1. 2025 Meeting
3. Sessions
5. UnspokenHistory

A Forgotten History: How Chinese Mathematics have Contributed to Modern Methods of Problem Solving — Kari Mays <kariormsby@gmail.com>

This paper explores the historical roots of modern mathematics. It compares ancient Chinese problem solving with contemporary methods. The paper compares multiplication visuals to area models used today. This paper also compares the Fengcheng rule for solving systems of equations to the Gaussian Elimination method. It emphasizes the contribution of Chinese mathematics to the solving of systems of equations long before the Gaussian Elimination method was used in Europe. Through analyzing the introduction to the commentary on Nine Chapters on Mathematical Art, this paper highlights the contributions of mathematician Liu Hui to the field of mathematics. This paper touches on the importance of studying non-Western contributions to mathematics. Exploring non-Western mathematical techniques furthers our understanding of the discovery of mathematics.

View Submission →

1. 2026 Meeting
3. Special
5. 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!

View Submission →

1. 2025 Meeting
3. Contributed

Impacts of Automation Technology on Customer Service Employment Rate in USA. — Dennis Kirui <dkirui@my.apsu.edu>

This paper investigates the impacts of automation technology on the employment rates of customer service representatives in the United States. While automation is recognized as a significant driver of economic growth, enhancing productivity and living standards, it simultaneously poses substantial challenges for the workforce. This duality raises public concerns regarding job displacement and the potential for increased unemployment in low-skilled positions. Utilizing R software for data analysis, the study draws on employment figures from the U.S. Bureau of Labor Statistics(https://www.bls.gov/oes/current/oes434051.htm) covering May 2011 to May 2022. The research focuses on the Business Support Service Industry, where customer service roles are prevalent, and analyzes percentage changes in employment figures to assess the risks associated with automation. Preliminary findings indicate a projected decline of 5% in customer service employment from 2022 to 2032. The paper underscores the critical need for upskilling and reskilling initiatives to prepare the workforce for the challenges posed by advancing automation technology and suggests that proactive measures are essential to mitigate the adverse effects on employment.

View Submission →

1. 2026 Meeting
3. Special
5. 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.

View Submission →

1. 2026 Meeting
3. Special
5. 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.

View Submission →

1. 2026 Meeting
3. 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.

View Submission →

1. 2026 Meeting
3. Special
5. 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.

View Submission →

1. 2026 Meeting
3. Special
5. 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.

View Submission →

1. 2025 Meeting
3. Sessions
5. UnspokenHistory

A Brief Story of the Chinese Mathematician Liu Hui — Charlie Liu <cliu97@utm.edu>

Liu Hui was one of the most renowned mathematicians in ancient China. He was primarily known for his approximation of $\pi$, the ratio of a circle's circumference to its diameter. In this submission, I will provide a summary of some life stories of him that are in general little known, including his work on $\pi$, one of his books named the "Sea Island Mathematical Manual", his commentary on the classic Chinese mathematics book "the Nine Chapters", his very clever approach of the proof of the Pythagorean Theorem, his work on the bicylinder or the double box-lid model and etc.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2025 Meeting
3. UGTalks

A Comprehensive Analysis of the Sequence X(n+2) = imX(n+1) + X(n) for X(1) = X(2) = 1 + i — Jasmine Stefano <stefanojasmine@yahoo.com>

This research investigates the recursive sequence given by $X_{n+2}=imX_{n+1}+X_n$, where $X_1=X_2=1+i$, with $i=\sqrt{-1}$ and $m$ being a parameter that assumes real values. We analyze the recursive sequence as a second-order difference equation with constant coefficients. By solving this equation, we derive explicit bounds on the parameter $m$ and obtain general equations to describe the resulting geometric shapes. Our analysis reveals how said bounds on $m$ influence the behavior of the sequence. We plot the sequence in the complex plane and as $m$ varies, we can see interesting geometric shapes formed from conic sections. When $m$ lies in the interval (-2,2), the sequence exhibits bounded behavior with points in the complex plane tracing two ellipses. For $|m|>2$, the sequence becomes unbounded, leading to hyperbolic trajectories. This work explores the geometric nature of the solutions, examining how the sequence's behavior evolves as the parameter $m$ varies.

View Submission →

1. 2025 Meeting
3. Contributed

A Concise Interpretation of Linear Regression Coefficients Based on Decoupling à la Random Data Analysis — J Donato Fortin <dfortin@jwu.edu>

There are multiple interpretations for the linear regression coefficients, ci, that result from the linear approximation of an output vector y based on multiple input vectors xi (i = 1 to n). A concise mathematical interpretation for the ci can be obtained by decoupling the input/output system via the techniques of random data analysis. In such case, each ck can be reinterpreted as the correlation coefficient resulting from the linear approximation of the conditioned output for y based solely on the conditioned input for xk. Here, conditioning refers to the removal of the linear contributions of the remaining inputs from both xk and y. In other words, ck is the correlation coefficient resulting from the single input/output system consisting of the residual of xk and the residual of y when the linear contributions of the remaining variables xi (i ≠ k) are eliminated from the system.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2025 Meeting
3. Sessions
5. DataLit

A Data Competency Quality Enhancement Plan — Crista Arangala <ccoles@elon.edu>

With a data focused 2020-2030 Strategic Plan, Elon University committed to a Data Competency QEP that harnesses the data-centric interdisciplinary work done across campus. This talk will highlight this work and a variety of ideas to achieve disciple specific advanced data competency for all.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2026 Meeting
3. 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.

View Submission →

1. 2026 Meeting
3. 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.

View Submission →

1. 2025 Meeting
3. UGPosters

A Formulation of the Union-Closed Sets Conjecture Using the Hamming Metric — Willoughby Caine <wcaine93@gmail.com>

A family of sets is union-closed if the union of any two sets in the family is also contained in the family. The Union-Closed Sets Conjecture, also known as Frankl’s Conjecture, posits that for any finite union-closed family of sets containing at least one nonempty set, there exists an element which belongs to at least half of the sets in the family. Although deceptively simple in its statement, the conjecture has defied a definitive proof, despite extensive study through various approaches and equivalent formulations, which have thus far yielded only partial results (Bruhn and Schaudt, 2015). We introduce a new formulation of the conjecture based on the Hamming distance (metric) between sets, which is defined as the cardinality of their symmetric difference. Using this framework, we derive multiple equivalent formulations of the conjecture and provide a complete characterization of the set of all elements that satisfy the conjecture. Furthermore, we demonstrate that our approach enhances the averaging method, a widely used approach that has led to numerous partial results. We also obtain a criterion that relaxes the requirement of the averaging method for verifying the validity of the conjecture. Our findings suggest that the Hamming metric provides a powerful perspective on the Union-Closed Sets Conjecture. By connecting structural properties of union-closed families to Hamming distances, this approach offers promising avenues for further exploration. Future research will focus on extending this framework to improve existing partial results and analyze larger families of sets, identifying additional equivalences, and hopefully progressing toward a complete proof of the conjecture.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2025 Meeting
3. UGTalks

A Hidden Pattern in the Co-Primes: A Journey Through an open Erdös Problem — Jonas Barfield <jonas.barfield@bobcats.gcsu.edu>

This presentation will delve into a fascinating open Erdös Problem, which poses the question: Is it true that there are no solutions to $$ n! = x^k \pm y^k $$ with $x, y, n, k \in \mathbb{N}$, $xy > 1$, and $k > 2$? We will show that a solution does indeed exist. However, in exploring whether this solution is unique, we uncover an intriguing pattern among the co-primes. This presentation will feature beautiful plots and reveal unexpected phenomena that invite deeper investigation. Join us as we navigate through these mathematical curiosities and uncover the hidden structures within.

View Submission →

1. 2026 Meeting
3. Special
5. 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.

View Submission →

1. 2026 Meeting
3. Special
5. 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.

View Submission →

1. 2025 Meeting
3. UGTalks

A New Generalization of the Continuous Bernoulli Distribution — Garrett Nix <gjnix22@gmail.com>

Many known distributions are useful in modeling data but often have limited shapes, such as only being right skewed, left skewed, or symmetric. These limitations make it difficult to use these distributions in broader applications, where data may not follow the shape of these models. By generalizing distributions, adding more parameters increases the flexibility of these distributions in most cases. This allows the new generalizations to have a wider range of applications than the original distribution. The aim of this research was to create a new generalization of the continuous Bernoulli (CB) distribution. In achieving this, a new family of unit-interval distributions could be created to model complex data. With this research, we propose a new generalization of the continuous Bernoulli distribution using the T-R{Y} framework, where we define random variables T, R, and Y that follow specified distributions. With this framework we introduce the T-CB{Cauchy} as well as the T-CB {logistic} families of distributions and investigate the properties of these families. We also investigate the properties of members within the families of these distributions, introducing the normal-CB{Cauchy} and the normal-CB {logistic} distributions. The flexibility of the distributions is observed by fitting the models to different data. Using the T-R{Y} framework, two families of generalized continuous Bernoulli distributions are defined. The properties are investigated, as well as the flexibility is observed in model fitting.

View Submission →

1. 2025 Meeting
3. Contributed

A New Mean? — Wei-Kai Lai <laiw@mailbox.sc.edu>

While studying some inequalities of fractions, we encounters a new value. For fractions $\frac{a_1}{b_1}, \frac{a_2}{b_2}, \cdots, \frac{a_n}{b_a}$, we define this new value by: $\bar{m}=\frac{a_1+\cdots+a_n}{b_1+\cdots+b_n}$. It can be proved that this value is bounded between the maximum and the minimum of these fractions, like all other means. In this talk, we will compare this value with one of the most commonly used means, the Arithmetic Mean, and introduce some properties of this new value.

View Submission →

1. 2025 Meeting
3. UGPosters

A Recursive Approach to a Multi-State Cylindrical Lights Out Game — Liwei Chen <lchen5@elon.edu>

Lights Out is a game featuring a grid of light-up buttons that begins with some lights on and some off. The goal is to turn off all lights but pressing a button changes its state and the states of the cardinal neighboring buttons. In this paper, we explore a Lights Out game in which the board is placed on a cylinder and the lights have $k$ states with a specific starting configuration. We try to turn off all lights using a light chasing strategy in which we methodically turn off the lights row by row. We model this process using recursive equations. A connection to the Fibonacci sequence then allows us to determine the number of rows of buttons the board should have in order for us to turn off all lights using our light chasing strategy.

View Submission →

1. 2026 Meeting
3. 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.

View Submission →

1. 2025 Meeting
3. Sessions
5. DataLit

A Second Wind of Mathematics Departments due to Data Ubiquity: A Proof of Concept — Ivan Dungan <ivan.dungan@fmarion.edu>

As Mathematics Departments have been adjusting over the last decade due to the ubiquity of data and the demand for data scientists, ML and AI have taken the world by storm. Fortunately, these fields’ reliance on data has made a data-centric shift more strategic and has even given a possible new heading. We have been slowly testing a conservative, curriculum restructuring approach in hopes of a proof-of-concept, at least for Math Departments with similar conditions which continue the data-centric focus but in a new form. The restructuring is based around the principle that mathematics plays a central role in ML and AI, and the mathematics in ML and AI touches every math class in a standard college math curriculum. The restructuring is conservative in the sense that the curriculum needs little formal change since most is a shift in material presentation and a continuation of these presentations externally through research projects. There are a few minor formal changes, but we will show how we have navigated those changes at least during the proof-of-concept period. In our talk, we will discuss the details of our approach to-date including motivation and anecdotes. We believe that the most enduring benefit of this approach (besides reinvigorating math departments a second time) is helping reduce a major limitation of future development of ML and AI: understanding the mathematics of ML and AI.

View Submission →

1. 2026 Meeting
3. Special
5. 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.

View Submission →

1. 2026 Meeting
3. 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.

View Submission →

1. 2025 Meeting
3. UGTalks

A Universal Chord Theorem for Triangulable Spaces — Kalev Martinson <kalev@gatech.edu>

Where $A$ is a topological space, let $f: [0,1] \to A$. Define the *Horizontal Chord Set* $D_f := \{\ell \in \mathbb{R} \,|\, \exists x \in [0,1 - \ell], f(x) = f(x + \ell)\}$. Let $\mathcal{L}A$ be the *loop space* of $A$. It has been previously proven that $\bigcap_{f \in \mathcal{L}\mathbb{R}}D_f = \{\frac{1}{n} \,|\, n \in \mathbb{\mathbb{N}}\} \cup \{0\}$. It has also previously been proven that the Lebesgue measure $\lambda(D_f) \geq \frac{1}{2}$ for $f \in \mathcal{L}\mathbb{R}$. For a topological space $A$, denote the constant $k_A = \inf \{\lambda(D_f) : f \in \mathcal{L}A\}$. In this paper we characterize $k_A$ for triangulable spaces, proving $k_A = 1$ when $A$ is 0-dimensional, and $k_A = 0$ when $A$ is more than 2-dimensional, or is 1-dimensional and has a cycle. When $A$ is 1-dimensional and has no cycles it is a tree, we prove that $k_A \leq \frac{1}{n}$ where $n$ is the number of leaves, and conjecture that $k_A = \frac{1}{n}$. We show that the map $f \mapsto \lambda(D_f)$ is not continuous, making the proof of this conjecture difficult. We finally generalize Paul Levy's Universal Chord Theorem by showing that for any tree $A$ with a vertex of degree three or more, $\bigcap_{f \in \mathcal{L}\mathbb{A}}D_f = \{0,1\}$.

View Submission →

1. 2025 Meeting
3. UGPosters

A study of the sequence $x_{n+2} = x_n + i mx_{n+1}$ where $x_1$ and $x_2$ that are orthogonal in $\mathbb{C}$ — Ryan Avallone <rgavallon@coastal.edu>

Let $x_n = a_n + b_n i$, where $a_n , b_n \in \mathbb{R}$, and $ n \in \mathbb{N} $, and suppose that the sequence $\{x_n\}$ is governed by the recurrence relation $x_{n+2} = x_n + i\,m x_{n+1}$, where $m \in \mathbb{R}$ . We investigate the conditions under which two subsequences $x_{2k}$ and $x_{2k+1}$ lie on perpendicular lines in the complex plane. Specifically, we express $x_1$ and $x_2$ as $x_1 = a_1 + b_1 i $ and $ x_2 = a_2 + b_2 i$, satisfying the condition $ a_1 a_2 + b_1 b_2 = 0 $. We show that there exist two perpendicular lines $ l_1$ and $l_2$ passing through the origin in the complex plane, such that for all $k \in \mathbb{N} $, the sequence alternates between the lines: $ x_{2k} \in l_1 $ and $ x_{2k+1} \in l_2$. This provides a geometric interpretation of the recurrence relation. Furthermore, the ratios $ \frac{b_{2k}}{a_{2k}} = \frac{b_2}{a_2}$ and $\frac{b_{2k+1}}{a_{2k+1}} = \frac{b_1}{a_1} $remain constant for all $k \in \mathbb{N} $.

View Submission →

1. 2025 Meeting
3. Sessions
5. FavoriteProb

AMC Problems from the Co-Editor-in-Chief's Perspective — Carl Yerger <cayerger@davidson.edu>

In this talk, an look inside the problem development process will be presented from one of the current Co-Editor's-in-Chief of the MAA AMC 10/12 Contest. What makes a problem interesting for a broad audience of students participating in the contest will be discussed, and a few favorite problems will be shared.

View Submission →

1. 2025 Meeting
3. Contributed

Active Learning on Basic Mathematics courses — Raju Bhusal <rbhusal@scad.edu>

As a math faculty member in an art and design school, I find the task of making mathematics accessible, relevant, and maybe even fun to our students to be uniquely challenging. This is especially true in our department’s MATH 100 course, which many students use to fulfill the math and natural science requirements for majors ranging from painting and illustration to fashion marketing and jewelry design. Unsurprisingly, hands-on projects and student-centered activities encouraging inquiry-based exploration help students connect math with their respective creative disciplines and overcome the math-related anxiety many of them bring to the classroom. I will share two projects I used in our MATH 100 and math 104 classes, indicating how these projects can be adapted to suit the needs of students in general education math classes at various institutions.

View Submission →

1. 2026 Meeting
3. 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.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2025 Meeting
3. Contributed

Affects of Climate Change the Belize’s Exports — Christopher Tillett <ctillett@my.apsu.edu>

This research delves into how climate change can affect Belize's sugar cane industry, increasing market, environmental, and credit risks. Belize is a small Caribbean country whose geographical location makes it vulnerable to various climatic events. This study aims to inform its audiences of the impact these natural phenomena have on the country's agricultural sector through an examination of the sugar cane industry. By utilizing a combination of historical data, case studies, and industry research, the research aims to assess the resultant market risks. By integrating quantitative assessments and qualitative perspectives, the study seeks to quantify and qualify the implications of these market dynamics. The outcomes of this research can reignite the discussion on minimizing the impact these storms have on the farmers and overall industry.

View Submission →

1. 2025 Meeting
3. UGTalks

Algebraic Methods for Exploring Phylogenetic Networks — Demmi Ramos <demmi.ramos@my.lr.edu>

Phylogenetics is the study of evolutionary relationships between organisms. Our goal is to reconstruct the evolutionary history of collections of species by building phylogenetic trees (family trees) from biological data. While mathematically interesting, trees are often too simple to model the complex nature of real gene transfers. This leads to the study of phylogenetic networks, which incorporate hybridization, allowing separate species to come together. This talk explores assigning algebraic invariants to phylogenetic networks in order to find the network that best explains the data given. One approach to assigning these invariants involves using matrices of conditional probabilities to describe models of DNA sequence evolution.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2025 Meeting
3. UGPosters

Alternative Probability Density Estimators for Navies Bayes Nearest Neighbor Machine Learning Method for Accuracy and Explainability in Wound Image Classification — Lanorah Hobbs <lanorah.hobbs@g.fmarion.edu>

We investigate classifying the stages of wounds from a dietetic wound imaging dataset with alternative machine learning algorithms to the standard approaches like Convolutional Neural Networks (CNN) and Support Vector Machines (SVM). Although these methods usually classify with high accuracy, we search for more explainable methods for clinician and patient interpretability. One approach previously studied in the literature is using a Bayesian Network model, specifically Naive Bayes Nearest Neighbor (NBNN). The goal of the authors was to make a computationally simple method while being competitive in image classification. We make some alterations to their method by trying alternative estimates of the probabilities in NBNN to improve the model's performance and equally important, its explainability. In particular, we consider K-Nearest Neighbor (KNN) for probability density estimation without using a kernel and then compare their classic NBNN to our approach using k-fold cross-validation. Ultimately, we address whether Bayesian Networks can be competitive in performance but also provide explainable wound imaging predictions.

View Submission →

1. 2025 Meeting
3. UGTalks

An Alternative Proof of a Sandwich Type Inequality — Wei-Kai Lai <laiw@mailbox.sc.edu>

In the book, *Algebraic Inequalities: New Vistas*, Andreescu and Saul proved an inequality in one of the exercises: for fractions $\frac{a_1}{b_1} ,\frac{a_2}{b_2},\cdots, \frac{a_n}{b_a}$ , if $m$ and $M$ are the smallest and largest of these fractions, we have $m\leq \frac{a_1+\cdots+a_n}{b_1+\cdots+b_n}\leq M$. Recently, while solving a problem in the journal, *MathAMATYC Educator*, Vol.15, No.3, Problem Section, we realized that the solution to this problem can be generalized to a proof of the inequality by Andreescu and Saul. In this talk, we will introduce the proof by Andreescu and Saul, and then we will present our new proof.

View Submission →

1. 2025 Meeting
3. Contributed

An Evaluation of Borda Count Variations Using Ranked Choice Voting Data — Brad Fox <foxb@apsu.edu>

The standard U.S. voting methods of plurality and ranked choice (or instant runoff) voting are susceptible to significant voting failures, including Condorcet and majority failures as well as monotonicity and no-show paradoxes. We investigate alternative ranked choice voting systems relating to the points-based Borda count which avoid monotonicity paradoxes, particularly variations based on how partial ballots are counted and on extending the values of the points assigned to each rank in the ballot. In this talk, we will discuss which voting failures are possible for each variation and then present an empirical study of 421 U.S. ranked choice elections from 2004 to 2023 where we determined the frequency of voting failures when using five Borda variations.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2025 Meeting
3. Contributed

An Investigation into the Tribonacci Sequence — Ashley Johnson <ajohnson18@una.edu>

I spoke at this meeting in 2024 on properties of the Fibonacci sequence in regards to a Math for the Arts class project. This year, I have a follow up regarding properties of the Tribonacci sequence: a recursive sequence in which the next term is the sum of the previous three terms, as opposed to the previous two for the Fibonacci sequence. In this talk I will go over properties of the Fibonacci sequence and show how some generalize to the Tribonacci sequence. This is join work with undergraduate student Logan Moore.

View Submission →

1. 2025 Meeting
3. UGPosters

Analyzing Pecan Quality and Yield Efficiency: A Quantitative Study of Three Pecan Trees — Tyanna Bastine <cyoung38@wildcat.fvsu.edu>

Pecans, known for their rich flavor and nutritional value, are a popular tree nut crop cultivated widely in the USA. The quality and yield of pecans are important factors for pecan farmers and growers, impacting both economic returns and consumer satisfaction. This research investigates the relationship between pecan size, weight, and quality, as well as the yield efficiency of three pecan trees located on Fort valley State University campus. The trees are not managed agriculturally and thus could be considered as wild pecan trees. Around the beginning of December 2024, we collected a total of 300 pecans, 100 from each tree, that were fallen naturally from the trees on the ground without shaking trees. Only intact pecans with no visible cracks were selected. Measurements of pecan length, diameter (using a caliper with 0.1 mm accuracy), and weight (using a scale with 0.1 g accuracy) were recorded. Each pecan was then cracked open to categorize its shelled quality as good (light brownish color and firm texture), blank, or bad (highly dried, mushy, or dark). Data were compiled in Excel for analysis. Both simple and multiple linear regression models were developed to explore relationships between pecan size (length and diameter) and weight. Statistical metrics, including minimum, maximum, average, standard deviation, and sample distribution, were calculated to characterize the yield of each tree. Yield efficiency was determined based on the percentage of good pecans produced by each tree. The initial analysis reveals that the average length, diameter, and weight of the pecans are 40.7 mm, 21.9 mm, and 7.6 grams, respectively. Correlation analysis showed relatively good relationships exist between length and weight (r = 0.54) and diameter and weight (r = 0.55). Simple linear regression showed linear trends between these variables. Furthermore, multiple linear regression using length and diameter as independent variables and weight as the dependent variable provided a better fit compared to simple linear regression models. The findings will provide valuable insights into tree management practices such as pruning, fertilizing, and pesticide application to enhance the quality and yield of pecan trees. This research highlights the importance of data-driven approaches in optimizing agricultural productivity.

View Submission →

1. 2025 Meeting
3. Sessions
5. UnspokenHistory

Ancient Algebra and Contemporary Conflict — Jared Kettinger <jkettin@clemson.edu>

While the contention over the forefathers of calculus is well known, many are unaware of a similar conflict over the progenitor of algebra. Some contend this title belongs to Diophantus with his introduction of symbols for unknown quantities; others argue the moniker is more properly suited to al-Khwarizmi who's work better embodies abstraction from specific numbers and a more comprehensive approach to algebraic problems. In this talk, we will explore the merits of both sides of this debate. In doing so, we will see how Eastern mathematicians preserved and improved upon Western results and methods as the latter entered a dark period in its mathematical history.

View Submission →

1. 2026 Meeting
3. Special
5. 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 $\mathcal Q$.

View Submission →

1. 2025 Meeting
3. UGPosters

Area Under a Rolling Ellipse — Nancy Scherich <nscherich@elon.edu>

The ElonU Tangential's student group solved the AMM problem 12476 which states: Let $C$ be one arch of the elliptic cycloid generated by the ellipse $x^2+\frac{1}{4}(y-2)^2=1$. That is, let $C$ be the curve traced by the vertex at the origin as the ellipse rolls without slipping along the $x$-axis for one revolution. What is the area under $C$ and above the $x$-axis? Our solution uses a clever change of perspective letting a tangent line roll around the ellipse, instead of the ellipse roll along the $x$-axis. The desired area turns out to be a surprisingly simple number.

View Submission →

1. 2025 Meeting
3. Contributed

Ascending Subgraph Decompositions on Tournaments of Order 6k+4 — Brian Wagner <bwagner@utm.edu>

A digraph $D$ with ${n+1} \choose {2}$ arcs has an ascending subgraph decomposition (ASD) if there exists a partition of the arc set of $D$ into $n$ sets of size $1,2,3,\dots, n-1, n$ such that the digraphs $D_1, D_2, \dots, D_{n-1}, D_n$ induced by the $n$ sets of arcs in the partition have the property that for all $i<j$, $D_i$ is isomorphic to a subgraph of $D_j$. We will outline a proof that almost all tournaments of order $6n+4$ have an ASD.

View Submission →

1. 2025 Meeting
3. UGPosters

Aspects of Bootstrap Percolation on the Random Geometric Graph — Ethel Sakyi <sakyie2@mailbox.winthrop.edu>

Bootstrap percolation (BP) is a process on a graph which can be used to model the spread of an infection throughout a graph. First, an initially active set of vertices is given. Then, loosely, vertices are activated if they’re in contact with enough active vertices. More precisely, suppose G is a graph, k is the bootstrap parameter, and a set of active vertices at time 0 is given. In the next time step, any inactive vertex with at least k edges to active vertices becomes active; the process continues until no new active vertices are created. To see how this can be used to model the spread of disease, take people as vertices, interactions between people as edges, and make “active” mean “infected”.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2025 Meeting
3. Sessions
5. UGRMentors

Balancing Structure and Flexibility: Implementing Course-Based Undergraduate Research — Kelly Buch <buchk@apsu.edu>

Course-based Undergraduate Research Experiences (CURE) provide an opportunity to engage students in undergraduate research, particularly in settings where external research support is limited. However, integrating this high-impact practice into coursework presents several challenges: while courses require structured syllabi and clear assessment criteria, research often demands flexibility to explore unplanned directions. Additionally, research is typically an open-ended and lengthy process, but in a course-based setting, projects must be completed within the constraints of a single semester. In this talk, I’ll share my experience incorporating student research into a mathematical modeling course, highlighting strategies to balance these competing needs and challenges. I will discuss how a scaffolded approach helped students navigate the research process while developing mathematical models using foundational frameworks. This approach to structuring student research is adaptable and can be applied to other courses or areas of mathematics to foster inquiry-driven learning.

View Submission →

1. 2025 Meeting
3. Contributed

Before the Clock and the Sun Parted Ways: An Explanation of the Astronomical Clock at Prague — Damon Scott <dscott@fmarion.edu>

The Astronomical Clock at Prague was built in 1410, with later additions, and is beautifully preserved and fully functioning. It shows time “by the sun,” as marked on an astrolabial dial, and also time “metronomically,” with an hand going round once every twenty-four hours. After explaining the (admirable) features of the astronomical clock, we list the sequence of departures from scientific sensibility that gave rise to the (not so admirable) modern clock as we know it now.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2025 Meeting
3. Sessions
5. UGRMentors

Beyond the Classroom: Guiding Student Research and Career Development — Laurie Zack <lmzack@ncat.edu>

As educators, our role extends far beyond simply teaching course content; we are also mentors who help students navigate the complex landscape of research, career development, and personal growth. This talk will explore strategies for mentoring students in mathematics, focusing on undergraduate research projects, internships, and career preparation. Drawing from 20 years of experience, I will share insights on how to support students in various research areas and finding REU's and internship opportunities. By cultivating trust and creating lasting relationships with students, mentors can help students not only excel academically but also prepare for success in their careers.

View Submission →

1. 2025 Meeting
3. Workshops

Beyond the PhD—A Career at PUIs — Shalmali Bandyopadhyay <sbandyo5@utm.edu>

Unlike larger research universities, primarily undergraduate institutions (PUIs) are smaller, privately or publicly funded colleges and universities offering unique resources and research experiences. As a PUI faculty member, your responsibilities are multifaceted, including substantial teaching commitments, typically ranging from six to eight courses per year. Join us for an inspiring workshop showcasing exceptional faculty members from Primarily Undergraduate Institutions (PUIs) who excel in teaching, research and service. Hear from educators at various career stages as they share insights and strategies for success. The speakers will be: 1. Blake Dunshee, Belmont University, on the integration fo cutting-edge active learning pedagogies to enhance student engagement, retention, and overall academic success. 2. Jason Devito, University of Tennessee at Martin, on effective interdisciplinary undergraduate research advising and securing external funding. 3. Nicole Panza, Francis Marion University, on navigating through university committees, departmental responsibilities, discipline-related opportunities and community-focused outreach, promoting mathematics awareness and education beyond academia.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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).

View Submission →

1. 2025 Meeting
3. UGPosters

Brocard’s Problem Abstract — Egor Maximenko <emaximen@highpoint.edu>

While exploring Brocard’s Equation $n! + 1 = m^2$, which is known to have 3 solutions, st. $m,n \in \mathbf{N} $, we develop an algorithm to effectively store factorials of large numbers. First, we begin by prime-decomposing the factorial with the help of Legendre’s Formula. Then, we convert the resulting product of prime powers into a sum by taking logarithms of convenient base. Finally, we implement the algorithm to search for potential solutions in $ \mathbf{N} $ for Brocard’s Equation up to $100 \,000!$.

View Submission →

1. 2026 Meeting
3. 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.

View Submission →

1. 2025 Meeting
3. Contributed

Building a culture of active student engagement in classroom — Sutandra Sarkar <ssarkar@gsu.edu>

In this session, we will share effective strategies for fostering active student engagement in introductory math courses at Georgia State University. Many of our students, primarily from early college backgrounds, are eager to pursue their major programs but often struggle to connect with prerequisite math courses. To bridge this gap, we have developed and implemented a range of dynamic teaching methods, both in and outside the classroom, that cultivate a community spirit and foster a deeper connection to the material. We will spotlight two proven, in-class techniques that have successfully maintained student engagement and motivation throughout the semester. Attendees will leave with actionable insights and practical strategies to transform their own classrooms into interactive, inspiring environments that support student success and enthusiasm for learning.

View Submission →

1. 2025 Meeting
3. Sessions
5. DataLit

Building and Supporting a Data Science Degree Program at a Primarily Undergraduate Institution — Zach Abernathy <abernathyz@winthrop.edu>

Over the past few years, mathematics faculty at Winthrop University have made efforts to infuse data science into the curriculum, culminating in the recent launch of an undergraduate degree program in data science. The program has been built with an applied focus to maximize student employability upon graduation, including features such as the use of real-world data sets throughout the curriculum, partnerships with industry and research groups, and an emphasis on domain knowledge in a student’s chosen field of interest. We will discuss how we built the program around our current curricular structure and challenges we’ve faced along the way. We will also explore several ongoing goals related to supporting the program, including the acquisition of biomedical datasets in collaboration with biology and chemistry faculty, expanding data science instruction across STEM disciplines, and mentoring undergraduate research projects in data science.

View Submission →

1. 2026 Meeting
3. 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.

View Submission →

1. 2025 Meeting
3. Sessions
5. UnspokenHistory

Celebrating the Achievements of Women in Mathematics — Denise Rangel Tracy <rangel.tracy@fmarion.edu>

The contributions of women to mathematics have often been overlooked, yet their achievements have shaped the field in profound ways. In 2021, the Association for Women in Mathematics (AWM) released the first of four planned card decks, titled EvenQuads, highlighting notable women in mathematics. EvenQuads cards are double sided; one side of the cards shows symbols that appear in varying colors and quantities used to play various pattern seeking games and the other side features a profile of a woman mathematician who has made significant contributions to the field of mathematics. In this talk, we will spotlight some of the remarkable women mathematicians featured in the EvenQuads decks. By uncovering their lesser-known contributions and some of the challenges that they faced we gain a deeper appreciation for their resilience and the roles they played in shaping the field of mathematics. We will also briefly describe the games that can be played with the profile side of the cards and explore how they can be used in a mathematics classroom.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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

View Submission →

1. 2025 Meeting
3. Contributed

Change Point Detection in Autoregressive Distributed Lag Models — Chao Gu <cgu@citadel.edu>

We propose a CUSUM-based testing procedure to sequentially monitor structural changes in Autoregressive Distributed Lag (ARDL) models using a penalized algorithm. Initially, this approach leverages historical panel data to simultaneously perform variable selection and estimation through a penalization method applied to the ARDL model. To detect any change point when new data is introduced, we conduct tests based on the CUSUM statistics. The consistency of this method, along with the oracle property of the resulting regularized estimators, is thoroughly examined. Additionally, we establish the asymptotic properties of the test statistics under both the null and alternative hypotheses. Simulations are carried out to demonstrate the effectiveness of the proposed method, and a real data application is presented to illustrate the detection procedure.

View Submission →

1. 2025 Meeting
3. Sessions
5. RecMath

Characterizing quad-free sets in the card game EvenQuads — Timothy Goldberg <timothy.goldberg@gmail.com>

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). We are most interested in quad-free collections of cards, which turn out to be Sidon Sets. We will describe an analog of the "Cap Set problem" for EvenQuads, and discuss known results. In particular, we will address the question of how many cards you must lay down to guarantee a quad.

View Submission →

1. 2025 Meeting
3. Contributed

Cheating in Online Math Classes — George Moss <gmoss@uu.edu>

Should faculty be concerned about cheating in online math classes? Is it worth our time and energy? Issues can range from students sharing information to having someone else take the class completely. We look at research on how serious the problem is, and we look at ways to discourage cheating and promote academic integrity. We discuss the pros and cons of proctoring using LockDown Browser and similar tools and examine alternative assessment methods.

View Submission →

1. 2026 Meeting
3. 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.

View Submission →

1. 2025 Meeting
3. UGTalks

Cohomogeneity two Bazaikin spaces — Rachel Flores <rflores8@ut.utm.edu>

We study the sectional curvature of all of the cohomogeneity two Bazaikin spaces with respect to a Riemannian metric construction due to Wilking. We show that, in contrast to the cohomogeneity one and homogeneous case, for all of the cohomogeneity two examples, the set of points with strictly positive curvature does not have full measure.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2025 Meeting
3. UGTalks

Comparing mathematical reasoning and logic across AI platforms — Abigail Hyatt <ahyatt@highpoint.edu>

In this presentation, we discuss a series of experiments designed to test the logical and mathematical reasoning skills of various AI tools. We present our experiments and some initial results, which so far have been conducted across three well-known LLMs.

View Submission →

1. 2026 Meeting
3. Special
5. 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.

View Submission →

1. 2025 Meeting
3. UGPosters

Complex Analysis in Fluid Dynamics: Visualizing Streamlines and Velocity Fields — Micah Chandler <mmchan4208@ung.edu>

One powerful application of complex analysis is the visualization of streamlines and velocity fields of irrotational and incompressible fluids using equipotential curves. With this poster, we aim to leverage the complex potential function to provide valuable insights for both theoretical research and practical applications. Our methods utilize complex analysis to determine solutions to the differential equations describing fluid flow, focusing on circular objects. These techniques offer an unparalleled ability to accurately describe flow around circular objects. We analyze planar velocity fields using conformal mappings and employ the Joukowski transformation to model flow around airfoils. Additionally, we construct ideal fluid flows confined within a given domain, known as "streamlining." These methods offer a robust framework for understanding and optimizing fluid dynamics problems. The findings have wide-ranging applications, including pollution spread, blood flow, aerodynamics, and water distribution systems, contributing to more efficient and sustainable designs.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2025 Meeting
3. Contributed

Configuration Spaces with Forbidden Partitions — James Dover <james.dover@ung.edu>

A configuration space models $n$ particles existing in a topological space $X$ with no collisions allowed. There have been many variations on these spaces, such as the "no-$k$-equal" type where collisions of fewer than $k$ particles are allowed. In this talk, we introduce a generalization where collisions are allowed or disallowed based on partitions of the $n$ particles. Depending on which partitions are disallowed, this framework yields many of the previously considered types of configuration spaces as well as new types. We also discuss the case where the space $X$ is a graph and provide discrete models for its forbidden partition configuration spaces.

View Submission →

1. 2026 Meeting
3. 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.

View Submission →

1. 2025 Meeting
3. UGTalks

Connectedness of Discretized Configuration Spaces — Justin Brentwood <jbrentwo@vols.utk.edu>

The discretized configuration space of a finite one-dimensional cell complex $G$ can be connected in many ways, few ways, or not at all, depending on $G$. This project begins to take an algorithmic approach to describe sufficient or necessary conditions to determine if a configuration space is connected through primarily graph properties and secondarily algorithmic abilities.

View Submission →

1. 2026 Meeting
3. Special
5. 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.

View Submission →

1. 2025 Meeting
3. Sessions
5. DataLit

Consumer Statistics Unit for 100-Level Quantitative Literacy Mathematics Courses — Laura Lembeck <lslembeck@wcu.edu>

In this session, I will describe how I teach the concepts of good and bad statistical practices. I will include lecture materials that have been created in collaboration with my students in an open resourced learning environment, as well as in-class and out-of-class exercises to allow for group work and interactive learning. I will describe the process we use for collecting, organizing and analyzing our own data set. Finally, I will describe how we work in groups to create research projects - oral presentations, utilizing our subject librarian’s expertise, and the rubric that promotes excellence, all under the umbrella of incorporating learning-centered inquiry methods to support each individual’s growth in their knowledge base.

View Submission →

1. 2026 Meeting
3. 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.

View Submission →

1. 2025 Meeting
3. Contributed

Counting Forests in Complete Graphs with the Tree Function — J.C. Price <jprice12@ggc.edu>

This talk investigates the enumeration of spanning forests in complete graphs, where each tree contains a fixed set of vertices. We begin with an overview of how the Tree function (Lambert W function) can be used to count spanning forests with a single fixed vertex per tree. Building on this foundation, we demonstrate how this approach can be extended to more complex fixed vertex sets, potentially revealing broader implications of the method. (This work was done in collaboration with Daniel Pinzon and Daniel Pragel at GGC.)

View Submission →

1. 2025 Meeting
3. Contributed

Counting Spanning Forests — Daniel Pragel <dpragel@ggc.edu>

A spanning forest of a graph G is an acyclic spanning subgraph of G. When a spanning forest has a single connected component, it is referred to as a spanning tree. A well known theorem from Kirchhoff uses the Laplacian Matrix of G to count the number of spanning trees of G. We extend this method to spanning forests.

View Submission →

1. 2026 Meeting
3. 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.

View Submission →

1. 2025 Meeting
3. Sessions
5. FavoriteProb

Crafting Challenges: Writing Competition Problems and Tests — Risto Atanasov <ratanasov@wcu.edu>

Drawing from my experience in crafting problems for various mathematical competitions, including the AMC, I will share examples of some of the most beautiful and elegant problems I've encountered. These examples will illustrate the blend of creativity and rigor that goes into problem creation. We will explore the art behind writing competition questions, discussing the key elements that make a problem both challenging and engaging. Additionally, we'll address the broader process of designing contest tests, ensuring a balanced and comprehensive assessment of participants' skills.

View Submission →

1. 2025 Meeting
3. Contributed

Creating an Undergraduate Learning Assistants Program for Calculus 1 and Introductory Statistics Courses — Kristen Mazur <kmazur@elon.edu>

We recently developed a learning assistants pilot program in which we train and mentor a team of undergraduate learning assistants to provide additional support for students in our calculus 1 and introductory statistics courses. The learning assistants attend each class to help facilitate active learning, promote metacognitive approaches, and help students adapt to new technologies in the courses. They also run weekly supplemental instruction sessions that provide structured and peer-led review of course content. After two semesters, feedback on the pilot program has been very positive, with students, learning assistants, and professors all reporting high satisfaction. In an end-of-semester survey, 60% of students who attended supplemental instruction sessions reported them being very helpful and 93% said they were at least somewhat helpful. Students largely said they would recommend sections with learning assistants and attendance of supplemental instruction sessions to future students. In this talk we discuss how we created the program and share further survey results demonstrating the positive impact that this program is having on calculus 1 and introductory statistics students at our university.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2025 Meeting
3. Sessions
5. FavoriteProb

Dandelin Spheres: the Unintended Benefits of Being Stumped — Stephen Davis <stdavis@davidson.edu>

A lack of personal insight regarding a problem from the 2019 College of Charleston Math Meet Level III Written Test (#25: about the area illuminated by a spotlight) led to an encounter with the spheres of the 19th century French mathematician Germinal Dandelin. In this talk, we learn about Dandelin spheres and how they could be used to solve the CofC problem (and maybe also see a sketch of a sphere-less solution).

View Submission →

1. 2025 Meeting
3. Sessions
5. DataLit

Data Literacy Course and Initiatives at Converse University — Amanda Mangum <amanda.mangum@converse.edu>

Converse University recognizes the increasingly important role of data literacy in educating tomorrow's workforce. With this in mind, I have created and taught a new general education course, Data Literacy. Converse has also recently approved a new general education program that includes a data component. This talk will address efforts to promote data literacy across campus and to create new courses that support this focus.

View Submission →

1. 2026 Meeting
3. Special
5. 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.

View Submission →

1. 2026 Meeting
3. Special
5. 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.

View Submission →

1. 2026 Meeting
3. 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.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2025 Meeting
3. Sessions
5. UnspokenHistory

Developing an Interdisciplinary Course on the History of Women in Mathematics — Brittany Riggs <briggs@elon.edu>

In this session, I will share my experience designing an interdisciplinary course on the history of women in mathematics, starting with Hypatia in Ancient Alexandria and extending to Maryam Mirzakhani, the first woman to win the Fields Medal. The presentation will include a summary of the women covered in the course, highlights of their contributions within and outside mathematics, as well as examples of math activities used in the course. I will also touch on lessons learned in the design and unexpected insights into the narrative of women in mathematics.

View Submission →

1. 2026 Meeting
3. Special
5. 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.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2025 Meeting
3. Contributed

Double-M Standards: a simple way to save time and support student success in Standards-Based Grading — Rachel Epstein <rachel.epstein@gcsu.edu>

In a course graded with Standards-Based Grading, students are given multiple opportunities to demonstrate proficiency in the course standards, often on exams where each problem is labeled with which standard it assesses. One drawback of Standards-Based Grading is that even though each problem is easier to grade than when using points-based grading, the increased number of exams can lead to a significant burden on the instructor’s time. Another concern with Standards-Based Grading is that since there is no partial-credit, students who have a basic but not a deep understanding of many of the standards may not meet enough standards to earn a passing grade. To address both of these issues, I chose a selection of standards to become “Double-M standards,” which are standards that appear twice on each exam, allowing for fewer total exams. Often, one of the problems would focus more on the basics of the standard and the other require a deeper understanding. In order to earn an A, students would sometimes need to answer both problems, to show they had a deeper understanding of the material. In this presentation, I will discuss how I implemented this strategy and how it worked out during the Fall 2024 semester in my Precalculus courses.

View Submission →

1. 2025 Meeting
3. UGTalks

Dynamic Flexible Tile Modeling of DNA Self-Assembly — Sloane Kinley <smkinley001@converse.edu>

Deoxyribonucleic Acid (DNA) is proven to be a valuable building block for constructing nanostructures capable of targeted drug delivery. DNA is also characterized as self-assembling; when a sticky end is introduced to complementary unbonded base pairs, DNA will hydrogen bond without any mechanical assistance. Graph theory can be implemented to model this phenomenon, and one such framework is referred to as the flexible tile model of DNA self-assembly. This model allows for symmetry and predicted bonding where it may not exist in the lab setting. We add to the flexible tile model in order to calculate the probability of self-assembly of certain graphs. If a specific graph type or family is desired, or even a single specific graph, the probability of this event occurring can be calculated. This theoretical experiment explores the possibility and probability that cohesive end types, in the flexible tile model, can bond to other end types when exposed to one another in a lab setting. This exploration specifically focused on small cycle graphs of order three and four.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2025 Meeting
3. Contributed

Emergency Brake, Please: Making Fast-Paced Courses Less Overwhelming — Jennifer Aust <jaust@utsouthern.edu>

The author will present a small collection of strategies for face-to-face and synchronous online courses that run in half-session, summer half-session, May-mester, and other shortened formats. All strategies can help mitigate the "drinking from a firehose" effect of accelerated content pacing and long class meetings. These strategies range from big to small, including a game-changing structural shift in content delivery, a few ways to help students manage their progress and feel empowered, and some "grab-and-go" ideas that can be implemented easily in any course.

View Submission →

1. 2025 Meeting
3. UGPosters

Energy Performance as a Part of Developing a Grazing Incidence Telescope Design System — Abigail Mervine <mervinea2@mailbox.winthrop.edu>

Prior to the development of optical systems, it’s essential to understand their potential performance, often allowing for easier testing of ideas and a smoother development process. The performance of grazing incidence optical systems, used to collect x-rays, is generally less understood than that of most optical systems. Thus, this research focuses on understanding and modeling the energy performance of grazing incidence mirrors as a step towards developing a grazing incidence telescope design system to assist in the development of grazing incidence optics. Currently, this work will assist in the development of metrics for the Lynx X-Ray Observatory: a novel x-ray system with the capability of achieving 10 times the effective area of the Chandra X-Ray Observatory at an equivalent or better resolution. Multiple linear regression and beta regression were used to generate a model for reflectivity given grazing angles of 0$^\circ$ to 2.5$^\circ$ and energies of 0.5 to 10 keV based on data from the Center for X-Ray Optics – X-Ray Database. The chosen model was then applied to data on grazing incidence mirror shells to calculate their reflectivity and thus effective area. Effective area was then analyzed as a function of energy and radius. It was found that energies of 0.5 to 10 keV and radii of 10 to 150 cm yielded effective areas of 0.03 to 220 cm$^2$. In general, lower energies and higher radii resulted in a higher effective area. Specifically, it was observed that effective area decreases rapidly as energy increases and decreases more steadily as radii decreases. Following this work, a ray tracing program for Wolter-I type optics is to be developed as the next step toward developing a grazing incidence telescope design system. This work is supported by the NSF REU solar physics program at SAO, grant number AGS-2244112.

View Submission →

1. 2025 Meeting
3. Contributed

Engaging Students Through Error Analysis Activities — Marcela Chiorescu <marcela.chiorescu@gcsu.edu>

Error analysis is an instructional strategy in which students are asked to identify, analyze, and correct errors in problems that contain intentional mistakes. Error analysis has many potential benefits, including enhancing critical thinking skills, promoting a deeper understanding of concepts, cultivating a growth mindset, and fostering collaboration and communication. This presentation will discuss how error analysis activities were implemented in a Precalculus course.

View Submission →

1. 2025 Meeting
3. Sessions
5. UGRMentors

Engaging Students in Math Research Through Games: Quads, Spot It!, and Beyond — Lauren Rose <rose@bard.edu>

Mathematical puzzles and games offer rich opportunities for faculty seeking to develop student research projects. By exploring math in a recreational context, students can naturally notice patterns, ask questions, make hypotheses, and delve deeper into mathematical investigations. We have used card games such as $\textit{Quads}$ and $\textit{Spot It!}$ to generate accessible projects for students at a variety of levels. We discuss the successes and challenges of both virtual and in-person research groups, highlighting the dynamics of collaborative work in different settings.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2025 Meeting
3. UGTalks

Error Analysis of a Symplectic Algorithm for a Hamiltonian System — Josiah Hays <triggs@uu.edu>

In a Hamiltonian dynamical system, ‘area’ in the phase space of the system is conserved over time. Symplectic algorithms are numerical algorithms that solve for the time evolution of a Hamiltonian system and are explicitly designed to preserve areas in phase space. Due to their area-preserving properties, symplectic algorithms often demonstrate much higher accuracy over long time intervals than the equivalent non-symplectic numerical algorithms for Hamiltonian systems. However, symplectic algorithms are still susceptible to rounding error as they use finite-precision floating-point numbers in their computations. We describe a modified symplectic method due to Robert Skeel that takes rounding errors into account, and we mathematically verify the accuracy of this method for the case of the simple harmonic oscillator.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2025 Meeting
3. UGPosters

Explorations of Machine Learning Methodologies to Enhance the Design of RNA-based Dopamine Biosensors — James Craven <cravenj6@winthrop.edu>

In this project, we seek to understand how we can utilize machine learning (ML) to inform the design of biosensors to emit a strong fluorescence in the presence of dopamine. Dopamine is a neurotransmitter and plays a role in a variety of functions such as memory, learning, and reward systems. Detecting dopamine levels could help with diagnosing addiction, mental illness, and neurodegenerative disorders. We develop a framework for one-hot encoding nucleotide sequences for training ML models, create a data preprocessing pipeline to pad sequences and normalize output values, and construct neural net model architecture for training on both sequence and numerical data. Using a published toehold switch dataset along with a ribosensor dataset, we explore the accuracy of several different regression models in predicting biosensor effectiveness by training on both nucleotide sequence data and calculated thermodynamic parameter data. We find that a neural network model, specifically a multilayer perceptron, typically outperforms other regression models such as linear regression, random forests, and support vector machines in both datasets, and that training on sequence data appears to be more predictive than training on thermodynamic parameter data. We also suggest potential directions to pursue transfer learning between the two datasets.

View Submission →

1. 2025 Meeting
3. UGTalks

Exploratory Analysis of the Top-Ranked Athletes' Performances in ATP Tour — Austin Hitt <ahitt@student.citadel.edu>

Exploratory Analysis of the Top-Ranked Athletes' Performances in ATP Tour Austin Manning Hitt Faculty Advisors: Dr. Bo Li and Dr. Chao Gu In this talk, we investigate the relationship between the overall scores of the top-ranked tennis players and the metrics provided in the database “Official Site of Men’s Professional Tennis/ATP Tour” through an exploratory statistical analysis. To improve the overall scores, it is the aim to identify the underlying predictor variables for the statistical model, since not all the metrics play a role in explaining the overall scores. We perform the step-down model selection algorithm to identify the underlying predictor variables. The statistical exploratory analysis result shows that the best evaluation of the overall performances are the adjusted values of the return points won, 2nd serve points won, and the total number of Aces.

View Submission →

1. 2025 Meeting
3. UGPosters

Exploring Clustering and Classification of 3M Electrical Tape Using FTIR Data — Emily Tester <emigtest@ut.utm.edu>

Current research supports the use of statistical methods in forensic science to analyze Fourier Transform Infrared Spectroscopy (FTIR) data for identifying polyvinyl chloride (PVC) electrical tape used in the construction of explosive devices. For this project FTIR data is collected for both the adhesive and backing sides of multiple rolls of black PVC electrical tape across the 3M brand’s product range. Principal components analysis is then applied to reduce the dimensionality of this FTIR data and cluster the rolls into similar groupings. This analysis is then used to classify other examples of similar PVC electrical tape, and the percentage of correct classifications is investigated.

View Submission →

1. 2026 Meeting
3. Special
5. 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.

View Submission →

1. 2026 Meeting
3. 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.

View Submission →

1. 2025 Meeting
3. Sessions
5. UGRMentors

Finding Projects and Managing Expectations — Zih-Syun FU <bbaker2@citadel.edu>

In this talk, we will consider several projects that undergraduates have worked on in the past several years. We will discuss how the problems were chosen as well as what the students were expected to accomplish in various time frames.

View Submission →

1. 2025 Meeting
3. Contributed

Flipped Learning Approach in College Trigonometry — Guanghua Zhao <guanghuaz@hotmail.com>

A flipped learning approach was implemented in my college trigonometry course. Before the start of the semester, the Canvas course site was redesigned to include video(s), PowerPoint, and other materials for each class meeting. Students were expected to watch the video(s) and/or study the PowerPoint prior to class, write down their study notes and questions, and submit their notes to the instructor at the beginning of class. During the first 15 minutes or so of class, the main points of the topics were addressed, and the students’ questions were answered. Then students worked on a worksheet in groups. While the students worked in groups, the instructor walked around to check for and answer any question they might have. At the end of class, worksheets were collected for grading. The previously graded worksheets were also returned to students at the end of class so that if there were any problems on the graded worksheets, The instructor could discuss them with students individually. The flipped learning approach showed very promising results: 1. Class attendance was improved. A traditional face-to-face class the instructor had taught has about 50% attendance rate. This is especially the case after midterm. But the flipped class had a higher attendance rate – almost 100% before midterm and 87.5% or better after midterm. The high attendance rate was mainly due to the requirements that students must work on a worksheet as groups and submit it at the end of class. 2. Students’ participation was increased, and thus active learning was achieved. While working on their worksheets in groups, students have more opportunities to communicate their ideas with each other. This helped students not only to understand the subject matters better, but also improve their communication skills, stimulate their interest in the subject, and sort the concepts involved straight and clear. 3. The flipped approach resulted in better learning outcomes and a lower DWF rate. 50% of the class received an A grade, 25% of students received a B, and another 25% students received a C, and thus a 100% passing rate was achieved.

View Submission →

1. 2025 Meeting
3. UGTalks

Food Insecurities in a Blooming Rural Town: A Statistical Analysis — Christine Jator <cjator@my.apsu.edu>

Food is an essential part of daily life, providing vital nutrition to the mind and body. The lack of an essential resource can significantly hinder one’s quality of life. In the south, “The state of Tennessee measures at 11.9% food insecurity” (Durnell, 2023, p.1). This statistic reveals that several people cannot acquire healthy food, decreasing their quality of life. Clarksville, a growing rural town in Tennessee struggles with the same issue. In this study, we seek to understand what factors classify food-insecure populations in Clarksville, TN, and how they compare on a smaller and larger scale. Using data from the United Census Bureau, we will analyze trends and formulate conclusions from Clarksville, TN data, and compare these results with Murfreesboro, TN, and USA data. The data contains food stamp information counts and percentages for different populations. This research aspires to aid food pantries and food-insecure populations in growing rural areas similar to Clarksville, TN. This project sheds light on remembering the impoverished and those who struggle to obtain healthy food in a progressing society.

View Submission →

1. 2025 Meeting
3. Contributed

Fraud Detection Using Logistic Regression — Alysia Norales <anorales@my.apsu.edu>

Fraud detection is a critical application of machine learning in the financial sector. It aims to find out fraud transactions with minimal impact on legitimate transactions. This project uses logistic regression, one of the most popular classification algorithms, to detect fraudulent transactions in a highly imbalanced credit card transaction dataset. This data contains 284,807 transactions, of which only 492 are fraudulent (Class 1), which accounts for less than 0.2% of the total data. This dataset had a highly imbalanced distribution between the classes, with only a tiny fraud class, which usually creates issues in developing an effective predictive model. This project will utilize various techniques, including SMOTE and threshold tuning of the decision, for better model performance and a balanced trade-off between precision and recall for the minority class.

View Submission →

1. 2026 Meeting
3. 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.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2026 Meeting
3. Special
5. 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.

View Submission →

1. 2025 Meeting
3. Sessions
5. DataLit

From small steps to giant leaps toward data literacy — Laurie Heyer <laheyer@davidson.edu>

Small steps -- a single workshop, a single course, a single tutor -- can create a launchpad for giant leaps in a data science program. We describe how data science courses, curricula and programming form a web of support for students across the disciplines at Davidson College.

View Submission →

1. 2025 Meeting
3. Invited

Fun with Fractions — Dan Yasaki <d_yasaki@uncg.edu>

The study of continued fractions goes back to Indian mathematicians in the 6th century. They came back into fashion in Europe in the 1600’s and were studied extensively in 18th and 19th centuries. They find their way into modern mathematics through their use in computing modular forms and computer recognition of rational numbers. In this talk, I will introduce continued fractions and discuss some of their modern applications.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2025 Meeting
3. Contributed

Gaming in Flux: Identifying and Mitigating Risks for Microsoft's Xbox Brand — Sikem Nkwawir <snkwawir@my.apsu.edu>

This paper examines the potential risks and advantages of Microsoft's strategic shift away from console development towards software development and the growth of Xbox Game Pass. Microsoft&#39;s recent announcement of releasing Xbox exclusives on rival consoles has sparked speculation about their future direction in the gaming industry. The study utilizes a multidimensional approach, combining data from sources such as Kaggle, news outlets, and legal proceedings to analyze the landscape of the video game and video streaming industries. The risks identified include potential losses in console and software sales, customer reluctance to subscribe to the platform on rival consoles, and the possibility of cloud gaming platforms failing all in relation to their potential losses. While the risk of console sales is considered low due to historical trends and Microsoft&#39;s console pricing strategy, the risk associated with software sales is more uncertain due to the fact that Microsoft makes money from third-party sales on their hardware. The risk of crossover appeal is considered low, as Microsoft already supports games on other consoles through acquisitions and now holds some of the most successful franchises in history. The risk of cloud gaming failing is also deemed low, given the industry's transition to digital and cloud-based gaming and Microsoft’s unique advantage in the industry. Considering these risks and opportunities, it is recommended that Microsoft seriously consider focusing on Game Pass and leaving the console space to leverage cross-platform availability and tap into a wider customer base.

View Submission →

1. 2026 Meeting
3. 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.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2026 Meeting
3. 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.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2025 Meeting
3. Sessions
5. UGRMentors

Guiding High School and Undergraduate Students into the World of Mathematical Research — Rigo Florez <rflorez1@citadel.edu>

In this talk, we explore strategies for engaging students with basic mathematical knowledge in research projects. This approach leverages open problems from respected academic journals. We will discuss methods for guiding students through problem--solving, publishing their results, and ultimately presenting their findings publicly. This technique can also benefit educators without prior research experience who wish to begin exploring research themselves. We discuss how to stimulate students' curiosity through visual tools, including classic experiments involving the Mo\"bius strip and the Klein bottle. These experiments involve constructing the objects, observing their properties, and using hands-on activities to show how altering the objects by cutting disrupts their inherent properties. At the end of the presentation, we will discuss problems our students have solved from journals as well as original problems related to our own research topics. Additionally, we will provide a list of current problems along with recommended books and articles to help students prepare for future projects. Join work with Drs. Chen, Mukerjee, and Swart.

View Submission →

1. 2025 Meeting
3. Invited

Hats, Hamming and Hypercubes — Mike Pinter <mike.pinter@belmont.edu>

During this interactive session, we will begin with a team strategy game followed by an error-correcting code with a corresponding link to hypercubes. Participants will explore how the game, code and cubes are connected to each other through examples and questions that arise. Come engage yourself with some contemporary mathematical topics that will be accessible regardless of the mathematics courses you have taken.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2025 Meeting
3. UGTalks

Higher Dimension Analogues for Pythagorean Triples — Cara Admiraal <c.admiraal@yahoo.com>

There is a known correspondence between rational points on the unit circle and Pythagorean triples. Using problem-posing strategies, such as those found in Brown and Walter's book *The Art of Problem Posing*, we will explore high-dimensional analogues of Pythagorean Triples such as by giving classifications or generalizing the generating formula. Beginning with a visual aid, in the form of a lattice, our generalization will proceed via the stereographic projection of rational points $S^n$ sphere.

View Submission →

1. 2026 Meeting
3. Special
5. 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

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2026 Meeting
3. Special
5. 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.

View Submission →

1. 2025 Meeting
3. Sessions
5. RecMath

How Many Dice Do You Need for a Bell Curve? — Jeffrey Clark <clarkj@elon.edu>

The Central Limit Theorem is one of the most fundamental principles in probability, stating that the probability distribution of the average of independent measurements of the same random variable has the ubiquitous bell curve as a limit as the sample size increases. This talk will use different numbers of fair dice to explore this convergence as one of the easiest examples of that convergence if not the quickest.

View Submission →

1. 2025 Meeting
3. Invited

How to Not Only Survive but Also Thrive as an Outlier — Hwayeon Ryu <hryu@elon.edu>

Navigating academia as an outlier—whether due to background, research interests, teaching philosophy, or identity—can be both challenging and rewarding. In this talk, I will share the challenges I have faced, as well as insights from my unique journey, reflecting on the strategies that helped me not only persist but also thrive in environments where I did not always fit the mold. Drawing from experiences in teaching, research, and mentoring, I will discuss the power of authenticity, resilience, and community-building in shaping my identity as a mathematician. Whether you find yourself feeling like an outlier or simply want to support those who do, this talk will provide practical takeaways for overcoming obstacles, embracing unique perspectives, and fostering a supportive community that values diversity and inclusion. Join me as we explore how the challenges of being an outlier can become a powerful catalyst for growth and success.

View Submission →

1. 2026 Meeting
3. 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.

View Submission →

1. 2025 Meeting
3. Contributed

Hyperbolic cords and wheels — andrew simoson <ajsimoso@king.edu>

The family of cycloid curves are generated in two different ways in the Euclidean plane: following a tack in a wheel rolling around a circular track and following a tack in a bungee cord whose ends are held by two runners on a circular track. What happens in hyperbolic space? Do the two approaches yield the same curve? Come and find out!

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2026 Meeting
3. Special
5. 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.

View Submission →

1. 2026 Meeting
3. 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.

View Submission →

1. 2025 Meeting
3. Contributed

It's NOT Cheating, It's Collaboration — Rodica Cazacu <rodica.cazacu@gcsu.edu>

Collaborative work is an essential part of learning and for the past couple of years I have tried to make it essential for all my classes. I want my students to feel that benefit not just when they work on some problems during class time or outside of the class for a group assignment, but also to experience the benefit of group collaboration during assessment time. In all my applications classes I have unit assessments during semester and each such assessment has an individual and a group component. This presentation will look into how I use group corrections and review for my unit tests and how I use that to strengthen the group relations, making my students feel more confident while learning to trust themselves and their group mates. I will also talk about how I determined a way of seeing if there is an improvement in my students’ work and how I used their results to motivate them to challenge themselves and their teammates

View Submission →

1. 2026 Meeting
3. Special
5. 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.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2026 Meeting
3. 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.

View Submission →

1. 2026 Meeting
3. Special
5. 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.

View Submission →

1. 2025 Meeting
3. Contributed

Learning Graph Theory: A Ropes Course Adventure — Ashley Suominen <asuomine@scad.edu>

A ropes course consists of a sequence of physical challenges that require participants to maneuver through obstacles constructed of ropes, cables, and wood. Successfully navigating these courses necessitates careful consideration of the route taken through each challenge. The objective is to participate in every obstacle without retracing your steps; thus, an effectively designed ropes course can be likened to an Euler path or circuit. Regrettably, course designers often lack an understanding of the mathematical principles that underpin these structures. In this presentation, I will elaborate on a class activity where my students, who are pursuing degrees in art and design, acquire fundamental concepts of graph theory by creating their own ropes course.

View Submission →

1. 2025 Meeting
3. Sessions
5. UGRMentors

Lessons learned from 30+ years of undergraduate research direction — Anant Godbole <godbolea@etsu.edu>

This is a personal tale of how I have directed undergraduate research at MTU and ETSU via NSF-REU awards. I was the sole advisor from 1991 to 2018, and have worked with Fernando Piñero and Pamela Harris since then. I retired in 2024. Some aspects of my talk are *How I used undergraduate research as a springboard to solidify and define my own research; *How I learned so much from my students while teaching them sophisticated and bread-and-butter techniques; and *The illustrious careers of my students.

View Submission →

1. 2025 Meeting
3. Workshops

Liberal Arts Math, Quantitative Literacy, College Algebra/Precalculus: A Novel Hybrid Curriculum — FirstName LastName <dan@dankalman.net>

**Participants are requested to bring laptops or other devices capable of opening and working with excel files.** This workshop will present an innovative curriculum that is a hybrid of the standard courses mentioned in the title. The mathematical focus is on discrete models defined by difference equations, and the continuous models that they reveal. The goal is to give students a realistic sense of how math actually gets applied. At the same time, the development and exploration of these models is an effective vehicle for having students review many of the ideas from standard college algebra courses. The presentation will follow this outline: 1. Motivation for the course: dissatisfaction with standard curricular options. 2. Principles underlying the curricular design. 3. Progression of mathematical ideas from arithmetic to logistic growth, climaxing with a new discrete version of logistic growth. 4. Pedagogy; Instructional approaches. 5. Technology. Available suite of excel-based exploratory tools. 6. Experiences of teachers using this curriculum.

View Submission →

1. 2025 Meeting
3. Sessions
5. DataLit

MAA’s StatPREP Project: Using Data-Centric Methods to Teach Introductory Statistics — Jenna Carpenter <carpenter@campbell.edu>

The MAA’s NSF-funded StatPREP Project had, as its mission to empower statistics instructors to create data-driven learning opportunities so that students can gain the skills and knowledge needed to work and live in a data-centric world. The forthcoming MAA Notes volume on the StatPREP Project showcases the tools and resources developed by the project, dives into examples of how to transform the introductory stats classroom (including lessons on common intro stat topics that use tools like the Little Apps to explain and explore topics using R online via a web browser), as well as other topics and considerations for improving and expanding data science education. We will explore these tools and ways they can be used in your classroom.

View Submission →

1. 2025 Meeting
3. Contributed

Making an MPAACT on Student Success in the UNC System — Catherine Payne <payneca@wssu.edu>

The MPAACT project is a collaborative effort across several universities in the UNC system to increase the success of African American males in introductory math courses. This talk will discuss the design of the project, including advising, mentoring, and corequisite support courses for introductory math classes. We will also discuss preliminary findings from data collected from the students and instructors of the support courses. Finally, we will share some challenges faced and lessons learned during the implementation.

View Submission →

1. 2026 Meeting
3. Special
5. 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.

View Submission →

1. 2026 Meeting
3. 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.

View Submission →

1. 2026 Meeting
3. Special
5. 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.

View Submission →

1. 2025 Meeting
3. Contributed

Mastery Grading in Calculus II and Calculus III — Chris Cyr <chris.cyr@covenant.edu>

During the 2024 calendar year, I transitioned my calculus classes from a traditional points-based grading system to a mastery grading system. In this talk, I describe my implementation of mastery grading in these classes, including how mastery of learning objectives was measured, the process for reattempting learning objectives, and the determination of final grades. I will also examine how students’ final grades under the new system compare to data from several previous years of teaching the same classes at the same institution with a points-based system.

View Submission →

1. 2025 Meeting
3. Sessions
5. RecMath

Math Engagement: Math is Fun! — Laura Steil <lsteil@mhu.edu>

This talk will focus on an initiative at Mars Hill University for co-curricular math exploration. Math faculty members use problems, activities, and puzzles from Math Circles to engage with students outside of the lecture classroom. The ideas used in the activities are applications that students would not necessarily encounter in the classroom but allow for exploration with patterns, strategies for games, and recognition of mathematics in everyday life. A large emphasis of the initiative is for students to realize that math can be fun!

View Submission →

1. 2026 Meeting
3. 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.

View Submission →

1. 2026 Meeting
3. 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.

View Submission →

1. 2025 Meeting
3. UGTalks

Mathematical Modeling of COVID-19 With a Focus on Asymptomatic Transmission — Lauren Beuerle <lbeuerle2@elon.edu>

In 2020, the global COVID-19 pandemic erupted. Without knowledge to combat the disease, hospitals around the globe were overrun. Scientists and mathematicians, using past information on extremely infectious viruses, began investigating the effectiveness of social distancing, facial coverings, and eventually, vaccinations. Mathematical models can be used to explore the quantitative effectiveness of vaccinations, facial coverings, and create predictive models to aid the creation of policies in order to prevent future surges in cases. This project will utilize the ordinary differential equation SIR model to explore susceptible (S), infectious (I), recovered (R) populations to explore impact of asymptomatic individuals. The products of this model can be used as a reference for preventative measures for future epidemics that follow a similar pattern to COVID-19.

View Submission →

1. 2025 Meeting
3. UGPosters

Mathematical Modeling of Immune Response to SARS-CoV-2 — Nicolas Alvarez <nalvarez2@elon.edu>

In response to the profound impact of the SARS-CoV-2 pandemic, the scientific community has focused considerable research efforts to understand the spread of the virus. Despite a tremendous volume of research in this area, the dynamics of the immune response to SARS-CoV-2 has been hampered due to limited analysis of the experimental or clinical information to date. Mathematical models that account for the interaction between SARS-CoV-2 and the human immune system will improve the scientific community’s ability to analyze the amount of data available.We develop a mathematical model for the immune response to SARS-CoV-2 to investigate the role of various pathways in successful viral clearance and the key mechanisms responsible for disease severity. These interactions are captured by a system of ordinary and delayed differential equations. We conduct parameter estimation based on experimental data and investigate model behaviors via computational simulations. Our model demonstrates key aspects of the immune response to SARS-CoV-2 which might be responsible for disease severity. Specifically, Natural Killer Cell dysfunction impairs its ability to eliminate infected cells effectively. This could be used to serve as a foundation for the development of therapeutic strategies.

View Submission →

1. 2026 Meeting
3. Special
5. 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.

View Submission →

1. 2025 Meeting
3. Sessions
5. UGRMentors

Modeling Bromeliads: An Ongoing Interdisciplinary Collaboration with Multiple Undergraduate Research Projects — Erin Bodine <bodinee@rhodes.edu>

Team Bromeliad is an ongoing seven-year interdisciplinary collaboration Dr.~Erin N.~Bodine (biomathematician) and Drs.~Rachel Jabaily, Brad Oberle, and Brian Sidoti (botanists) to study the growth, reproduction, and population dynamics of bromeliads (a plant family of rosette-structured flowering plants that includes the pineapple and Spanish moss) using greenhouse and field experiments in conjunction with mathematical modeling. The long lifespan of many bromeliads (up to 100 years in some species) can make it difficult to study individual rosettes \textit{in situ} over their lifetime. However, this provides fertile ground for developing mathematical and computational models that can simulate and predict growth, reproduction, and population dynamics over many decades. These models have the additional benefit of allowing for simulations that consider the impact of changing environmental conditions, such as climate change or the introduction of invasive species. In this talk, we will tour a selection of mathematical models of bromeliad growth, reproduction, and population dynamics that have been developed and analyzed in collaboration with undergraduate students from a variety of institutions. From simple single equation continuous functions and discrete difference equations to more intricate models of systems of differential equations and agents-based models, each model provides a different lens from which to view and understand bromeliad growth and reproduction. Additionally, this talk will reflect on the elements of this collaboration that have enabled it to persist and evolve over time, and to provide research opportunities for over 20 undergraduate students.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2025 Meeting
3. UGPosters

Modeling Dendritic Solidification of Crystal-Like Structures Through Diffusion-Limited Aggregation — Daniel Olopade <daniel.olopade@bruins.belmont.edu>

This poster presents a Diffusion-Limited Aggregation (DLA) model in the context of crystallization. The DLA model describes how particles randomly diffuse until they come in contact with the existing cluster. The underlying physics that creates DLA is Brownian motion, which is simulated stochastically through random walks. This model explores the formation of crystal structures through dendritic solidification. Dendritic solidification is a process where a liquid cools and forms a solid with tree-like patterns, known as dendrites. This principle is fundamental in forming naturally occurring patterns and structures, such as metal castings and ice crystals. By understanding how dendrites form, the microstructures of these materials can be optimized for improved mechanical properties such as strength and durability. With this model we demonstrate how changes in expansion rate and particle fusion probability affect the structural integrity of dendritic materials.

View Submission →

1. 2025 Meeting
3. UGPosters

Modeling Granular Flow Dynamics Using the Discrete Element Method — Jeremiah Poston <jeremiah.poston@g.fmarion.edu>

The Discrete Element Method (DEM) is a numerical technique used to model interactions between discrete particles. DEM simulates the behavior of granular materials by calculating the forces and motions resulting from particle collisions, friction, and cohesion. Newton’s second law of motion, combined with force-displacement laws, maintains a crucial role in enabling accurate simulation of particle interactions in DEM. Applications of DEM encompass various fields including civil engineering for simulating soil mechanics, pharmaceuticals for optimizing powder mixing processes, and geophysics for studying natural phenomena like landslides and earthquakes. Building on these diverse applications, this research seeks to enhance the understanding of granular flow dynamics by leveraging DEM to analyze the interactions within granular materials. A series of simulations were conducted by using Python to explore how particle shape, size distribution, and contact properties influence flow behavior.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2025 Meeting
3. Contributed

Modeling Sound Waves in a Battery — Jeffrey Landgren <jeffrey.landgren@ung.edu>

Experiments in the field of Electrochemistry demonstrate that sound waves act as a catalyst for chemical reactions. A model is developed using conservation of momentum and mass, a boundary motion equation, and a surface tension equation. Chemically, it is clear that the catalytic phenomenon is derived from the sound waves and how they are affected by the top boundary in the cell. When combining all four equations we arrive at a boundary condition that strictly involves the top boundary. Throughout the problem a self-adjoint invertible operator derived in the top (Neumann) boundary condition is established. Then a discussion ensues regarding regularity and formalizing all other boundary and initial conditions. These conditions are then applied to the wave equation. The specific chemical reactions where this phenomenon is observed can be found in batteries, capacitors, and solar cells. The reaction takes place at an interface or boundary in each device. Making these devices more efficient can help decrease our negative impact on the environment.

View Submission →

1. 2026 Meeting
3. 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.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2026 Meeting
3. Special
5. 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?

View Submission →

1. 2026 Meeting
3. 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.

View Submission →

1. 2025 Meeting
3. Sessions
5. DataLit

New Courses and Programs to Promote Data Literacy — Ellen Breazel <ehepfer@clemson.edu>

In an increasingly data-driven world, fostering data literacy has become essential for students across disciplines. This presentation describes the steps the School of Mathematical and Statistical Sciences has taken to promoting data literacy through the development of an undergraduate major, specialized courses, and an online Master’s program. By integrating data literacy into the curriculum, students will not only gain essential analytical skills but will also learn to apply data-driven decision-making in diverse fields. The general education undergraduate course focuses on foundational data concepts, while the major offers an in-depth exploration of data analysis, programming, and ethical implications in a wide variety of disciplines. The online Master's program was designed for working professionals, providing flexible access to advanced data literacy training. This session will explore the rationale behind these initiatives, the curriculum design, and the impact on both academic and professional communities.

View Submission →

1. 2025 Meeting
3. UGPosters

Nonlinear BVP on Discrete Time-Scale — Kyle Byassee <kylhbyas@ut.utm.edu>

We study nonlinear boundary value problem on discrete time-scale with continuous nonlinearity on the boundary and inside the domain. We define upper and lower solution for the problem and use Brower fixed point theory to prove existence of positive solution.

View Submission →

1. 2026 Meeting
3. 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.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2025 Meeting
3. UGTalks

Numerical Simulation of Jellyfish Swimming — Jillian Thomas <jthomas61@elon.edu>

Jellyfish are considered the most energetically efficient swimmers to have ever existed, so their propulsion method can be researched to improve our own underwater vehicle designs. These unique animals need to be very efficient because of their untraditional bodily components, and because most consume limited food while they prey passively during swimming. Jellyfish accomplish their efficiency through vortex propulsion. The contraction of a jellyfish’s bell generates a vortex ring as it swims, which due to its axial symmetry we simplify into two dimensions using two point vortices. We model these vortices using a system of differential equations, for which parameters can be selected to adjust the strength, location, and direction of their rotation. To numerically solve the system, we use the fourth order Runge-Kutta method in MATLAB. The first goal of the project is to examine the jellyfish's propulsion and maneuvering mechanism, which involves creating simulations for various parameter values in the system of differential equations. Secondly, we study the material transport in the vicinity of jellyfish and its implication on food acquisition. Massless particles are inserted into the fluid flow to observe how the jellyfish and particles around it move through the water as affected by the vortices. To work towards these goals, we have implemented bell shapes to represent moon jellyfish, Pacific sea nettles, cannonball jellyfish, and lion’s mane jellyfish to provide a breadth of bell shapes and sizes. Each of these bell shapes serve as a barrier to material transport, so the jellyfish can capture particles from the surrounding environment. These results have significant implications for fields such as biomimetic engineering, including improvements to sub-aquatic vehicle efficiency and reliability, especially in cases when speed is not a priority.

View Submission →

1. 2026 Meeting
3. 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.

View Submission →

1. 2025 Meeting
3. Contributed

On Conditions for Weak Convergence Concerning Quasi-likelihood Estimation with an Application to a Mutagenicity Test — Bo Li <bli@citadel.edu>

Over-dispersion has been well-known often besetting counting data analysis. In this talk, we assume that data follow the quasi-likelihood distribution that the variance is proportional to a known function of the mean, such that the scale parameter captures over-dispersion. When data fit the generalized linear models, we propose the generalized Huber’s condition, under which the root for inference based on quasi-likelihood estimation converges weakly, along with the other regularity conditions. Based on the large-sample approximation, we apply the simultaneous confidence interval method to the Salmonella data obtained from a mutagenicity test, using the proposed theory.

View Submission →

1. 2025 Meeting
3. Contributed

On Galois Groups, Resolvents, & an Application to Nonic Power Compositional Polynomials — Frank Patane <frankapatane@gmail.com>

We begin our discussion with a brief summary of methods for determining the Galois groups of cubics & quartics. This discussion will lead us to the notion of resolvents which is a central tool in the computation of Galois groups. We then apply these tools to the family of irreducible $f(x)=x^9+ax^6+bx^3+c$ defined over $\mathbb{Q}[x]$. We conclude with a computation Gal$(f)$ in select cases.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2026 Meeting
3. 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.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2025 Meeting
3. UGTalks

Orientable Quadrilateral Embeddings of Cartesian Products of Cycles — Matthew Farnsworth <matt.farnsworth@bruins.belmont.edu>

In the spirit of Pisanski (1989) we consider orientable quadrilateral embeddings of Cartesian products of cycles on surfaces. We offer a constructive example of such an embedding of three low-order cycles. Then we show more generally that such embeddings exist for products of the form $C_2 \times C_{2n} \times C_{m}$. We represent our graphs using rotation schemes to show this existence. Use of rotation schemes led to the ultimate characterization of our findings visually, providing conjectures for generalizations of products of three cycles.

View Submission →

1. 2026 Meeting
3. Special
5. 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.

View Submission →

1. 2025 Meeting
3. Contributed

PRICING OF ASIAN OPTION USING FINITE DIFFERENCE METHOD — Michael Kipngeno <mkipngeno@my.apsu.edu>

This study employs a numerical method for pricing Asian options using the finite difference methods. It approximates the partial differential equation. The price of the option price is obtained by discretizing the underlying asset price and time dimensions into a grid, allowing for the calculation of the option value based on the average price of the underlying asset over a specified period. This provides a robust and flexible tool for evaluating complex Asian option structures. 

View Submission →

1. 2026 Meeting
3. NExT

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

TBA

View Submission →

1. 2025 Meeting
3. Contributed

Patient-Specific Models of Transcatheter Aortic Valve Replacement Using the Immersed Finite Element-Difference Method — Jordan Brown <jordan.brown@belmont.edu>

Transcatheter aortic valve replacement (TAVR) is the implantation of an artificial aortic heart valve without an open-heart surgery. Computer modeling and simulation is an important tool in the process of transcatheter aortic valve (TAV) device design, regulatory approval, and indication in the care of specific patients, since there are still many open questions surrounding post-implantation complications. Improved computational models beyond those in the existing literature have the ability to provide more accurate performance predictions for individual patients. We present computational fluid-structure interaction models of TAVs using the immersed finite element-difference method. We perform dynamic simulations of crimping and deployment of the devices as well as their behavior across the cardiac cycle in a patient-specific aortic root anatomy reconstructed from CT image data. These IFED simulations incorporate biomechanics models fit to experimental tensile test data and automatically capture the contact within the devices and between the stents and native anatomies. We apply realistic driving and loading conditions based on clinical measurements of human ventricular and aortic pressures and flow rates, and our models provide informative clinical performance predictions, such as pre- and post-procedure transvalvular pressure differences, detailed flow patterns, leaflet dynamics, and valve orifice areas.

View Submission →

1. 2025 Meeting
3. UGPosters

Patterns in a Number Triangle — Zih-Syun Fu <dannyfuesalin@gmail.com>

We introduce a triangle of numbers, similar to the Fibonacci Triangle and the Pascal Triangle and discuss some of its properties. As an open question, this triangle was given as an OEIS Challenge (P419) from “The Playground” in the Math Horizons magazine. The triangle is constructed in the following way: The entries of the first diagonal from the left (or the first back slash diagonal) of the triangle are all equal to 2, and the second back slash diagonal is made up of the Fibonacci numbers. Any entry in a particular back slash diagonal after that is obtained using a recursive formula that involves adding up all previous entries in the respective diagonal along with a constant which depends on the position of the entry that is being computed. We provide a formal definition for the entries of the triangle using a recursive formula. We also discuss how an L-shaped pattern in the triangle gives rise to a formula for the entries of the third slash diagonal (or third diagonal from the right), involving entries of the previous slash diagonals and Triangular numbers. We finally provide a generalized proof of this formula using Mathematical Induction. Other patterns are also included.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2026 Meeting
3. 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.

View Submission →

1. 2025 Meeting
3. Sessions
5. RecMath

Phun with “Phractals” and Phi for 100-Level Quantitative Literacy Mathematics Courses — Laura Lembeck <lslembeck@wcu.edu>

In this session, I will describe how I introduce fractal mathematics with iterative processes and focus on key aspects of the golden ratio and transcendental number Phi. I will include some of the video clips I use to get students engaged with the concepts, examples they practice in the classroom to further their understanding, and assignments that align with the learning objectives of this course - “Students will craft written and/or oral communication demonstrating organization, clarity, logic and skill for various audiences.”

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2025 Meeting
3. Sessions
5. RecMath

Playing with Proof: Combinatorial Game Theory in Liberal Arts Mathematics — Bill Shillito <bshillito@oglethorpe.edu>

Proof lies at the heart of mathematical reasoning, yet teaching proof in a liberal arts mathematics course poses a unique challenge. How can we showcase the power and utility of axiomatic reasoning while keeping the content accessible to students from diverse majors and backgrounds? A simple game involving blue and red poker chips can offer the perfect balance of accessibility and depth, inviting students to explore axiomatic reasoning in an engaging yet rigorous way. With just three axioms, students can discover hidden structures within the game and even determine their optimal next moves. We will introduce the game and its axioms, and then we will discuss how it can be used as a classroom activity to demonstrate the elegance of mathematical proof through play.

View Submission →

1. 2026 Meeting
3. 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!

View Submission →

1. 2025 Meeting
3. UGPosters

Predicting Heart Failure Outcomes Using Deep Learning and Explainable AI — Kwatcho Mahinanda <kmahinanda@unc.edu>

Heart disease remains the leading cause of death in the United States, with heart failure contributing significantly to these mortality rates. Defined by the CDC as the heart's inability to pump sufficient blood and oxygen to support other organs, heart failure affects over 6 million Americans, with a five-year post-diagnosis mortality rate of nearly 50%. This study leverages deep learning to predict mortality risk in heart failure patients using a dataset of 299 records with 17 clinical features. Deep neural networks (DNNs) and convolutional neural networks (CNNs) were developed and optimized through hyperparameter tuning to enhance prediction accuracy. Model interpretability was achieved using SHapley Additive exPlanations (SHAP), which identified key predictors such as follow-up duration, ejection fraction, serum creatinine, and diabetes. These findings align with prior research highlighting ejection fraction and serum creatinine as critical factors, while also emphasizing time, diabetes, and age as significant predictors. This work demonstrates the potential of combining explainable AI with deep learning to support clinical decision-making in heart failure management.

View Submission →

1. 2025 Meeting
3. UGPosters

Predicting Hitter Success Using Bat Tracking Metrics in the MLB — Jakub Michel <jmichel2@highpoint.edu>

In this study, we examine the predictive power of seven key bat tracking variables in determining Expected Weighted On-Base Average (xwOBA), a widely accepted measure of hitter success. xwOBA is considered a more reliable indicator of a player’s skill than traditional Weighted On-Base Average (wOBA), as it removes defensive factors from its calculation. Unlike wOBA, which depends on actual outcomes, xwOBA estimates a hitter's performance based on batted ball characteristics—exit velocity, launch angle, and other relevant factors—assigning probabilities for singles, doubles, triples, and home runs based on contact quality. To identify the most predictive variables for xwOBA, we utilize multiple linear regression (employing forward and full-subset selection) alongside decision tree models, including random forests and boosted trees. Model performance is evaluated via Root Mean Square Error (RMSE), and we identify the most influential metrics in predicting hitter success. These findings offer valuable insights for player evaluation and development.

View Submission →

1. 2025 Meeting
3. Sessions
5. UnspokenHistory

Primes and Pyramids — Satish C. Bhatnagar <satish.bhatnagar@unlv.edu>

This article was written is a reflective mode after visiting the Grand Pyramid of Giza on January 02, 2025. Prime numbers and pyramid constructions are poles apart, yet an effort is made to build a bridge over them. In life, a bridge is only known for its one of the longest spans.

View Submission →

1. 2025 Meeting
3. Invited

Projective and Non-Abelian SET (MAA AWM Lecturer) — Catherine Hsu <chsu2@swarthmore.edu>

Mathematicians love SET. On the surface, this classic game is a con test of pattern recognition, but it also presents an interesting way to visualize the geometry of a torus over a finite field. In this talk, we will discuss some of the mathematics connected to SET and then explore several new versions of the game, including one arising from projective geometry and one arising from non-abelian groups. In particular, we will see how these non-abelian variations on SET can give intuitive visualizations of abstract group structures.

View Submission →

1. 2026 Meeting
3. Special
5. 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.

View Submission →

1. 2025 Meeting
3. UGPosters

Properties of Eigenvalues of Fractal Laplacian — Andrew Chincea <achincea@students.kennesaw.edu>

We investigate the properties of the eigenvalues of the fractal Laplacian. We begin by defining the fractal Laplacian operator in one dimension and formulate the corresponding Dirichlet eigenvalue problem. Analytical solutions are obtained for specific fractal parameters, and computational results illustrate the structure of eigenvalues and their associated eigenfunctions. We extend our analysis to two dimensions using separation of variables. Our findings contribute to a deeper understanding of how fractal geometry affects the spectral characteristics of differential operators.

View Submission →

1. 2026 Meeting
3. 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.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2025 Meeting
3. Contributed

Pythagorean n-ples — Dan Kalman <kalman@american.edu>

Pythagorean Triples such as (3,4,5) and (5,12,13) are a familiar topic in college mathematics. They represent integer sided right triangles, as well as rational points on the unit circle (eg (3/5,4/5), (5/13, 12/13)) and integer vectors with integer lengths (eg (3,4), (5,12)). This talk discusses extensions of these ideas to higher dimensions: Pythagorean 4-ples, 5-ples, n-ples. Though these extensions are not new (for example they can be found in wikipedia), they are not nearly as well known as they deserve to be.

View Submission →

1. 2025 Meeting
3. UGTalks

Quad Packing — Taiki Aiba <taiba3@gatech.edu>

Quads or EvenQuads is a pattern-recognition game similar to Set. The goal of the game is to find "quads", which are sets of 4 cards that satisfy a particular pattern. In this talk, we will discuss our research into the maximum number of quads in a $k$ card layout. Specifically, we will demonstrate an upper bound for the number of quads in a $k$ card for all $k$ and prove this bound is tight for when $k$ is a power of two. Furthermore, we will share the results for $4 \leq k \leq 6$.

View Submission →

1. 2025 Meeting
3. Sessions
5. RecMath

Quad-free sets in the card game Quad-128 — Lauren Rose <rose@bard.edu>

Quad-128 is a game played with two distinguishable Quad-64 decks; for example, each deck has a different background color. The game play is similar, but the combined deck is now a model for the affine geometry $AG(7,2)$ rather than $AG(6,2)$. We define a $\textit{cap}$ to be a quad-free set of cards. We determine the maximum size of a cap, which tells us how many cards we must lay out to guarantee a quad. More generally, we classify all caps in $AG(7,2)$ up to affine equivalence.

View Submission →

1. 2026 Meeting
3. Special
5. 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.

View Submission →

1. 2025 Meeting
3. Contributed

RISK FACTORS ASSOCIATED WITH COVID-19 — mohammed Talukder <mtalukder@ecsu.edu>

COVID-19 is a viral disease that began impacting the world in the latter part of 2019. In early 2020, the world would be in a state of pandemic due to the rapid spread of the disease. Statistical analysis has been an extremely useful tool in determining the impact of COVID-19. Some discussion about the COVID-19 pandemic is how medical and non-medical factors can influence i the severity of the infection of a person. A case study was conducted regarding cases that occurred in Wake County, North Carolina. The relationship between demographic factors (age, sex, and race) and both ICU admittance and death were investigated using the chi-square test of association and binary logistic regression. Age and race were determined to have some significant relationship with severe cases of COVID-19 while sex did not. Binary logistic regression also produced model equations that can be utilized to predict the likelihood of ICU admittance or death of an individual as the result of COVID-19 based on these factors.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2026 Meeting
3. 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.

View Submission →

1. 2025 Meeting
3. Contributed

Recognizing Algebraic Properties from Multiplication Tables — Dan Scofield <daniel.scofield@fmarion.edu>

Machine learning algorithms, such as neural networks, are rapidly gaining popularity as tools for research in pure mathematics. In one application, a classifier is trained on a set of multiplication tables with the goal of detecting property P, where P may be an algebraic property such as commutativity or associativity. We present evidence that relatively small neural networks can solve these problems with high accuracy. We also analyze these models by varying the structure of the training data and show that they likely achieve this accuracy by detecting consequences of property P, rather than property P itself.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2025 Meeting
3. UGPosters

Related Identities for the Fibonacci and Lucas Sequences — William Knuth <wknuth@student.citadel.edu>

We solved Problem B-1337 from The Fibonacci Quarterly. In this problem, we show that the sum and difference of ratios of Fibonacci numbers is equivalent the product of two consecutive Fibonacci numbers. We prove a similar result for Lucas numbers. We use the Gelin-Cesaro Identity as well as a related identity to prove the equations of Problem B-1337.

View Submission →

1. 2026 Meeting
3. 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.

View Submission →

1. 2026 Meeting
3. 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.

View Submission →

1. 2025 Meeting
3. Invited

Rigor Starts with Imperfection — Anne Duffee <laduffee@sewanee.edu>

In this talk, I explore the tension between mathematical rigor and perfectionism, particularly how the fear of failure can hinder their engagement with rigorous mathematical thinking. Drawing on Imre Lakatos' book Proofs and Refutations, which describes a dialectical process of conjecture, proof, and refutation, I argue that just as historical developments in mathematics emerge through a cycle of failure and refinement, our students develop their own rigorous thinking through their experiences of failure. As a result, a large barrier to developing mathematical cognition stems from a rise in maladaptive perfectionism. I will discuss pedagogical strategies, including course structure and historically motivated problems, to help students navigate the discomfort of not knowing and cultivate genuine mathematical rigor.

View Submission →

1. 2025 Meeting
3. Contributed

Running a Preceptor Program — Hope McIlwain <mcilwain_mh@mercer.edu>

In this talk, I will describe the Preceptor Program in Mathematics at Mercer University. Topics will include the motivation for the program, the structure of the program, and the benefits of the program. In addition, plans for the improving the program will be discussed.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2025 Meeting
3. UGPosters

Simulating the Spread of Norovirus with a Cellular Automata SIR Model — Najma Ismail <najma.ismail@bruins.belmont.edu>

Norovirus, a highly contagious illness, affects the digestive system and is a common cause of morbidity globally. This study explores the spread of Norovirus using a hybrid SIR model integrated with cellular automata. Our simulation models the transmission and recovery processes in a sampled population under varying probabilities of susceptibility and infection. By employing cellular automata, the model captures localized interactions and provides a visual representation of spatial disease progression. Our model assumes a static population, deterministic state transitions, and fixed durations for infection and immunity. The simulation outcomes demonstrate how initial conditions, such as high susceptibility or infection rates, influence epidemic patterns over time. High susceptibility results in rapid disease spread due to limited initial immunity. Conversely, high initial infection rates lead to rapid saturation with immune individuals, followed by cyclical reinfections as immunity wanes. The findings highlight the interactions between susceptibility, infection, and temporary immunity, offering insights into effective epidemic control measures.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2025 Meeting
3. Invited

Skibidi, Jabberwocky, and Grationality (MAA-SE Section Lecturer) — Jeneva Clark <dr.jenevaclark@utk.edu>

*“When I use a word, it means just what I choose it to mean — neither more nor less.” - Humpty Dumpty* Creating new words can clarify mathematical communication and logic, especially when forging new pathways. In this session, a few new words will help us approximate rationality in a purely geometric context. These proofs will not use high-powered tools, so leave your slithy toves at home. Instead, we will rely on geometric constructions, proportional reasoning, tiling, dissection, and proof by descent. We will determine whether 3, 4, 5, 6, and 9 are “grational,”as defined below. We will use the stealth of geometry to sneak up on number theory, such as proving all perfect squares are grational. Define a nice-gon to be a regular polygon with integer side lengths in Euclidean geometry. A nice n-gon is a nice-gon with n sides. An integer n is grational if and only if there exists a nice n-gon such that its area equals the sum of areas of n congruent nice n-gons. Open questions about grationality will follow you home and may inspire your next mathventure. What would grationality look like with higher values or with higher dimensions? How is grationality related to rationality? Might grationality be related to the work of Hippasus of Metapontum, described by Plato?

View Submission →

1. 2026 Meeting
3. Special
5. 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.

View Submission →

1. 2026 Meeting
3. 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.

View Submission →

1. 2025 Meeting
3. Sessions
5. RecMath

Some aspects of combinatorial game theory — Tolulope Oke <oket@wfu.edu>

Combinatorial game theory is a branch of mathematics and theoretical computer science that typically studies sequential games with perfect information. Study has been largely confined to two-player games that have a position that the players take turns changing in defined ways or moves to achieve a defined winning condition. In this talk, I will present some ideas about the structural properties of a combinatorial game - in particular, the subtraction game.

View Submission →

1. 2025 Meeting
3. Contributed

Some benefits of co-teaching — Nick Kirby <kirbyn@apsu.edu>

Adopting a new mode of instruction or a new mode of assessment can feel intimidating and isolating as a faculty member. Given the chance to do this with a colleague, I embraced co-teaching as a chance to innovate. Our partnership combined my active learning strategies with my colleague’s expertise in standards-based learning, allowing us to explore how these approaches complemented one another. In this talk, I will share how co-teaching benefited my students and me. Some benefits of co-teaching were expected, but some were only realized in retrospect.

View Submission →

1. 2025 Meeting
3. UGPosters

Speeding Cars and Mixed Distributions — Jadon Jones <jadon.jones@vikings.berry.edu>

In this project, we model the time advantage of speeding on a highway with traffic lights as a stochastic process. The object of study is the sequence of random variables $\{T_k\}$, representing the time benefit of the speeding car at the $k$ th traffic light. For simplicity, we assume identical traffic light cycles with independently distributed initial phases and constant distance between lights. With this simplified model, we investigate the distribution of $T_k$, proving results on the expected value of $T_k$ and deriving the conditional distribution $T_k\vert T_{k-1}$. The first result gives some intuition on the situation being modeled and the second result shows that $T_k\vert T_{k-1}$ and thus $T_{k}$ are examples of mixed distributions. Though the model serves more as a toy model, it provides an interesting example of a family of distributions having both a continuous and discrete part that arises from a simple mathematical model.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2026 Meeting
3. Special
5. 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.

View Submission →

1. 2025 Meeting
3. Sessions
5. DataLit

Statistics Start-Up — Nicole Panza <npanza@fmarion.edu>

Employers are demanding more statistical and data analysis skills from our graduates. In an effort to meet that demand, our Mathematics Department at Francis Marion University implemented a minor in statistics. This talk will discuss how we came to that decision, how we implemented the minor and how it has worked out so far.

View Submission →

1. 2025 Meeting
3. Workshops

Strategies for Targeting and Assessing Conceptual Understanding in Undergraduate Mathematics — Hwayeon Ryu <hryu@elon.edu>

Co-organizer: Aaron Trocki, Elon University, (atrocki@elon.edu) Research on teaching and learning in introductory mathematics courses has identified a need to address underpinning concepts during instruction and on assessments. Faculty teaching these courses are challenged with addressing a plethora of learning objectives in a limited amount of time, which may lead to a focus on lower levels of cognitive demand. All students deserve opportunities to develop their understanding of foundational concepts in mathematics. This workshop highlights innovative practices designed to foster and effectively assess conceptual understanding. We will showcase strategies recently implemented in Calculus I courses that include developing classroom routines to explain concepts; emphasizing application questions; and revising assessments for higher cognitive demand. Workshop participants will learn about these efforts and engage with others to adapt and develop actionable strategies and assessments for the undergraduate mathematics course they teach.

View Submission →

1. 2025 Meeting
3. SectionNExT-SE

Tactile Visualization Techniques for Teaching Calculus — Andrew Miller <andrew.miller@belmont.edu>

In this session, we will look at a wide variety of hands-on activities that could be used to help students better visualize and understand calculus. Many of these activities use fun props, like feather boas, toys, food, and craft items. We will discuss how to use these kinds of activities in your class, how these activities benefit students, and how to modify or develop new activities for your teaching needs. We will physically do most of these activities throughout the session as well.

View Submission →

1. 2026 Meeting
3. Special
5. 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.

View Submission →

1. 2025 Meeting
3. Sessions
5. RecMath

Temari Projections on Assorted Surfaces — Shemsi Alhaddad <alhaddad@email.sc.edu>

Temari is a traditional Japanese fiber art in which designs are stitched to the surface of a ball. Many Temari designs begin with a geometric partition of the sphere. Temari designs can be viewed through the lens of recreational math as it is a leisure art with mathematical properties. In this presentation, I will first describe a standard procedure for partitioning Temari balls. I will then demonstrate application of this procedure to difference surfaces. Finally, I will compare the results to standard mathematical projections, such as stereographic and cylindrical projections.

View Submission →

1. 2026 Meeting
3. Special
5. 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.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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

View Submission →

1. 2025 Meeting
3. SectionNExT-SE

The ABCs of Alternative Ways to Assign A's, B's, C's... — Amanda Mangum <amanda.mangum@converse.edu>

This session will give an introduction to alternative grading methods. The basics of two alternative grading structures and some of their variations will be detailed, and examples from courses taught under these parameters will be shown. Participants will have the opportunity to think through the structures and discuss how they might apply them to courses they teach.

View Submission →

1. 2025 Meeting
3. UGTalks

The Danceability Index — Lila Snodgrass <lsnodgrass@elon.edu>

In this presentation, we will introduce a new knot invariant, the danceability index, which draws inspiration from the dynamic movement of dancers across a stage. We will examine the connections between this invariant and two other fundamental knot invariants: the braid index and the bridge index. Designed with an undergraduate audience in mind, this talk will offer a brief yet informative overview of the key concepts and foundational ideas within the field of knot theory.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2025 Meeting
3. Sessions
5. RecMath

The Gauss-Bonnet theorem and triangular Tangles — Doug Torrance <dtorrance@piedmont.edu>

A Tangle is a smooth closed curve formed by the union of arcs of congruent circles, known as links. We use the Gauss-Bonnet theorem to prove an interesting result about the number of concave v. convex links in a Tangle. This in turn allows us to show that all "triangular Tangles" (planar Tangles formed from sixths of circles) may be constructed by a sequence of fundamental operations starting from a circle.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2025 Meeting
3. Sessions
5. UnspokenHistory

The Life and Work of Shing-Tung Yau — Zachery Keisler <zkeisler@saludaschools.org>

Shing-Tung Yau is one of the most prolific geometers alive today, from being awarded the Fields Metal in 1984 for his contributions to partial differential equations and his proof of the Calabi Conjecture in algebraic geometry to publishing his book titled The Shape of Inner Space: String Theory and the Geometry of the Universe’s Hidden Dimensions with Steve Nadis in 2010. Today's talk will examine the major life events that molded Shing-Tung Yau into the geometer he is today while also examining the many contributions he made in the field of mathematics as a whole.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2025 Meeting
3. Contributed

The Maximum Likelihood Degree of the $\beta$-Stochastic Blockmodel — Jennifer Garbett <jennifer.garbett@lr.edu>

Statistical network models are used across the sciences and social sciences in settings such as modeling microbiomes and understanding protein interactions in biology and understanding friendships and strategic alliances in the social sciences. The $\beta$-stochastic blockmodel is a statistical network model that is useful in describing relational data that exhibit homophily, the tendency for certain individuals to group together. In the $\beta$-stochastic blockmodel, individuals are represented by nodes in an undirected graph which are grouped into blocks based on shared characteristics, and each edge is equipped with a parameter that measures the likelihood that the individuals represented by the nodes at each end interact. Ideally, one would like to determine the model parameters for the model that best fits a given dataset. We can measure the algebraic complexity of this problem by computing the maximum likelihood degree, the number of solutions to a set of likelihood equations associated with the model, for generic data. We explore the maximum likelihood degree for the $\beta$-stochastic blockmodel culminating in a multiplicative formula. Relevant background will be included in the talk, and the talk should be accessible to most.

View Submission →

1. 2026 Meeting
3. 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.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2026 Meeting
3. 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.

View Submission →

1. 2026 Meeting
3. 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.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2025 Meeting
3. UGTalks

Theory to Identity: The Role of Mathematical Modeling in Shaping Graduate Students as Mathematicians — Christina Anderson <cande140@vols.utk.edu>

Students have a rare opportunity to combine fundamental concepts with practical applications in the mathematics classroom, even at the graduate level. In order to understand how their courses, interactions with peers, mentors, and multidisciplinary projects contribute to their developing sense of self as mathematicians, this study looks at the experiences of graduate students and instructors who are actively involved in advanced mathematical studies. In addition to addressing the difficulties students encounter in striking a balance between mathematical precision and real-world application, the study highlights the crucial role modeling plays in promoting competence, confidence, and professional purpose. These results highlight how important it can be to incorporate mathematical modeling as an instructional method and not just a course. This will foster identity formation and get students ready for meaningful employment in mathematics and related disciplines.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2025 Meeting
3. Contributed

Two refinements of Fubini numbers — Kyle Celano <celanok@wfu.edu>

The Fubini numbers (aka ordered Bell numbers) F_n (A000670) count the number of ways n runners can place in a race, with ties. In this talk, we consider two refinements of F_n: first, by grouping placements by the number of pairs of runners where the runner with the higher bib finishes before a runner with a lower bib; second, by how many runners tie at each place. The former refinement leads to a polynomial refinement of F_n and the latter leads to a symmetric function refinement of F_n. We derive simple generating functions and recurrence relations for both refinements. Moreover, we show that the symmetric function results implies the polynomial results through a general theory on word enumerators. We further view these results in the same sphere of results of Konheim--Weiss (1966) and Haiman (1994) on parking functions by interpretting Fubini words as unit interval parking functions of Harris--Hadaway (2021) and Bradt et al (2024).

View Submission →

1. 2025 Meeting
3. Sessions
5. UGRMentors

Undergraduate Research: Recruitment, Retention, Mentoring — Shalmali Bandyopadhyay <sbandyo5@utm.edu>

This presentation shares my experiences and insights from undergraduate research mentoring at my current institution, UT Martin. I discuss the challenges and successes of integrating multiple disciplines, navigating the mentor-mentee relationship and promoting student autonomy in team-based research. This reflective analysis aims to contribute to best practices in undergraduate research mentorship, highlighting the benefits and complexities involved and challenges faced as an entry-level faculty member.

View Submission →

1. 2025 Meeting
3. Contributed

Use of AI Models to Detect Handwritten Digits — Cameron Tillett <ctillett1@my.apsu.edu>

My presentation introduces an AI model to detect and accurately classify handwritten digits from 0 to 9. The model utilizes a neural network architecture trained on a large dataset of handwritten numerals to achieve high accuracy in digit recognition. The model is optimized to consider handwriting style deviations and noise through preprocessing methods like normalization and data augmentation. The results present great efficiency, with the model performing near-human accuracy on standard datasets such as MNIST. This project displays possibilities for deep learning in practical applications such as digit recognition for forms, checks, and automated data entry systems.

View Submission →

1. 2026 Meeting
3. Special
5. 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.  

View Submission →

1. 2026 Meeting
3. Special
5. 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.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2025 Meeting
3. Sessions
5. FavoriteProb

Using High School Competition Problems to Create Rich Mathematical Tasks for Undergraduate Mathematics Students — Doug Ensley <dougensley@gmail.com>

In this talk we will share some specific problems from MAA competitions (pitched at middle- and high-school students), and we will show how these problems can be deconstructed and adapted to create engaging content for undergraduate students that promote active learning by intentionally addressing communication and problem-solving standards. Topics will include elementary number theory, combinatorics and probability in the context of an introductory course in discrete mathematics.

View Submission →

1. 2025 Meeting
3. UGTalks

Using Math to Win Fantasy Football — Gabe Boone <gabriel_boone@mhu.edu>

This presentation explores how mathematical strategies can give one an advantage in fantasy football. It covers key aspects of success, including drafting strategies, managing lineups, and making trades, while emphasizing the importance of adapting to changing player performance and injuries throughout the season. The presentation also discusses playoff preparation and analyzes the role of probability and projections in improving one’s chances of success. Through examples and statistical insights, it demonstrates how consistent, informed decision-making leads to better outcomes in fantasy football.

View Submission →

1. 2026 Meeting
3. Special
5. 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.

View Submission →

1. 2025 Meeting
3. Contributed

Using Polypad in university mathematics content courses — Kevin LoPresto <klopresto@fmarion.edu>

This session will showcase the utilization of Polypad, an online collection of virtual manipulatives, to facilitate the instruction of diverse mathematical concepts in mathematics content classes for students pursuing early childhood and elementary teaching certification. The demonstrations will encompass self-assessment activities, the dynamic utilization of pattern construction, and the implementation of drag-and-drop functionality. The subsequent discussion will focus on integrating this tool within the Desmos platform or as a standalone application.

View Submission →

1. 2026 Meeting
3. Special
5. 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.

View Submission →

1. 2025 Meeting
3. Contributed

Using teacher.desmos to help mathematics students write papers — Julie Barnes <jbarnes@wcu.edu>

While teaching our capstone class in Fall 2024, I realized on an early assignment that many of my students were so used to writing proofs that they assumed writing a math paper meant pasting a bunch of proofs together with little to no exposition between proofs. To help them bridge the gap between proving a homework problem and writing a paper, I developed an activity in teacher.desmos that broke down portions of the writing process into smaller steps. Students responded real-time in class to various prompts and could see each others’ responses anonymously. This generated a class discussion about how best to connect ideas in their papers. The activity generated positive feedback both in the moment and on end of course evaluations. In this talk, I will explain how to use the free resource teacher.desmos to do an activity like this, show details on how I organized it, share samples of what the students wrote, and quote some comments from evaluations. If possible, we will end the talk with a short audience participation demonstration of how it works.

View Submission →

1. 2026 Meeting
3. Special
5. 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.

View Submission →

1. 2025 Meeting
3. Contributed

Voting Theory to Blow Your Mind — Adam Graham-Squire <agrahams@highpoint.edu>

Many college courses teach Voting Theory, including topics like Ranked-Choice Voting and voting criteria failure. Students sometimes ask if these voting anomalies have ever occurred in real-world elections, which is hard to answer because the underlying data is often hidden. In this talk, we pull the curtain back and discuss some interesting recent elections in which voting anomalies have occurred. We will also have this data available for any instructors who want to use it in their classes.

View Submission →

1. 2025 Meeting
3. Contributed

What a brain injury taught me about accessibility in mathematics — Megan Powell <mpowell4@unca.edu>

In 2020 I suffered a traumatic brain injury from a fall. While I have been lucky enough to be able to keep doing and teaching mathematics, the sudden change in my brain’s ability to process information presented an immediate need for accessibility tools and accommodations for myself which gave me a new perspective of accessibility in mathematics in general. In this talk, I will discuss simple ways to support student learning in the classroom and present existing tools and the need for additional tools to help move towards everyone having equal access to learn and do mathematics.

View Submission →

1. 2026 Meeting
3. Undergrad
5. 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.

View Submission →

1. 2026 Meeting
3. Special
5. 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.

View Submission →

1. 2026 Meeting
3. 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.

View Submission →

1. 2026 Meeting
3. Special
5. 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.

View Submission →

1. 2025 Meeting
3. UGTalks

“Using Multiplication and Addition to Manipulate Sequences Equating to 0 modulo n” — Ryan Legg <rlegg@student.citadel.edu>

This poster was created from Mathematics Magazine Problem 2204. In any sequence, does there exist a way to manipulate how the terms of the sequence are added and multiplied to form a solution equivalent to 0 mod n, where n is the number of terms in the sequence? We look at whether this was possible by examining several sequences of numbers, differing in length and combination. Using techniques such as trial and error, as well as picking up on several different patterns, a method was formed to help prove that any sequence can be multiplied and added together in such a manner that the sequence could always come out to a remainder of zero. We prove that any sequence of numbers could be arranged in a certain way so that when multiplied and added together, there would always be a remainder of 0 modulo n.

View Submission →