Considering a Math PhD & Computer Science Professorship: Pros & Cons

[mathcompsci]

Hi.

I have a question about careers.

I'm graduating this semester with a bachelors in pure math. I've been accepted into a computer science masters.

I plan to study AI for my masters, and hopefully some applied math.

What I would like to do is this, go for my Ph.D. in math afterwards, and then go be a computer science professor.

Is that absurd? I really love math and want to do math all the time, but I really love AI (we'll know soon if I do).

My fear is that if I don't do the math ph.d I won't know the math I want to know, nor will I be able to contribute with math research (I hope to find my own field someday).

My other fear is I won't be able to get a comp sci professorship with a math ph.d

The reason I want to be a comp sci professor is because of the freedom to move back and forth, but the reason for a math ph.d is I really want to focus on math alone for 5 or 6 years.

Really I'd love to be in both worlds. I want to be a mathematician who does research in math, but I also want to be an AI researcher too.

What do you guys think?

 

[maverick280857]

There is a considerable overlap in theoretical computer science and mathematics, and also an overlap of mathematics with "applied" fields such as AI. Many university professors in computer science departments have PhDs in Mathematics. I am also a student like you, so I cannot give an authoritative answer, but I believe you can do either.

Recently, a professor with a bachelors, masters and PhD degree in Computer Science got recognition for solving a problem that is as mathematical as it is computational, viz. that of finding an efficient algorithm for primality testing.

Imho, computer scientists will generally concern themselves with mathematics which seems to be applicable to the solution of problems in computer science (someone please correct me if I am wrong). Fields like computational geometry, algorithms, numerical analysis, computational number theory, computational algebra, cryptography are just some areas which are explored by both "pure" mathematicians (with PhDs in mathematics if you wish) as well as computer scientists and applied mathematicians.

Also, I must state that mathematics is all pervasive...we can't say that a particular field of mathematics is not relevant to computer science. So, obviously the above list is not exhaustive. Topology, graph theory, randomized algorithms are other overlapping fields.

I will leave this for a more experienced person to answer...these are just my own views.

 

[mathcompsci]

Thanks Maverick. Yeah it does seem like I could do either. But I feel strongly pulled towards both - really strongly pulled.

Today, despite having graduated last Friday, I have studied both algebra and differential geometry (two of my favorite subjects) and I have studied genetic algorithms and genetic programming.

There has to be a way to get both of these entirely. I just haven't figured it out yet.

I'm nervous about taking too much math with my masters in computer science. I have very relaxed core courses, actually only two, and that's awesome. But I really want to focus on the theory of AI more than the programming end of it. And if I get too close to math I want to just study that too for the fun of it.

If I choose to go computer science then I don't want to disqualify myself from applying to ph.d programs by having taken too much applied math with my masters in computer science.

Thanks.

Any more thoughts?

 

[maverick280857]

There has to be a way to get both of these entirely. I just haven't figured it out yet.

Have you spoken to your teachers? I'm sure you can find someone in the Math department who works on computer science related areas of your interest, such as AI. (Genetic Algorithms seems interdisciplinary..in my school, some professors from Mechanical Engineering work on it too.)

Maybe someone on the forum here has graduated in Math and is working in AI?

If I choose to go computer science then I don't want to disqualify myself from applying to ph.d programs by having taken too much applied math with my masters in computer science.

I think if your interests lie in mathematical fields of CS (like those I mentioned in my previous thread) you should be fine. Why do you think you would disqualify yourself in PhD programs? I am sure CS depts believe that the more applied math you have, the more diverse your set of skills is.

At the same time, when you apply to a PhD programme in Computer Science, a Masters in Computer Science means you have a Masters thesis in CS and some CS courses...anything else you have done (in Math) could be a bonus but cannot be a disadvantage/downside.

Are you going to do these Math courses during your CS Masters instead of some CS courses? If yes, are those CS courses which you can opt out of related to your Masters thesis and/or your areas of interest for PhD? Even then, you can do them as part of your PhD coursework.

So, imho, you really can do both...I somehow see a strong overlap. Maybe you can do a PhD jointly with two professors--from CS and Math departments. Again, talking to faculty in your own school will definitely be helpful.

 

[yoran]

Here is another example that will convince you. My professor for Operating Systems did his undergraduate in Mathematics, his PhD in Theoretical Physics and now he's at the Computer Science department doing research in AI. So everything is possible!