Math Research
Research is a fundamental aspect of our mathematical lives. Mathematics is about asking questions and searching for answers. Students do this in class and in assignments, and the faculty do this preparing for class and pursuing their own mathematical interests outside of class. Here are some of our interests.
Adam Childers: parameter estimation. Given the general structure of a mathematical process is known, the goal is to use a small number of data points to determine the fine details of the model.
Chris Lee: genetic programming. Starting from a number of random guesses, the computer program quickly converges to a solution by modifying the best of the guesses and continuing to improve the guesses.
Roland Minton: sports science. The golf tour measures all shots to the inch; the analysis of the resulting data set reveals patterns in performance and allows a ranking of professionals.
Maggie Rahmoeller: Lie algebra representation theory. This field represents sets of matrices (Lie algebras) as certain types of functions and studies these representations.
Hannah Robbins: associated primes of local cohomology modules. This area of commutative algebra studies the properties of mathematical structures such as polynomials to find useful patterns.
Karin Saoub: graph coloring. This area of graph theory focuses on connections of entities that can be distinguished ("colored"), with applications in scheduling and network analysis.
David Taylor: games and gambling. The determination of optimal or near-optimal strategies for various games creates interesting and intricate probability calculations.
We strongly encourage students to participate in research projects. Topics for independent studies often come from the students, either from a topic mentioned briefly in a class or from discussions of possibilities with the faculty. Here are some of the recent topics that have been explored.
Mathematics of Games: Jon Marino studied the occurrence of familiar number patterns in Blackjack probability calculations.
Mathematics of Gambling: Heather Cook studied optimal strategies in a new variant on a card game, Blackjack Switch.
Mathematics of Cell Dynamics: Paul Vines developed a model of iron metabolism in breast epithelial cells.
Mathematics of Networks: Sarah Witt studied various measures of influence in social networks (Facebook).
Mathematics of Plant Growth: Akram Sublouban studied L-systems, a fractal model of plant growth.
Mathematics of Sports: Sky Weber computed and compared the expected runs matrix for ODAB baseball to major league values.
More examples of independent studies can be found at this link.