Canada/USA Mathcamp is an intensive 5-week-long summer program for mathematically talented high school students, designed to inspire and motivate mathematically talented high school students by exposing them to the beauty and variety of mathematics, and to impart valuable knowledge and skills for the pursuit of mathematics in high school, university, and beyond.
The environment of Mathcamp tends to be relaxed in terms of rules; in fact, Mathcamp officially has only four rules (generally invoking common sense and respect). Students have the freedom and flexibility to choose what classes and activities they wish to participate in: everything at Mathcamp is optional. This system works only because of the maturity of its participants, and the admissions process looks for evidence of emotional maturity as well as mathematical maturity.
Mathcamp was founded in Vancouver, Canada in 1993 by Dr. George Thomas. At that time, there were only two students. By 1994, there were eleven students. However, by 1996 the enrollment list grew to over 90 students, as Mathcamp had moved to the United States. Dr. T (as he is known) later left in order to establish MathPath, so Mira Bernstein became the new Director in 1998. The third generation of leadership began in 2008, with Marisa Debowsky formally stepping up as the Director in 2016.
So far, Mathcamp has taken place at (in order of appearance): the University of British Columbia, the University of Toronto, the University of Washington, Babson College, Colby College, Colorado College, the University of Puget Sound, Reed College, Mt Holyoke College, Lewis & Clark College, and Colorado School of Mines. The location rotates around regions of North America, typically on a 3-year cycle.
Students hoping to qualify for admission start their applications with an 5-10-question "Qualifying Quiz" of open-ended proof questions. Completion of all of the questions is definitely not a requirement; instead the selection process is more interested with the proofs and the manner in which the problems are attacked.
In addition, two recommendations (academic and personal) are required, as well as a short essay written by the student about why they wish to attend camp.
Once a student has qualified for camp, they need not apply again: alumni are invited to return without reapplying.
Mathcamp provides financial assistance to any student who needs financial support to attend the program, including full scholarships and travel grants. Every student is eligible for financial aid, including both new and returning students, and including both domestic and international students. No student is turned away for lack of funds, and financial aid requests are not taken into account during the admissions process at all.
Every day of the Mathcamp week (Tuesday through Saturday), there are four periods of 50 minutes each in which students may take classes. Note that classes are not mandatory, and in fact it is encouraged that students do not fill up their schedules so that they have greater time to ponder the ideas they are studying.
In the afternoon, there is a 2 hour period known as TAU (Time, Academic -- Unscheduled), where students work on homework and ask questions (to mentors or peers) regarding mathematical topics. Then there is Colloquium, a one hour lecture often delivered by an invited mathematician.
Classes tend to have an emphasis on subjects in mathematics that are normally beyond the scope of high school math; instead, most of the subjects are more likely to be found in college math classes.
Outside of the academic week, field trips are organized for weekends (Sundays and Mondays); typical field trips include hiking, white water rafting, sea kayaking, amusement parks, museums and trips to nearby cities (like Seattle and Boston). There are many other non-mathematical events of all sorts. Games like Ultimate Frisbee, strategy board games, and Bughouse tend to be popular. Singing and dancing activities (like the camp a cappella group and salsa dancing classes) recur every year, as do cooking and baking activities. One perennial favorite is the annual day-long Puzzle Hunt.