William (Alex) Toussaint
For the coming spring 2003 semester, I hope to work with Professor Russel Carlson as an Undergraduate Research Assistant. The project that he and I have selected is a practical application of relatively simple Linear Algebra concepts toward the world of sports (specifically, NCAA Basketball). It is my goal to develop an effective way to rank college basketball teams (the system could then be used for any other sporting event), and hopefully to have the rankings that it determines published in the sports section of the Daily Wildcat.
Numerous mathematical schemes exist for ranking teams based on their results using matrices known as “tournament matrices”. As the first step of my research project, I will do background research into the different ranking systems that have already been developed, and the relative merits of each. For example, one of the largest challenges is the creation of a system that can break ties between two teams with equal records, without creating the possibility of inconsistencies where teams with less wins are ranked higher than teams with more wins. Once I have researched the various methods that have been developed previously to solve similar problems, I will use what I have learned to develop an effective system for ranking teams within a certain conference, and possibly ranking all teams in the country, using technological aids such as Maple. It is my goal to develop a system that is both relatively easy to use and which gives results that make logical sense (in other words, which avoid the common problem outlined above). Hopefully his system can then be applied and improved upon in the future.
I am personally very excited to participate in the unique opportunity that an Undergraduate Research Assistantship provides. I look forward to working with Dr. Carlson, and to having the chance to explore one of the many real-world applications of mathematics, that I most likely would not be introduced to as a part of standard classroom instruction. I look forward to building upon my great experience these previous two semesters as an Undergraduate Teaching Assistant (UTA) with another great semester of working with the math department.