It is important to realize that not all summer math programs are organized the same way. Some are quite structured; some allow a lot of choice. All of them require more hours of math per day than MathPath, as befits a camp for older students who have longer attention spans.

We have started collecting statements from some MathPath grads who have gone on to high school math camps. We asked these grads to highlight the similarities and differences from MathPath, so that MathPathers who go there will know what to expect. So far we have three statements, one about AwesomeMath, one about Hampshire, and one about Mathcamp. Here they are:

As one of the few who have attended both the camps, I think I can compare both the programs. MathPath and AwesomeMath are both excellent summer math programs for bright students with excellent aptitude as well as strong interest in Math. However, they have slightly different objectives, mode of operation, and student population. MathPath is aimed at primarily middle school students within age range 11–14, while AwesomeMath is aimed at primarily early high school students. MathPath also has plenary sessions, where several distinguished Mathematicians lecture about some special topics in Math.

If someone is a middle school student in the age range 11–14, I strongly recommend going to MathPath, where (s)he can get an introduction to various areas of Mathematics, which they never get either in their school curriculum or other math programs I know. MathPath is undoubtedly the best math summer program for middle school students. It has the best blend of Math, other intellectually stimulating activities and lots of fun. I'll rate MathPath a 10 in a 10 point scale. Also, in MathPath, as the kids are middle schoolers, they make sure that kids are always under supervision and well taken care of.

If someone is a high school student, (s)he can go to either MathCamp, where they can get in-depth exposure to subjects that are typically not covered even until graduate school in a normal math curriculum or AwesomeMath, where they can get in-depth exposure to two specific areas of Math, such as Number Theory, Combinatorics, Algebra and Geometry.

Once again, I thank you for giving me an opportunity to go through MathPath. I'll cherish the experience forever (and I'll never forget Dr. Convey's antics such as eating the bag).

Talking about my Hampshire experience, it's 6 weeks, adequate for students to go deep enough on at least one topic. The schedule for HCSSiM is tough.

• 8 hours of math a day, Monday to Saturday
• 4 hours class, an hour lecture by a staff or guest speaker (usually), and 3 hour problem session.


• First three weeks: Workshops (A senior staff; 2~3 junior staff in a class; 3 separate classes)
• Remaining three week: Maxi (17-day course), two Minis (8~9 days each)

1. High school camps are demanding
   
2. A course per week, as at MathPath,is not enough for a student to understand the course material fully. One of the things about HCSSiM was that they taught us upto graduate, Ph.D level because we could take time understanding it over three weeks.

At MathPath I tried to avoid much of the Mathcount/ARML courses. It turned out to be a very good choice for me, since such courses as graph theory, and Dr.V/Dr.Su courses are also taught/recommended in high school programs. More camps in high school wants students to pursue their career in math major or related fields instead of contests. Hence, I recommend students to take something new, and topics which can be used for future research subjects, other than focusing on competition classes.

Note: What I felt this year, the level of maturity at Hampshire was a great deal for rising sophomores, because the camp is mostly juniors and seniors. I was second youngest this year. My opinion regarding the camps might be different from others because of this.

Going to Mathpath (2008 and 2009) over the summer was certainly an eye-opening experience. After exploring intriguing, fascinating branches of mathematics as well as creating a network of friends among like-minded math nerds, I found that my school environment at home was notably lacking in appreciation and support for people like me. Once I turned 15, I was eager to continue being a part of a loving, intellectual community and went to Mathcamp in 2010. I had heard several great reviews of the camp from my friends and was interested to see Dr. T's first camp for mathematically-inclined students. I was not disappointed when I arrived; even from just the first week, I felt like I was home again: from taking classes on theoretical computer science and ring theory to making jokes about Stephen Wolfram and the triviality of problems, it was obvious that the same quirky spirit that made me love Mathpath lived in Mathcamp as well.

Strictly by the numbers, Mathcamp is a bigger and more internationally-accepting camp than Mathpath. There are around 120 campers here ranging from the US to Europe to India and Southern Asia. This does not impact the friendships or culture at camp in any negative way; I still felt that I got to know the entire camp as well, and international students gave a more global perspective to the universality of mathematics. Financially, the cost of Mathcamp is considerably less than that of Mathpath, and Mathcamp also offers greater financial aid than Mathpath. Again, this did not create an obvious difference between the environment of the two camps; social status never came up as an issue and no one felt very conscious about these things.

The classes at Mathcamp, similarly to Mathpath's, worked on a scoring system: this time with chili peppers (to show the spiciness of the course) rather than stars. The work week ran from Tuesdays to Saturdays, while Monday and Sunday were left for excursions. In an average day, there were 4 breakout-style sessions which were simply called classes and only 1 plenary session called Colloquium. We were encouraged to not attend all class sessions but instead to take a break to not burn out or stress. There was planned-in time in the schedule to do homework or independently study math called TAU, Time: Academic Unscheduled, where all teachers were free to discuss the course material. Some students used this time to work on their Project. About midway through the camp, Project Fair was given instead of Colloquium, where campers could check out the various types of Projects suggested by the teachers, ranging from programming a game on the Hyperbolic Plane to studying Markov chains. Projects can also be independently formulated, such as the student-run inquiry into quantum mechanics.

Mathcamp is clearly geared more towards high schoolers, not just in subject difficulty but in overall freedoms given to campers. The structure is considerably laxer than Mathpath's: students are not required to go to class, there is not set bedtime (though there is a quiet hour), and campers are allowed to go off campus. Likewise, there are no limits to class size; students simply show up to the classes that they want to go to. Rather than have all of the classes have about the same number of attendees, classes range from 4 students to 50 students. Essentially, Mathcamp gives college-esque permissions to its campers, whereas Mathpath gives a more high school permissions. Both are still relatively free compared to the home environment and are appropriate given the maturity and responsibility of the campers. Similarly, at Mathcamp, organized activities are scheduled by both counselors and students, rather than just by the counselors. A wall is dedicated off from the main lounge as a scheduling board, and campers are encouraged to put up whatever zany events they wish, ranging from chess tournaments to Human Turing Machines to a campaign to get New York bagels to camp.

One of the greatest things that I appreciated at Mathcamp was this sense of freedom and equality; campers, teachers, and counselors were all equal, only settling into a hierarchy to reflect the respect of knowledge that the campers had for the elders. Though looking back, Mathpath seems more regimentalized, it was appropriate for me at the time, so that now I can appreciate the responsibilities given to me. I felt that I had greater freedom to pursue any branch of mathematics rather than just the ones offered as a class. The quirkiness, however, still lives equally brightly in both camps. Whatever crazy ideas that materialize at camp come directly from the students, and no infrastructure differences can change them.

All in all, I loved my time at both camps and strongly recommend both programs to any gifted student interested in mathematics.

Actually, this is Lilly's second statement comparing the two camps. It is aimed at students who have already been to MathPath. Earlier she wrote a statement aimed more at parents and students who had not yet been to either camp. If you want to read Lilly's earlier statement, look here.