Ended up applying to:
- CSUSB REU for knot theory
- SMALL Number theory/probability
Lots of people say to apply to many programs, but really, I would not want to go to a program I'm not interested in, so I think only applying to four this year is fine. There were maybe 2-3 other programs I would have liked to attend, but their projects were too advanced for me. I'd rather wait 1-2 years then apply when I think I can actually contribute.
Applying to only 4 programs was also nice because I got to write personalized letters of interest/intent.
For the reference of future REU applicants, I'll give some of my 'stats,' which I would have found helpful when I was applying.
Large public, well-respected for its math department, I'd say T20 for math.
4.0 (only a semester's worth of courses, though)
I got two letters, each from the professor of the two math courses I took last semester: linear algebra and number theory. The Fields Institute sent me my letters after they were submitted for some reason, so I got to read them. They were both very strong. One is from a 15+ year tenured professor who has done a large amount of work in number theory; it was very specific and supportive, put me among 'the top handful' of undergraduates he has worked with. My second letter came from a younger professor, but was similarly specific and supportive; best in class, top among students ever taught. Both wrote extensively on their trust in my ability to do actual research. So those were fun to read!
I have no documented research experience. But, I did work with my n.t. professor last semester (which was what he talked about in the letter) and I ended up generalizing something related to random matrices and their eigenvalues, extending results for Q to Q(sqrtD). In my letters, I explained what exactly we did, and said a paper intended for publication on this work was in preparation.
My written submissions: