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I am enrolled in a university close to my home in a bachelor of electrical engineering and a bachelor of data science. The university I am attending does not offer a lot of math courses. The only math courses they offer are first year calculus, discrete math, vector calculus, differential equations, linear algebra, abstract algebra, real and complex analysis. I am intending to do all these math courses as electives for my bachelor of data science (they are not core courses). My university does not offer any courses such as topology, analytic number theory, differential geometry, measure theory and other advanced math courses which undergraduate students in other universities have access to.

The only option I can think of is to transfer to a university where they offer the math courses I need but that requires me to travel about 6 hours each day (3 hours each way). Also, moving out is not an option since accommodation is expensive and I can not afford it. So that only leaves me with studying in my current university.

What options do I have to learn and do more advanced math courses?

I may be going to graduate school in math and I do not think that the math courses my university offers is suitable for graduate level math since other students have done a lot of advanced courses not available to me. What can I do to ensure
that I am a good candidate despite the fact that my institution does not offer any advanced math courses? Would self studying suffice? How can I then convince the graduate admission committee that I am ready for graduate level math courses?

I live in Australia and I like to do my graduate school in USA.

It is very unlikely that your university will start giving full-fledged advanced math courses at one person's request. However, there are multiple things you could try instead. I suggest discussing these with your program supervisor. (or whoever you can best talk to about your course program)

Take a single course at another university

It might be possible to follow a course at another university without enrolling there. Advanced mathematics courses tend to be highly specialized, so it is not uncommon that a single university is unable to provide a diverse program of advanced math courses. For this reason, some universities have programs to 'share' their advanced math courses. (see e.g. the Mastermath program in the Netherlands)

It is possible that your university does not have such arrangements with other universities, but you may be able to make arrangements for yourself.

Guided self-study

While self-study is an option, feedback from a teacher is be very useful when learning. You could ask a faculty member at your university whether they would be willing to have a short weekly meeting where you can ask them questions and they look at your progress. An additional advantage of this is that while you will not have this 'course' listed on your diploma, you can mention it during applications, as there is someone who can 'verify' that you have learned this topic.

There may be no faculty at your university that can or is willing to help you here, but they probably know someone at another university who would. It never hurts to ask around.

Research project

Since you mention you want to do research, consider approaching someone to do an undergraduate research project. This may not work out due to a lack of pre-knowledge, but as there is usually an expectation that some self-study is required, you might be able to find a project that fits.

Since you say that transferring (which sadly would be by far the best option, see the note at the bottom) is not feasible, the next best solution might be to just will those courses into existence. From your question I get that you haven't done the available courses yet, so start doing those as soon as possible. Most of them are soft prerequisites for the more advanced courses anyway. Try to excel in those courses, in order to get noticed as a bright and interested student. (I assume that you are good enough to do so, otherwise going to grad-school will be a bad idea.)

Then, once you are finished with some of those courses, talk to the professor and tell them what you told us. Make sure that the focus is on you being interested in learning about things, not in padding your transcript (which is just the means to study more math in graduate school). Teaching the same old basic level math year in and year out to students only interested in their grades can be quite boring, so at least some should jump at the chance to break the monotony.

From there on, I see several different options you might discuss, in rough order of desireabilty:

• The course you want is actually created, at least as a one-off. This is more likely if you find a few other people which are interested as well, but don't be disappointed if it doesn't happen, as preparing and holding a new course takes quite a bit of time which simply no professor might have.


• You do the advanced topics as a "reading course". This is not a common format, but the basic idea is that the professor assigns you a textbook to read and you periodically meet up to discuss your understanding and any problems you might have had. Then in the end you do an oral exam to determine a grade. I'm not sure about Australia but at least here in Germany this can count as equivalent to a regular course and is sometimes done in this exact situation if there aren't many interested students and the prof has not enough time.


• The prof might just assist you in studying the topics on you own, by giving you some hints and opportunities to periodically discuss things together. Sadly you will not have formally passed a course, but this might be the only solution in the not completely unlikely case that bureaucracy simply doesn't allow for a certain course to exists in your university.

In any case, an important goal will be to get a good personal letter of recommendation. This won't get you to your top choice of place but could at least open up some possibilities at places where the professor is known. So to maximise your chances, before you choose a professor to ask, have a look at their CV. Find out under whom they did their PhD and with whom they have collaborated in recent years. If those people are still actively involved in some graduate program, your prof might be able to send you there even with holes in your transcript. Just never tell him that this is the reason you chose him...

Footnote:
But all this being said, the harsh truth is, if you truly want to have a career in math, try to transfer to a university with a proper maths program as soon as you can. You'll be able to learn much more at a much faster pace by having more proper courses and by simply having other math students around you.

Also while it might be a prejudice, math courses from some applied university without a proper maths program are generally seen as second rate and lacking in depth. So given the choice between a student who passed introductory math courses for engineers with perfect grades and a student who only got mediocre grades in identically named courses at a place renowned for its math program, many will choose the latter. In the same way, your professors generally won't be the best mathematicians, both in terms of ability as well as in terms of connections, otherwise they would teach at some "better" place.

So I'd suggest to think about transferring again. There might be a scholarship program that you could get into, which would pay for accommodation or a way to condense your physical presence at the other university only to certain days in order to make traveling more feasible. Even if you decide to stay at your university for now, keep looking for opportunities.

I will put in a minority view that complements the answer suggesting doing a guided study etc.

Your list was "first year calculus, discrete math, vector calculus, differential equations, linear algebra, abstract algebra, real and complex analysis." It is true that for an elite PhD program in the United States (which you mentioned as your goal), that would not be enough.

On the other hand, very few people get into such programs at all (by the numbers). There are plenty of smaller regional universities which have PhD programs that might be eager for "the best maths student in a generation at our college" (if that is you) to apply, and get a full assistantship. Some (not all) of the domestic students getting into these programs may not have significantly more theoretical preparation than these courses (though they may have more math total).

Nowadays there are more and more ambitious people coming from other than the "usual suspects" who are pursuing research careers (granted, also pursuing working in finance or risk analytics) so if this is your goal, it is plausible to do so without being at a "top-10" place (as might not have been the case 30-40 years ago).

So I wouldn't necessarily say you need to transfer. Abstract algebra and real analysis will show you can do proofs. Crush the math subject test GRE (which basically has the topics you mention), do as many of the other things mentioned as possible - particularly an undergraduate research experience or two. Then work hard to find a program that will be interested in you and want to invest in you succeeding.

Final note: In the US there are also many (even) smaller regional universities which have master's (but not PhD) programs that would offer a lot of the types of topics you are mentioning. Some of these also have assistantships. I don't know whether that would be the case in Oz, though, nor whether the ones I'm thinking of typically have overseas applicants. That is a possible route as well, though not one I'm as familiar with people eventually going to a PhD using (I do know of some very successful examples of this).