YesLetter: Summer: Articles

The Math Camps of America

by Bernie

Do you get out of the last day of school and see nothing but a bleak, mathless summer ahead of you? Are you fascinated by math, but do you feel your high school courses (and even college courses you are able to take) fail to challenge you? Does the idea of studying math intensely at a university for up to eight weeks during the summers titillate you?

Then you're not alone. Every summer for the past forty-seven years, hundreds of students like you have packed their bags and headed for top universities nationwide to explore new places, make friends, and study like it's nobody's business.

These programs started in 1957, when the late Arnold Ross, then a professor at the University of Notre Dame, took advantage of the funding for math and science education made possible by Cold War paranoia, and created a summer camp for kids who wanted to learn math. The Ross program has been running every year since then, and its alumni have since formed two similar programs, the Program in Mathematics for Young Scientists (PROMYS) at Boston University in Boston, Massachusetts, and the Southwest Texas Honors Summer Camp (HSMC), at Southwest Texas State University in San Marcos, Texas. The Ross program lasts eight weeks, while PROMYS and HSMC each run six weeks.

These programs all focus on number theory. Don't spend your summer at one of these programs if all you want is to ace the AP Calculus exam; number theory is worlds separated from the Calculus or, for that matter, anything taught in most high schools, with the possible exception of axiomatic Euclidean geometry. Number theory has proven extremely successful as a starting point for aspiring mathematicians, though, because it consists of deep problems which are very easy to state yet which take years to understand fully.

These programs move very quickly. Only the first lectures for each of these programs can really be considered elementary. The problem sets, which form the core of learning in all these programs, are intense (no one is expected to finish even half the problems given each day; caveat lector). The first few form a relatively mild introduction to rigorous theorem-proving, (which students can only recognize in hindsight), and after that, the problem sets move on to cover number theory at such a furious pace that even the most intense undergraduate courses on the subject do not compare. After all, the problem sets, which average fifteen to thirty problems each day (and more on the weekends), and which increase in difficulty exponentially as each program progresses, gives a taste of a hard reality of college life: there's always work to do, completing all the problems, takes months, if not years.

While most of students' time is spent doing math, these programs encourage very active social lives. Only a few hours a week are spent in class, which gives students a lot of free time. Everyone is encouraged to work on problem sets in teams, and many students stay up all night doing so - in addition to playing Mafia, a strategy game suitable for large groups of players, and engaging in other social activities. Counselors, extremely enthusiastic math majors drawn mainly from colleges like MIT, Harvard, Princeton, and the University of Chicago, live in the dorms with the students and form an integral part of the social life there. Their responsibilities range from grading problem sets to organizing weekend outings for students to teaching hot mathematical topics in nighttime mini-courses. The atmosphere at these programs is collegiate; while the counselors are clearly "in charge", and while there is a curfew at some of these programs, students are free to otherwise do whatever (legal) activities they desire.

And this experience can be tremendously rewarding in other ways, too. These are the most highly regarded summer mathematics programs in the nation, and they hold commensurate respect at the nation's top universities. The faculty at these programs write letters of recommendation for top students; these letters can hold unbelievable sway at schools like Harvard and MIT. Furthermore, the friends students make at these programs last years and years - and when freshmen arrive at Ivy League schools (or even when graduate students arrive at Ivy League schools), they almost always find that they have instant connections with their comrades from summers past. Alumni of these programs are now among the most renowned mathematicians in the world and hold positions at top research universities.

These programs attract a special group of students. Admission is not easy - at PROMYS, the program I attended for two summers in high school, Glenn Stevens, the program director, personally reads and evaluates each application for admission. Applicants must show a particular enthusiasm, as well as an aptitude, for mathematics. If they do not, they will neither succeed in the program, nor will they get much out of it. None of these programs are for everyone.

And picking programs is also nontrivial. While they are fundamentally similar, there are some big differences. PROMYS is held at the BU campus, which is a very urban setting. The T, Boston's subway system, stops less than a block from the dorm in which PROMYS students stay. Ross and HSMC are not. Likewise, Ross lasts eight weeks and covers a little more material than the other two programs.

There are other summer math programs in the country. They are quite diverse in length and content. I chose to go into detail only on these because they have the reputation of being the most challenging and intense - and for holding the most sway with colleges. For more information on the other programs, see the references below.

References:

The Ross Program at the Ohio State University.
http://www.math.ohio-state.edu/ross/

The Program in Mathematics for Young Scientists (PROMYS) at Boston University.
http://www.promys.org/

The Southwest Texas Honors Summer Math Camp.
http://www.txstate.edu/mathworks/student/HSMC/HSMC.html

Other programs:

Qualification for inclusion: program must have received funding from the American Mathematical Society epsilon fund.

All Girls/All Math at the University of Nebraska. A five-day residential program for high school girls, focusing on a single topic.
http://www.math.unl.edu/~agam/

Canada/USA Math Camp, held alternating years in Canada and the US. A five-week program covering many topics, yet without much depth.
http://www.mathcamp.org

Hampshire College Summer Studies in Mathematics at Hampshire College. A very reputable, six-week program where students spend more time in class than at other programs.
http://www.yp17.org/

Stanford University Mathematics Camp at Stanford University. A four-week program focused on undergraduate analysis and algebra.
http://math.stanford.edu/sumac/main-sumac.htm

University of Chicago Young Scholars Program at the University of Chicago. A three-and-a-half week program for Chicago Public School students.
For information, call Paul Sally at (773)702-7388 or Dianne Hermann at (773)702-7332.
Email: diane@math.uchicago.edu