Richard "Ricky" Magner, a senior studying mathematics at Eastern Connecticut State University, is the University's first Undergraduate Research Fellow. The research fellowship program provides undergraduate students with a stipend and the opportunity to research with experienced professionals in their field. During his freshman year, Magner met Professor Mizan Khan of the Mathematics Department and was invited to take part in the research that Khan was undertaking in the field of Number Theory.
"The interesting part of the experience was that the original question we started out with wasn't answered in the end," said Magner. "We realized that it was not the most successful question to ask, so we had to modify things as we went along." The research in the field of Number Theory is about phenomena known as modular hyperbolas, which are sets of points in a plane. The original goal of the research, according to Magner, was to show when three or more points passed through a line, which proved to be unsuccessful.
Magner and Khan modified their experiment to test for only two points passing through a line and that proved to be a more successful operation. "The research is pretty much self-contained and probably won't change anyone's lives except for mine," said Magner, "but it is good practice and résumé building experience for the future." Magner also spoke to the nature of math research. "It is not too uncommon in math research to go for a long time and not get anything and then have it all come tumbling out in a great realization."
Khan was Magner's research supervisor and mentor throughout the process and helped introduce him to the topic more than 18 months ago. Magner presented his research at two research conferences this past summer. The first was at the "Combinatorial and Additive Number Theory 2013" at the Graduate Center of the City University of New York (CUNY); the second was the 2013 Young Mathematicians Conference at Ohio State University (OSU), which was funded by the National Science Foundation. Only a third of the abstracts were accepted at the OSU event.
The research has culminated in two manuscripts. The first, "Two combinatorial geometric problems involving modular hyperbola," (http://arxiv.org/abs/1304.6943v2) has been submitted to a research journal. The authors are M. Khan, R. Magner, A. Winterhof and S. Senger. The second, "An application of modular hyperbolas to quadratic residues," co-authored by Khan and Magner, has been accepted for publication in the American Mathematical Monthly, the flagship journal of the Mathematics Association of America and will be published in late 2014. The Monthly accepts less than 10 percent of submissions, and publication of the research represents a major milestone for Magner. He believes being a research fellow will serve him well when he applies to a prestigious doctoral program in mathematics.