Mount Holyoke Undergraduate Mathematics Summer Research Institute

Mount Holyoke College, South Hadley MA

Investigators

Abstract

Mount Holyoke College proposes to continue operating a mathematics and statistics summer research site for undergraduates. Each summer, for the next five years, we envisage selecting ten students from a diverse array of U.S. colleges and universities to engage in mathematical or statistical research. These students shall work in groups of five, each group carrying out a different project under the supervision of a faculty member. The projects will be rooted in mainstream areas of mathematical or statistical research and will often involve computer experimentation and computation. One of the messages we intend to communicate strongly to the students is the power of examples to illuminate, and possibly transcend, current impasses in purely theoretical strategies. The two groups will meet separately several times a day but there will also be ample (structured and unstructured) opportunities for students in the different groups to exchange ideas. Students will organize and participate in their own speaker series, give weekly talks/reports in the program's research seminar, and will be encouraged to attend and participate in local and national meetings. We intend to simulate, as best we can, what life at a research institute feels like. For summer of 2009, Jessica Sidman's group will investigate questions in computational algebraic geometry and commutative algebra while Giuliana Davidoff's group will be involved with a number theory investigation. Our research projects are substantial and mainstream. The intense exposure that we provide, along with the intimacy of small working groups, facilitate and support learning of very deep and abstract concepts in a concrete and non-superficial way. Through the REU the students are strengthened in their enthusiasm for mathematics and statistics; they learn how to effectively communicate mathematical or statistical ideas; they develop confidence in their ability to take a new concept and, through experimentation with examples and questioning, build intuition for it. This experience also serves as a bridge to graduate school for those students who pursue that path. Often the foundational material that is covered in the first couple of weeks of the program coincides with courses that students encounter during their first year of graduate school. Finally, each student will be encouraged to prepare a preprint of his or her work by the end of the program. These preprints are made available on the program's website. It is not uncommon for honors theses as well as journal publications to result from the summer projects. The intense research experience provides an opportunity for students to see for themselves what life as a researcher can entail. Thus it may help them answer (or reaffirm their position on) questions about their potential for a career in mathematic or statistics. Additionally, we seek to increase our program's visibility among students who may otherwise not consider attending an REU. In particular, we intend to recruit heavily from historically black colleges and universities. In this way, we hope to contribute to the diversification and subsequent improvement of these disciplines.