Applying to a PhD in Pure Math with an undergraduate degree in physics

[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). I worked hard in my master’s study and managed to publish a conference paper and a journal paper (one more currently requiring revisions for publication, 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 lecturers/professors from my university as well as other universities at different countries, and I had been getting mixed opinions. I was told that transitioning to pure math is not that hard, I was told that my background is more qualified for applied math instead, some told me that I should consider PhD programs in the US since they generally offer coursework that can bridge the gaps in my background. 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?

 

[Vanadium 50]

This made me feel that my achievements in my master’s study are not helping me in the admissions at all.

Sure seems that way.

My undergraduate CGPA is not great (2.92/4.0).

That's not "not great". That is "too low to get into pretty much any grad school".

I am aware that my background is not qualified for pure math.

You're right. It's not.

You should look at admission requirements. For example, from UCLA "they must have completed at least 12 quarter courses (or eight semester courses) in substantial upper division mathematics, particularly advanced calculus, algebra, differential equations, and differential or projective geometry." Here's DePaul's (and they don't even have a PhD program) "For full admission, applicants must have already completed the following undergraduate-level coursework: Two semesters (or three quarters) of single-variable calculus, One semester (or two quarters) of multivariable calculus, a course in logic and proofs, a course in linear algebra, \a course in abstract algebra, a course in real analysis"

And the GRE does not replace coursework. It doesn't take much mathematical knowledge to get a very good score: it's half single-variable calculus.

For US schools you are, frankly, unprepared for a graduate curriculum in pure math, and have a GPA so low as to preclude getting into most places even if you had an excellent GPA and the proper preparation. From your name, it sounds like you are Chinese. Why would a graduate school admit you and not another student from China with the proper preparation and a 4.0 GPA? I think you need a very good answer to that question and it needs to come out in your application.

I can't say if other countries will evaluate your application differently or not.

 

[gwnorth]

@Vanadium 50 the OP states that they have a Master of Engineering Science degree and while they did not state their GPA from that program, would it not replace their undergraduate GPA when applying to Ph.D. programs?

 

[Vanadium 50]

He doesn't say, and I am not going to guess.

 

[zhenyong]

@Vanadium 50 the OP states that they have a Master of Engineering Science degree and while they did not state their GPA from that program, would it not replace their undergraduate GPA when applying to Ph.D. programs?

He doesn't say, and I am not going to guess.

My masters degree was by research. This means that there was no coursework and there were no grades. I took on a research project from the start and got stipends while doing it. I was under the impression that research abilities should matter the most in grad schools. After all, the goal is to do research, and my publication history should demonstrate my research ability.

 

[Vanadium 50]

My masters degree was by research. This means that there was no coursework and there were no grades.

That doesn't sound like much of a masters degree. I think this is not helping you.

After all, the goal is to do research, and my publication history should demonstrate my research ability.

Why do you think that? You've nor told us about any pure math research, just something that may or may not be considered applied math - but probably not.

 

[PeroK]

What area of pure mathematics are you thinking of?

 

[andresB]

I know engineers that went into an applied math Ph.D, so that shouldn't be impossible for a physicist.

Pure math on the other hand... I'm from a third world country, so not sure how are Ph.D is other places, but math people here (irrespective of their research topic) had to pass a very though exam that covers analysis, modern algebra, geometry and a 4th thing that I don't remember at the moment. Do you think you can handle those topics at graduate level?

 

[zhenyong]

That doesn't sound like much of a masters degree. I think this is not helping you.

Ungraded masters degree is not uncommon outside of the US. It is called masters degree by research/research master degree. On the other hand, graded masters degree is called masters degree by coursework/taught masters degree. Masters degree by research is like a mini phd, you get paid by stipends, work on a research project with a narrower scope than that of phd projects, for a maximum duration of two years.

Why do you think that? You've nor told us about any pure math research, just something that may or may not be considered applied math - but probably not.

Because I have been told that, by graduate directors/professors from reputable universities. I have no research experience in pure math, my undergraduate research was in Einstein's Field Equations, it involved linear algebra and tensor calculus. My masters research was in signal processing. Particularly single-pixel imaging with compressed sensing. It involved optimization.

I am not naively thinking I can simply get into pure math phd programs right off the bat, I am trying to explore options where I might be able to narrow the gaps.

What area of pure mathematics are you thinking of?

I don't think I am well informed enough to pick a field yet. I studied discrete math and I found logic, proofs and combinatorics interesting. Then I started studying real analysis and I find it even more interesting. So I think it's not realistic for me to say what field I am interested in yet.

I know engineers that went into an applied math Ph.D, so that shouldn't be impossible for a physicist.

Pure math on the other hand... I'm from a third world country, so not sure how are Ph.D is other places, but math people here (irrespective of their research topic) had to pass a very though exam that covers analysis, modern algebra, geometry and a 4th thing that I don't remember at the moment. Do you think you can handle those topics at graduate level?

I've personally known a professor in my university who has a physics degree and applied math phd too. Applied math has always been my backup plan.

I am from Malaysia. I have always been surrounded by science/engineering majors so I am not sure what math majors have to do. I sure can't handle those topics at graduate level, I haven't taken them at undergraduate level.

 

[Keith_McClary]

There is "Mathematical Physics", for example here or here . Rigorously solving problems that Physicists usually don't care much about.

 

[Dr. Courtney]

A GPA of 3.0/4.0 is pretty much a hard lower limit for those aspiring to PhD programs. For good PhD programs, ones GPA needs to be significantly higher than that.

 

[Vanadium 50]

I was told that transitioning to pure math is not that hard,

By someone who knew anything?

some told me that I should consider PhD programs in the US since they generally offer coursework that can bridge the gaps in my background.

By someone who knew anything?

Because I have been told that, by graduate directors/professors from reputable universities.

Again, by someone who knew anything?

I am afraid I am going to have to be direct. Math grad admissions (especially pure math) in the US are extremely competitive. Your application is not:

• The best school in Malaysia is on par with universities like Iowa State or the University of Cincinnati. That's a mid-tier research university. The second best school is on par with maybe Kansas State, a lower tier research university. You're not starting from the same place as a Harvard or Princeton grad.
• In grad school, below a 3.0 GPA is considered failing. You have demonstrated that you can't hit a 3.0 GPA taking easier, undergraduate classes at a less strong college. A masters without grades or evaluation doesn't compensate. A high GRE score doesn't compensate. As Dr. Courtney points out at many - likely most - schools, below a 3.0 is an automatic reject.
• You are unprepared. Not by a class or two. By about two years. As far as I can tell you have not taken a single real math class: upper-division proof-based. Nobody is ready for grad school without taking a single serious course.
• Who will write your letters and what will they say? You want someone who has gone to math grad school themselves (preferably in ths US or Canada) and who can say that you are likely to succeed. But you're not likely to succeed. You're unprepared.
• It sounds like you want funding. That just makes everything harder. Not many places will support someone for two years while they catch up. They would rather accept someone who better prepared themselves.

I don't know if a non-US degree is possible or not. But a US degree is not likely.

 

[Vanadium 50]

Let me add that I am a lot more prepared than you for math grad school, and I do not think I am prepared.

• I have a PhD in physics
• My undergrad was from a top insitution - usually ranked #1
• I have taken more math classes than required for a math BS (although I do not have one.)
• I don't think I ever got below in A in any math class, although I'd have to check. There may be an A- in there.
• I took one class (Linear Algebra) which was "proofy" - it was kind of a mix with Abstract. Prof was a pure mathematician and he got ambitious.
• I didn't do the entire practice math GRE, but I did the toughest 5 problems and got 5 for 5. I would expect to score well.
• I have a strong publication record in physics.

Even with all this, I would not expect to get into a pure math program.

 

[zhenyong]

There is "Mathematical Physics", for example here or here . Rigorously solving problems that Physicists usually don't care much about.

Mathematical physics has always been my backup plan. In fact, I have an interview next week for a scholarship and admission to a phd in mathematical physics. I do wonder though, people often say that a lot of applied math research involve pure math as well, how much of that is true?

A GPA of 3.0/4.0 is pretty much a hard lower limit for those aspiring to PhD programs. For good PhD programs, ones GPA needs to be significantly higher than that.

By someone who knew anything?

By someone who knew anything?

Again, by someone who knew anything?

I am afraid I am going to have to be direct. Math grad admissions (especially pure math) in the US are extremely competitive. Your application is not:

• The best school in Malaysia is on par with universities like Iowa State or the University of Cincinnati. That's a mid-tier research university. The second best school is on par with maybe Kansas State, a lower tier research university. You're not starting from the same place as a Harvard or Princeton grad.
• In grad school, below a 3.0 GPA is considered failing. You have demonstrated that you can't hit a 3.0 GPA taking easier, undergraduate classes at a less strong college. A masters without grades or evaluation doesn't compensate. A high GRE score doesn't compensate. As Dr. Courtney points out at many - likely most - schools, below a 3.0 is an automatic reject.
• You are unprepared. Not by a class or two. By about two years. As far as I can tell you have not taken a single real math class: upper-division proof-based. Nobody is ready for grad school without taking a single serious course.
• Who will write your letters and what will they say? You want someone who has gone to math grad school themselves (preferably in ths US or Canada) and who can say that you are likely to succeed. But you're not likely to succeed. You're unprepared.
• It sounds like you want funding. That just makes everything harder. Not many places will support someone for two years while they catch up. They would rather accept someone who better prepared themselves.

I don't know if a non-US degree is possible or not. But a US degree is not likely.

Let me add that I am a lot more prepared than you for math grad school, and I do not think I am prepared.

• I have a PhD in physics
• My undergrad was from a top insitution - usually ranked #1
• I have taken more math classes than required for a math BS (although I do not have one.)
• I don't think I ever got below in A in any math class, although I'd have to check. There may be an A- in there.
• I took one class (Linear Algebra) which was "proofy" - it was kind of a mix with Abstract. Prof was a pure mathematician and he got ambitious.
• I didn't do the entire practice math GRE, but I did the toughest 5 problems and got 5 for 5. I would expect to score well.
• I have a strong publication record in physics.

Even with all this, I would not expect to get into a pure math program.

By people whose research is in pure math. Thanks for being straight with me. Glad that things worked out so well for you. Getting into top tier grad school is important, but I care more about doing research in the field I am interested in. If that means I have to go to low tier grad schools, I can live with that.

 

[gwnorth]

but I care more about doing research in the field I am interested in. If that means I have to go to low tier grad schools, I can live with that.

Hypothetically speaking supposing you could get admitted to a program at a low tier grad school, what are your plans once you graduate?

 

[zhenyong]

Hypothetically speaking supposing you could get admitted to a program at a low tier grad school, what are your plans once you graduate?

My plan is to stay in academia, my plan is the same regardless of the field of the phd program I got in. If that failed I'll do whatever that keeps me alive.

 

[gwnorth]

I ask because I wonder at your chances of actually being able to stay in academia with a degree from a lower tier school.

 

[zhenyong]

I ask because I wonder at your chances of actually being able to stay in academia with a degree from a lower tier school.

Yeah, I wonder just the same to be honest. I guess I'll only find out when I get there.

 

[andresB]

Yeah, I wonder just the same to be honest. I guess I'll only find out when I get there.

As a half-unemployed Ph.D here, I'd say that not a good plan.

 

[zhenyong]

As a half-unemployed Ph.D here, I'd say that not a good plan.

Can you elaborate more? I am always interested to listen to other people's experience.

 

[andresB]

Your case is somewhat different because you have a master in signal processing, so you already have an option outside academia. But, you should think about employability before committing the time and energy (and money?) to a Ph.D.
For example, how feasible is to get a full professorship post in Malasya?

 

[zhenyong]

Your case is somewhat different because you have a master in signal processing, so you already have an option outside academia. But, you should think about employability before committing the time and energy (and money?) to a Ph.D.
For example, how feasible is to get a full professorship post in Malasya?

Unclear, but that's a good point. Thanks for the advice, I'll certainly keep that in mind.

 

[MidgetDwarf]

There are dual PhD applied math/engineering degrees. Maybe this can be a better avenue given your undergraduate and engineering background? Pure math seems like a stretch at this point. Unless you are willing to pay for classes (ie., post bachelors) in pure math, then see what the admissions say. With those grades, this last option seems to have a higher chance of success into a MS Math program...

 

[zhenyong]

There are dual PhD applied math/engineering degrees. Maybe this can be a better avenue given your undergraduate and engineering background? Pure math seems like a stretch at this point. Unless you are willing to pay for classes (ie., post bachelors) in pure math, then see what the admissions say. With those grades, this last option seems to have a higher chance of success into a MS Math program...

Understood. Thanks a lot for the advice.