenge traditional approaches to quantification. These irregularities are frequently fractal in nature, exhibiting self-similar patterns that complicate conventional measurement techniques. This study investigates the fractal dimension of Arctic terrain as a metric for describing surface roughness and detecting environmental change. Using the box-counting method applied to Digital Elevation Models (DEMs) sourced from ArcticDEM satellite data (2008–2025), we analyze select Greenland regions to assess how fractal geometry can enhance terrain monitoring. By constraining data to July samples within a 10 km radius, we reduced confounding factors such as seasonal variation. Python-based algorithms generate two-dimensional slope estimates and three-dimensional visualizations, enabling fractal dimension estimation across varying box sizes. Preliminary results confirm that smaller box sizes yield more reliable representations of terrain complexity, though challenges arise from incomplete box coverage. This approach demonstrates potential for identifying subtle terrain shifts linked to climate change, such as glacial retreat and erosion, that may be missed by conventional metrics. Beyond the Arctic, the methodology offers broader applicability for analyzing diverse landscapes affected by environmental pressures. Ultimately, fractal dimension analysis provides a bridge between mathematics and climate science, offering a sensitive, scalable tool for detecting and quantifying terrain change in an era of accelerating global transformation.

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1. Special
3. Practical AI

Exploring the Impact of Automated Assessments in a Quantitative Methods Course — Raluca Clendenen <raluca.clendenen@belmont.edu>

This is a preliminary report on a study investigating the effectiveness of self-grading Excel spreadsheets as a feedback tool in STEM education, particularly focusing on their impact on student learning outcomes, engagement, and satisfaction. By providing students with instant feedback on assignments, these self-grading spreadsheets are intended to enhance students’ understanding and mastery of mathematical concepts. The study gathers student feedback to explore their perceptions of how these tools influence their learning process, confidence, and comprehension in mathematical contexts. Giving students the tools they need to develop confidence is critical to their self-efficacy and performance. Additionally, this research identifies and addresses the challenges of designing and implementing self-grading assignments, offering insights into best practices for integrating technology-driven feedback tools in STEM education. Preliminary findings suggest that self-grading spreadsheets may serve as a valuable resource in promoting active learning, with implications for improving student engagement and satisfaction. Student quotes on the positive effects for their learning from the assignments, obtained via in-semester surveys and end-of-semester course evaluations, will be shared. References Blayney P., Freeman M. (2004). Automated formative feedback and summative assessment using individualised spreadsheet assignments. Australasian Journal of Educational Technology, 20(2), 209–231. https://doi.org/10.14742/ajet.1360 Kovačić Z., Green J.S. (2012). Automatic grading of spreadsheet and database skills. Journal of Information Technology Education Innovations in Practice, 11, 53–70. Laing G., Kirkham R., Kampen T. V. (2020). An Automated Assessment Marking Approach: Using Excel to Grade an Accounting Practice Assignment. e-Journal of Business Education & Scholarship of Teaching, 14(3), 12-24. Mays T. (2015). Using spreadsheets to develop applied skills in a business math course: Student feedback and perceived learning. Spreadsheets in Education, 8(3). Fyfe, E. R., & Rittle-Johnson, B. (2016). The Benefits of Computer-Generated Feedback for Mathematics Problem Solving. Grantee Submission, 147. https://doi.org/10.1016/j.jecp.2016.03.009 Kangaslampi, R., Asikainen, H., & Virtanen, V. (2022). Students’ Perceptions of Self-Assessment and Their Approaches to Learning in University Mathematics. LUMAT: International Journal on Math, Science and Technology Education, 10(1), 1–22. McCarron K.B., Park T., Ellis Y. (2023). Intermediate accounting students’ reaction to Excel® homework assignments with a feedback (self-check answer) function. Journal of Instructional Pedagogies, 28. LoSchiavo F.M. (2016). How to Create Automatically Graded Spreadsheets for Statistics Courses. Teaching of Psychology, 43(2), 147-152. DOI: 10.1177/0098628316636293.

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1. Contributed

Families of Prime Sequences — Antara Mukherjee <antara.mukherjee@citadel.edu>

For fixed positive integers a and c, the prime sequences of the form ap_n + cb, where p_n is the nth prime and gcd(a,cb) = 1, can share terms as b varies. When the sequences share terms, we say that they overlap. Furthermore, when the sequences overlap with each other or another common prime sequence of a similar form, we say that these prime sequences are in the same family. We show that when a and cb have opposite parity, the number of families of prime sequences is Φ(a), where Φ(a) is Euler’s totient function. In other words, the number of families depends only on a. Several of these overlapping prime sequences, their families, and the pseudocode used to generate the sequences will be included in the presentation.

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1. Contributed

From Laminations to Julia Sets: An Undergraduate Research Collaboration — Brittany Duncan <brittany.duncan@ung.edu>

This presentation highlights two key components of a joint undergraduate research project conducted by Duncan and Worley with undergraduate students. First, we will outline the collaborative research process and the roles students played in exploring the mathematical concept of laminations. Second, we will describe the method used to generate the corresponding Julia sets from specific laminations studied during the project. To provide context, we will introduce the foundational definitions of laminations and discuss the technology and tools employed to visualize and compute the associated Julia sets.

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1. Undergrad
3. Undergrad Posters

From Solar System to Strata: Modeling the Atmospheric Heating of Cosmic Dust — Richard Britton <rbritto3@utsouthern.edu>

Cosmic dust particles continuously enter Earth's atmosphere, and knowledge of the thermal dynamics of differently sized particles is a crucial first step in understanding the distribution of extraterrestrial matter that ultimately reaches the surface. Some groups seek to link the composition of strata to that of cosmic dust being accrued by the planet during that same time period. To do this, establishing which particles entering the atmosphere will be fully ablated during their journey to the surface is an important distinction, as ablated material will have less predictable trajectories and be more randomly scattered. This study mathematically models the vertical atmospheric descent and resulting heat accumulation of spherical cosmic dust particles of different compositions as well as initial velocities. Three models are developed using Newton's Second Law to simulate particle trajectories from the mesosphere to the surface. An initial analytical model uses separation of variables under the assumption of constant atmospheric density and negligible gravity. Two subsequent models, solved via numerical integration, introduce variable atmospheric density and explicit gravity to improve heat profile accuracy. Comparative analysis across initial velocity regimes reveals that at high velocities, aerodynamic drag heavily dictates the heat profile as kinetic energy is converted to heat, whereas in low-velocity particles, gravitational acceleration dominates heat generation due to the eventual conversion of potential energy to heat. Ultimately, these preliminary models provide a foundational mathematical framework to predict the thermal survivability of cosmic dust and aid in the interpretation of geological strata.

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1. Special
3. Teaching Logic

From Truth Tables to Trees: Strengthening Logical Reasoning Through Semantic Tableaux — Ashley Suominen <asuomine@scad.edu>

Logic and formal reasoning are foundational to mathematics, yet students often struggle to connect symbolic notation with conceptual meaning. This presentation explores the pedagogical value of semantic tableaux as an integrated approach that reinforces truth tables, normal forms, and tautology analysis while deepening conceptual mastery of propositional logic. Semantic tableaux offer a visual and algorithmic method for decomposing well-formed formulas into subformulas and atoms. This tree-based representation complements traditional truth-table reasoning by applying the rules for logical connectives to determine whether a statement is satisfiable. By making the logical structure visually explicit through a branching tree, this method reveals the conditions for tautologies and contradictions while naturally bridging to normal forms (CNF and DNF). In doing so, it also reinforces case-based reasoning that underpins probability models and proofs by cases. Ultimately, semantic tableaux move students beyond procedural symbolic manipulation and table-reading toward a deeper understanding of logical form, laying a rigorous foundation for advanced reasoning in mathematics and computer science.

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1. Undergrad
3. Undergrad Posters

Fun with Wasserstein Distance for Self-similar Measures — Hunter Johnson <hunmjohn@ut.utm.edu>

We explore different discrete approximations for the 2-Wasserstein distance between self-similar measures defined on the unit interval.

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1. Contributed

Gaps between central lattice points on hyperbolas — Tsz Chan <tchan4@kennesaw.edu>

Let $n$ be a positive integer. Suppose $(x_1, y_1), (x_2, y_2), \dots, (x_k, y_k)$ with $\sqrt{n} \le x_1 < x_2 < \dots < x_k$ are integer lattice points on the hyperbola $x y = n$ near the center $(\sqrt{n}, \sqrt{n})$. In this talk, we will discuss repulsion among these lattice points through a lower bound on $x_k - y_k$. It turns out that this lower bound is sharp when $k = 2$ and $k = 3$ but not $k \ge 4$. We apply elementary, Pell equation, and Diophantine approximation techniques. This is joint work with Jorge Jim\'{e}nez-Urroz.

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1. Undergrad
3. Undergrad Papers

Graph Families and Their Conflict-Free Coloring — Joseph Pope <jpope7@una.edu>

Motivated by frequency-assignment problems in cellular networks, we study complete conflict-free colorings of graphs. A coloring of a graph $G$ is conflict-free if every vertex has a uniquely colored neighbor in its open neighborhood. The minimum number of colors required for such a coloring is the conflict-free chromatic number, denoted $\chi_{CF}(G)$. We determine the exact values of $\chi_{CF}(G)$ for several graph families such as paths, cycles, trees, complete graphs, and windmill graphs and provide conjectures on circulant and grid graphs.

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1. Featured

Graph Pebbling: More than just moving stuff around (MAA-SE Section Lecturer) — Carl Yerger <cayerger@davidson.edu>

This talk will begin with a brief discussion of motivations for conducting research in mathematics and why the presenter believes that graph pebbling is an appealing research area. It will continue with an introduction to graph pebbling. A survey of several streams of pebbling research, including cover pebbling, optimal pebbling and Class 0 graphs will be discussed. A number of accessible results (many involving undergraduates) and some open problems will also be presented. *Graph pebbling* is a combinatorial game played on an undirected graph with an initial configuration of pebbles. A pebbling move consists of removing two pebbles from one vertex and placing one pebbling on an adjacent vertex. The *pebbling number* of a graph is the smallest number of pebbles necessary such that, given any initial configuration of pebbles, at least one pebble can be moved to a specified target vertex.

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1. Undergrad
3. Undergrad Papers

Graph representation of parking sequences — Thien-Phuoc Phung <pphung@cbu.edu>

Ehrenborg and Happ introduced the concept of parking sequence, an extension of parking function for cars of different sizes. A graph presentation for parking sequences will be introduced, and this yields another proof for the theorem proved by Ehrenborg and Happ that enumerates the number of parking sequences.

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1. Undergrad
3. Undergrad Posters

Helmholtz Equations with Variable Potentials on Fractal Measures — Jerry Liu <zliu19@students.kennesaw.edu>

We study a one-dimensional Helmholtz equation of the form (-\Delta_\mu + k(x)^2)u = \lambda u, where \mu is a finite Borel measure on [0,1], possibly singular or fractal, and k(x) is a continuous potential. This framework extends the theory of the fractal Laplacians studied by Bird, Ngai, and Teplyaev to include spatially varying potentials. We derive a Volterra–Stieltjes integral formulation for the eigenvalue problem and prove existence, uniqueness, and differentiability of solutions under minimal assumptions on k and \mu.

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1. Special
3. AI-Resistant

Homework-Video-Reflection System for Calculus I and DE — Shalmali Bandyopadhyay <sbandyo5@utm.edu>

Traditional homework-based assessment in undergraduate mathematics has been destabilized by AI tools, producing a familiar pattern: flawless homework, failed exams. This talk presents an integrated homework-video-reflection system implemented in Calculus I and Differential Equations that addresses AI-assisted academic dishonesty without punitive measures. Exam problems are drawn directly from homework, making transparency itself the accountability mechanism

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1. Undergrad
3. Undergrad Papers

Homomesy for a Family of Posets — Samantha Morrison <sdmorrison5@catamount.wcu.edu>

Given a group action on a set of combinatorial objects, a statistic on these objects is called homomesic if its average value is the same across all orbits. The notion was coined in 2015 by Propp and Roby, who were motivated by earlier examples of this phenomenon from chip-firing on graphs (2008) and rowmotion on antichains (2009). In this talk, we will present a family of posets whose number of inversions are homomesic with respect to the promotion action.

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1. Special
3. Practical AI

How Alternative Assessment Can Change the AI Conversation — Kristi Rittby <kerittby@peace.edu>

What if, instead of trying to prevent students from using AI, we designed assessments that require collaboration with it? At a small liberal arts college, mathematics assessment for non-majors was reimagined through alternative grading and structured revision cycles. When assessment shifts from point accumulation to iterative feedback and proficiency-based revision, students begin to use AI not to produce answers, but to ask better questions, test ideas, and clarify their thinking. This session explores the evolving partnerships between students, instructors, and AI in redefined learning spaces, striving to increase a sense of belonging. Let’s explore redesigning assessment to sustain rigor, preserve human connection, and invite authentic mathematical curiosity in the age of generative AI.

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1. NExT

How to be Successful in Undergraduate Research — Chad Awtrey <cawtrey@samford.edu>

This interactive talk is designed for beginning college mathematics professors who want a practical, evidence-informed roadmap for mentoring undergraduate research. Participants will learn why mentored undergraduate research matters, what effective mentors do, how to choose problems that are appropriately challenging, how to recruit and support students, how to help students grow in independence, and how to guide them in writing papers and delivering professional presentations. Participants will leave with a clearer philosophy of mentoring, a starter plan for implementation at their own institution, and a set of questions and resources for continued growth.

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1. Undergrad
3. Undergrad Papers

Ice Bucket Challenge vs. Rice Bucket Challenge, the differences that distinguish the trends — Seunghee Chu <chuseungh2@gmail.com>

Viral social media campaigns can generate millions of dollars in donations, yet predicting their spread remains challenging. This study applies epidemiological models to analyze the 2014 ALS Ice Bucket Challenge (IBC) using published data, which models the campaign using Susceptible-Infected-Recovered (SIR) differential equations, branching process theory, and network epidemic frameworks. Using the reported values for the basic reproduction number R₀=1.43 and serial interval τ=2.1 days, I calculated the transmission rate and recovery rate. I also used branching process and SIR eigenvalue analysis to verify R₀. Using graph theory metrics (degree centrality, clustering coefficient, and network heterogeneity), I analyzed how a scale-free topology can amplify spread. Extending this framework, this study considers why the similar Rice Bucket Challenge (RBC) did not achieve comparable global impact. I develop an exponential barrier model p(b)=p₀e^(-b) to quantify participation costs. This model predicts a reproduction number R₀ ≈ 0.70 < 1, which is consistent with observed limited diffusion. The comparison highlights five factors associated with viral success: 1) R₀ > 1; 2) short serial intervals; 3) favorable network topology; 4) low participation barriers; and 5) strategic seeding among highly connected individuals. These findings suggest that epidemiological models can provide a useful framework for forecasting the virality of social media campaigns.

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1. Special
3. History

Inspired by Notable Women in Math: An Assessment in Abstract Algebra — Denise Rangel Tracy <rangel.tracy@fmarion.edu>

In this talk, I will describe a project based assessment created for an abstract algebra course that centers the mathematical work of women algebraists highlighted in the Association for Women in Mathematics (AWM) EvenQuads playing card project. Rather than presenting algebra as a finished body of results, this assignment invited students to explore topics such as geometric group theory, elliptic curve groups, and tropical algebra through the work of mathematicians whose contributions are often absent from traditional undergraduate coursework. Students completed individualized structured problem sets connected to each honoree’s research area, developed a short biography, and gave a presentation linking the mathematics to the mathematician’s contributions. I will discuss the goals of the assignment, share examples of the algebraic tasks designed for the project, and reflect on how integrating these mathematicians into assessment broadens the historical narrative students encounter in upper level mathematics.

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1. Contributed

Integration: AI vs CAS vs People — Barrett Walls <bwalls@gsu.edu>

Why do we have to learn to integrate when Computer Algebra Systems (CAS) or Artificial Intelligence (AI) can do it for us? This talk looks at some tricky integration problems that even AI and CAS struggle with and how people can solve them. We also look at some tips for ensuring our answers are correct whatever method we use.

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1. Special
3. Spoon!

Kitchen Physics: Teaching Quantum Mechanics & General Relativity With Spoons. — Jonathan Clark <jclark@tnwesleyan.edu>

Advanced physics utilizes mathematical concepts which are often inaccessible to both undergraduate and unprepared graduate students. In keeping with the theme of teaching with spoons, this talk will illustrate examples of presenting advanced modern physics concepts with only using low-level tools accessible to typical math or science majors. In particular, we will derive gravitational time dilation without using the differential geometry of general relativity, we will solve the quantum harmonic oscillator without using Schrödinger's equation, and we will present a conceptual proof of Bell's theorem using only Venn diagrams. The intent of this talk is to inspire physics teachers to try utilizing spoons in their classrooms to illustrate otherwise unavailable content using more accessible intuitive tools.

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1. Undergrad
3. Undergrad Papers

Lagrangian Coherent Structures and Network Approaches on Interannual Time scales in the Subpolar North Atlantic — Micah Chandler <mmchan4208@ung.edu>

The Atlantic Meridional Overturning Circulation (AMOC) plays a crucial role in regulating Earth’s climate by transporting heat and nutrients throughout the ocean. Warm, saline surface waters flow northward, where cooling in subpolar regions increases their density, causing them to sink and return southward as part of the deep ocean circulation. Over the past century, rising greenhouse gas concentrations have begun to alter this circulation, leading to gradual changes in its structure and variability. Within the subpolar North Atlantic, regions such as the Labrador Sea, the West Greenland Current and Disko Bay play a key role, as deep convection, where surface waters cool, sink, and mix into the deep ocean, strongly influences AMOC variability. Improving our understanding of the processes that control convection in these regions will enhance our ability to assess ongoing changes in the AMOC, with the broader goal of informing climate policy. This work develops a new, computationally efficient framework that combines Finite-Time Lyapunov Exponents, Lagrangian Coherent Structures, and graph-theoretic measures to find regions of coherent flow to diagnose how deep convection redistributes water within the subpolar North Atlantic.

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1. Contributed

Largest Square Divisor of a Random Integer — Michael Liu <1217656778abc@gmail.com>

For $x \ge 1\$, we define the expected value of the largest $k^{\text{th}}$-power divisor over integers $n \le x$ by $E_x(r^k) := \frac{1}{x} \sum_{n \le x} \max \{\{ r^k : r^k \mid n \}\}.$ Motivated by a question on MathOverflow concerning the square case ($k=2$) and a heuristic argument of Yuval Peres, we study the asymptotic behavior of $E_x(r^k)$ as $x \to \infty$. Peres’ heuristic predicts that $E_x(r^2)$ grows on the order of $\sqrt{x}$, but the associated error term is too large to determine the correct leading constant. We prove that $ E_x(r^2) = \frac{\zeta(3/2)}{3\zeta(3)} \sqrt{x} + O(\log x), $ where $\zeta(s) = \sum_{n=1}^{\infty} 1 / n^s$ is the Riemann zeta function. This result identifies the correct leading constant supported by numerical evidence. More generally, for any $k \ge 2$, we show that $ E_x(r^k) = \frac{\zeta\\left(\frac{k+1}{k}\right)}{(k+1)\zeta(k+1)}\, x^{1/k} + O(\log x). $ The constants arise naturally from zeta functions associated with $k$-free integers and quantify the average size of the largest $k^{\text{th}}$-power divisor.

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1. Special
3. History

Latin America's Hidden Contributions to Mathematics — Zachery Keisler <zkeisler@saludaschools.org>

In this talk, we’ll trace the development of mathematics in Latin America, using precise examples to anchor a broader story. We’ll start with the Mayans' vigesimal positional numeral system—remarkable for its early and systematic use of zero—which enabled sophisticated calendrical calculations and astronomical observations. Fast forward to the present, and we encounter the work of Carolina Araujo in birational geometry, particularly her contributions to the theory of Fano manifolds and rational curves within Mori theory. These cases serve as guideposts for a deeper discussion spanning Indigenous mathematical traditions, the influence of colonial-era education, and the emergence of active research communities in Mexico, Brazil, and Argentina. By sharing these stories, we’ll see how Latin American mathematics has been shaped by creativity, exchange, and resilience, and why its contributions matter in today’s global mathematical landscape.

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1. Special
3. Recreational

Manimating Formal Definitions and Theorems — Robert DeYeso III <robldeye@gmail.com>

We use the community version of Manim (created and popularized by Youtuber 3Blue1Brown) to animate mathematical concepts and theorems that are traditionally very difficult to convey. Examples include animations of the derivative, the $\varepsilon$-$\delta$ definition of the limit, and the fundamental theorem of calculus. If time permits, we will play with an interactive example where students can dynamically adjust animations of integrals.

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1. Contributed

Markov Chain Monte Carlo Methods for Curve Reconstruction and Point Cloud Data Analysis. — Asir Intesar Tushar <aintesar@vols.utk.edu>

Point cloud data have become increasingly vital due to their ability to capture detailed, multi-dimensional representations of physical objects and their surrounding environments. Point clouds are nowadays central to applications across industry and academia that range from robotics, navigation systems, and 3D printing to architecture, manufacturing, and agriculture. Despite its importance, the analysis of point cloud data faces several limitations, including high computational cost due to large data volume, contamination with localization noise and inaccuracies caused by sensor limitations, and missing points due to environmental factors or sensor positioning. Moreover, unavailable uncertainty quantification in reconstructed structures remains a critical gap in applications requiring reliable estimation. We present a fully Bayesian framework for point cloud data analysis and curve reconstruction. Our framework models a cloud’s points as noisy perturbations of latent positions constrained to lie on closed polylines, jointly inferring polyline vertices and connectivity, latent coordinates, and noise characteristics. Posterior inference is performed via a specialized Markov chain Monte Carlo sampler tailored to point cloud data processing. Experiments on synthetic data demonstrate accurate curve reconstruction while providing uncertainty quantification.

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1. Special
3. Practical AI

Mastery Based Assessment in a Remedial Math Course — Sarah Eskew <sarklock@utsouthern.edu>

We will discuss how the remedial math course at our university was converted to mastery based assessment. This will include how we decided on the learning targets, how we handle the logistics of additional attempts, and what is mastery graded and what is not. Initial reactions from student surveys will also be included.

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1. Featured

Math as Cognitive Training (Distinguished Lecture for Students) — Blake Dunshee <blake.dunshee@belmont.edu>

The work that you do changes the way that you think. Your problem-solving approach will shift dramatically over years of work studying math. In this session we’ll investigate how several groups of students and faculty with varying mathematical backgrounds approached solving the same problem (and you’ll get to try this fun puzzle for yourselves!). We’ll attempt to characterize some of the differences in their approaches. Then, we’ll take time to share our stories of how mathematics has shaped the way we think, learn, and interact in the world. Come ready to reflect on how you think and solve problems.

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1. Featured

Math in the field: Diffusion models and the minimum habitat size for bobwhite quail (Distinguished Lecture for Students) — Jerome Goddard <jgoddard@aum.edu>

Habitat fragmentation breaks continuous habitat into smaller patches separated by a less suitable “matrix.” For many species, persistence depends not only on births and deaths within a patch, but also on movement across patch boundaries and that movement can change when a patch becomes crowded. In this talk I’ll introduce a mathematical framework for fragmentation using reaction diffusion models. The reaction term describes local population growth, while diffusion captures movement that resembles random walk-like movement. We’ll begin by introducing diffusion (how a concentration spreads in space) and then translate the same idea into animal dispersal across a landscape. A key modeling choice is how individuals behave at habitat edges. We’ll discuss emigration (leaving a patch) and density-dependent emigration, where departure rates increase with local density. These assumptions lead to “rules at the boundary” (boundary conditions) that represent how animals cross edges which is an ingredient that strongly influences persistence predictions. We’ll end with a conservation-focused application to Northern Bobwhite quail: estimating a biologically meaningful minimum patch size needed for persistence. Using movement and demographic rates reported in field studies (and simple fitted components when needed), we’ll see how mathematics can test common rule-of-thumb recommendations and identify which movement assumptions matter most.

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1. Special
3. History

Mathematics Behind African Art — Kari Mays <mays_kari@hcde.org>

Mathematics, at its heart, is African. Unfortunately, much of ancient African traditions and customs have been lost due to colonization and slavery, including their knowledge and practice of mathematics. However, artifacts uncovered by archeologists confirm the understanding of math principles by African artisans. African art holds the secret behind the history of mathematics in Africa. With a focus on Sona sand drawings, this presentation will explore the beauty of mathematics that can be pulled from the ancient customs of the Tchokwe people of Angola. By exploring the work of Paulus Gerdes, a mathematician known for his work with the Tchokwe people, a discussion of mirror curves and symmetry arises from the analysis of the Sona sand drawings. He takes the patterns created by these curves to make what he coins as Lunda-designs. In this presentation, you will learn how to create your own Lunda-design and learn why they are mathematically beautiful.

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1. Undergrad
3. Undergrad Papers

Modeling Chart Metrics: Statistical and Machine Learning Analyses of Billboard Number One Hits — Samuel Whitaker <swhitaker10@students.apsu.edu>

This project comes from utilizing my major of math and statistics to study a passion of mine: music. With this project, I aim to highlight possible patterns, shifts, and broader trends within popular music in America over the past several decades. Using a historical dataset of all Billboard Hot 100 number one hits, I explore how artist gender, musical genre, audio characteristics, and more relate to chart success and longevity. To connect my statistical training with my interest in music, I built regression and machine learning models incorporating audio features, musical key, genre indicators, and temporal information. I also examined broad associations in the data, such as the uneven distribution of gender across genres. Throughout the project, I use cross validation, temporal splits, and sensitivity analyses to ensure that the results are robust and reproducible. More broadly, this work reflects my commitment to applying mathematical and statistical tools to questions in music research—showing how data can deepen our understanding of the cultural forces behind the music that define different eras.

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1. Undergrad
3. Undergrad Posters

Modeling NBA Championship Probability Using Linear and Logistic Regression — Nadeem Madyun <nadeem.madyun@g.fmarion.edu>

Modern professional basketball relies heavily on advanced statistics to evaluate team performance. This project examines whether regular-season data can be used to estimate a team’s probability of winning the NBA championship. Using team-level data from the 1995-1996 season through the present, collected from Basketball-Reference.com, we apply regression modeling to analyze championship outcomes. Using IBM SPSS, multiple linear regression is first used to identify the statistical factors that contribute most strongly to overall team strength. These factors include offensive and defensive efficiency metrics such as shooting percentage, turnover rate, and free-throw rate. Building on this analysis, logistic regression is then used to estimate the probability that a team wins the championship based on its regular-season performance and playoff seeding. This study demonstrates how classical statistical methods can be applied to modern sports analytics, illustrating how mathematical modeling helps explain and predict competitive success in professional basketball.

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1. Contributed

Morphisms of Boolean Network — FABRICE RAZAFIMAHATRATRA <frazafi@clemson.edu>

Boolean networks (BNs) have become quite popular since their proposal as models of network regulation. Every BN can be decomposed into coordinate functions and thus defines a signed, directed graph, called a wiring diagram, that describes the variable dependencies. We will explore what it means for two BNs to be equivalent and how to define a structure-preserving map between them. In particular, maps that are topologically conjugate or semi-conjugate need not preserve locality of the functions or the wiring diagram. We will illustrate this with examples and non-examples, involving commutative diagrams with extra structure. Finally, we will discuss how to define a category of Boolean networks and explore some of its basic properties.

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1. Undergrad
3. Undergrad Posters

Multiplying Rabbits: Introduction to Rabbit Laminations — Michaela Carter <michaela.carter@lander.edu>

The presentation will cover the main components of Julia sets and their laminations. Laminations are a topological way of modeling the dynamics of Julia sets. It will begin with defining Julia sets and unicritical laminations. Next, images will be provided in reference to these definitions, as well as some guidance on how to read them. Following these will be a deeper explanation of how to identify the correct Julia set when given a lamination. More diagrams will be provided to assist with visualization and stress the significance of making the correct identification. This is joint work with Dr. Brittany Duncan from University of North Georgia and Dr. Chase Worley from Lander University.

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1. Special
3. Spoon!

N Our 2D Era — Cara Admiraal <c.admiraal@yahoo.com>

In our previous work, we explored the higher dimensional analogues for Primitive Pythagorean Triples (PPTs) both algebraically and geometrically. In this session, we take a curiosity driven exploration of primitive Pythagorean results in two dimensions, emphasizing the recognition of patterns within differently defined collections of PPTs and observing predictable frequencies and occurrences of non-PPTs. What possible connections exist between this creative exploration and the higher dimensional analogues?

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1. Contributed

Nationwide Epidemiologic and Healthcare Burden Analysis of Chemotherapy-Induced Neurological Disorders — Yiran Xu <kathyyiran@foxmail.com>

Chemotherapy-induced neurological disorders (CIND) represent a serious side effect of cancer treatment. They can exist long after treatment ends and significantly impair functional independence and daily life. While this toxicity is well known in oncology, its epidemiological and cost burden features among various cohorts remain understudied. To better understand the current gap, we conducted a retrospective cohort study using de-identified administrative claims data from the IBM MarketScan research database. Our study included 258,410 adult patients undergoing chemotherapy and 4.7 million adult patients without chemotherapy. The chemotherapy group was stratified by cancer behaviors and treatment routes to examine CIND patterns and healthcare utilization. Survival analysis and Cox proportional hazards models showed that approximately one-quarter to over one-third of cancer patients receiving chemotherapy developed CIND. All malignant cohorts showed higher CIND probability than their benign counterparts across all treatment routes, with the highest rates observed in patients receiving both intravenous and oral chemotherapy. Cox modeling adjusted for demographic characteristics, comorbidities, and baseline medications showed that chemotherapy increased the risk of neuropathy by approximately 40% compared to cancer patients not exposed to chemotherapy, with female and older age as critical risk factors. A healthcare burden analysis showed that patients with CIND had significantly higher opioid use, CIND-specific medication use, and rehabilitation service needs compared to the general population, resulting in about 2 times higher healthcare costs per patient. These results indicate that CIND influences a considerable proportion of cancer patients experiencing chemotherapy, with chemotherapy administration route being a key determinant of risk. Our findings emphasize the clinical importance of comprehensive neurotoxicity monitoring and highlight the significant economic burden that CIND places on the healthcare system.

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1. Contributed

Novel Methods of Untimed Testing in Upper-Level courses — Josie Ryan <pryan@lander.edu>

Upper-level mathematics courses are widely regarded as challenging due to the complexity of their material. These courses often assess students’ understanding of course concepts through timed examinations. Because advanced mathematical concepts require critical thinking and problem-solving, students approach problems differently and may need varying amounts of time to reach solutions. Students with documented disabilities can request extended time; however, this accommodation often necessitates taking the test in a separate location, removing them from direct access to their professor. In this paper, we address the issue of test-time stress and explore strategies instructors can adopt to help students perform at their best. Our methodology involves gradually presenting test material over several days, eliminating standard time constraints for each component. We document student behavior and performance as compared to timed tests. Students are given a defined period over several days in which they can complete and submit individual components of the test as they progress. We observed student behavior, collected performance data, and analyzed the outcomes in comparison with classes from previous years that used standard timed testing methods. This paper discusses our findings and instructional strategies in detail, with the goal of providing fellow faculty members with practical approaches to reducing test-related anxiety and improving student outcomes.

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1. Undergrad
3. Undergrad Posters

Numbers with Four Close Factorizations — Laura Holmes <lholme10@students.kennesaw.edu>

Consider n = 99, 990, 000, a number that has two close factorizations: 10, 000 · 9, 999 and 11,000 · 9, 090. Generalizing this to k close factorizations, we have n = AB = (A + a_1)(B − b_1) = (A + a_2)(B − b_2) = · · · = (A + a_{k−1})(B − b_{k−1}) where 1 ≤ B ≤ A as well as 1 ≤ a_1 < a_2 <· · · < a_{k−1} ≤ C and 1 ≤ b_1 < b_2 < · · · < b_{k−1} ≤ C. Here, C is our closeness measure. Our faculty mentor, Dr. Tsz Chan, previously studied numbers with three close factorizations and identified an optimal ratio R_3 = A / C^3 ≤ 0.25. The scope of our project this summer was to expand on his work and study numbers with four close factorizations. The optimal closeness ratio here was calculated to be R_4 = A / C^3 ≤ (6+√ 6) / 9(2+√ 6)^2 = 0.04742.... Arriving at this ratio involved proving identities and inequalities, deducing intermediate lemmas, transforming our original question into a generalized Pell-type equation, determining which numbers should be entered into that equation, and eliminating cases that we knew would yield no solutions.

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1. Contributed

Obstructing Klein bottle surgeries using immersed curves — Robert DeYeso III <robldeye@gmail.com>

Dehn surgery is a topological process that creates new 3-dimensional manifolds from the 3-dimensional sphere by excising and regluing a thickened knot in interesting ways. We study when specific surgeries using fibered knots can contain a Klein bottle. We use Heegaard Floer topological invariants in their more tractable immersed curves form. This talk is aimed at undergraduates interested in accessible research topics in geometry and topology.

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1. Undergrad
3. Undergrad Papers

On a Simple Geometric Problem — Tyrique Lambert <tyriquel@email.sc.edu>

For a random parallelogram ABCD with AB parallel to DC, if BD intersects CE at F, where E is a random point on AB, what is the area of ADFE if the areas of CBF and EBF are provided? This geometric problem seems simple, but finding the solution is not easy. In this talk, we will explore some properties regarding area of triangles, area of trapezoids, and similar triangles. We then will use these properties, including one only requires middle school mathematics knowledge, to find the solution.

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1. Undergrad
3. Undergrad Posters

On the Gonality of Kneser Graphs — Willoughby Caine <cartwris+wcaine@fvsu.edu>

The Kneser graphs KG(n,k) are a classically studied family of graphs, wherein vertices are subsets of size k from a set of n elements, and vertices are connected if the sets they correspond to are disjoint. The chip-firing game is a combinatorial game played with poker chips relevant to various fields of mathematics and physics (see the dollar game, probabilistic abacus, Abelian sandpile model). Gonality is the graph invariant corresponding to the minimum number of chips needed to win the chip-firing game after one chip has been removed from one of the vertices of the graph. Gonality has applications in various mathematical fields, from combinatorics to algebraic geometry and coding theory, relating most notably to finding solutions to equations defining algebraic curves. Various techniques for upper and lower bounding gonality exist; using one such technique, we give (n-1) choose k as an upper bound for the gonality of KG(n,k) when n > 2k. We also apply the recent result that the invariant scramble number is a lower bound for gonality to show that the gonality of KG(n,k) is exactly (n-1) choose k when n is greater than (3k 2 + k + 2)/2, and improvement on existing results towards the conjectured n > 4k. Finally, we conjecture that an even stricter polynomial bound may hold by considering a specific scramble.

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1. Contributed

On the Implementation of a Two-Dimensional Finite Element Least Squares Algorithm for the Navier-Stokes Equations — Keith Brauss <dbrauss@fmarion.edu>

We discuss the Navier-Stokes equations (NS equations) and the implementation of a well-known least squares finite element algorithm in an object-oriented framework. We review the conjugate gradient method (CG method) utilized in solving the least-squares formulation as well as the corresponding key components specific to the application of the CG method with respect to the NS equations and the natural application of the finite element method resulting from the components. We discuss the application of the implemented solver toward several standard benchmarks, we visualize benchmark results, and we discuss computational aspects of the implemented solver with respect to benchmark results.

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1. Undergrad
3. Undergrad Posters

On the equivalence of the weak and integral formulations for a variable coefficient Helmholtz equation associated with fractal measures — Nischal Regmi <nregmi@students.kennesaw.edu>

We study a one–dimensional Helmholtz-type equation with a variable coefficient k(x) . The problem is formulated as a Volterra–Stieltjes integral equation, allowing the inclusion of singular measures beyond the continuous setting. An equivalence is obtained between weak formulations, integral representations, and derivative identities, providing an analogue of a result of Bird–Ngai–Teplyaev in the variable-coefficient setting. These results extend known analysis of fractal and measure-based Laplacians to variable-coefficient Helmholtz operators.

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1. Special
3. Practical AI

Our class SI is the "infamous" AI — Rodica Cazacu <rodica.cazacu@gcsu.edu>

It is well known that one big issue students have in math classes is related to solving word problems. So, what can we do in a class like Quantitative reasoning or Mathematical Modeling, where most of the problems they have to solve are word problems? How many examples could an instructor show their students to make sure they understand how to approach such problems? This presentation will look into how I use the AI in my Quantitative Reasoning classes as a tool that will help my students understand the process of solving word problems, creating examples and understanding the mathematical logic while applying it in real life. I will talk about what I call Unit Workshops, where my students work in groups to discuss different methods, they find using the AI and compare them to what we worked in class before, looking for errors that may affect the results and/or interpretation of the results. All these workshops are guided, and each group must write a report.

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1. NExT

Panel on Innovative Teaching Methods — Melinda Lanius <melinda.lanius@auburn.edu>

TBA

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1. Undergrad
3. Undergrad Papers

Periodic Nature of Julia Sets and Laminations — Kent McCathern <mccathernkent@gmail.com>

This presentation will discuss the periodic makeup of laminations and Julia sets. First, I used the original polynomial to create our Julia sets. Next, displaying additional functions over the image, helping to explain the periodic makeup of the Julia sets created. Finally, I’ll explain how this strategy helped me to understand the behavior of our generated Julia sets to identify the Julia set to lamination correspondence more easily.

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1. Contributed

Permutations with only reduced co-BPDs — Adam Gregory <gregory@wcu.edu>

Bumpless pipe dreams (BPDs) are combinatorial objects used to study Schubert and Grothendieck polynomials. In 2025, Weigandt introduced a co-BPD object corresponding to each BPD and used them to prove change of bases formulas between these polynomials. She posed the open problem of characterizing which permutations have only reduced co-BPDs associated to their BPDs. In this talk, we present a pattern-avoidance characterization of these permutations. This is joint work with Josh Arroyo.

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1. Undergrad
3. Undergrad Posters

Physics-Based RNN for IMU-Based Sensor-to-Segment Alignment — Zeyad Chatila <zeyad.chatila@g.fmarion.edu>

In this work, a Recurrent Neural Network (RNN) model is used to predict the joint center of a one-degree-of-freedom mechanism in 2D rotation from inertial measurement unit (IMU) data. The model is trained using synthetic data and tested using experimental measurements. In half of the trained models, an additional physics-inspired signal is calculated from the IMU data and used to examine whether it can improve prediction accuracy. The results demonstrate that the RNN with physics-inspired feature engineering can effectively learn the relationship between IMU measurements and joint center location, suggesting that neural networks are a promising tool for improving kinematic estimation from sensor data.

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1. NExT

PreTeXt and Prefigure for Accessibility — Steven Clontz <steven@scholarlattice.org>

With new legal requirements for accessibility beginning in April (https://www.ada.gov/resources/2024-03-08-web-rule/), it is important for faculty to know how to author and share accessible mathematical documents and images. We will explore the free and open-source PreTeXt and Prefigure software solutions which produce print materials, accessible HTML, and even braille!

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1. Special
3. AI-Resistant

Promoting Genuine Engagement through an AI-Resistant Assignment: Evidence from Student-Created Video Solution Homework in Undergraduate Mathematics — Wonjin Song <wsong@ung.edu>

The rapid advancement of artificial intelligence has created new challenges for mathematics educators seeking assignments that promote authentic student engagement rather than AI-assisted completion. This study examines student-created video solution homework as an AI-resistant assignment in undergraduate mathematics. Implemented across four undergraduate mathematics courses, the assignment required students to explain their problem-solving processes verbally and visually. Classroom-based empirical evidence was collected through two measures: (1) comparisons of exam performance by video homework completion and quality, and (2) a student perception survey. Across courses, students who consistently earned full-credit video scores demonstrated higher average exam performance than peers with incomplete or lower-quality submissions. Survey responses further indicated that students perceived improvements in conceptual understanding, organization of reasoning, and confidence in explaining mathematics. Together, these findings suggest that structured video explanation assignments can promote genuine engagement and deeper learning while serving as a practical AI-resistant assessment strategy in undergraduate mathematics.

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1. Contributed

Properties of Uniformly F-Compatible Ideals — Jiamin Pan <jpan4@student.gsu.edu>

In [Schwede 2010], uniformly $F$-compatible ideals were introduced as a generalization of centers of $F$-purity in prime characteristic, revealing deep connections to classical Matlis duality. When the underlying ring is Gorenstein, this notion coincides with the well-studied $F$-ideals of [Smith 1995] and [Kimura 2025]. In this talk, we will introduce the definition and core properties of uniformly $F$-compatible ideals and see its applications in the study of Frobenius complexities of rings.

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1. Undergrad
3. Undergrad Posters

Prüfer Transformation and Spectral Analysis for a Sturm–Liouville-Type Equation — Bailyn Hall <bhall76@ut.utm.edu>

The Prüfer transformation is a classical technique that converts a second-order differential equation into a pair of first-order equations using polar-like coordinates. By separating a solution into amplitude and phase components, the oscillatory behavior decouples from the growth of solutions — the zeros are determined entirely by the phase. This makes it a powerful tool for studying eigenvalue problems arising in vibration analysis, quantum mechanics, and mathematical physics.

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1. Special
3. Recreational

Quad-packing in the game EvenQuads — Taiki Aiba <taiba3@gatech.edu>

_EvenQuads_ is a _SET_-like card game published by the AWM whose goal is to find "quads", which are sets of four cards satisfying a particular pattern. The cards can be viewed as points in the finite affine geometry $AG(6,2)$, and a quad in the card game corresponds to a plane in $AG(6,2)$. An interesting puzzle is to consider what the largest number of quads is that we can possibly pack into a specified number of cards/points, if we are allowed to choose them however we wish. In this talk, we will explain the rules and geometric underpinnings of EvenQuads, and describe some current work and open questions about quad-packing.

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1. Undergrad
3. Undergrad Papers

Rational-value of polynomial on $S$-unit of prime integers. — Thien-Phuoc Phung <pphung@cbu.edu>

Theorems by Thue, Pólya, and Mahler show that if a polynomial with integer coefficients $f(x)$ has at least two distinct complex roots, the greatest prime factor of $f(n)$ tends to infinity as $n$ approaches infinity. Consequentially, for every finite set of prime $P$, the intersection of $f(\mathbb{Z})$ and the $S$-unit of $P$ is finite. An extension on $f(\mathbb{Q})$ will be explored, by mimicking the technique used by Pólya, and applying a corollary of Falting's theorem for quartic binary forms.

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1. Contributed

Rationalizing the Cantor Set and Its Progeny — Douglas Daniel <ddaniel@presby.edu>

After reading a few articles about the rational points that could be found in the well-known Cantor set, I wondered if I could similarly find rational points in generalized Cantor sets too. Many years ago, I worked with a student to see what we could find. In this talk, I will briefly describe the Cantor set and the motivation for this project. After that I will discuss two different types of generalizations of the Cantor set and how to think about finding what lies inside of these sets.

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1. Undergrad
3. Undergrad Posters

Reconstructing Weighted Directed Graphs from Dynamical Systems — Donnell Wilkins <jbarnes+donnellwilkins@email.wcu.edu>

Analyzing dynamical systems is challenging due to their high dimensionality and chaotic, nonlinear behavior. Motivated by this challenge, we develop graph representations of these systems that track both the structure of states and their temporal evolution. More precisely, we introduce two reconstruction methods: a direct binning approach that discretizes phase space into grid-based nodes, and a k-nearest neighbors (k-NN) approach in which nodes are defined by local neighborhoods. In both cases, directed edges encode temporal transitions between nodes. These graph constructions capture local geometric organization, recurrent behavior, and transition structure in the discretized state space. Consequently, graph-theoretic techniques such as community detection and loop detection can be used to identify structural signatures of the underlying dynamics.

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1. Contributed

Restricted Configuration Spaces of Metric Graphs — James Dover <james.dover@ung.edu>

A traditional configuration space of a metric graph *X* models *n* particles existing in a network of tracks with no collisions allowed. If instead of *n* particles, there are *n* "robots," then the resulting space's type depends on the robots' sizes and other distance restrictions given by a restraint parameter **r**. In this talk, we discuss the homotopy and homeomorphism types of these restricted configuration spaces $\{X^n_r\}$ over the domain of the parameter **r** and provide polynomial upper bounds (in the number of edges of the graph *X*) for the number of types.

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1. Contributed

Ricci flow on homogeneous spheres — Jason DeVito <jdevito1@ut.utm.edu>

Hamilton proved that positive sectional curvature, sec > 0, is preserved under Ricci flow in dimensions 2 and 3. However, as shown by Bettiol and Krishnan, this is no longer true beginning in dimension 4. In fact, Cheung and Wallach and, later, González-Álvaro and Zarei showed that sec > 0 is not preserved under the added assumption that the starting metric is homogenous. We will show that, in contrast to these results, Ricci flow does in fact preserve the set of homogeneous sec > 0 metrics on a sphere of any dimension. This is joint work with David González-Álvaro and Masoumeh Zarei.

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1. Undergrad
3. Undergrad Posters

Shor’s Algorithm: A Mathematical Approach to Quantum Computing — Porter Allen <portera.1308@gmail.com>

In 1994, Dr. Peter Shor developed an algorithm for finding the period of large prime numbers. This algorithm is called Shor’s Algorithm and it enables quantum computers to calculate the period faster than classical computers. Classical computers implement a “brute-force” strategy for calculations by systematically trying every possible value. Alternatively, Shor’s algorithm sequentially tests the most probable number instead. An exploration of this algorithm’s implemented mathematics and a comparison with classical computing will be the focus of this poster.

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1. Undergrad
3. Undergrad Papers

Simultaneous Inference of Factors Affecting Home Prices in Charleston — Aiden Raab <araab@student.citadel.edu>

Rated Charleston as best city in north America to travel and live by Travel magazine, the home prices of Charleston area became to soar. It is demanding from home buyers to address the factors affecting home prices in Charleston area. We selected several candidate factors contributing to the home prices: regions, number of bedrooms, number of bathrooms, square feet, median income, and waterfront view or not. The data are collected from a sample of 210 homes on Zillow. We fit data to a general linear model. Among the candidate factors, the analysis results show that all except the number of bedrooms/bathrooms significantly affect the home prices. We further apply the Bonferroni method for simultaneous testing of the region effects vs. the baseline effect of home prices from downtown Charleston. Even though the estimates of home prices of the non-downtown regions are lower than that of downtown, such difference is not significant between the pair Isle of Palms and downtown Charleston.

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1. Special
3. Practical AI

Some AI solutions to a math professor's problems — Nick Kirby <kirbyn@apsu.edu>

The use of AI in the professor's office can be a source of great fun or great aggravation. This presentation shares specific, prosaic problems that were solved well by generative AI. In particular, we will explore three distinct success stories: 1. Administrative efficiency: building LaTeX files for class notes; 2. Assessment design: using AI to generate diverse, standards-aligned exam questions; and 3. Programmatic visualization: using AI-assisted coding to build Mathematica animations of poles of Padé approximants. The presentation will also candidly address the dead ends of generative AI, discussing failed attempts at posing research-level open problems and the frustrations of iterative assignment design.

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1. Contributed

Some Side Benefits of Euclid's Algorithm — Stephen Davis <stdavis@davidson.edu>

We look at three results that use Euclid's algorithm as a backbone, producing side benefits apart from the computation of a GCD.

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1. Undergrad
3. Undergrad Papers

Stagewise comparison — Dulanjana Amarasekera <damarasekera@students.apsu.edu>

The traditional pairwise comparison voting method is not widely used, as evidenced by the fact that no national-level elections use it. One of the main reasons for this is that, unlike in elections with few candidates, national elections tend to have a large number of candidate, which dramatically increase the time required to evaluate the votes and determine the winners. In this research, we propose a new method for conducting elections, the stagewise comparison method, to hold elections with a large number of candidates and return results faster than using the traditional pairwise comparison method. This method requires dividing candidate pools into successively smaller pools and making pairwise comparisons among the candidates. We conclude by demonstrating the effectiveness of this approach in terms of time and resources required to conduct such an election.

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1. Special
3. Practical AI

Standards-Based Grading: First Day Activities to Promote Student Buy-In — Rachel Epstein <rachel.epstein@gcsu.edu>

Standards-Based Grading (SBG) has many potential benefits for students, since it gives them multiple opportunities to demonstrate their understanding and doesn’t penalize taking longer to learn something. However, since most students have only experienced points-based grading in math courses, they are often wary of and confused by SBG. In this presentation, I’ll discuss how I introduce SBG on the first day of class, using small group discussions to help them identify issues with traditional grading and understand the benefits of SBG. This presentation is intended to be useful both for those already using SBG and those interested in learning more about it.

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1. Special
3. Recreational

Tangles and computational algebraic geometry — Doug Torrance <dtorrance@piedmont.edu>

A simple closed space curve that is comprised of quarter circles of fixed curvature with continuous tangents is known as a Tangle, after the popular fidget toy. We show that all Tangles of a given length n (or n-Tangles) correspond to the solutions of a particular system of polynomial equations. Using the software platform Macaulay2, we prove the nonexistence of 5-Tangles and describe all 6-Tangles.

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1. Special
3. Spoon!

Tennenbaum's Spoon — Jake Mealey <mmealey@vols.utk.edu>

Mathematician Stanley Tennenbaum demonstrated a geometric proof of the irrationality of the square root of 2 in the 1950s using a lesser known theorem called Carpets Theorem. Using a “spoon”, I plan to show Tennenbaum’s proof in an easy to understand light. However, to avoid steering away from the more mathematical aspects of such a proof, I will show the core algebra and math as well. Both of these points of view will be viewed from a geometric lens just as Stanley Tennenbaum did.

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1. Undergrad
3. Undergrad Papers

The $d$-Armed Turtle — Robert Risdon <rnlrisdon@gmail.com>

This presentation shows the process of finding a corresponding Julia Set from a particular lamination and delves deeper into the understanding of a specific Julia Set, the “Sea Turtle.” The presentation will cover the manipulation of the Sea Turtle, aka the “$d$-Armed Turtle” and the proof of showing affine conjugacy as well as prediction of the amount of solutions to the Turtle. 37E10 Dynamical systems involving maps of the circle

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1. Undergrad
3. Undergrad Papers

The Distribution Along the Ellipse of the Complex Number Valued Sequence X_n+2 = imX_n+1 + X_n — Keith Bullard <kjbullard@coastal.edu>

Uniform distribution under irrational rotation is a classical result in dynamical systems. If a point on the unit circle is iteratively rotated by an irrational multiple of 2π, its orbit is equidistributed with respect to arc length measure, a consequence of the equidistribution theorem and the circle’s rotational symmetry. This research stems from a difference equation in the complex plane that creates an ellipse when -2 < m < 2. Applying an irrational rotation to the ellipse, it is found that although the resulting orbit remains dense, approaching every point on the ellipse arbitrarily closely, it fails to be uniformly distributed with respect to arc length.

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1. Undergrad
3. Undergrad Papers

The Interplay Between Relaxation time, Damping, and Blowup in the Breakdown of Solutions to an Equation from Fluid Dynamics — Shae Jolivette <shaejolivette@gmail.com>

We consider two nonlinear (damped and undamped) partial differential equations which model, among other systems from fluid dynamics, special solutions of the n-dimensional incompressible Euler equations. We show that the incorporation of damping effects may or may not suppress the finite-time blowup that occurs in solutions of the associated undamped equation. In particular, we discuss how the amount of damping required to suppress blowup is determined by a relaxation time which depends on the blowup time of solutions of the undamped system.

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1. Undergrad
3. Undergrad Posters

The Kelly Criterion Used in Betting and the Stock Market — Johnny Drouillard <jdrouil1@cbu.edu>

This project compares the mathematical structure of the Kelly Criterion, meant to maximize expected logarithmic wealth in two settings: a repeated biased coin toss model and the stock market modeled as a stochastic process. This project derives the optimal fraction in each case and demonstrates that both solutions follow the same structural principle: optimal allocation equals expected excess return divided by variance. By looking at both examples side by side, this project shows how the same mathematical idea can be applied to simple games of chance as well as real-world investing decisions.

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1. Undergrad
3. Undergrad Posters

The Life of Srinivasa Ramanujan: Partitions and Infinite Pi Series — Jamion Carter <jamion.carter@lander.edu>

This project is a study on the life of Ramanujan. We cover topics including a general description of life, his work in partitions, and the infinite pi series. The closest people to Ramanujan were his mother Komalatammal, his wife Janakiammal, and G.H Hardy (his mentor/partner). We will start by discussing his relationship to these people and the impact they had on him. Then once we get into mathematics, we can explain how Ramanujan did a lot of work in number theory with partitions. Number Theory is a subset of mathematics about studying the patterns and relationships between integers and other number groups/sets. Partitions are all the ways to add a number using non-negative integers. The poster will have photos and a description of the 3 partition congruences Ramanujan proved, and the partitions formula he created with Hardy. Partitions is significant in mathematics by giving us all possible combinations that we can apply to topics in statistics and graph theory. Finally, we will explain how Ramanujan’s infinite pi series is applied everywhere in math and physics by giving us more digits of pi.

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1. Contributed

The Method of Brackets for the Evaluation Certain Definite Integrals — Ghanshyam Bhatt <gbhatt@tnstate.edu>

The mathod of bracket is useful in evaluating some definite integrals. In this talk we present the method of brackets and provide some examples.

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1. Undergrad
3. Undergrad Posters

The Plus Topology on $R^2$ — Griffin Duncan <duncangs@appstate.edu>

This poster session will highlight the use of visualization tools for understanding calculus and topological concepts. We take a novice's view of understanding open sets in the plane in order to define continuity of functions. This highlights why continuity within a neighbourhood is important for differentiability. In multivariate calculus, we expand on differential calculus notions of derivatives and the limits that define them, by growing from one dimension with two directions of movement towards a point, to two dimensions and an infinite number of ways to move towards a point. This work is done on top of the backdrop of the usual topology on the real plane. This research project is an investigation of applying the Plus Topology on the plane as a backdrop for continuity and differentiability as discussed in a multivariable calculus class.

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1. Featured

The Shears Know: Creative Assemblage with 3-D Change of Basis Vectors (Faculty Plenary Speaker) — Hortensia Soto <hortensia.soto@colostate.edu>

In this presentation I will share on a research project where we explored how undergraduates, enrolled in an introductory linear algebra course, collectively created an assemblage of a shear using 3-D change of basis vectors. For this study, I used a theoretical perspective that falls under the umbrella of embodied cognition–inclusive materialism. This lens posits that learning is the invention of a new creation that manifests through imagination in unusual and unexpected ways. It describes mathematics as an assemblage between the body of participants and the body of their materials that give shape to an activity, where affective and aesthetic features contribute to the virtuality of the body of mathematics. Our findings suggest that the class created an assemblage of a shear by (a) introducing or catalyzing the new and (b) showcasing how aesthetics and affect inspire intra-actions. As part of my presentation, I will describe the students’ intra-actions with their own fabricated material.

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1. Featured

The Tortured Metaphors Department: An Educator's Confession, Investigation, and Love Letter (2025 Teaching Award Winner Lecture) — Melinda Lanius <melinda.lanius@auburn.edu>

What makes a math metaphor land and what makes it crash? In this talk, I reflect on my journey as a mathematics educator through the lens of one of teaching's most powerful and perilous tools: the conceptual metaphor. We begin at the University of Illinois at Urbana-Champaign, where, as a graduate teaching assistant, I deployed some genuinely tortured metaphors with the full confidence only inexperience can provide. We then move to the University of Arizona, where as a postdoc I discovered the subtler danger of mixed metaphors, where individually reasonable analogies placed side by side can quietly undermine each other and students’ developing understanding. And finally, we arrive at Auburn University, where I stumbled upon a metaphor that actually worked beautifully, and found myself compelled to understand *why*. Along the way, I will draw lightly on cognitive theories of mathematics learning to ask: what is a metaphor really doing for a learner? What happens when the wrong one takes root? The talk will include penguins, binoculars, a poorly drawn summary of *The Terminator*, and a live encounter with the surprisingly rich metaphorical life of the equals sign. I will also invite the audience to consider a new and thought-provoking question: in an age of large language models that can generate metaphors fluently and instantly, what does that reveal about what makes a math metaphor genuinely *good*? This talk is equal parts a confession, an investigation, and a love letter to the craft of teaching. P.S. As a lifelong Swiftie, I could not resist naming this talk after a certain album. But I promise that the parallel is more than cosmetic.

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1. Undergrad
3. Undergrad Papers

The Visual Encoding of Thick Data — Jai Grant-Williams <jgrant27@student.scad.edu>

"Thick data" captures the qualitative richness of human experience including emotions, behaviors, and perceptions, and while it is central to the design process, synthesizing it risks losing nuance as researchers cluster experiences into discrete themes. This data is often identified as unquantifiable, but through modern natural language processing (NLP) techniques, the bridge between qualitative and quantitative is shortened. This research introduces a methodology for identifying sentiment between speakers in an interview study. The process includes (1) partitioning a sentence sequence into subsequences representing each speaker (2) embedding sentences into vectors representing sentiment polarity using a BERT-based embedding model architecture, and (3) softmax normalization to produce probability distributions used for visualization. This process is then expressed through new visualizations and explores various visual encoding characteristics to create effective visuals, defined by three principles: consistency, accuracy, and meaningfulness. The goal is to provide a new synthesis methodology for real-world research operations.

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1. Undergrad
3. Undergrad Papers

Total Prime Labelings — Joseph Spaeth <jspaeth@students.apsu.edu>

A *total prime labeling* of a graph is an extension of a prime labeling in which we distinctly label the vertices and edges with the integers $1, 2, \ldots, \lvert V \rvert + \lvert E \rvert$. In a total prime labeling, the labels on adjacent vertices are relatively prime, and for each vertex of degree at least 2, the greatest common divisor of the labels on its incident edges is 1. In addition to introducing total prime labelings for various classes of graphs, this talk will highlight certain classes of graphs that do not allow a total prime labeling.

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1. Undergrad
3. Undergrad Posters

Tracking the Trajectory: Time-Series Analysis of Inflation From 2020 to 2025 — Jaela Adams <jadams56@wildcat.fvsu.edu>

In this study, we investigated how the COVID-19 pandemic influenced inflation trends in the United States from the year 2020 through 2025. This topic is especially important because inflation directly affects the everyday lives of citizens and plays a crucial role in shaping the economy’s overall health. High inflation can reduce purchasing power, increase the cost of goods and services, and place additional strain on households and businesses. During the pandemic, the economy faced unprecedented disruptions, including breakdowns in global supply chains, changes in consumer demand, and fluctuating energy prices. These factors significantly influenced inflation rates, making it essential to track and understand the trends that followed. To explore this, we collected monthly data on the Consumer Price Index (CPI) and Producer Price Index (PPI) from credible sources such as the U.S. Bureau of Labor Statistics. Using Microsoft Excel, we organized the data, created charts, and applied linear regression analysis to observe how CPI and PPI shifted over time. Our results showed a sharp increase in inflation from 2020 to 2022, largely driven by supply chain disruptions, changing consumer behavior, and external shocks to food and energy markets. This supported our first hypothesis that inflation in the early pandemic years was heavily influenced by logistical and production challenges. However, contrary to our second hypothesis, inflation did not significantly decline between 2022 and 2025, despite government interventions and partial stabilization in energy markets. This finding suggests that recovery from global crises like COVID-19 is neither immediate nor linear. Economic variables are interconnected, and a single policy or market correction may not be enough to reverse inflationary trends. These results also emphasize that inflation impacts individuals differently based on factors such as income, geographic location, and spending behavior. Therefore, it is critical to continue monitoring inflation indicators like CPI and PPI in real time. This allows policymakers, economists, and the public to respond proactively and avoid long-term economic instability caused by unchecked inflation.

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1. Special
3. Practical AI

Using AI to Enhance Mathematics Classes and Departmental Functions — Julie Barnes <jbarnes@email.wcu.edu>

As teachers, we are always looking for ways to work smarter, not harder, and AI can assist with that.  In this talk, we look at a collection of ideas from AI used in calculus and introduction to proof classes.  These ideas include some nuts and bolts topics like creating review sheets with solutions, writing creative word problems with useful diagrams, and generating a large collection of possible exam questions to choose from.  We will also look at some more artistic ideas, like developing an image for the class's Canvas tile, generating playing cards about historical mathematicians, and creating a slide show about departmental graduates.  

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1. Special
3. Teaching Logic

Using Authentic and AI-Generated Debate to Teach Logic and Argumentation — Andrew Miller <andrew.miller@belmont.edu>

At Belmont University, our Global Honors Program curriculum includes a Mathematical Inquiry Seminar as the only required mathematics course for students in this program. Since its inception, this course has included a unit on logic, argumentation, and critical thinking. We share recent course activities that attempt to bridge the gap between mathematical approaches to logic and real-world argument analysis. These include discussing authentic debates hosted by the nonpartisan, nonprofit organization Open to Debate and arguments created with the assistance of generative AI tools.

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1. Undergrad
3. Undergrad Posters

Using Bioinformatics to Characterize Missense Variants of SERPINA1 Associated with Bronchiectasis — Joseph Pope <jpope7@una.edu>

Bioinformatics is the intersection of statistics, biology, and computer science. The abundance and open-source nature of data from clinical submissions of genome sequencing can allow one to study genetic mutations without the need for expensive lab equipment and wet-lab time. Bioinformatics research is an important tool for lowering cost and reducing time to wait for genomic results. This study investigates missense swaps of the *SERPINA1* gene. *SERPINA1* is the gene that carries the instructions to produce the Alpha-1 antitrypsin (AAT) protein. AAT is a protease inhibitor created in the liver that protects the airways from pollutants. Mutations in *SERPINA1* can cause not enough AAT to be produced, halt creation of AAT altogether, or deform the folding of the protein causing it to not reach its intended destination; the lungs. Such a deficiency in AAT can cause non-cystic fibrosis bronchiectasis. This study aims to predict the pathogenicity of the missense swaps S38F and S69F. These swaps were chosen due to their proximity to an alpha-helix, their possible harmful effects on other bonds throughout the protein, and their relationship to the pathogenicity of other serine to phenylalanine swaps. Pathogenicity scores were compared to the known pathogenic swap S77F and the average of all known benign scores using the *in-silico* prediction analysis from SIFT, PolyPhen, REVEL, MetaLR, and CADD scores. ConSurf modeling over 150 homologues revealed conservation scores and predicted if the amino acid positions of interest were exposed, buried, structural, or functional. Molecular dynamic simulations were used to predict the movement of the protein, comparing the wild type and the selected variants of uncertain significance to determine differences in movement. These simulations indicate a statistically significant increase in movement for the selected uncertain variants. These findings contribute to the understanding of genetic factors influencing non-cystic fibrosis bronchiectasis and define the importance of further investigation of these variants for improved diagnostics in clinical diagnosis.

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1. Special
3. AI-Resistant

Using Oral Exams to Enhance Conceptual Understanding — Chris Cyr <chris.cyr@covenant.edu>

It is often said that the best way to understand something is to try to explain it to someone else. Based on this, would asking our students to explain important course concepts in their own words be an effective learning technique? To test this hypothesis, a few years ago I introduced oral exams as an alternative assessment method in some of my upper-division courses. In this talk, I will describe how I conduct oral exams in my Real Analysis and Abstract Algebra courses, giving examples of the types of questions I ask, criteria for evaluation, strategies for alleviating student anxiety, and some benefits of assessing students using this method.

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1. Special
3. Teaching Logic

Using Specifications Grading in a Transition Math Course. — Jeff Hildebrand <jhildebr@ggc.edu>

A course to introduce mathematics majors to upper level mathematics courses requires the students to develop familiarity with and the ability to use many mathematical tools. Because of this, the course lends itself to the use of specifications grading. This talk will discuss one attempt to implement this method of grading and describes some of the benefits and the drawbacks found will teaching the courses with this approach.

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1. Special
3. AI-Resistant

Visual Algebra, Intro to Proofs, and other AI-resistant upper-division math courses — Matthew Macauley <mattmacauley@gmail.com>

Before AI, my students submitted weekly homework sets written by hand. Today, they use LaTeX to write and typeset their own professional-looking textbooks. Somewhat ironically, the emergence of AI has helped them strengthen, rather than weaken, their mathematical writing skills. I'll tell you all about this, and more. If time permits, I will show you how I have AI-proofed my abstract algebra class by infusing hundreds of visual elements, along with feedback from former students who have gone on to PhD programs. For those unable to attend, additional details and materials are available on my course webpages.

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1. Undergrad
3. Undergrad Papers

When Data Breaks the Formula: Problems for Rarefaction Curve Calculations — Timothy Campbell <tcampbell12@gardner-webb.edu>

Ever since Newton and Kepler, science has made extensive use of mathematical models for systems, at times in fields where they are probably simpler than useful. Ecology is among the fields where formulae are useful, but can never be truly precise. One of the more common metrics calculated about an ecosystem is the rarefaction curve. This curve approximates how many species within a specified group will be found, with sample size as the independent variable. They may be used to compare species richness between sites with differing levels of sampling, approximate the total diversity of a site, estimate the total global diversity of a clade, or perform other similar calculations. They are generally assumed to follow either an inverse decay curve—\(\hat{s}=a(1-e^{-bx})\)—or a logarithmic curve—\(\hat{s}=a\ln({bx})\). Much of my research work has been focused on documenting the fauna of the early Pleistocene Carolinian Waccamaw Formation. As part of this, I have also done systematics/taxonomy and paleoecology. Since much of the material for the faunal documentation consists of bulk samples, this allows for calculation of a rarefaction curve across a very wide range of sample sizes. Plotting these data points reveals that they match neither of the expected types of curves, but have a much longer slow increase than expected. The closest match found so far is the integral of a cumulative lognormal, however, suggestions of other possible curves are welcome.

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1. Special
3. Spoon!

When are Two Polygons Fold-Congruent? — Elena Ruiz <ellie.c.ruiz@gmail.com>

Hilbert's Third Problem, presented in 1900, asked: given two polyhedra of equal volume, are they scissors-congruent? That is, can one always be cut into a finite number of pieces and be reassembled into the other? In two dimensions, it is clear that two polygons have equal area if they are scissors congruent, but the converse was proved in 1807. The parallels between flat origami and polygonal decomposition suggest a common framework, which motivates us to define a notion of fold-congruence. We pose the question: are two polygons of equal area always fold-congruent? In this talk, we discuss preliminary investigations into this seemingly difficult question.

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1. Contributed

Word-based global dynamics of vibro-impact pairs in bistable regimes — Lanjing Bao <lbao1@student.gsu.edu>

Vibro-impact systems are central to many engineering applications, including energy harvesting; yet, unlike smooth dynamical systems, they still lack broadly applicable methods for global dynamical analysis. We develop a novel word-based first-return map framework to study the global dynamics of a vibro-impact pair, modeled as a ball moving up and down inside a harmonically forced capsule. Because impacts define the system’s evolution through discrete collision events, symbolic dynamics provides a natural representation. We encode impacts with the bottom and top of the capsule as B and T, respectively, and describe trajectories through finite words formed from these symbols. In our recent work (Bao et al., SIAM Journal on Applied Dynamical Systems, 24 , 1891, 2025), we focused on short word sequences associated with 1:1 responses (e.g., BTB). Here, we extend the approach to longer words (e.g., BTBB and BBTB) to capture regimes in which 1:1 and 2:1 solutions coexist. This extension demonstrates that the word-based first-return map remains effective in more complex settings and can be used to identify basins of attraction in bi-stable regimes. Moreover, by characterizing the global dynamics of energetically favorable states in the bi-stable regime, we identify parameter regions that maximize energy output in vibro-impact systems and clarify how noise may play a constructive role by triggering switches from low-output to high-output attractors.

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1. Special
3. Recreational

Wreath Cards & Cube Rotations — Stephen Davis <stdavis@davidson.edu>

As part of her 2025 MAA-SE plenary talk, Catherine Hsu introduced cards that represented elements of the group $S_2\wr S_3$ for a game similar to SET. We call these cards *Wreath cards* and pull out the 24 cards (the $\mathcal{R}$ deck) that correspond to the group of rotations of a cube. We propose a ``game" to express a drawn card from the $\mathcal{R}$ deck as a product with factors chosen from three designated generators for $\mathcal{R}$. The player is also challenged to physically manipulate a cube to demonstrate the product.

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