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Marquis Scholar Brian Kronenthal ’07 (Yardley, Pa.) is exploring the prevalence of non-tying behavior in dice games this summer through EXCEL research with Lorenzo Traldi, Metzgar Professor and head of mathematics.
“We are looking at the relationships among different dice which have the same average value when rolled, but different configurations of numbers,” says Traldi.
Traldi has studied the mathematical connections between dice games and elections involving three or more candidates for a number of years. He has published three articles on dice games.
As part of his research, Kronenthal is trying to figure out why dice games which tie over the long term are actually surprisingly rare.
“The goal is to prove that whenever a pair of dice from a given set is tied, a third die from that set exists that neither ties,” says the math major.
Kronenthal has completed research for three-sided dice and has proven the theorem for that set with one exception.
Traldi has been impressed with Kronenthal’s progress.
“Brian is a very successful math major and is particularly interested in combinatorial games,” he says. “So this project seemed to be right up his alley.”
Kronenthal also believes that this project will help him in the long run.
“This research is definitely important,” he says. “After Lafayette, I plan to attend graduate school to obtain an advanced degree in mathematics, where research is a critical component. Having had research experience as an undergraduate is a significant asset.”
Kronenthal researched linear algebra and vector space in another EXCEL project with Derek Smith, assistant professor of mathematics, in spring 2005. He is the president of Math Club, and a member of Pi Mu Epsilon and Phi Betta Kappa. He is also on the dean’s list and received the James P. Crawford Prize in Mathematics at the annual All-College Honors Convocation, April 30.
Traldi, who joined the faculty in 1980, has worked with many Lafayette students on independent studies, honors theses, and EXCEL projects. He has also worked with undergraduates from other colleges doing mathematics research at Lafayette through the National Science Foundation’s Research Experience for Undergraduates (REU) program.
“The EXCEL program has been useful to me in supporting students who contribute to my research,” says Traldi. “I hope it’s also been useful to them by giving them the opportunity to find out what it’s like to do mathematical research.”
In Lafayette’s distinctive EXCEL Scholars program, students conduct research with faculty while earning a stipend. The program has helped to make Lafayette a national leader in undergraduate research. Many of the more than 160 students who participate each year share their work through articles in academic journals and/or conference presentations.