Hello all, I am a senior undergraduate Mathematics student who is thinking about where to go for my PhD. I actually was planning on graduating last spring (in 3 years) but I ended up getting denied from ALL the programs to which I applied so I decided to stay for a 4th year of undergraduate education. Let me give some information about myself.

My favorite courses have been in probability and analysis so I think I want to do work in those fields. I really do enjoy and probably prefer working out proofs and doing theoretical math over more computational stuff but I think at least for a while I want a profession working in applied math. I'm not sure if that makes sense to most people but I feel like pure math is going to be more like a hobby in my life and I'd rather work more closely with real life problems. Something tells me though that I can get into applied math after working closely with pure math easier than the other way around and perhaps someone can confirm this or correct me if I am wrong.

Here are my "stats"

GPA:3.56

Math GPA: 3.96

Quant GRE: 800 (94th %)

Verbal GRE: 590 (84th %)

Writing GRE: 4.5 (45th %)

Math Subject GRE: 820 (87th %)

When I applied to schools last fall, I think applied to far too good of programs and I am certain far too few. My biggest problem is that I have no idea what sort of schools to look at with my test scores and coming from a small school that most schools have never heard of and with no research experience. I also don't know whether I should apply to applied math programs or pure math programs or both. Most of the students at my school that go to grad school enter programs in nearby universities that "know about" my school and will frequently accept our students but I don't want this at all. I am willing to basically go to school anywhere in the country as long as it is a good fit for my mathematical interests and aspirations.

I don't know any students in my school that have similar interests, all the students that like probability seem to hate working on proofs and all of the students who are more theoretically focused don't like probability. So I find that I have no one in my life to compare my experience to or to discuss this with.

Anyway, if someone can point out some schools that I can possibly get accepted to that seem to be a good fit for my interests or if anyone just has any sort of advice at all for me, it would be much appreciated.