I’ve never been to HCSSiM, but I know five or so kids who were there in 2014. They all really enjoyed it. It’s a lot of math, but it’s structured in a way that there’s no stress over the math. It seems like a very welcoming, quirky place, and the girls I talked to loved it.
I’m not sure if there’s a skewed girl/guy ratio, but I can say, coming from Ross, which was 2/3 male, that it’s generally okay to be a girl in the minority at math camps – people look at you for you who are and what you bring, and forget a lot of external stuff. I felt impostor syndrome for about two days at Ross, as a fairly underprepared white female-presenting person, but I doubt that even that small bit of “I shouldn’t be here” would be present at HCSSiM, from the things that the HCSSiM girls said. (And, by the way, I consider Ross to be the best and most formative six weeks of my life and miss it daily, so even if there is a rocky start, there’s also time after that .)
HCSSiM is different from PROMYS or Ross because there’s designated “not math” time and more actual instruction – the other two are working alone or with peers on number theory problems 24/7 with some pressure to finish the set before the next day. It’s way more intense than MathILy, though, and I think you get greater continuity at HCSSiM than at Mathcamp.
Admission to HCSSiM is primarily based on the Interesting Test (and probably essays – I don’t have a sense of how much those matter to Hampshire), which is a series of interesting math questions that you’ll write up solutions to. I’d imaging that ability shown on the Interesting Test matters quite a bit more than your current math class. These math camps are typically looking for mathematical maturity, not scores.
Definitely poke around on the HCSSiM website if you haven’t already; it give a pretty good picture of what Hampshire is all about. Even at Ross, the last year HCSSiM kids started caroling on Yellow Pig Day and making references to the number 17. You’ll learn a lot of abstract math unlike any you’ve encountered before, and have a fun time while learning it. Apply if you love math with your heart.
There’s also SUMaC. Look at http://talk.collegeconfidential.com/discussion/comment/15408627#Comment_15408627.