SMALL is one of the larger REU's, with fifteen students working in five groups under five different professors on five different problems. Unlike other REU's, SMALL takes a lot of students (about two-thirds) from Williams College itself; snotty as it may sound, a Harvard math department education will prepare you very well. SMALL also takes a relatively large (one-third) number of women.

The research at SMALL is from a variety of fields; my year the projects were in geometry, knot theory and hyperbolic manifolds, commutative algebra, algebraic geometry, and ergodic theory. The projects are generally research that the professors are currently working on; though my group did the research by ourselves, other groups did the research collaboratively with their professors. Most people were happy with this arrangement; I actually became interested in a side topic (geometric measure theory) and, though we still worked on the same two problems we started with, I managed to tug the focus of our research in a different direction. Most of the groups obtained results which they plan to publish. My year, two of the groups went to the joint AMS/MAA math meetings in July; one of them is also attending the winter meeting. After you are accepted to the program, you will receive a more detailed list of the projects (with half-page descriptions) and they try to assign you based on your preferences. My year, it worked out so that everyone got one of the top choices. Be warned that the sort of experience you have will greatly depend on the other people in your group; but no one had a negative experience. You're expected to spend a full day doing research; most people held regular 9-5 (ish) hours, although I rarely came in before 11, which was fine too.

Williams College is located in Williamstown, MA, about three hours west of Boston and three hours north of New York. Williamstown is just a small town, and very different from Cambridge, but is a great place to spend a summer. Williamstown has been described as the densest rural cultural center in America, and it really is true. Every summer there is a large theater festival; there is also a good art museum just down the road. There are many good hiking trails nearby, including an access to the Appalachian Trail. Another nice thing is that a large portion of Williams students stay at Williams over the summer, so there are plenty of people around and plenty of campus-wide happenings, from weekly pick-up soccer and ultimate frisbee games to a weekly colloquium of various scientists describing their research. (And if, like me, you haven't learned how to cook, you can get on their meal plan; the cafeteria is similar to Harvard's dining halls.)

All of the students in the REU occupy a single dorm, and it's nice to have the whole building to ourselves. (All the rooms are singles, though they vary in size.) The dorm is poorly lit but comes with a couple of common rooms and a cable TV. (So for instance there was a group of us watching the World Cup together.)

There will likely be people with cars; we had five or six among all the students, so could drive to Stop & Shop, take road trips, etc. There are various organized and unorganized social activities, including outings to the movie theater (at Burlington Mall -- forty minutes away), the bowling alley, and a local swimming hole; the number and frequency depends on what the students are interested in and willing to organize. There is also a Fourth of July parade, in which a SMALL contingent traditionally participates; if you've never seen a small-town parade, it's worth seeing.

Overall, I would highly recommend Williams. The research, while not Duluth-caliber, is still good, and I found the summer's social/relaxation experience to be very enjoyable. Please feel free to email me if you have any questions.