Undergraduate Research in Mathematics

Senior Projects 2015

Cathie Bisher - An Examination of Mathematics Anxiety and Self-Efficacy in Preservice Teachers, Advisor Dr. Carla Gerberry Assisted by Dr. Max Buot

We look at the significance of mathematics anxiety and mathematics self-efficacy and the role that each plays with respect to pre-service teachers. This study includes an examination of the differences between the levels of math anxiety and math self-efficacy for pre-service middle school teachers and pre-service elementary school teachers with respect to various Number Sense topics. The results from a variety of statistical tests are compared and the validity of each result is examined with a particular focus on the issues that arise due to a small sample size.


Anne Farwick - Fixed Point Iteration, Advisor Dr. David Gerberry

A fixed point for a function is one such that f(p) = p. Iterative techniques that can find or approximate these fixed points are referred to as fixed point iterations. In this paper, we will discuss the theory of fixed point iterations as well as some common applications. We discuss convergence results for a basic one-dimensional fixed point problem with applications that involve root finding and its use in discrete population models. We generalize this method for use in solving linear systems with a focus on large, sparse linear systems. Specifically, we use the Jacobi and Gauss-Seidel iterative methods to find a solution to the equation A~x = ~b, that arise from discretizing partial differential equations.


Veronica Fatoyinbo - Mathematical and Algorithmic Applications of Linear Algebra, Advisor Dr. Esmeralda Nastasee

Linear Algebra is a useful tool in modeling and solving a variety of mathematical problems. In this project, we researched problems from combinatorics, graph theory, and analysis and used clever linear algebra techniques to determine their solutions. In this paper, we introduce a few of these problems, and present the linear algebra techniques employed, and how these lead to their solutions.


M'Kai Folley - The Linear Algebra Behind Rankings, Advisor Dr. Minnie Catral

The aim of this project is to study applications of the Perron-Frobenius Theorem for nonnegative irreducible matrices. The first half of the project discusses how Google applies the Perron-Frobenius theorem to study of systems with unique rankings, non-unique rankings, and dangling nodes to calculate importance scores. The second half of the project is an application of the Perron-Frobenius Theorem to find the most common played genre of music played.


Matt Jones - Applying Time Management to Computer Go, Advisors Dr. Liz Johnson and Dr. Bernd Rossa

In games where each player is allowed a certain amount of time to play, allocating this time effectively is important. This topic, time management, has been researched in many games, but relatively little in the field of computer Go, where Monte Carlo Tree Search has become the dominant algorithm.

I introduce a new time management formula that significantly improves the strength of a modern Go program. I also introduce new time management heuristics that provide even further significant improvement.


Mark Miller - Modeling Harmful Algal Blooms in the Western Basin of Lake Erie and an Economic Solution, Advisor Dr. Hem Raj Joshi

In August of 2014, the city of Toledo, Ohio (population approximately 500,000) was without drinking water for roughly three days due to a harmful algal bloom of Microcystis aeruginosa lingering around the city's water intake. A major ecological control of algal species is Dreissena polymorpha, more commonly known as the Zebra Mussel. The purpose of this paper is to compose a mathematical relationship between algal species and the Zebra Mussel through an ecological predator-prey model-the Lotka-Volterra model-and explore possible economic solutions to the issue.


Alexandra Mueller - A Stochastic Cellular Automata Model for Criminal Behavior, Advisor Dr. David Gerberry

While criminal activity in a city has certain fixed characteristics (i.e. high and low crime areas), there is also a temporal component that forms hotspots. I have created a cellular automata model for burglary that includes the dynamics of burglars and attractiveness landscape, which changes based on criminal activity. Using different parameters, the model shows different spatial hotspot dynamics. To determine its applicability, I have parameterized the model for San Francisco.


Evan Weaver - Application of Variable Selection and Ridge Regression Using Commuting Data, Advisor Dr. Max Buot

This project studies different linear regression methods within the context of commuting and traffic fatality data collected in the United States. Specifically, I investigate various model selection techniques, such as forward stepwise regression, and examine the differences between selection statistics, such as the Akaike Information Criterion (AIC), the Bayesian Information Criterion (BIC), and adjusted R2. As these tools are used to identify a constructive subset of explanatory variables for regression, we also compare ordinary least squares estimation to ridge regression, a method that generally decreases the standard errors for parameter estimates.