Hello! I am about to enter my senior year of undergraduate and am planning on applying for Ph.D. programs in pure mathematics this fall. I am wondering if there is an effective way to go about searching for programs/how I can compile a reasonable list of schools given my credentials. I currently attend a small liberal arts college. My academics are fine but far from stellar (3.603 overall and 3.677 in math as of the end of junior year), I have one summer of research in chemistry, will be participating in a math REU this summer, and I have a position as a Learning Assistant (kind of like a TA on an undergrad level) for Calc II at my school. I'm planning on taking the GRE and GRE subject test this fall- I'm assuming I'll perform fine, but not great. I think my main concern is my lack of research experience in combination with my not-too-great GPA. Is one REU with no other math research enough? Will my experience in chemistry research mean anything at all? (This research only lasted for one summer after my freshman year, not published). Will my GPA knock me out of consideration from the get-go? I expect to have 2 very good, and one decent letter of recommendation.

I'm also concerned about the lack of courses I've had access to given the school I attend. The only higher level classes I will have completed by the time I graduate (in addition to the lower level required courses) are abstract algebra (my school only offers one course in this), number theory (this class is what killed my math GPA lol), complex analysis, chaos and fractals, advanced geometry, combinatorics and graph theory, applied mathematics and modeling, real analysis (my school also only offers one course in this as well), plus two electives in my final semester (not sure what they'll be yet, potentially a second course in linear algebra, and codes and ciphers). It actually sounds like a decent list when I write it all out in one place, but I will have taken every math course that my school offers upon graduating, aside from two statistics courses, and operations research which I have no interest in taking, and I feel as if my coursework is lacking if I look at the undergraduate courses that are offered at bigger schools. Will this be a detriment to me in the application process? I know there's nothing I can really do about it, but I know I will be up against super successful students at large research institutes who simply have a more developed program than I have access to.

As of now, I'm thinking of looking for programs in algebra- I really enjoyed abstract algebra last fall and I would love to learn more about it, but what I'm seeing basically everywhere are things like algebraic geometry, algebraic topology, algebraic number theory, commutative and noncommutative algebra, etc. How do I know if I should apply to programs that have these research topics if I haven't had the opportunity to learn about them yet? Some programs I've found list group theory or algebra more generally, but this is not what I've been seeing in most cases. Should I be looking into these more specific fields of algebra (ha ha no pun intended) before narrowing down my list? Should I be deterred from applying to programs which have research I haven't been exposed to yet? Are there any specific schools with a strong algebra focus that I should be looking at? On another note, should I perhaps consider more than one field of mathematics when searching for programs? Putting all my eggs in one basket seems like not the best idea- what if I take more advanced algebra classes and find that I'm not enjoying it as much as I anticipated? I did also enjoy my complex analysis course a lot more than I expected to, and would love to learn more about that. However, if I had to pick one right now, I'd go with algebra.

As a final thought, finding programs in the first place is proving to be very daunting. I've used the AMS search engine to try and filter my results, but I'm still left with an overwhelming number of schools. Should I be considering location as a major factor in narrowing down this list? It seems like a trivial thing to consider, but it would greatly help in shrinking the list, and I'm having a hard time thinking of any other way to do this.

This post is kind of all over the place, but any input regarding anything I mentioned in here would be greatly appreciated! Thank you so much!