# Math Camps

One summer option that has traditionally been popular among math majors is to work at a math camp for high school students. Typically, undergraduates serve as counselors, helping students with problem sets, providing general supervision, and serving as older friends and mentors to the students. Many find the job to be both fun and rewarding, and some Princeton students have chosen to spend most of their summers at camps like this. The most popular by far among Princeton students are the Ross Mathematics Program, held at Ohio State University, and PROMYS, held at Boston University.

#### Ross Mathematics Program

The Ross Mathematics Program, pretty much universally called just “Ross,” is an intensive six-week course in number theory for high school students. Over the course of the program, the students work through a huge chunk of fundamental number theory, starting with an axiomatic construction of the integers and culminating with a proof of Gauss’s quadratic reciprocity theorem. The emphasis is on solving problems—there’s a problem set every day and the problems guide the students step-by-step through proofs of many tricky results, including quadratic reciprocity—and learning to think mathematically, which is to say, both intuitively and rigorously. Counselors live in the dorms with the students and take charge of a small “family” (four to five students) and sometimes a junior counselor, an advanced returning student who is ostensibly in training for the role of counselor. If you work here, you’ll be expected to grade your students’ problem sets quickly and provide useful feedback that will allow them to progress as far and as rapidly as they can. All in all, it’s a rewarding job that leaves plenty of time for personal interests, and the Ross community is wonderful.

#### PROMYS

PROMYS is the child of the Ross program and is similar in many ways. The program parallels that of Ross, starting with an axiomatic construction of the integers and ending with a proof of Gauss’s quadratic reciprocity theorem. Again, the emphasis is on problem solving and thinking mathematically, and a problem set is assigned daily. Student “families” consist of 4-5 students, usually with one advanced returning student, who take advanced courses like Algebra, Galois Theory, Geometry and Symmetry, Combinatorics, and Modular Forms. Counselors’ roles includes grading family members’ problem sets quickly, guiding students through the program, and marking for an advanced course. There is spare time, however, and fun activities for both participants and counselors. It’s a rewarding job that, like Ross, has traditionally been popular with Princeton undergraduates.