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.
The Mount Holyoke College REU in mathematics and statistics is an intense eight-week summer research experience for undergraduates. This project was in place from 2009-2013, covering five summers. Each summer, students were selected from a diverse array of U.S. colleges and universities. The students worked in groups of five, each group carrying out a different project, under the supervision of one or two faculty members. Projects were selected from mainstream areas of mathematical or statistical research and typically involved computer experimentation or computation. Over the five years of this REU project, 50 students and nine faculty mentors took part in the program. The mentors were a diverse group of faculty, 3 Asian females, 1 Asian male, 1 black female, 1 white female and 3 white males. The applicant pools for students were reasonably large; the smallest was 147 in 2011, and the largest was 205 in 2013. The 50 students who were accepted into the program (24 women, and 26 men) were from 42 different institutions and nearly all had completed their junior year. Each year, at the end of the program, students were asked to complete evaluations. These have been overwhelmingly positive. Over the 5 years of program there were 37 (out of 45 respondents) that said they were "Very satisfied" with the overall program, with 7 selecting "Somewhat satisfied" and 1 indicating "Somewhat dissatisfied". The lowest rated aspect of the program was consistently the "Living arrangements" while the highest rated aspects were the "work environment" and "lectures by visitors" and "lectures by faculty". When asked to rate the extent of improvement in particular abilities, students reported the greatest improvement in the ability to "Work as a member of a group", "Use computers as an investigative tool", "Organize and give a mathematical talk", and "Tackle research with confidence". In addition, it’s clear from the open ended comments that the students find that the program helps them to "solidify", "confirm", or "reinforce" their plans to attend graduate school or to continue as a researcher in the field. Topics for the five summers included: number theory (theory of quadratic forms, the arithmetic of cubic fields over the rational numbers), algebraic geometry, differential invariants for Sub-Riemannian geometries (with application to understanding the visual cortex), a comparison of clustering techniques on three real datasets, the motion of human respiratory cilia, and rigidity theory in computer aided design. The problems were rich and open-ended leaving room for the creativity of the students. Students are deeply immersed in learning mathematics or statistics, but in addition they are improving their ability to work collaboratively and to exchange ideas with other students and with faculty. Students practice both oral and written communication by preparing and giving more formal presentations throughout the program. Students are encouraged to shape their own experience, and assist in the planning of the weekly schedule. Activities such as daily afternoon tea, field trips to graduate programs and meals with speakers, all help to foster a sense of community, and the sense of belonging to a research institute. The majority of students give presentations or posters based on their REU projects at area REU Mini-Conferences - gatherings of REU institutions in the area. They may also speak at or have posters at MathFest, the Young Mathematicians Conference, Women in Mathematics in New England Conference, or the Joint Mathematics Meetings and many give presentations after returning to their home institution. Sometimes, projects also result in jointly authored published work. In the summer of 2013, we applied for and received a supplement to support a weekend conference on the occasion of the 25th anniversary of Mount Holyoke’s first REU. Fifty-eight people attended the weekend conference entitled "New Directions for Undergraduate Math Research." Experienced REU faculty joined former students and others, for a series of panel discussions. Topics included the impact of REUs on the student researchers, the impact on the fields within mathematics, and envisioning the REU of the future. Contributions are being collected and will be published by World Scientific.
