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My story is a long one to tell, so I will just say my current situation and leave out how I got here. I am interested in studying mathematics but I do not have the opportunity to attend a university due to being hired soon. Recently I learned that I can take college-credit courses without having to enroll in a program. There are two highly reputable schools that offer online upper-level undergraduate math courses: UIUC and Johns Hopkins.

I have no problem investing the money and I foresee no issues on learning the material since I am very motivated and have already studied some of the subjects on my own. The only issue is how to build relationships with professors so that I can apply to graduate schools later in life. Online courses are generally run by instructors who are not doing research. Most graduate schools require 3 letters of recommendation. I'm thinking that investing money in these courses may be pointless if I cannot build relationships with professors.

Does anyone know if professors are willing to help someone not affiliated with a university? Should I try emailing professors at UIUC or JHU?

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    You're correct that most on-line courses are not (actively) taught by tenured faculty, but by adjuncts, whose letters of recommendation would have less weight... Still, "certifying" your competence in things is worthwhile, especially if you otherwise have no official evidence of what you're learned. Yes, you'd still want something stronger to get to grad school... The latter is harder to arrange...
    – paul garrett
    Commented Oct 22, 2022 at 0:57
  • @paulgarrett Enrolling in an online BS program may give me a higher chance of collaborating with faculty. Some schools have capstone project as part of their requirements. However, this will be more expensive as I would need to complete more credits (including lower-level courses and other gen-ed requirements), doesn't have the leisure of completing courses at my own pace, and typically these programs are only offered at less prestigious brach campuses such as LSU Alexandria and UI Springfield. Seems like a Catch 22. Life is tough for those who didn't find their passion when they were young.
    – ngc1300
    Commented Oct 22, 2022 at 1:37
  • What level math courses are you taking now? Starting at Calc II will be a lot different than starting from Galois theory.
    – Terry Loring
    Commented Oct 22, 2022 at 19:25
  • @TerryLoring Now? None. I am not in school. A year ago I completed my PhD in Engineering (throughout I thought about quitting due to my greater interest in math) and before that I got my BS in physics (I don't count this toward my actual education though since I had no study habits when I was younger). Outside of school I have studied linear algebra, analysis, abstract algebra, topology, and first-order logic up to Godel's theorems. I studied these with a mentor. He is a retired math professor but he no longer has connections to academia.
    – ngc1300
    Commented Oct 23, 2022 at 2:37
  • Even if he did, all graduate programs that I have seen, including the lesser reputable one, require around 18 credits of upper-level math on a transcript. I don't have this despite having the knowledge.
    – ngc1300
    Commented Oct 23, 2022 at 2:37

1 Answer 1

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Basically you are asking for a "back door" into academia.

It is not impossible. But there is, quite naturally, no official path to it. You are going to have to improvise.

There are two bits of advice I can be pretty sure will apply, though I can't necessarily tell you how to apply them.

1 - Don't make a pest of yourself. Nobody likes ants at a picnic. Whatever method you find to get yourself a relationship with a prof, don't try things that annoy, harass, waste time, and most especially, don't do anything that will make them worry about their safety. Or any other person's safety. Or the safety of the university.

2 - Find some way to make yourself look good to a prof. Typically students do this by producing outstanding work on their assignments. And by being useful in class interaction. (As opposed to being, for example, a know-it-all. See point 1.)

If you could find a class you are especially interested in and take that in person, it might be a good chance. Especially if the class was taught by a prof you might be interested in working with.

If there is some area of math that you are especially interested in, and you have done some work on your own, you might get somewhere by "cold calling" (cold emailing) a prof and asking for help on some point. If you are pleasant about it, and if you are interesting, the prof might respond. And then you might be able to start a relationship.

This is the autobiography of John Moffat. He was living in Paris, an artist doing paintings. And studying general relativity on his own. He decided one day to write a letter to Einstein to ask a question about relativity. Einstein wrote back. Moffat wrote again, and Einstein responded. Eventually Einstein asked why Moffat was not asking his own professor these questions. When Moffat explained his situation, Einstein helped him get into Cambridge. Directly into the PhD program with no undergrad degree.

So it is possible. It is certainly not the usual pattern.

And once again, be nice about it.

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  • Thanks for the advice. The only problem I see with 2) is that any online classes will be taught by instructors who are not doing serious research. So I will probably have no opportunities to make myself look good to faculty members with higher prestige. Also, how would I even begin to do work on my own? To do that I would need the guidance of experienced faculty to give me a research question which is doable at my skill level.
    – ngc1300
    Commented Oct 23, 2022 at 14:03
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    When Moffat was studying GR on his own, there was no internet. You have the opportunity to obtain very nearly all of human knowledge on line. You might have to pay for a subscription to a journal or two. You might have to buy a text or two. You might have to watch some of the on-line videos of profs explaining things to their regular classes.
    – BillOnne
    Commented Oct 23, 2022 at 15:36
  • I have already done the latter two but not the first. I'll see what I can find.
    – ngc1300
    Commented Oct 23, 2022 at 16:31

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