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I will be applying to CS PhD programs coming fall. I have a BA in Mathematics right now.

I am hearing that it is harder to get into a CS PhD program if I state I want to study Theoretical Computer Science because there are less funding opportunities for the area. So if I state I want to study TCS in my SOP, I might have a hard time getting in to a program as opposed to something like Systems or AI that have lots of funding and faculty who are willing to take students. Is this true at all? I am talking about getting into a CS PhD program in the first place by indicating my interest in TCS. I am kind of worried because I do want to pursue TCS in grad school and have done undergrad research in coding theory and also number theory.

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    What country is this?
    – Buffy
    Jul 10 at 22:06
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    It is probably true that you will have a better chance of getting in if you are willing to study AI/ML. However, if you want to study TCS, what will be the point of saying that you want to study AI/ML? Jul 11 at 8:06
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    Can only agree with @AgnishomChattopadhyay - if you are accepted into the program saying you want to do AI, would you actually do AI when accepted, or are you hoping you will be allowed to switch to TCS?
    – Sabine
    Jul 11 at 8:56
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    Think of graduate admissions as not only a process to be gamed strategically by the applicant, but also as a process of fitting students to the programs that suit them best and vice-versa.
    – Bryan Krause
    Jul 11 at 14:47

5 Answers 5

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This is a US-based answer.

Theoretical computer science is indeed less well-funded, but it is also less popular, and the effect of this on graduate admissions is complicated. You should also consider the effect on your eventual chances for jobs after you finish your PhD.

The main effect of TCS being less well-funded is that many lower-ranked, smaller departments do not have anyone in TCS at all and have no plans of hiring anyone, because the people they can hire in TCS would not be able to get funding. If your record can only get you admitted to, say, University of Georgia, then you are out of luck; they don't have any faculty with primary interests in TCS as far as I can tell.

On the other hand, if you are competitive for admission at University of Illinois at Urbana-Champaign, then you probably need a slightly less impressive record to get admitted in TCS, because they have a lot more applicants interested in AI/ML than their faculty can advise, whereas they only have somewhat more applicants interested in TCS than faculty availability.

You should make sure you are only applying to departments with several faculty primarily interested in TCS, but if you are doing that (and competitive for admission in those departments), then mentioning an interest in TCS probably helps your application.

You should also consider the other end. Once you get a PhD, only the best researchers in the TCS will eventually get faculty jobs at research universities (or research jobs in industry), whereas merely good researchers in other areas frequently manage to get faculty jobs.

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  • Thanks for that answer! I am looking for faculty whose research areas are around "design and analysis of algorithms". I am aiming for mostly top 30-40 ranked CS PhD programs. Should I be fine with TCS at these schools? I see about at least 3-4 profs doing TCS (some kind of coding theory, algorithms, complexity etc) at most of these programs. Jul 11 at 1:49
  • You have to be a little careful here. Say a department has a professor who primarily works on network protocols, and somewhere in their work they needed to develop an algorithm to solve some network optimization problem which they couldn't find in the literature, so they write an algorithms paper that gets in some second-or-third-tier algorithms conference (or just for a journal). Now their department advertises them as working in algorithms as well as networking, but that's a bit misleading, and they're not going to be a good advisor for someone who just wants to do algorithms. Jul 11 at 2:10
  • So how do I find someone who works just in algorithms? Will they be in related fields? Like graph algorithms, complexity etc. If I see a prof who does "algorithms, optimization, complexity, coding theory" etc, then can I count them as a prof who does TCS? How do I actually know who would be the right advisor? This is to, of course, mention their name in the SOP. Jul 11 at 2:42
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    Look at their actual CV/publication list. Jul 11 at 3:00
  • Thank you! Do you mind taking a look at my SOP after I am done writing it? Do you have experience reading SOPs written by CS (or TCS in particular) applicants? Jul 11 at 13:37
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Graduate studies are no cake-walk. You will likely be totally on your own, motivation-wise. Your advisor will advise you, but very likely it will be up to you to develop the motivation to actually get through - do not expect your advisor to pull you along.

Doing things that interest and motivate you in themselves makes a huge difference when the going gets tough. In the best case, the time will fly by and you will be sad when it's over. If instead you study something that does not really interest you, chances are you'll not get through the darker phases.

Another aspect: If I were on the committee that interviews graduate applicants, I would strongly look for people that show great interest (and somehow give me the feeling that they are able to do it, of course). Especially because that field has less funding, they will try to pick the cherries amongst the applicants. And vice versa - if you apply to a ML/AI course, and the board notices that you don't really feel like it's the most interesting thing for you, your chances of getting taken might diminish significantly.

So, do what your heart tells you. Of course, don't be blind to realities, but if you burn for TCS, then study TCS.

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I am hearing that it is harder to get into a CS PhD program if I state I want to study Theoretical Computer Science because there are less funding opportunities for the area. So if I state I want to study TCS in my SOP, I might have a hard time getting in to a program as opposed to something like Systems or AI that have lots of funding and faculty who are willing to take students.

The statement about AI is not correct. In fact, AI/ML widely considered the most competitive field to apply in right now, and much more competitive than theory and systems, because there is an explosion of applicants interested in pursuing a PhD in AI/ML, with generally far fewer faculty available than can advise all those interested.

Zooming out a bit: your ability to get in to a PhD program in an area X is roughly a function of (1) your application strength in X (rec letters, profile, and interests), (2) funding in area X, (3) the number of candidates interested in X. You are very focused on (2), but (1) and (3) are probably more important, especially if you are open to being funded through TA-ships rather than RA, which typically doesn't need the faculty to have as much external funding.

Comparing between theory and systems, it's less obvious; as far as I have seen, neither theory nor systems is especially hot at the moment, so they may be roughly equivalent (for metrics (2) and (3)).

This is all besides the point, though: if you are interested in theory research, why not give yourself a chance and apply? By far the most important factor to do a successful PhD is that you are working in a field you believe in. Without a doubt, your interest and excitement at this stage will take you further than just following the money. Good luck!

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Actually, in the US, you have a lot of time after entering a doctoral program with a bachelors to choose a specialty. The first years are advanced coursework leading to comprehensive exams. You get to look at both areas of specialization and faculty members who might advise you.

Whether a university is more interested in theoretical CS or hot topics like AI depends on the faculty and also on which of the faculty are looking for doctoral advisees.

I wouldn't be too concerned, but it would probably be good to keep your options open for the moment and project some flexibility in a statement of purpose. Saying that your current interests are in more theoretical aspects is almost certainly fine.

Note that acceptance in the US is broad based. A single thing, especially a statement of interest in theory, is likely to have very little weight compared to things like GPA, letters of recommendation, specific courses, and such.

Also note that funding is less for many theoretical fields is less because less is required. If you don't need expensive labs/equipment then there are few funding requirements. Most students in such fields are supported as teaching assistants, which provide a service to the university and are adequately funded. TCS and math are similar in this regard. Even in physics, some theoretical aspects require little if any funding beyond salary. Einstein didn't require an experimental setup to come up with special relativity. (IIRC he was terrible at experimentation.)

Don't overthink it.

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  • So overall, it wouldn't be a problem if I wanna study Theoretical CS (algorithms, graphs, complexity etc) as opposed to ML/AI? It wouldn't hurt my chances of getting in, right? Jul 11 at 14:18
  • Generally, not a problem. But specific programs might have specific needs, so not a universal. The US is pretty flexible about such things at your stage.
    – Buffy
    Jul 11 at 14:20
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I am a TCS grad student. Yes, it is noticeable that there is much more funding for ML/AI right now. My advice is to do (or at least try) what interests you. However, I will point you to another field that recently seems to have a hype going on and might be an option for you -- Quantum Computing.

This is not my area of research and so I am not that much into it, and it is definitely a broad field. But in certain areas of QC there is much of TCS involved -- BQP; QMA; the recent result MIP* = RE; Quantum fine-grained complexity, ...

As said, I do not know much about this field, but from what I do know your math background might be beneficial here -- Hilbert spaces, Unitary Matrices, the Spectral Theorem, all stuff that pops up there (to be honest in a finite-dimensional toy variant most of the time, but anyway, depends on how much you want to delve in) and you probably already have learnt (some of) this stuff as a mathematician.

As far as I heard, it is not expected that this QC hype ends soon. Companies are already establishing use cases, consulting companies evaluating applications and in general it is expected to have an impact on industry in the near future (some say next 10 years, some say next 30 years). Furthermore, there is some kind of a national competition between the US and China on quantum supremacy (and also Europe is investiging a lot recently, but as far as I know they buy their hardware in the US).

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  • So if you are interested in studying algorithms, complexity theory, is it harder for you to be admitted into the program in the first place? (going straight from an undergrad) Jul 11 at 14:04
  • To be honest I do not know anything about specific QC PhD programs, I just wanted to help you broaden your perspective and show you another option. Some universities that are into QC (where you might find further information): Texas Austin, University of Waterloo, QuTech (at Delft University), MCQST (Munich) -- just a few (big?) names that came to my mind. There are probably much more, but that should give you a start. I am really not into this community, I am just an outsider who tries to keep up.
    – StefanH
    Jul 11 at 14:13
  • Thank you! But I wanted to ask you about TCS in general, not QC. Lets say I wanna work with professors specializing in designing algorithms, studying computational complexity, coding theory etc. Will I have a harder time getting in if I state I am interested in these fields, since they are typically less funded? Jul 11 at 14:17
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    I do not think so, it might get harder after the postdoc phase maybe. But there are a lot of professors and institutions doing research related to what you have mentioned.
    – StefanH
    Jul 11 at 14:25

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