Applying to a PhD in Pure Math without a background in Math

[zhenyong]

Not from the US. I have a Bachelor of Science in Physics and a Master of Engineering Science.

 

Mid-way through my undergraduate study, I realized that I am more interested in pure math than physics and wanted to apply for a PhD in pure math after my graduation. I had done research and written a thesis related to math (related to general relativity) for my undergraduate final year project under the supervision of a math lecturer. Unfortunately, after graduation I could not find a math research project for master’s degree and had to apply for a masters in another field. I ended up working on a project related to signal processing.

 

My undergraduate CGPA is not great (2.92/4.0), so I worked hard in my master’s study and managed to publish a conference paper and a journal paper (one more currently under review, and one more has not been submitted yet). This allowed me to graduate earlier. Now that I have completed my master’s degree, I want to apply for a PhD in pure math. I had consulted several professors from different universities, and I was told that my background is more qualified for applied math instead. So, I applied to five universities for PhD in applied math last year. I got rejected from four of them, the remaining one is still under review. This made me feel that my achievements in my master’s study are not helping me in the admissions at all.

 

But deep down, I am still more interested in pure math. Given my background, is it possible for me to get admitted to a PhD in pure math? I am aware that my background is not qualified for pure math. From what I have learned, it seems that I could either:

1. Take the GRE general and math subject test (uncertain due to the pandemic) and apply to grad schools in the US or

2. Apply to a master’s in pure math in other countries.

Did anyone have a similar experience? Or this is just a pipe dream?

[Stat Assistant Professor]

You may be able to get better advise on MathematicsGRE.com, where you'll find a lot more pure math PhD applicants. However, I do have a few comments.

You say that you are interested in pure mathematics, but have you actually taken classes in pure math? Pure math PhD programs will want to see that you have taken courses in abstract algebra, real analysis, proof-based linear algebra, complex analysis, number theory, topology, etc. If you do not have these classes, then you might be totally out of luck, and the immediate course of action is to somehow take a few of these classes (at the MINIMUM, abstract algebra, real analysis, and proof-based linear algebra) OR obtain a Masters degree in math where you take these classes. A lot of Math PhD programs have a preliminary exam that all first year PhD students have to take that tests these subjects at the undergrad level (at least on proof-based linear algebra and real analysis). PhD students who cannot pass this exam at the PhD level are dismissed from the program. So you'd actually need to be really solid in these subjects otherwise you won't even be able to reach the research phase of your PhD program.

Scoring decently on the Math Subject GRE is also quite important for getting into a decent program in Pure Math. If you can score well on this exam, that might assuage some adcoms' reservations about your low undergrad GPA. However, a good score on the Subject GRE is no substitute for coursework. You need to demonstrate strong abilities in math through getting good grades in the relevant classes.

Edited June 5, 2021 by Stat Assistant Professor

[zhenyong]

15 hours ago, Stat Assistant Professor said:

You may be able to get better advise on MathematicsGRE.com, where you'll find a lot more pure math PhD applicants. However, I do have a few comments.

You say that you are interested in pure mathematics, but have you actually taken classes in pure math? Pure math PhD programs will want to see that you have taken courses in abstract algebra, real analysis, proof-based linear algebra, complex analysis, number theory, topology, etc. If you do not have these classes, then you might be totally out of luck, and the immediate course of action is to somehow take a few of these classes (at the MINIMUM, abstract algebra, real analysis, and proof-based linear algebra) OR obtain a Masters degree in math where you take these classes. A lot of Math PhD programs have a preliminary exam that all first year PhD students have to take that tests these subjects at the undergrad level (at least on proof-based linear algebra and real analysis). PhD students who cannot pass this exam at the PhD level are dismissed from the program. So you'd actually need to be really solid in these subjects otherwise you won't even be able to reach the research phase of your PhD program.

Scoring decently on the Math Subject GRE is also quite important for getting into a decent program in Pure Math. If you can score well on this exam, that might assuage some adcoms' reservations about your low undergrad GPA. However, a good score on the Subject GRE is no substitute for coursework. You need to demonstrate strong abilities in math through getting good grades in the relevant classes.

No. I haven't taken any pure math classes in undergrad. My institution was strict, I was only allow to take classes that were predetermined by the university. I have self studied discrete math and I am currently studying real analysis. But I understand this won't help me in the admission. So I am considering getting a masters in pure math to bridge the gaps first, but I guess this would makes my current masters useless.

[Stat Assistant Professor]

6 hours ago, zhenyong said:

No. I haven't taken any pure math classes in undergrad. My institution was strict, I was only allow to take classes that were predetermined by the university. I have self studied discrete math and I am currently studying real analysis. But I understand this won't help me in the admission. So I am considering getting a masters in pure math to bridge the gaps first, but I guess this would makes my current masters useless.

Then I think your chances for PhD programs in pure math are fairly low. You would have to get a Masters where you take courses like real analysis, abstract algebra, complex analysis, etc. and get all A's to demonstrate to admissions committees that you can succeed in a pure mathematics PhD program. Without having taken *any* of these classes, you might not be able to pass the PhD preliminary exam anyway. Scoring very well on the Math Subject GRE would also help your case a lot, especially since your undergrad was not math.

Even if you were to do all these things, I would guess that you still have to apply to mainly mid-to-lower ranked PhD programs, on account of your undergrad GPA (although your publications in a journal and a conference may be definitely seen as a plus, since it demonstrates some research ability).

I agree with you that it would be a very long road ahead of you if you wanted to pursue a PhD in pure math. But if that is your passion, then I say go for it. But you need to be realistic about what schools you can get admitted to. The folks over at the MathematicsGRE forum might be able to help you out more. Best of luck.

[zhenyong]

12 hours ago, Stat Assistant Professor said:

Then I think your chances for PhD programs in pure math are fairly low. You would have to get a Masters where you take courses like real analysis, abstract algebra, complex analysis, etc. and get all A's to demonstrate to admissions committees that you can succeed in a pure mathematics PhD program. Without having taken *any* of these classes, you might not be able to pass the PhD preliminary exam anyway. Scoring very well on the Math Subject GRE would also help your case a lot, especially since your undergrad was not math.

Even if you were to do all these things, I would guess that you still have to apply to mainly mid-to-lower ranked PhD programs, on account of your undergrad GPA (although your publications in a journal and a conference may be definitely seen as a plus, since it demonstrates some research ability).

I agree with you that it would be a very long road ahead of you if you wanted to pursue a PhD in pure math. But if that is your passion, then I say go for it. But you need to be realistic about what schools you can get admitted to. The folks over at the MathematicsGRE forum might be able to help you out more. Best of luck.

Thank you so much for the advice. I learned a lot.