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[I originally posted this is the Mathematics Stack Exchange and was told to post it here instead]

This might seem like an odd topic for this forum, but I'm losing my mind. I am about eight months away from completing a Bachelor's degree in Mathematics. I am what you would call a "nontraditional" student - I am an adult who decided to change careers and I'm pursing my current degree online. My school, despite having a physical campus, has zero support in the realm of undergraduate research or mentorship. I've tried connecting with a number of my instructors, but as the program is exclusively online, it seems that they are not particularly interested in helping.

I hope to attend graduate school where I would also study Mathematics - I would opt for on-campus learning for this. Since I have no support, I have no idea how to prepare for the application process nor do I have any primer for how to jump into the world of mathematical research. I have a very high GPA and have aced all of my math classes, but this seems trivial when reading about how difficult it is to get into a graduate math program. I recently applied for a short-term research program for undergraduates, for which I was soundly rejected (I can only assume what about my background seemed inadequate). I've tried perusing papers to get a sense of the research landscape, but all of it seems well beyond my own abilities. I'm in quite the low place and it seems that things are quite hopeless. Does anyone here have any insight that might point me in the right direction?

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  • $\begingroup$ Welcome to matheducators.SE! "Support" is a broad word that could include all kinds of things like tutoring or financial aid. Reading your question, it seems like you have in mind support for undergraduate research. I edited the title to reflect that. If I'm wrong, please feel free to edit further to clarify what you meant. $\endgroup$
    – user507
    Commented Jun 19, 2020 at 15:33
  • $\begingroup$ See also the author's post at academia.stackexchange.com/questions/150738/… which has a little more detail. $\endgroup$
    – kcrisman
    Commented Jun 19, 2020 at 18:11
  • $\begingroup$ I wouldn't feel too bad about not getting into REU programs. I find they are more competitive for my students than graduate school itself. There are many more positions to fill in graduate school than in REU programs. I've had students with excellent performance on above and beyond coursework not get any bite from REUs. Sometimes it's just relational. For example, the student who had done a bit less, but was good, got into a program that my colleague happened to know someone at. It's annoying, but relationships and networking do pay off. Online classes are not supported to encourage such care. $\endgroup$
    – James S. Cook
    Commented Jun 22, 2020 at 1:59

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It seems like some of the other answers are aiming at PhD programs. I would suggest (as your question on academia.sx suggests) that you may wish to look at a Master's program (at a non-PhD-granting institution). Obviously not all have the same quality, but a lot of them have high-quality coursework, with assistantships of various kinds. I regularly see emails saying "we still have positions available".

And many of their faculty are going to be quite involved in the research world, and be interested in bringing you into research, and be able to write quality letters of recommendation - which is likely to be what you are missing right now for admission, if your grades are great and your GRE is acceptable. (The issue of the GRE subject test not necessarily measuring readiness for research is a separate one, but for now is part of the ecosystem.)

This might not work for you - for instance, you may have geographical considerations to keep in mind that make this harder - but at any rate is worth considering. And I'm sorry your current institution is not supporting you, at least morally, in pursuing your adventure. That is a real shame.

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    $\begingroup$ I strongly second this. If you did well in an online degree program you should be able to get into an on ground masters program (probably paid, but possibly with scholarship), even at a PhD granting institution. Once there do excellently in your courses and then talk to your professors about research opportunities with them. You're already good at teaching yourself if you did it on online, leverage that. I think this would really be the best option. Good luck! $\endgroup$
    – Nate Bade
    Commented Jun 21, 2020 at 17:41
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You could look around for a program like CalTech's SURF, which takes visiting students from other undegraduate institutions. However, I suspect that it's too late to do those for this summer or (since you're graduating) next summer.

So failing that, my suggestions would be the following:

(1) Line up the best recommendations you can from the people you've been taking classes from, who sound like they're all adjuncts being paid poverty wages. These recommendations will basically say not much more than "A student, did all the work."

(2) Figure out a self-directed project of your own that interests you and is within your ability. It doesn't have to be cutting-edge, publishable work at the forefront of the field. For example, when I was an undergrad, I got interested in the problem of what happens if you take a polyhedron and shave off its vertices to form new faces. What happens if you repeat the process? Does it always converge to a spherical shape? I wrote some code to compute examples and made some pretty pictures that I hung on the wall in my dorm room. Now this was not at all publishable work. However, for someone in your situation, a project of this type is something to point to that shows your ability to work creatively and independently.

Good luck!

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Are you in the US?

It is probably true that you will not get into grad school in math at Princeton or MIT with no undergrad research. But many other US universities will gladly admit you with: good grades, good recommendations from undergraduate instructors, and good results on the Graduate Record subject exam in math.

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  • $\begingroup$ I am in the US. Of course, with my background, even with a perfect academic record, I have zero hopes of getting into a good program. So, I'm not even aiming that high. On the issue of recommendations, do you have any insight about how I should go about finding people to nurture relationships in order to be able to get recommendations? I've hounded all of my professors and they are very much not interested (again, I think it's because this is just a side gig for many of them). Are there outside resources? $\endgroup$
    – Drew Dias
    Commented Jun 19, 2020 at 11:40
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    $\begingroup$ @Drew Dias: I don't know what "good program" means to you, but for me it would include quite a few departments besides the top 5 or 6 in the USA. The vast majority of graduate math students do not attend the top 5 or 6 departments. $\endgroup$
    – Dave L Renfro
    Commented Jun 19, 2020 at 17:19
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How are your test scores? General as well as subject. The good thing about those is they identify smart people from less fancy schools.

Oh...and just apply. Mention your work background. I got into a top science grad school with no undergrad research as I did college in the military. But was a smart cookie. And had a TAD that was sort of research related. No publication but showing an interest.

It's not as hard as you think. They need more people every year. Grad school at MIT is easier to get into than undergrad. Just realize the job prospects can be worse.

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  • $\begingroup$ "Grad school at MIT is easier to get into than undergrad." Truly? How so? Just curious. $\endgroup$
    – user155
    Commented Jun 20, 2020 at 2:45
  • $\begingroup$ I haven't taken the GRE yet (general or subject) - that's later this year. I'll be doing a fair amount of preparation for that. I understand that GRE scores are not the end all of graduate admissions, but I do understand that the society that we live in is inherently discriminatory from a meritocratic standpoint. I'll need to blow that test out of the water if I even want a chance. I'm glad you brought up work experience, but I believe (whether or not it's the case) that work ethic and determination can count for something when demonstrating ability to diligently research something. $\endgroup$
    – Drew Dias
    Commented Jun 21, 2020 at 1:01
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The sad fact is that your mathematics preparation may very well be inadequate for graduate school. My department admits with some frequency people from small regional public universities or unknown private liberal arts colleges whom their faculty recommend as the best student they've had in 10 years, and sometimes we find their preparation woefully inadequate (and sometimes they are quite good). The truth is that many universities simply do not have any students who are capable of succeeding in a course that would prepare students for grad school, and hence don't teach such courses. This is not a matter of the subject matter covered, but rather of the creativity and depth of understanding demanded of the students.

Can you come up with a proof on your own for the following statement? Let G be a finite group and H a subgroup of G, with |H| = (1/2) |G|. Prove H must be normal.

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  • $\begingroup$ I appreciate you taking the time to answer my question. I'm not sure how you could know that I'm ill suited for graduate school. At any rate, you may be touching on something that is a reality - the type of program I am in is not necessarily geared toward preparing students for that. I do find myself having to do work on my own to delve deeper than the courses do. As fas as the proof, I haven't gotten to algebra yet (next term), so I would need definitions. I'm at a loss at what I can take away from your comment other than trying to discourage me from pursuing mathematics. $\endgroup$
    – Drew Dias
    Commented Jun 21, 2020 at 0:54
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    $\begingroup$ I wrote "may very well be" which is not the same as "is". I chose every word carefully. Generally, I discourage everyone from graduate school in mathematics. The academic job market has fallen through the floor and shows no signs of recovering. Graduate programs in mathematics are academic programs, not professional ones, and, except for the rare jobs in industry that actually involve mathematical research, don't provide any more preparation for a job than a bachelors degree. $\endgroup$
    – Alexander Woo
    Commented Jun 21, 2020 at 17:33
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    $\begingroup$ Clarification noted, and I understand your position as it concerns graduate programs in mathematics. I just hope that if someone else asks a similar question that you simply discourage them based on career prospects rather than infer that they are too stupid to get into school, much less succeed at it. $\endgroup$
    – Drew Dias
    Commented Jun 21, 2020 at 21:15
  • $\begingroup$ Though I get why @DrewDias would read this as about stupidity, I think it is important to be able to distinguish between "preparation" and "talent". Many students who have the ability to do well (even quite well) in grad school cannot be given the preparation that a given grad school assumes for their introductory courses. Which is why some grad schools outside the "top 20" (or whatever) still admit students but require them to take the "honors undergrad" version of certain courses that are assumed to be background. $\endgroup$
    – kcrisman
    Commented Jun 25, 2020 at 14:45

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