1. Sessions
3. 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.

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1. 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.

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1. Sessions
3. 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.

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1. 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.

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1. 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.

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1. Sessions
3. 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.

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1. 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.

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1. 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.

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1. 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.

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1. 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.

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1. 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.

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1. Sessions
3. 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.

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1. 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, $\bigcap_{f \in \mathcal{L}\mathbb{A}}D_f = \{0,1\}$.

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1. 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} $.

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1. Sessions
3. 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.

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1. 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.

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1. 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.

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1. 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.

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1. 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.

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1. 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.

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1. 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.

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1. 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.

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1. 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.

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1. Sessions
3. 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.

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1. 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.

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1. 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.

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1. 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”.

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1. Sessions
3. 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.

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1. 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.

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1. Sessions
3. 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.

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1. 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.

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1. 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 $100 \,000!$.

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1. 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.

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1. Sessions
3. 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.

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1. Sessions
3. 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.

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1. 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.

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1. Sessions
3. 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.

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1. 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.

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1. 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.

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1. 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.

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1. 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.

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1. 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.

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1. 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.

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1. Sessions
3. 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.

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1. 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.)

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1. 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.

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1. Sessions
3. 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.

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1. 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.

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1. Sessions
3. 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).

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1. Sessions
3. 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.

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1. Sessions
3. 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.

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1. 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.

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1. 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.

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1. 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.

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1. 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.

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1. 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.

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1. Sessions
3. 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.

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1. 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.

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1. 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.

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1. 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.

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1. 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.

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1. Sessions
3. 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.

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1. 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.

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1. 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.

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1. 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.

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1. Sessions
3. 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.

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1. 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.

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1. 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.

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1. Sessions
3. 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.

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1. 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.

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1. 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.

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1. Sessions
3. 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.

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1. 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.

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1. 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!

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1. 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

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1. 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.

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1. Sessions
3. 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.

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1. 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.

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1. Sessions
3. 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.

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1. 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.

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1. 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.

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1. Sessions
3. 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!

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1. 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.

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1. 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.

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1. Sessions
3. 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.

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1. 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.

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1. 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.

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1. 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.

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1. Sessions
3. 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.

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1. 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.

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1. 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.

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1. 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.

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1. 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.

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1. 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.

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1. 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. 

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1. 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.

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1. 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.

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1. Sessions
3. 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.”

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1. Sessions
3. 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.

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1. 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.

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1. 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.

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1. Sessions
3. 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.

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1. 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.

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1. 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.

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1. 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.

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1. 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 $4 \leq k \leq 6$.

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1. Sessions
3. 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.

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1. 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.

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1. 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.

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1. 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.

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1. 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.

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1. 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.

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1. 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.

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1. 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?

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1. Sessions
3. 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.

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1. 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.

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1. 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.

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1. Sessions
3. 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.

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1. 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.

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1. 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.

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1. Sessions
3. 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.

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1. 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.

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1. 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.

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1. Sessions
3. 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.

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1. Sessions
3. 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.

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1. 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.

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1. 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.

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1. 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).

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1. Sessions
3. 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.

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1. 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.

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1. Sessions
3. 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.

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1. 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.

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1. 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.

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1. 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.

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1. 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.

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1. 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.

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1. 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.

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