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As the title suggests, I am a CS undergraduate who wants to apply to math PhD programs in the US. I should also mention that I live and study outside the US.

The problem is that my undergraduate program does not have many math courses, in fact I think it has the bare minimum amount. Obviously I self-study a lot (and I think I can get a good subject GRE score) but I don't think this plays any role. Aside from the very few and simple math courses, I have only my thesis (which is more or less mathematics) to show.

How will that affect my application? For example, I have a very good GPA but this could not even matter since my curriculum does not cover many math subjects.

I love mathematics but my research interest are mostly in the intersection of CS and maths, so I am thinking that maybe the best choice is choosing CS+Math PhD but perhaps there aren't many such programs.

The other option is staying in my university and doing Master's in the Mathematics Department. However I want to avoid this if I have better options (I would prefer to do all of my graduate studies in good programs).

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    You may want to conider getting a masters degree in math first.
    – Dimitri Vulis
    Commented Jan 5 at 13:15

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I work in the boundary area of mathematics and CS, and am in a CS department. In general, I don't think it is a good idea to embark on a PhD in this area with a BSc in CS that was light on mathematics. (I'd be much more comfortable with a BSc in Mathematics without any CS-stuff in it). It doesn't matter for this whether the PhD is formally in Mathematics or in CS.

The primary obstacle is a decent understanding of what a proof is, how to write one, and how to come up with a new proof. Learning this is hard, and learning this by yourself is something only very few people could do.

Now maybe you actually have those skills and your thesis shows it. This could be enough to get you into a PhD programme in places where you directly start with a supervisor (who could read your thesis and confirm), but I don't see this working out for a US programme with decent standards.

What I recommend is pursuing an Masters in Mathematics first, ideally one with a significant research component.

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  • I would guess that my thesis is rigorous and "mature" enough so as to suggest that I understand, as you put it, "what a proof is". However, aside from very few exceptions, it mostly consists of known and simple proofs etc. and does not have anything trully unique. Do you think reaching out to some professors (supervising in such programs) specifically from my country (since I think I've read that proferssors take more students from their country) is a good idea?
    – Yuumita
    Commented Jan 5 at 15:11
  • A remark, for whatever it's worth: CS has more marketing heft at the moment than math, and it seems to me more demand including in academia. Easier at the end to go that route through a PhD if you're split between the two.
    – user176372
    Commented Jan 6 at 1:07
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I don't entirely agree with the answer of Arno or a similar comment. That would be entirely true in Europe, I think, but this a US view.

An undergraduate math program in the US has about 40 semester courses of which about half are in mathematics. The rest cover a variety of topics in science, the humanities, writing, etc. Those courses are generally light in research as is the program overall (most places). One or two CS courses might count in that math major (algorithmics, say). The math courses also cover a broad range of math topics including analysis, algebra, topology, and some others. In other places, the undergraduate program seems to be much more focused on a single field. I believe this is the case in UK (Arno can comment) and Germany at least and perhaps generally in Europe.

Next, note that it is relatively common for students to change majors/focus when going directly from a BS to a doctoral program and admissions committees are used to dealing with that fact.

Third, the most common path in the US is directly from BS to a doctoral program, with a MS possibly earned along the way, sometimes just by filing a form, sometimes with a modest additional task or two. The first task of such a student is to prepare themselves for comprehensive examinations through coursework at an advanced level. One seldom starts math research immediately, even if they have a MS since comprehensives are still a gate.

Finally, the only way to know if your record stands up is to make application to a few places and see how far you get in the process. If you apply only to "top" schools, you may not get very far, but the US has many, many, research universities at which you can find a good/great advisor.

A strategy might be to simultaneously apply to both masters and doctoral programs so that you have a backup that still advances your goals if you aren't accepted into a doctoral program. But before you sign up for a masters, be sure that the coursework is likely to also enable passing comprehensives, which can be very difficult. Typically they cover a broad range also (analysis, algebra, topology, ...)

See the answer for the US here: How does the admissions process work for Ph.D. programs in Country X?

Forty courses for a bachelors degree is common in US. Another scheme has about 32, but still only about half in the "major". The coverage is about the same, but the dividing lines between things a bit different. Top students might take a few extra courses.

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  • The problem with masters in the US is that I think they don't usually support you financially (at least not fully). I can maybe secure a scholarship from an organization in my country but I am not sure if this is enough, I have to research this a bit. So you think also applying to masters (with the intention to apply for a PhD afterwards) is a more viable option? How probable is it to actually get accepted for the PhD afterwards? Can I skip or speed up the starting stages of a PhD if I have a masters?
    – Yuumita
    Commented Jan 5 at 15:26
  • Phd funding in the US is usually via a teaching assistantship, especially in math. There is little funding for masters programs here. Another reason to apply for a doctorate. You need English skills and familiarity with entry level undergrad courses. The masters only "speeds up" the process if it gets you close to the point of passing comprehensive/qualifying exams.
    – Buffy
    Commented Jan 5 at 16:01

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