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Whatever you do over the summer for summer programs, ask yourself how it will be useful to you 10 years down the road.
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<p>Well, maybe not that extreme. I'm pretty sure I've forgotten the Abstract Algebra that I learned at Mathcamp 4 summers ago.</p>
<p>Don't go to a summer program just because you want to get into MIT. Going to a summer program is not a guarantee of admission, and if you end up hating your summer, wouldn't it be a bit too tortuous to put yourself through 6 weeks of pain and may still end up not getting accepted?</p>
<p>If you like math, consider Canada/USA Mathcamp or PROMYS.</p>
<p>I went to Mathcamp my freshman summer and I must say it really opened my eyes to the possibilities of math. The camp itself is also fun, filled with crazy activities and games. Even though it's been 4 years since Mathcamp, I still remember those crazy games we played (and still do play, to a certain degree, at MIT - since a lot of us ended up here).</p>
<p>PROMYS is a program held at BU that emphasizes Number Theory. The whole program is based around NT, so I'd say go only if you are interested in the field. The scope is definitely more narrow than Mathcamp, but I've also heard good things about people who attended PROMYS.</p>
<p>SUMaC is a math program held by Stanford Uni. It's also very NT-based. I only know one person who went there and his experience was very negative, so I can't comment much about this.</p>
<p>For junior year, don't apply to RSI or TASP unless you really think you can make it in. Their acceptance rates are way too low (ridiculously low, at that). Instead, check out SSP. I went to SSP in Ojai in the summer of 2006 and had the best summer of my life thus far. You spend 6 weeks in a California valley observing the tracks of asteroids with your teammates at all hours of the night, taking pictures on telescopes. At the end, you write your own program that simulates the path of your asteroid. Aside from the academic side of it all, there's crazy field trips (including one to Caltech's JPL), amazing people, and a ton of very random games. The best thing about SSP is its relative size. Only 36 people get accepted to either campus, and you really get to know everyone in your program very well by the end of the summer. 7 of my SSP Ojai peers ended up in my class at MIT, and the bonds we formed over that summer 2 years ago still did not fade. It is really an amazing experience.</p>
<p>Also, if you can, you can consider NJ Governor's School. I didn't go to school in the States so I don't know what it is actually like, but I know several people that went to NJGS and they really enjoyed the experience...it is quite prestigious also (but then, stop thinking about prestige!)</p>