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I was a former math college student with a 3.9+ GPA (overall, and in my math classes). I took most of the key classes to go to grad school, e.g. groups, rings, and fields, upper-level real analysis, graduate-level complex analysis, mathematical logic, point-set topology, etc. I chickened out of applying to math graduate programs because I was intimidated by my peers and didn't think I had a shot at a top program. I wasn't an Olympiad winner, didn't do research, etc. I'm now realizing that was a mistake. In retrospect, while I wasn't about to get into MIT or anything, I definitely should've given graduate school applications a meaningful shot before chickening out.

Now, I'm at a great law school. It's fine, but it's definitely not where I feel like I'm meant to be. I'm signing up for math classes next year at the Faculty of Arts & Sciences in algebraic topology, groups, rings and fields (to brush up), and topology (again, to brush up).

I'm wondering if someone could give me a realistic picture of what applications will look like. I want to apply to math programs now. I'm considering both Masters (to wet my feet again, and buy myself some time) and PhD programs. I will have good references. The school I'm at has a top math graduate department, so hopefully good grades in my math classes next year will give a slight boost to my application to this particular school.

There's a part of me that is still unsure whether lack of research experience or a contest math track record will significantly disadvantage me from getting into a top PhD program. I don't think it would be a good decision given my priorities to go to any PhD program I get into. It'd just set me back a few years to get into roughly the same jobs in industry/law/finance, but I would definitely set aside the law for a few years to "indulge" my passion if I get into a top program that could promise a meaningful academic career or a very math-heavy career in industry/government, e.g. NSA, robotics, AI, etc. My peers, whom I outperformed, are at great schools (top 20), but not the best. I wasn't very confident in college, but I'm wondering if that means I have a decent shot at a top 10 program. (This is not to put them down! I guess I just had a very fragile sense of self-esteem then...)

As far as my interests go, my comparative advantage and my biggest passion was in abstract algebra and complex analysis, so I'm leaning towards algebraic topology, algebraic geometry, or a related field.

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closed as primarily opinion-based by user370967, Xam, Lord Shark the Unknown, Glorfindel, Antonios-Alexandros Robotis Jul 24 '17 at 21:27

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ I've no advice to give other than to cheer you on, so this is a comment, not an answer. There are lots more good grad students and happily employed math professors than there are mathematicians who won competitions and did research as undergraduates. You'll find a good place. $\endgroup$ – Ethan Bolker May 2 '17 at 23:00
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    $\begingroup$ Prepare for the GRE subject test in mathematics. If you do well, you will have no problem. I don't think a fresh law degree earned right after college will hurt in the slightest. $\endgroup$ – Mark McClure May 2 '17 at 23:00
  • $\begingroup$ It sounds like you have a good shot. Sure, undergraduate research, contests, etc. are helpful but they are not required for grad school. And law school will not hurt your chances. A friend of mine started and completed a math PhD after completing a law degree and passing the bar. $\endgroup$ – Jair Taylor May 2 '17 at 23:24
  • $\begingroup$ Thank you! You're all very kind. I really hope that I'll have a successful application cycle. I'll start preparing for the math subject test ASAP. This helped relieve a lot of nervousness I had about my contest math record, unusual status as a law student applying to grad school, etc. $\endgroup$ – MR1992 May 3 '17 at 4:26
  • $\begingroup$ I wonder what career you are actually trying to pursue. $\endgroup$ – Obinna Nwakwue Jun 17 '17 at 22:52

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