Students who want to take higher courses early 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.
You may consider:


Transferring to another South African school that would be of a similar level but more flexible about the upper level classes.
See if you can find a way to go abroad.
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:


Do some tutoring/mentoring/teaching.  This can be rewarding and can help you break your isolation.
Take some classes in fields where one might be able to apply some tools of applied math or statistics.
Get started with one or more interdisciplinary projects with folks in other departments.
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.