I just recently got back from attending the Ross Mathematics Program in Ohio and I would like to give a review. I came back from the airport giddy with excitement, and I wish that the Ross Program could go for another week to distract me from school.
On the Ross Website, it makes it seem like you will do nothing but math for 6 weeks, and I can say that the Ross Program is exactly as advertised. You will get 6 weeks of mathematics. The main curriculum in number theory was very interesting, and gave me a deeper appreciation of the integers. You may think that proving that if a is divisible by b, then b < a might be a trivial task, but at the Ross Program, we go FULL RIGOR, meaning that every proposition must be directly from the axioms with minimal inference or hand waving (the student's response: "full rigor leads to rigor mortis"). All the problem sets have interesting problems that test your conceptions of numbers.
All the counsellors at the Ross Program are excited to help you with math and discuss any math topic (Shoutout to Jon!). Just say "I have a math problem" and 10 heads will snap in your direction. Problem sets are graded daily by the counsellors. Being in a 4-person "family" with a consellor creates a sense of camaraderie, which is good because I arrived at Ross not knowing anyone.
Special lectures are given by the counsellors and professors from OSU. These are very exciting and you do not want to miss them. They cover eclectic topics ranging from modular forms to computation theory. I made the mistake of missing out on Vitaly Berglesson's Pigeonhole lecture series in the first week and I regret that I did not go. The lectures introduce you to new subjects and really broadened my conception of what I thought math encompassed. My favourite talk might have been Oscar's talk on the hyper-reals
The community was my favorite thing about Ross. It is one thing to solve interesting problems, but it is quite another to collaborate on problems with people who are just as obsessed with math. We all sort of egged each other on to solve more problems and inspired each other. I feel that the biggest advantage of the Ross Program is that it prepares you for how life will be in university. I.E. in university, you will likely specialize in a subject and hang out with people in a similar major to discuss your shared passion.
I'd rather not dwell on this subject for too long.
If you are going to the Ross Program, I have some tips for you.
If you would like to do math for 10 hours a day, for 7 days a week, for 6 weeks straight, then apply to the Ross Program. I was a bit intimidated at first because I had never done that much math before, but I really liked the experience.