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I'm a first-year undergraduate student (studying Pure Mathematics) at a university that has a mediocre mathematics department, in a country where there are no really good math departments compared to other countries abroad (as an example, there are only 2 known professors in my country that work on research in Algebraic Geometry)

Through what I've studied on my own, currently I have completed everything up to mid 3rd year courses at my university and I shall within the next 6 months/1 year have learned the content offered in all undergraduate honors (fourth year) courses and some graduate-level courses.

I however feel that the courses offered by my university's mathematics department are not at all challenging for me, and that is quite frustrating. I currently achieve 100% on every paper I write and I do not attend any lectures. Instead I opt to study on my own.

I spoke to the head of our university's mathematics department, explained my situation, and asked if I could be granted permission to take higher courses, and his response was essentially 'Who are you to ask me such a question?'

The difficult part is that there is almost nobody whom I can talk to about mathematics that I'm studying. It feels as if I'm working in complete isolation. The only people I can really talk to are some of the Masters and PhD students, who are perhaps the sole reason I even go to university to study.

I feel that this lack of competitiveness and being forced to go through courses that have content which I've already studied on my own is hindering my development. What's more, my university's math faculty does not have any official undergraduate research program, nor do faculty members interact much with undergrads (apart from lecturers taking questions from students of their courses).

I feel stuck, frustrated and depressed as if I'm being held back. In the US I've heard that it's fairly common for students to take courses at higher levels as they choose to do so, but alas I'm not in the US and don't have this option at any of the institutions in my country.

So in my situation, is there any advice one can give me? Also if there are any students who've been in the same situation as I find myself in, I'd be highly interested to hear how you managed to stay motivated and competitive.


(As a side note, I would like to mention that I learned what I learned not to complete courses but out of a genuine interest in what I was learning, it just happened to be that what I learned were the courses offered by my university.)

Also I do plan to move abroad for my graduate studies, if I receive a scholarship to do so, however if I don't, I won't have the necessary finances to pursue this.

My main problem is on how to stay competitive and motivated, and pushing myself in an environment that is not challenging nor conducive to research or to those who want to progress faster than the normally accepted rate.

  • Can you add the country? For example here in Austria you get a list of lectures you need to finish to get your degree and no one cares about what you do when (except for some lectures you have to do before laboratory exercises). – DSVA Dec 8 '16 at 22:42
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    You've left out important information: why are you studying math? Anyway, it seems likely the solution is to move to a more suitable institution. – Anonymous Physicist Dec 8 '16 at 22:45
  • Well I'm studying math to become a mathematician. In South Africa (the country I'm from as per the prev. comment), there are no really stand out institutions, especially not for Pure Mathematics, for Applied Mathematics however there are certain institutions which stand out more than others. – Proven Dec 8 '16 at 22:51
  • You make it sound like there are some possible courses of interest at your university, even if the environment is not ideal, but you struck out asking the head of the department. Have you tried asking through another professor? Either someone who teaches a course you are interested in, or a professor you have already completed a course with? Particularly someone you have taken a course with may be a good person to enlist because they know your capabilities. – Bryan Krause Dec 9 '16 at 2:44
  • Dear @Proven hopefully you have solved your problem in the mean time, if not read on. I was in a very similar situation just 2 years ago. The best solution is to move to a different institution, but some other things can be done as well. Please feel free to send me an email at afdago AT hotmail.com and I will try to help you. – Lee Wang Apr 6 '17 at 11:19
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You may consider:

  1. Transferring to another South African school that would be of a similar level but more flexible about the upper level classes.

  2. See if you can find a way to go abroad.

  3. Stay where you are but try to get into those higher level classes.

    3a. Try to get permission directly from the instructor. Maybe you won't get credit for the class -- but if you are permitted to sit it (audit) the class, that's progress. A good way to start working on this would be to visit the instructor's office hours with a couple of good questions that will show your aptitude, level of knowledge, and communication skills. After getting to know the instructor in this way, you could then ask for permission to attend his or her class.

    3b. Try going above your department head.

I personally favor method 3b as the preferred approach -- if it works.

Now, what to do about your feeling of isolation? Here are some ideas for you to consider:

  1. Do some tutoring/mentoring/teaching. This can be rewarding and can help you break your isolation.

  2. Take some classes in fields where one might be able to apply some tools of applied math or statistics.

  3. Get started with one or more interdisciplinary projects with folks in other departments.

  4. Interact with mathematicians in other countries with email, letters, etc. Here's one way to get started with this: read some papers you're interested in. Write to an author of one of the papers, to say that you read the paper with interest; say what you found most interesting; ask something. You could mention that you would be very glad to be able to correspond with grad students. Then see if a correspondence relationship develops.

  • Thanks for your answer and advice. The only problem with 3b is that I run the risk of damaging my relationship with the head of my university's math department. This becomes a problem as I plan to move abroad to do my graduate studies, and scholarship applications would require recommendation letters from faculty members or the head of the mathematics department, who I think would hesitate to do so if I go with this option. – Proven Dec 9 '16 at 13:42
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    @Proven - That sounds like an excellent reason to cross 3b off the list. Glad to hear you are taking such things into account. – aparente001 Dec 9 '16 at 16:23
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I'm also an undergraduate at a South African university, in my second year though. I'm in a pretty similar situation to yourself but I've managed to have some limited success with what you're trying to do.

I did manage to get permission to take some higher level courses this year but what I think was much more valuable is that I started doing a unofficial reading course with a professor. Essentially I just asked if I could and they were willing. While there might not be many explicit opportunities for undergrads I suspect that some of your professors might be quite happy to help informally, just begin asking.

That said you should probably still keep trying to take higher level courses. Perhaps try asking different people as another commentator mentioned but don't ruin any relationships.

Staying motivated and competitive has been a struggle. Being forced to take loads of courses covering work you already know sucks but it seems like one just has to endure. At this point I view courses as just something I have to do to get a degree and learning mathematics as a more or less separate activity I do because I want to.

One advantage is that you now have plenty of time to learn all the math that interests you instead of just the boring stuff they shove in the curriculum.

It also helps to feel you're at least a little competitive internationally so try to hold yourself to international standards, for example I always try to work through my years Cambridge exams at the end of the year to gauge how I'm doing.

Otherwise if your university has a math club, join that, take the SATMO and try to find professors you can talk to.

Also if it helps, there are students who have managed to get somewhere. I know of one student who went to Princeton and one who went to Cambridge from my university, yours should be similar, so there is hope.

  • It's great to hear from another fellow South African student, but quite sad that we both find ourselves in this similar position. I wholly agree with everything that you've said. I'm curious, were you credited for the higher-level courses or just permitted to sit in? – Proven Dec 10 '16 at 11:30
  • Initially I sat in on a class and took all the tests but wasnt officially registered for it. The arrangement was that I would then be given those marks next year when I was officially allowed to take the class. Since then another professor has helped out a bit and made arrangements for me to officially take some classes and waive some prerequisites. – PorcineBodine Dec 10 '16 at 12:05
  • That's good to hear! It's great to see some progress is being made in your case. Again, purely out of curiosity, which areas of math are you most interested in? – Proven Dec 10 '16 at 13:39
  • A lot of it, but I'd say mainly Analysis and differential geometry. For example I'm quite enjoying Riemann surfaces right now. – PorcineBodine Dec 10 '16 at 14:10
  • Same with me, mainly at the moment though I'm quite enjoying Analysis and General/Algebraic Topology. I'll be working through Spivak's books on Differential Geometry once finals are complete (in another week's time), and if you're still studying Differential Geometry at that time, perhaps we could exchange email addresses and discuss problems and solutions iff it is mutually beneficial to both of us? – Proven Dec 10 '16 at 16:48

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