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).