Schools Should I Choose Math, Computer Science, or an Interdisciplinary Grad Program?

[Bourbaki1123]

I am currently a junior undergraduate and I am interested in too many areas, or I don't know how to reconcile my interests. I have a lot of interest in algebra and algebraic geometry but also mathematical logic and theoretical computer science. I am taking independent study courses for Algebraic Geometry and I will have a minor in computer science plus I will have taken Theory of Computation, graduate level mathematical logic, independent study in theory of recursion(hopefully) and independent study in advanced set theory.

I have developed a pretty strong interest in theory of recursion and I want to look into algebraic methods in computer science (I see that there are apparently a lot of applications of abstract algebra to computer science). I also am interested in automated theorem proving(to a lesser extent), and set theory (by grad school I will probably have covered forcing and the ideas surrounding large cardinals, though I am not at that level yet).

I have read the first few chapters of J. Donald Monk's book Mathematical Logic, and a good part of Smullyan's book on Gödel's Incompleteness theorem. I plan on beginning Smulyan's book on Theory of Recursion soon. As far as general mathematical logic, I am familiar with the basic ideas of proof and model theory and the completeness theorem and the Löenheim-Skolem theorem.

I suppose my interests could be broadly divided between algebra/algebraic geometry and mathematical logic with a focus on computer science.

So should I go math, or computer science or something in between? What kind of programs might suit me (ignoring the difficulty of getting in, I'll worry about that myself)? Any assistance will be greatly appreciated.

 

[twofish-quant]

So should I go math, or computer science or something in between? What kind of programs might suit me (ignoring the difficulty of getting in, I'll worry about that myself)? Any assistance will be greatly appreciated.

For graduate work, you need to think in terms of professors rather than in terms of subjects. Go to the library, pull up papers that seem to be related to the fields and topics that you are interested in, and then see where those professors are, and apply to those programs (and mention that you did this in your statement of purpose.)

One thing that is very different between different schools is which departments talk to each other, and which departments don't talk to each other. You are probably looking for a school in which the math and CS professors have offices next to each other, take each other out to lunch, co-author papers together, have joint seminars, etc. etc. It's pretty much impossible to figure this out from the department name, but it usually becomes obvious if you look at the research output and the schools web pages.

 

[MathematicalPhysicist]

You're in luck Algebra and Logic complement each other.

P.S
Smullyan's great, I stopped somewhere in my reading of incompletness' textbook, hope to reread it someday.

 

[Bourbaki1123]

Thanks for the advice. I know Carnegie mellon seems to have a great correspondence and they even have a phd track for pure and applied logic that has people from math, philosophy and computer science. It seems pretty promising, especially coming in as a math candidate since it seems a lot less competitive than going in for computer science (you can do the program as a philosophy(I think), math or computer science candidate). there are definitely a couple people there I would like to work with.

Questionow much would it affect my chances of getting into a grad program if I find a professor who I can keep in correspondence with whose work is interesting to me? It seems as though building a relationship with a professor ahead of time would boost my chances plus it might get me the adviser I want. Does anyone know about this?