Getting into maths PhD program

Question

I would like to get into a mathematics MSc or PhD program. My undergraduate degree is in physics and I have completed the most basic mathematics courses, like calculus, linear algebra.

In the final year of my physics degree I found a new interest in differential geometry. I even completed a graduate course on the subject and have been studying on my own. This eventually resulted in getting bad grades for my physics modules (few Fs).

What can I do to improve my chances on getting into a graduate program in mathematics? I don't really want to take any courses on analysis, or topology as I've studied them on my own.

Answer 1

You have to consider your competition -- that is, the people schools can choose from as they are applying at the same time as you are.

First, they will generally not have "a few Fs" -- that's going to look rather bad on your transcript, in particular since it is at the end of your studies. If you had had a semester of this sort at the beginning, it would be possible to explain it away in your essay as "I needed to grow up, but as you can see in my transcript, I have gotten through this phase of my life and my recent semesters were all As". So that is an issue you have to think about how you can address or remedy.

Second, most of your competition is from people who were math undergraduates, have taken all foundational math courses with good grades, and have typically taken a few graduate math courses. You have taken one -- that's good --, but it will remain unclear to anyone looking at your application how broad your math undergraduate education really is, and how you would do with the graduate math breadth requirement most departments have.

So, long story short, I'm afraid what you currently have isn't particularly safe as far as getting admitted is concerned. I would see whether you can stay at your home institution for another year, for example, to fill in the holes in your transcript (more breadth in your math courses, maybe more graduate math courses, good grades).

Answer 2

Impressive GPA

If your GPA is really impressive, then many universities will give you admission.

Pre-requisites

Mathematics MSc or PhD program may require you to take some undergraduate math courses as pre-requisite and then you can carry on with the program.

I would suggest that you contact the math department and ask them about your situation. Contact with more than one universities.

Answer 3

The best thing for you to do is apply to a Master's program abroad to raise your competitiveness for PhD programs down the line--and sadly, you can expect to fund it yourself. Simply consider that there are very few graduate schools that would fund a student from a foreign university in a small country, who has a few failing grades on their transcript (even if in a different field; after all, physics and math are very closely related). If you can get into a master's, you have the opportunity to really build up your mathematical background and make up for this deficit, hopefully making yourself more competitive. It will be a significant struggle, but it is possible.

To me, the most alarming part of your question is the fact that you don't wish to take analysis or topology. You should absolutely be looking to strengthen your math background, especially in such fundamental topics--I would suspect that, like any young student self-studying these topics, your background in them is not as strong as you expect. And if your background truly is very strong, and these classes prove easy, that's great! They will be a useful review and an easy A to add to your transcript (you need proof somehow that you know these topics, as no one will believe you've read the book), and you can use the extra time to focus on less familiar topics like algebra.