2024 COES Design and Research Conference

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Mathematics and Statistics Senior Projects

Integrated Engineering and Science Building 126.

1:00 p.m.	Internal Consistency in NCAA Gymnastics Scores Advisor: Nathan Ponder The aim of my research is to examine internal consistency in relation to the validity of scores in NCAA Women’s Gymnastics. This study focuses on scores from the now infamous 2024 Tennessee Collegiate Classic. Patterns from several different deviations and correlation coefficients are analyzed, and a “gold standard” score to test against is created. This allows me to identify several patterns in results that could signify invalid scores.
1:30 p.m.	Handle Number of Toroidal Graphs Advisor: Stacey McAdams We define a characteristic of toroidal graphs called the handle number. The handle number is the minimum number of edges which must traverse the handle in a toroidal embedding of a graph. After defining the char- acteristic, flat polygon projections are used to explore efficient toroidal embeddings. Using this exploration we then show an upper bound for the handle number of toroidal graphs. Finally, we prove an inequality between the handle number and graph skewness and conjecture an equality.
2:00 p.m.	Faculty Diversity and Minority Enrollment in Advanced STEM Courses: A Case Study at Neville High School Advisor: Stan McCaa This study investigates the correlation between the diversity of STEM faculty and the enrollment rates of minority students in honors, Advanced Placement (AP), and dual enrollment STEM courses at Neville High School. Recognizing the long-standing underrepresentation of minority students in advanced STEM education, this research explores whether a more diverse faculty positively influences student participation in these courses. Using a quantitative correlational design, data on faculty demographics and student enrollment patterns were analyzed through logistic regression and chi-square tests of independence. Comparative data from the English department served as a control to assess discipline-specific effects. Results are expected to provide insights into the role of faculty diversity in fostering equitable academic opportunities. The findings may inform educational policies and encourage recruitment and retention of diverse educators, ultimately contributing to a more inclusive learning environment in STEM education.
3:00 p.m.	Quarterback Statistics vs. Season Success Advisor: Stan McCaa The purpose of this research is to determine which quarterback statistic most significantly impacts team success in the National Football League. By analyzing data from quarterbacks with at least 100 pass attempts per season from 2006 to 2023, we examine the relationship between quarterback rating, passer rating, completion percentage, and TD-INT ratio with end-of-season power rankings. We ran the data through multiple linear regression models to identify which statistic has the strongest correlation with team performance. Our model considers variations across different seasons and accounts for statistical trends over time. With over 17 seasons of data analyzed, further exploration could refine the findings by incorporating additional variables or alternative modeling approaches.
3:30 p.m.	An Analysis of the Alaskan Salmon Harvest Advisor: Xiyuan Liu The objective of this paper is to analyze the annual Alaskan salmon harvest and the variables that affect the harvest differently each year. Every year, thousands of workers livelihoods depend on the annual salmon harvest to provide for themselves and their families. This paper takes this reality and aims to use data gathered from previous fishing seasons to understand what variables affect the salmon population. To analyze the salmon harvest, multiple linear regression will be used over a 41 year period with variables including water temperature, air temperature, yearly harvest, and species of salmon. By modeling these and other variables, we should be able to understand which variables affect the salmon population positively and negatively.
4:00 p.m.	Explorations of Plane Graphs with No Odd Faces Advisor: Galen Turner In this paper, we will explore the intersection of two classes of graphs which are foundational in graph theory. The class of planar graphs, P, and the class of bipartite graphs, χ2. In particular, we will explore the edge-maximal graphs in the intersection. Excluded minors are well studied, and the two fundamental operations of deletion and contraction have become core to the field. The focus of our work is to consider the operations in reverse – that is, through single-edge extensions and single-edge co-extensions in the class P ∩ χ2, namely those graphs that are planar having chromatic number 2.