What to do if my university does not offer any advanced math courses?
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.