The raison d’être of Mathcamp is to take mathematically talented teenagers—many of whom exhaust the resources of their high schools long before graduation—and deliver them the most powerful tool we know: the ability to take charge of their own educations. We offer courses on an enormous range of topics (from Complex Dynamics to Public-Key Cryptography) and formats (from interactive lectures to inquiry-based), varying in pace and difficulty from "recreational" to "graduate seminar." We offer support and guidance, and then students forge their own paths.
In order to create this smorgasbord of mathematical opportunities, we hire a large, highly-talented teaching staff of graduate students, postdocs, and professors. Our instructors have a diverse set of mathematical interests and pedagogical approaches, but each one is passionate about both mathematics and teaching.
Each week, we teach 20+ courses, and invite students to choose 2–4 classes they'll be taking that week. (The Mathcamp "week" is slightly shifted: classes meet Tuesday through Saturday, and we take field trips and relax on Sundays and Mondays.) You don't have to register formally for classes, so if a class turns out not to be the right fit, you can change your mind. Some courses continue from week to week, but many are self-contained week-long explorations on a particular topic. Classes typically offer optional homework, and students typically opt to do the problem sets! But this isn't school: there are no exams, nor are there textbooks. Instructors will distribute handouts with any information students need.
The course topics vary widely in pure math, applied math, and even a few classes in related fields like computer science and physics. Competition math is not our focus, but we do teach one or two problem-solving classes per week, and offer two problem-solving contests each week for fun.
We publish our course catalogue at the start of camp, and students make their first course selections on orientation day. There's no specific preparation or training that you need to do in advance of camp; when we admit students, it's because they're ready for Mathcamp classes! Note that while we welcome students from all over the world, students should be comfortable both discussing mathematics and socializing in English.