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I am about eight months away from completing a Bachelor's degree in Mathematics. I am what you would call a "non-traditional" student - I am an adult who decided to change careers and I'm pursuing my current degree online (read: I work for a living at the moment and have adult responsibilities). My school, despite having a physical campus, has zero support in the realm of undergraduate research or mentorship (this is no program for any student looking to do research). 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. It doesn't necessarily have to be a Ph.D. program, though I know that some schools do not offer Masters's degrees - I would opt for on-campus learning in either case. 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 superlative 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 (outside of my school), for which I was soundly rejected (I can only assume the many things about my background that seemed inadequate). I've tried perusing papers to get a sense of the research landscape, but all of it seems well beyond my abilities to dissect on my own. I'm in a really 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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    If there aren't any nearby universities with graduate programs, you can also connect with graduate students online. For example, I'm organizing an online math mentoring program for Fall 2020 (sites.google.com/view/twoples), where undergrads are paired with grad students to work on a reading project for the semester. This is based on the Directed Reading Program that is run at many universities. – Stephen McKean Jun 19 at 15:52
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    This is a pretty common question - you're not alone. See for instance academia.stackexchange.com/questions/8026/… and the other questions that appear in its "Linked" sidebar. – Nate Eldredge Jun 19 at 16:30
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    You might like to look into postbac programs. These are intended for just this situation - you've finished a bachelor's degree but without sufficient coursework / research experience / faculty relationships to be ready to apply to a PhD program. They typically last one year. – Nate Eldredge Jun 19 at 16:32
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    @GrayLiterature Yes, I am very open and able to move. It's a very interesting suggestion that you bring up. I think I had the impression that I should only be contacting institutions once you are 100% set in your research path (with research/publications already under your belt). It sounds like you're saying that there may be some schools that are willing to work with people who seem driven/bright enough to add something to their program. Is that a fair assessment? – Drew Dias Jun 19 at 19:06
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    @DrewDias The expectation of having already been published prior to applying to graduate school is a bit outlandish, but perhaps not so much if you were applying to Ivy league and were exposed to research very early on. What I am saying is that you want to try and connect with professors prior and then apply to the program. The reason being is that you could apply to a math program, get in, and then realize they do not have any research areas that suit your interest. – GrayLiterature Jun 19 at 19:08

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