Math REU for Summer 2010: Tips to Improve Your Chances

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PieceOfPi
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I am a math major and a junior, and I'm interested in doing REU during next summer. I've been looking through some of the REU programs for math, and while most of them still show the summer 2009 information, a lot of them sound pretty interesting.

So what are some tips to get accepted to this program?

Are there any math courses that I should take to increase my chance?

What will I be most likely doing in an REU site?

Any comment/suggestion is welcome.

Thanks.
 
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They usually keep the programs small. From what I've read they only accept 10-15 students, and some of the programs get 150+ applications. So, in short...apply to many of them and don't be picky.

Get your letters of recommendation in order. If you don't know your professors well, impress them this semester. Again, from what I've read, the letters play a major role in your chances of acceptance.
 
Thanks. I realized they are quite competitive, so not being picky sounds like a great idea. I'm interested in various mathematical topics so far (e.g. linear algebra, graph theory, combinatorics, dynamical systems, etc), and I might get a little picky with geography, but at least I won't be living there for a long time, so I think I can tolerate that as well.

Fortunately, I am familiarizing with some of the professors/instructors at my school. I don't know if they're really "impressed" about me, but hopefully some of my efforts would count. I hope I can get a few professors to write me a letter by the end of fall quarter...

I'll be also doing Putnam exam this year, which should be fun and something I can write down on my application (well, maybe not if I got something like 0 or 1...).

Thanks, and more comments are appreciated. But I'm starting to think I asked this question too early...