Description: The program runs for eight weeks, starting in early June. Each student receives \$3,000 for the eight weeks of work. Their housing is paid for by the program but they must buy and cook their own food, although the program does arrange at least one dinner (after the student seminar) and two lunches (one with invited speakers and one after the weekly reporting seminar) each week. We try to feed the students as much as possible. The student's all live in the same Mount Holyoke dorm with other Mount Holyoke summer research students from different disciplines. They share a kitchen with the other research students. In the mathematics department, each research group is assigned a large room equipped with a conference table, a blackboard, several comfortable chairs, desks, a library of relevant texts and papers, and dual-boot Windows/Linux computers. (Apple computers are available as well.) Other rooms are available for study and quiet. A refrigerator, microwave and coffee-making facilities are available in the department office. The entire area is air-conditioned.
Each group begins the morning by meeting with the faculty advisor to plan the day's activity. A group's daily schedule might begin with a presentation by the faculty member of new material, a presentation by students of their own progress, a discussion summarizing what has been done, or a restatement of the project's short- or long-term goals. The faculty advisor remains in touch throughout the day. The day ends with afternoon tea in the common room.
Once a week each group gives a formal progress report. The inexperience of undergraduates is never more painfully apparent than in their first presentations. We have learned over the last few years how valuable it is for them to have repeated opportunities to say what they are doing, and in the process to clarify for themselves and their friends in the other groups what their problem is about and how they approach it. In the course of the summer everyone speaks regularly and each group becomes familiar with the other group's problems.
There are also visiting speakers, most of whom are paid for with Mount Holyoke funds. In the summer of 2005, for example, there were six such visitors: David Cox on Origami Constructions (Amherst College), Tom Weston on Fermat's Last Theorem (University of Massachusetts at Amherst), Jean Steiner on Geometric Analysis (then a Post-doc at NYU), Thomas Wright on the ABC Conjecture (Graduate student at Johns Hopkins, REU 2002), Seth Sullivant on Algebraic Statistics (Harvard University), and Jason Starr on Diophantine Equations (MIT, REU '97). The visitors do not just give a talk, but also spend the day with the students discussing the projects, graduate school, and mathematics in general. Some summers the visitors will bring their own summer research students with them.
The students also run and speak in their own weekly seminar series with a pizza dinner afterwards. One student volunteers to run the seminar and that student lines up the others to give talks on some unusual topic they have learned about from courses, independent work, or other summer REUs. In 2005 we had six such talks and some of the topics were: Tilings of the plane, Ramsay numbers, Galois theory, the fundamental group and the universal covering space, representation theory, and singular homotopy.
Visits with other undergraduate research sites are often arranged during the course of the summer and almost every summer the students arrange to borrow the Mount Holyoke van for a two or three day trip to visit graduate schools. They have found that visiting graduate schools in a group is very valuable. In the past the whole REU has visited other REUs like the groups at Williams, Worcester Polytechnic Institute, Amherst College, the University of Massachusetts, and Boston University. In 2006, for example, the whole REU attended and spoke at the Young Investigator Conference at Ohio State in August. We encourage the students to present their results in the undergraduate sessions at mathematics meetings during the following year. We ask for a modest amount in our NSF grant to provide travel support so that the students can attend these meetings as well as travel during the summer to visit other REU groups. Since our travel funds are very limited, we ask the students' home institution to pay travel to the January conference and use our NSF funds only when the home institution does not have the funds available.
Five students in a group seems to work best. This size allows for diverse interactions and division of labor, yet is small enough so that no one is lost.