My apologies if this question has been asked before. I found some that were similar, but the advice offered addressed mid- to upper-tier schools, and the tools/rankings didn't seem to fit what I was looking for very well. I'm also sorry if this post is super long or comes off as mopey.
I'm an undergrad in mathematics. Recent events mean that I unexpectedly must graduate at the end of the upcoming school year. I hoped to take yet another year after, so as to have the best shot possible at getting into a Ph.D. program. That said, I still hope to try and get in somewhere.
Unfortunately I don't have a very strong case for application. Looking into how competitive math Ph.D. and masters' programs are has left me feeling in genuine crisis about my life goals. I'll put my academic details at the bottom of this post for anyone who wants to look them over to give any kind of advice. But mainly I have one question:
How might I go about finding mathematics graduate programs that are "easier" to get into?
I've seen the AMS website for grad programs, but unless I'm missing something it's mainly just summaries. Then there's PHDs.org, which allows sorting by a couple different criteria that conceivably might correlate with acceptance standards, but not to an extent that I'd base such an important decision on them. These are the only resources I've come across.
I suppose this just isn't a readily answerable question. With small pools of applicants and a lot of factors coming in to play, I know you can't rank this very clearly. But all the same: Some programs are harder to get into than others, and I need to find a few that are not that.
Thanks a ton for anything anyone might share!
Here are the details about me and my academics:
Firstly I have indeed given thought to what would be a good fit for me. I'm drawn to two particular subjects (dynamical systems, harmonic analysis) and harbor well-developed opinions on where I'd like to be geographically. But I would give up most anything, to just keep studying math.
My big worry is my GPA: Mine is at ~3.2, a bit higher for math-specific. I'm especially concerned about how my transcript looks chronologically. It comes off like the only time I do well is when I'm not attempting university level work:
I dropped out after a single very poor (~2.9) year at my first institution. Two years later I returned to community college and earned a 4.0 for the year before transferring. I kept up the A grades during fall- and winter-quarter at my current school, but around then experienced severe trauma and let everything slip: That spring term I got a C- in 400-level (first-year graduate) linear algebra, and needlessly withdrew from my other 400-level math course. I had mixed A/B grades the year after, including another (also pointless) withdrawal.
After a year of psychiatry I feel I can definitely do well again. But I'll only have this coming fall quarter (maybe winter?) to show for it on applications. After GPA, here are my other credentials:
Good lower-level math: Core requirements completed with A's: LinAlg, vector calc (retaken), analysis, proofs. B- in discrete math, and B- in a vector calc class, both during my first year.
Checkered 400-level Coursework: Complex Analysis (A-, B+); Combinatorics (B+); Linear Algebra (C-); ODE's & Dynamical Systems (A-); PDE/Fourier Analysis (B); Abstract Algebra (A+, B, B-). This coming fall I start year-long sequences in both Analysis and Topology.
Research Experience: Also very worrisome. I passed on applying to REU's (thinking I'd have another summer after) in favor of continuing a year-long reading I'm engaged in with a faculty member, which is aimed at producing research. I now am in serious doubts about writing in time for applications. What results I do have are of some real interest though.
Personal Recommendations: My two best options for references both relate to my reading. One is apparently well known in functional analysis, the other is now at U Maryland to work in the same field. Both references will be much stronger if I can write in time.
So far that is it. I only just now scheduled my GRE tests. Written personal statements to come. I at least know I interview well.
First, while your transcript is not great, it not necessarily so horrible. Actual research results are not typically a bit deal (see this answer: https://academia.stackexchange.com/a/67732/19607), though letters from your research supervisors can be very helpful. You've done well in some advanced course and less well in others. If you have good recommendations, you have a good shot at mid-level PhD, and certainly master's, programs. (For instance, my program has admitted students with transcripts similar to yours.) Strong letters can overcome a lot of blemishes.
For how to find programs you have a good shot at, first ask your letter writers for suggestions. After all, their opinion will be one of the main things admissions committees will look at. Second, you can try looking at math grad program rankings (e.g., phds.org or US News), and pick some schools that seem interesting at various ranges between 20 and 100, say. (Also, some programs on their webpages will indicate typical expectations of applicants in terms of GPA, coursework, GRE scores.) Then you're likely to get into some schools, and you can choose the best school that accepts you. (Most candidates aren't good judges of what programs they can get into.)
Edit: Note the rankings aren't a perfect gauge of quality or selectivity, but they give some indication---one other factor is that schools in less geographically desirable/less populous locations tend to get fewer applicants, so are generally easier to get into. E.g., a 70th ranked school in New York City will probably be more selective a 70th ranked school in Wyoming, because the latter doesn't get as many applicants.