Senior Projects 2025

Spencer De Tenley, Maximal Green Sequences of Circulant Quiver, Advisor Dr. Eric Bucher

My research explores circulant graphs, graphs oriented in a circular fashion, and specifically directed circulant graphs called circulant quivers. In exploring these circulant quivers I look specifically at their framed quiver counterparts which add additional vertices in a specific way. The framed quivers then allow for maximal green sequences, a sequence of mutations which transform a quiver, to be found. In this presentation I will discuss the process of mutating framed quivers to find their maximal green sequences and specifically look at a strategy I found for a subset of circulant quivers.

 

Delaney Doorhy, Teaching Geometry vs. Precalculus: A Comparative Study of Pedagogical Approaches, Advisor Dr. Carla Gerberry

This study presents a comparative analysis of the pedagogical techniques employed in teaching high school Geometry and Precalculus. By examining instructional strategies, methodologies, and learning outcomes in both subjects, the research identifies key differences and similarities in teaching approaches. Additionally, the research explores the types of assessments and questions used to measure student understanding and achievement. The findings reveal that while Geometry emphasizes conceptual foundations, logical reasoning, and proofs, Precalculus focuses more on application and problem-solving. Despite these distinct approaches, both subjects are interconnected, with Geometry serving as a critical foundation for the concepts explored in Precalculus. Ultimately, the study highlights how these differing pedagogical strategies shape students' readiness for more advanced mathematical studies.

Brandon Launer, An Introduction to Partition Theory, Advisor Dr. Danny Otero

This research provides an introduction to partition theory, focusing on its fundamental definitions and applications. We will analyze the structural composition of partitions, the role of generating functions under various constraints, and the use of visual representations in understanding partition properties. Furthermore, we will examine the application of pentagonal numbers in partition theory and review the foundational contributions of Euler and the subsequent advancements made by mathematicians such as Sylvester, MacMahon, and Subbarao.

Will Scheske, A Bijection Between Matrix Representations of Ascent Sequences, Advisor Dr. Eric Bucher

Mtxn and Mtxn' are two types of upper triangular n x n matrices with non-negative integer entries. These matrix types were defined and shown to be in bijection with ascent sequences by Dukes and Sagan and Dukes and Parviainen, respectively. However, Dukes and Sagan left the direct bijection between the two types of matrices without using ascent sequences as an open question in their paper. Thus, this project will describe a direct bijection between Mtxn and Mtxn'.

 

Jenna Wagner - Predicting the “Perfect” Bracket for the NCAA Women’s Basketball Tournament Using R Studio, Advisor Dr. Max Buot

The NCAA Division I Women’s Basketball Tournament, also known as "March Madness," takes place annually, following the regular season and conference tournaments. In my project, I focused on developing a statistical model to predict a "perfect" bracket. Season and tournament data from 2010 through 2015 were used to develop a multiple logistic regression model in R, which incorporated differences in rankings and percentages across multiple statistics. Additionally, I tested the model using data from this year’s women’s tournament, applying the same statistical methods to evaluate the first-round matchups and season stats to make predictions.