The Mathematical Association of America Maryland-District of Columbia-Virginia Section

Running undergraduate research at a smaller university can create roadblocks ranging from lack of faculty, funding, and student excitement. This talk will outline the triumphs and tribulations we have faced in conducting research with undergraduates at our university. We will go through anticipated timelines and research expectations our students experience and how we collaborate with other departments. The talk will finish with a group discussion for others to share their own experiences.

Math Theme: Let A and B be mxm matrices and let n>1 be given. Then AB=BA implies (A+B)^n can be expressed using the binomial theorem. The implication is not bidirectional. That is, the binomial expansion may be valid even when AB is not equal to BA. Families of examples will be presented. Methodology Theme: investigated collaboratively with the Google AI agent. The agent carried out finicky algebra (mostly correctly), composed summaries of discussions as latex documents with no coding errors, and contributed algebraic and logical insights the human author missed.

In this talk, we will present a way to parametrize all integer triangles with a given rational cosine. We will also touch on approaches that already exist in the literature. Our parametrization gives rise to linear transformations that can be used to generate integer triangles with a given rational cosine.

We often meet students that say that they don't like math. If you hear their stories, however, it is more of a story about how they felt frustrated when they were not able to understand the math that they had to learn. No one likes the feeling of being confused in the classroom. As educators of mathematics, it is our duty to teach mathematics, whatever level it is, in a way that the students can understand and follow. Once we can do this, with carefully selected fascinating topics, we can truly share the beauty and importance of mathematics to a broad audience. In this talk, I will talk about how I was able to spark students' interest in mathematics in my courses of various levels from General Education classes for non-STEM majors to upper-level math courses such as Numerical Linear Algebra. I will also talk about how mathematics and programming can be used together to accomplish this goal.

Quantum computing is fundamentally a mathematical subject, grounded in linear algebra, probability, and abstraction rather than physics hardware. This talk argues that quantum computing fits naturally within the mathematics curriculum, where concepts such as vector spaces, tensor products, and unitary transformations take on new computational meaning. Drawing on my experience teaching a quantum computing course this semester, I will highlight how the subject enriches core mathematical training while preparing students for a rapidly emerging interdisciplinary field.

In a typical second semester calculus course, Taylor polynomials can be introduced earlier and used to understand several topics with greater depth and understanding. We will illustrate one example of this and discuss other possibilities if time permits.

In this talk we will discuss two math/art/code projects that use crochet as a medium for "stealth outreach" to nontraditional audiences. The recently completed "Granny Life" project engaged over 100 crafters in a community math/art project that is currently in an exhibition in Paris, France. Our new project "AutoScarf" uses customized 1D cellular automata to create self-generating scarf patterns that participants around the world will use to generate one million hand-crafted algorithmic stitches. At the end of the talk we will provide an open invitation to participate in this new project.

This study investigates the density estimation of the Continuously Compounded Returns (CCR) for five major U.S. stocks over a four-year period (April 2022 – April 2026). Given that financial returns often exhibit non-normality, we employ Variance Mixtures of Normals to capture the underlying market regimes of the CCR. Using approximately 1,000 daily closing price observations, we compare three estimation frameworks: a Bayesian approach, the Expectation-Maximization (EM) algorithm, and the UNMIX model. The performance and fit of these models are evaluated and compared using Chi-square tests and other goodness-of-fit metrics. Our findings aim to identify the most robust modeling approach for better capturing both the body and the tails of the CCR density.

In this talk we will present a one dimensional functional, which is used in modeling materials with memory effects. We will start with a demonstration of such shape memory alloy. The patterns, formed in it, minimize certain nonconvex, singularly perturbed energy functional. By means of sharply matching upper and lower bounds, we show that this functional admits a unique, explicit minimizer - a rare finding in nonconvex minimization problems of this type!

Generalized Linear Models offer a cohesive, diverse and easy to use framework for statistical modeling. Unfortunately, they lack a continuous finite domain probability distribution. In this project I compare two plausible models: beta regression(a flexible regression model that deviates from the GLM framework) and binomial regression(a more rigid, but still plausible generalized linear model). I collected data by surveying 25 general education classrooms in Shenandoah University to find predictors of various positive and negative emotions. The survey asked questions relating to motivation, experience, and confidence which were used alongside some classroom information like subject and time as features to predict emotions. Correlations were modeled using beta regression and binomial regression and the two models were compared.

The study of baseball through data and statistical analysis has been an ever-increasing phenomenon. It stems from the urge to increase knowledge about strategy and player effectiveness. This work aims to investigate three distinct states of the game and report on the trends that appear during them and what they mean for the Virginia Military Institute’s baseball team and the sport as a whole. Specifically, it will address the noticeable trends in VMI pitchers in terms of their predictability for pitch type and pitch location, trends in the signs of an expected run value when modeled by physical and game-state variables, and how batting physics relate to outage percentage.

Let \(G = (V, E)\) be a graph with adjacency matrix \(A(G)\) and Seidel matrix \(S(G) = J - 2A(G) - I\). We examine the characteristic polynomial, \(\phi(S(G))\), of the Seidel matrix. We prove a general form for the coefficients of some terms of \(\phi(S(G))\) for all graphs on \(n\) vertices. We also prove a general form for the Seidel characteristic polynomial for the complete bipartite switching class and its complement.

Every year the population for English Learner (EL) students increases in K-12 classrooms. This has raised questions about how teacher preparation programs can better equip future educators to support linguistically diverse learners in mathematics classrooms. This study examines whether education majors and non-education majors support requiring education majors to complete at least two Spanish courses as part of their teacher preparation. Spanish is the second largest language used in the United States, which means a large portion of EL students' primary language is Spanish. Using a cross sectional survey design, undergraduate students will be recruited, surveyed, and categorized as education majors and non-education majors. Participants will rate their level of support using a six point Likert scale. A two sample t-test will be conducted to determine whether a statistically significant difference exists between the mean levels of support reported by the two groups.

Testing water quality is critical to measuring environmental change and ensuring the health of an ecosystem. With the necessity of expensive equipment to measure water quality directly, environmental stewards implement citizen-led macroinvertebrate bioassessment programs, like Virginia Save-Our-Streams as a "canary in the coal mine" to identify environmental stressors in aquatic systems. The proportion of mayflies, caddisflies and stoneflies in a freshwater ecosystem has been shown to be an effective proxy for water quality. But the process of identifying these species requires extensive training and time investment. For this reason we have developed an image-based convolutional neural network (CNN) capable of classifying the three taxa from field photographs, eliminating the need for expert identification. Our initial results demonstrate promising classification accuracy across the three taxa, laying the groundwork for a deployable field tool.

Classical ciphers are a symmetric form of encryption, meaning they require the same key to be used for encryption and decryption. The Key-Sharing Problem is the challenge of securely sending and receiving these keys in a public channel. We consider methods of overcoming this problem for several ciphers by making use of Elliptic Curves (ECs). We then examine implementations of the resulting asymmetric key-exchange algorithms in python and discuss the trade-offs between traditional approaches and the EC key exchanges.

Math anxiety is a persistent issue among college students that can negatively impact performance, confidence, and motivation in math courses. The goal of this research study is to examine which academic support methods Shenandoah University college students use to help themselves with math anxiety and which methods students perceive as most effective in helping them succeed. Research was conducted using two surveys, one at the beginning and one at the end of a semester, with questions related to math anxiety, the three outlined support methods, and students' perceived effectiveness of those methods. The key findings of this research study are that low levels of confidence in math lead to more math anxiety, students feel their low math confidence stems from a lack of foundational skills, it doesn’t matter how effective students think a support method is if they still choose not to use it, if you have liked your past math teachers you’re more likely to be confident and less anxious in your current math class, and anxiety and confidence play a role in students deciding whether or not to make steps to help themselves in math. These findings helped inform the development of two proposed intervention programs for students to be more confident and less anxious when going into their math classes. The first proposed intervention is a structured review program at the beginning of every semester, which is focused on building and reviewing basic math skills so students feel prepared for their class. The second intervention program requires or gives an incentive to students to get tutoring so they are more proactive in their learning and less reactionary.

Modern AI development has two primary bottlenecks: hardware limitations and the architectures running on top of them. As transistor scaling slows, traditional silicon-based and von Neumann architectures struggle to meet growing computational and energy demands of large machine learning workloads. The widespread adoption of AI in business and consumer applications means that routine AI training and testing workflows have become a common business requirement. Data center energy consumption has risen as natural language processor and large language model implementation continues to grow. Resource consumption is projected to increase, with data center projects to be constructed nationwide within the next 10 years, specifically dedicated to AI training and research. To mitigate the computational and environmental impact of this growth, researchers have begun exploring biologically inspired alternatives that utilize properties of neural systems. Two methods have emerged from these experiments: synthetic biological semiconductors, and brain organoids derived from stem cells. Both methods utilize characteristics of neural networks, like parallel processing and nonlinear dynamics. Researchers have begun examining neural structures as dynamical systems using living neurons cultured from stem cells into small brain-like organoids. Organoids may provide parallel, dynamic, energy-efficient compute power suitable for machine learning applications. Early studies show that integrated neurons may be able to more efficiently support machine learning workloads using a fraction of the energy requirements of a traditional CPU/GPU architecture. This review synthesizes current research in neuromorphic and biological computing to evaluate their potential as a sustainable next generation in AI architecture.

Mathematical origami is a theoretical extension of paper origami where the complex plane can represent an infinitely large piece of paper, and the “folds” of this paper are represented by a set of allowed angles. We study the structure of the set of intersection points between all pairs of angles. This has been well described in 2 dimensions; however, little is known about them in multidimensional space. We determine how an origami set that generates a lattice in three-dimensional space is altered by introducing an additional allowed angle. We also implement an algorithm in SageMath that computes the intersections of pairs of allowed angles from given starting points. The algorithm then computes the projections from the new intersection points back onto the real number line.