Mathematics is incredibly broad, but that's not very apparent in what's taught in school. One of the best ways for students interested in math to learn more about it is to attend summer math camps. Just as importantly, those camps provide a community of math-loving people who usually share lots of other interests, as well. Some of my best friends are people I met at math camp.
Here, I'll go through some summer math programs that focus on theoretical or pure math as opposed to problem solving math. One, MathPath, is for middle schoolers. The others are all high school programs. There's a little more detail about Mathcamp social life because I'm a Mathcamp alum, so I know more, but all of the programs have excellent community aspects. All of the websites have much more information than I could list here, including daily schedules and course offerings from previous years.
MathPath
MathPath is a four week program for middle school students. About 100 students attend each year. MathPath offers both theoretical math and problem solving classes, though there are fewer problem solving classes. Each week, students choose two breakout classes to attend, and there are other lectures (called plenaries) that all students attend.
MathPath's website is www.mathpath.org. MathPath 2013 will be at Macalester College from June 30th to July 28th. Admissions is rolling and camp could be full by the end of March. The application involves a qualifying test, a recommendation from a math teacher/coach, and a non-academic recommendation.
Mathcamp
Canada/USA Mathcamp is a five week program for high school students that offers classes in a huge variety of areas. There are about 120 Mathcampers per year, and many people return for multiple years, creating a continuing culture. Each week, Mathcampers choose what classes they want to take (up to four classes). They can choose classes in related areas or topics that are entirely different. Most classes are taught by mentors, who are math grad students. Mathcamp has a big social component -- most campers spend a lot of time in the main lounge playing games or hanging out. There's a lot of freedom at Mathcamp; camp basically runs on the rules "Be excellent to each other" and "Don't do stupid stuff."
My two summers at Mathcamp were amazing. I learned about so many different areas of math, fell in love with graph theory and logic, and met some of my best friends. I also learned to dance -- contra, salsa, and swing!
Mathcamp's website is www.mathcamp.org. Mathcamp 2013 will be held at Colby College in Maine from June 30th to August 4th. The application involves a qualifying quiz with lots of fun problems, a recommendation from a math teacher and another adult who knows the student well, and a personal statement. The application deadline is in mid April.
HCSSiM
Hampshire College Summer Studies in Mathematics (HCSSiM) is the oldest math summer program for high schoolers in the US, as far as I know. It's also known for its traditions involving yellow pigs and the number 17. (HCSSiM breakfasts at the Joint Math Meetings are at 7:17 am.) HCSSiM is six weeks long, and it's all theoretical math. Classes are in the morning with lectures and problem sessions in the evenings. The afternoons are free for doing non-math things!
For the first three weeks, students are split into Workshops for their classes, and then for the second three weeks campers choose a maxi-course and two mini-courses, which can cover all kinds of things!
HCSSiM's website is www.hcssim.org. It takes place at Hampshire College in Massachusetts every year, and in 2013 the dates are June 30th to August 10th. The application involves an Interesting Test and some personal statements as well as a recommendation letter from a math teacher/coach/someone else who knows the applicant mathematically.
MathILy
MathILy is new in 2013! It's a five week program for high school students that focuses on discrete math -- combinatorics, graph theory, and theoretical linear algebra -- and the courses are discovery/inquiry based. This year they expect to have about 30 students. The name is short for Math Infused with Levity, and one of the organizers/professors, sarah-marie belcastro, has written a discrete math textbook called Discrete Math with Ducks.
MathILy will be held at Bryn Mawr from July 7 to August 10. The application involves a personal statement, a math recommendation, and an Exam Assessing Readiness. The website is www.mathily.org.
SUMaC
SUMaC (Stanford University Mathematics Camp) is a four week program for current 10th-12th graders (ages 15-17). SUMaC is split into two programs. The first covers some abstract algebra and number theory. The second has single-variable calc as a pre-req and covers topology.
SUMaC is always at Stanford. In 2013 it's from July 14 to August 10. The application deadline is in mid March, and the application involves an admission exam, a personal statement, and a math recommendation. The website is http://math.stanford.edu/sumac/.
International Summer School for Students
The Modern Mathematics International Summer School for Students is a two week long program for students in the last two years of high school or first two years of college. Knowledge of calculus is required. The program is organized around mini-courses and lectures with lots of visitors.
In 2013 it takes place in Bremen, Germany, but all instruction is in English. The program takes place from 2 July to 12 July. The application involves one or two math recommendation letters and a fairly extensive personal statement. The website is http://math.jacobs-university.de/summerschool/2013/index.php.
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