What Are Math REUs Looking for in Essays and Statements of Intent?

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hsetennis
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I'm a high school student who will be graduating this spring and I'm applying to the various Math REU's that accept pre-freshman undergrads. I'm confused about the essays and statements of intent. What exactly are they looking for in this component of the application? What constitutes a good statement?

Also, what can I do to compete with the undergrads that I'll be applying with?

My background:
high school math + AP Calc BC + AP Stat
(via Stanford) Diff Eq, Calc III, Calc IV, Linear Algebra, Modern Algebra
I'm enrolled in Real Analysis and Complex Analysis this spring.

Technical skills: Java, VB, C++, Mathematica, SPSS, SAS, R, Matlab

Research experience: worked 10 weeks as a paid researcher at a large state school
Authored 1 paper, Coauthored 1 paper (which will be publishing this spring).
 
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In my experience, they almost always say what they want, but it is usually about your educational background, interests, and academic and career goals. And any other information you think is pertinent.

As for what you can do to compete, there isn't much you can really do at this point. You definitely have enough background but it is pretty rare for programs to accept people who have finished freshman year, let alone haven't started yet. I have never heard of it happening. I'm curious, what programs are you looking at that accept pre-freshman applications?
 
Stengah said:
In my experience, they almost always say what they want, but it is usually about your educational background, interests, and academic and career goals. And any other information you think is pertinent.

As for what you can do to compete, there isn't much you can really do at this point. You definitely have enough background but it is pretty rare for programs to accept people who have finished freshman year, let alone haven't started yet. I have never heard of it happening. I'm curious, what programs are you looking at that accept pre-freshman applications?

IU also accepts pre-freshman http://www.math.indiana.edu/reu/faq.phtml .

Regarding academic/career goals, some of them ask if I plan on PhDing in math. Do they give higher consideration to those who want to do graduate work?

I want to do research as a career, but I don't know if I can commit to academia so soon.
 
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I think it may be possible since a lot of people doing REUs are trying to see whether they are interested in going to grad school (whether this makes sense or not is another story). Many jobs involving research in industry have people who went to grad school work there. However, I'm not very knowledgeable on this so I can't really comment. Another thing is that I don't think going to graduate school necessarily confines you to academia. If you are also interested in going into industry you can try different things over the summer like trying an internship one year and an REU in another.