- #1

Bourbaki1123

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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.