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I'm a final year computer science undergrad and I'm looking to pursue a PhD in theoretical computer science in the long term. I've been admitted to some great schools to do theory like Princeton and Berkeley but right now, I'm looking to defer all my admits to study math for a year since I've been admitted to study Part III at Cambridge on a full scholarship.

I'd very much appreciate your thoughts on the following couple of questions.

  1. So, given that I'm not really sure what sort of theory I want to be doing at grad school (as of now, algorithms and combinatorics) what sort of things should I be looking to study there?

  2. As someone who has studied computer science and not pure mathematics for the last few years, I want to take the next few months to prepare myself for the course. Can anyone recommend areas (and/or books) to bone up on before going there? (Since for instance, I never formally studied abstract algebra or complex analysis)

Thanks a lot.

EDIT :

I realize that my question as previously stated was too dependent on my personal specifics and here's a restatement that I hope fares better -

What things, that most mathematics undergraduates learn, do you think a Computer Science major should make sure he knows if he plans on following a masters course in pure mathematics with a focus on discrete mathematics (things like extremal or additive combinatorics) and some algebra?

Thanks again.

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 Isn't your first question saying: 'Given that I don't know what I want to study, what should I study?'. I don't know any CS so I can't rule out the possibility that someone who does might come along and say: 'Secret Tip: Make sure you learn field X really well', but my take would be that it really is up to you which courses you take at Cambridge. If you've got a PhD place already sorted then you are very lucky and can just have fun, meet people, broaden your outlook, learn what takes your fancy. Things that are somewhat relevant will probably naturally fall under these criteria. – Spencer Mar 24 2011 at 0:58
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 But your concerns are reasonable! I could say a lot more on the topic but I'm not sure MO is the right place for the question in the first place and so I will resist. – Spencer Mar 24 2011 at 1:00
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 -1: "too localized": Part III at Cambridge – Hans Stricker Mar 24 2011 at 1:37
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 Thread opened at meta if people want to argue the case for or against closing this question: meta.mathoverflow.net/discussion/993/… – Yemon Choi Mar 24 2011 at 2:17
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 One slight problem with inviting discussion here is that Part III is a peculiar and atypical beast (or at least it was when I took it) and the content & presentation of some courses can depend heavily on who teaches them. I would get hold of the list of offered courses ASAP and then do some diplomatic asking around ("so, what's that lecturer supposed to be like") - but that isn't something that can really be done here on MO! – Yemon Choi Mar 24 2011 at 2:55
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closed as too localized by Hans Stricker, Ryan Budney, Will Jagy, Daniel Moskovich, Andres Caicedo Mar 24 2011 at 3:21

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