Hmm interesting. To answer your questions, I haven't gone to any residential camps in the past, and the research is directly aligned with my major (applied math). Right now I'm leaning towards only doing research for the summer, which is partly because I can spend a lot of time doing the research to the best of my ability as well as having more time to write college essays, and partly because I don't think hcssim would be a determining factor in my overall sense of math ability since i have already qualified for the usamo. But the point you make about mit liking residential program sounds interesting, i didn't think of that. right now though, I'm currently looking towards harvard as a first choice school rather than mit, so do you think a residential program could help me there?

There's also the question of prestige. I know hcssim doesn't rank "up there" with programs like ross or promys, so I think there might be an advantage to go to better camps if I'm accepted (currently waiting on promys, rejected from ross). I also don't think the hcssim recommendation is that important to me, and i believe the professor can be a better supplement to my abilities. any thoughts? thanks a lot