Last summer I worked as a counselor at PROMYS (Program in Mathematics for Young Scientists). PROMYS is a six-week program run by Boston University, and is funded by the NSF. The director of the program, Glenn Stevens, is a mathematics professor at BU. Last summer there were eighty students, mostly from high school, who had strong interests in math.

The purpose of PROMYS is to develop the students' interest in math. Each morning the students attend an hour lecture in number theory where they are given the day's problem set: numerical calculations, statements that they are asked to "prove or disprove and salvage if possible" and some tricky problems labelled "miscellaneous." Students look for patterns and make conjectures ("any conjectures?" is perhaps the most frequently asked question in the program.) The students never recieve scores on the problem sets. They are instructed to finish as much as they can, and recieve comments. Finishing the problem sets becomes steadily more difficult as the program progresses, and few students come close to finishing the problem sets in the second half of the program. The lack of grades enables the program to keep competition to a minimum. Students constantly work together and discuss the problems.

This brings us to the role of counselors. PROMYS hires 20 college students, some of whom were themselves students, to guide students through the program. Like the other counselors, I was assigned five students whom I was primarily responsible for (numbers varied slightly from counselor to counselor.) I commented on their problem sets, and discussed their work with them. We talked about the course and tried to resolve some difficulties. Besides his or her five students, the counselor is responsible for all of the students in the program. In the evenings, many students and counselors work together in a room called the "basement". Students work with students, students work with counselors, counselors work with counselors.

The students at PROMYS are very smart and motivated; working with them was one of the best parts of PROMYS. Working with the other counselors was also a great experience. The program at PROMYS can be taken at all different levels; it is hard to imagine anyone being bored by it! The number theory problem sets are extremely interesting, both in the problems themselves, and in the way that they are organized to lead up to important results. There are several more advanced courses that are taken by the returning students in addition to the number theory (all students take the number theory course, there is easily enought material there for several summers).

As a counselor, there is much opportunity to learn a lot of math. Besides the number theory problem sets, the more advanced courses are of interest to counselors. There are also seminars that counselors put on for themselves. Last summer's Modular Forms seminar developed a particularly cultish following.

Contrary to what it may seem from this description, we didn't do math all the time. The flexible nature of this program allows for much socializing. Counselors organized social events that range from somewhat normal to bizarre, but were always fun. Trips to surrounding colleges are also organized by counselors (if you've ever wanted to give a tour of Harvard, now might be the time to do it), as are games of ultimate, trips to Boston, etc. You won't get much sleep, but you will have an exciting and fun summer.

-- Jessica Wachter '96 (wachter@math.harvard.edu)