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Next October I start a year long course in Cambridge, intended as preparation for a PhD.

I chose mainly pure disciplines as an undergrad (particularly topology and analysis) but I'd really like to pursue a PhD in one of the current areas of research towards a GUT. I don't know that much about anything besides String Theory, but input from those with knowledge in other areas would be fabulous!

I'm trying to decide which courses to take, but I don't know whether to stick with pure, or switch to applied. Undoubtedly there will be things I need to pick up while pursuing a PhD. But is one or other option preferable? Or does it really not matter? Should I do a mixture of both?

Here are some broad course areas that I reckon might be relevant, just as a reference.

Pure: Algebraic Geometry, Commutative Algebra, Algebraic Topology, Differential Geometry, Kähler Manifolds, Functional Analysis

Applied: Quantum Field Theory, Supersymmetry, Standard Model, String Theory, General Relativity

Any advice or general comments would be greatly appreciated. Many thanks!

Edit: I've attempted to make this much more general. I'm basically looking for any advice from people who've been through a similar situation!

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Isn't this more suitable for one of the physics sites on the SE network? –  Asaf Karagila Jul 12 '12 at 22:16
@AsafKaragila: My point is precisely that this lies on the borderline between Maths and Theoretical Physics, and I definitely see myself as a mathematician than a physicist. I guess this is a question of pure maths vs. applied maths. –  Edward Hughes Jul 12 '12 at 22:24
Ooh - why the downvote/close vote? I'll edit the question if necessary! –  Edward Hughes Jul 12 '12 at 22:29
I see this question as quite similar to this one which has many upvotes. Could those voting to close tell me what I've done wrong?! –  Edward Hughes Jul 12 '12 at 22:32
Even if this was a good fit for this site (it isn't IMO), I'm not convinced it's a good question. The "pure" classes are really the minimum anyone should know, even including professional physicists. And obviously you'll need to know the "applied" material if you want to work on GUT. To me, the question isn't much different from "which should I take first, real analysis or abstract algebra?" My answer: it doesn't matter much and you'll need to learn both eventually. –  Logan Maingi Jul 13 '12 at 4:15
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closed as too localized by William, Leonid Kovalev, Brandon Carter, BenjaLim, Quixotic Jul 13 '12 at 13:35

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