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Redsummers

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So, to get an idea, I am currently studying a Physics B.Sc. in Germany (taught in English). My grades are fine so far (A-ish? German grading is weird). And I will be graduating next year (i.e. June 2012). So, I would not be worried if I had to apply to a physics graduate program...

HOWEVER, this past year I have become really attracted to pure mathematics. By this I don't mean that I want to pursue a graduate degree in Theoretical physics; I want to pursue a graduate degree in pure mathematics.

Now the problem is, in Germany, the universities where you can pursue graduate studies in English for Mathematics are two: the BMS (Berlin) and Uni Bonn. Obviously, Uni Bonn is one of the top notch universities for Mathematics in Europe. They have the max Planck institute for mathematics there, etc... And the BMS is quite well known in Europe, so that I don't know whether I would really have a shot or not.

That said, since I want to broaden my chances, I have considered applying to the US. Now, my problem is that I don't really know how does a 'changing plan' like this would work in the US.

Can physics students apply to a mathematics department? Or they just get rejected right away? Do you think I should apply to an undergraduate math-degree, instead? (in that case, would I need to take the SAT? could I take the M-GRE to get into an undergrad math program?)

I have been doing some searching in different Math dept., but I don't see anything related being mentioned...

The branches I am most interested with, are Algebraic topology, category theory (specially the notions of Topoi) and some aspects of Algebraic Geometry. But that's definitely not all, of course. The familiarity with such branches comes from me reading books in the library.

Do all the departments in the United States have Algebraic Geometry and Algebraic Topology seminars? (I don't think that's the case, though...). Do you know of *reasonable* universities (i.e. where I would not get rejected right away) with such seminars?

I tried to find a list in google, but couldn't find any... Do you know if such a list exists? Or, say, a list with research interests arranged by universities?

If somebody has answers to this questions regarding Canada instead of the States, I would be pleased to hear them too. I have actually been considering Dalhousie university, but I think it is really well-known, so that my chances wouldn't be too high either. Well, that's my impression. Never been to Canada.

And for the UK... really, UK has a complex system. Because I think I would have to take the masters first (like in Germany), but they consider a master as the 4th undergrad year, and it's somehow of a transfer, etc. So I don't know if I should really consider UK..? (maybe it's easier than what I think!)

I would really appreciate your input on this matter. I have been googling too much, but I am sure that people here have such information already in their heads. Thanks!

P.S. For the ones wondering about background info.:

My math courses here in Germany consisted of Real Analysis I (sequences, differentiation), Real Analysis II (integration, integration in R^n, vector Analysis), Complex Analysis (Cauchy-Riem. eq., Liouville's thm., Cauchy's thm. cauchy's formula, Runge's thm., etc.), Measure theory (σ-Alg, etc.) together with Integration theory (Lebesgue's etc.) and its generalization to Functional Analysis (Hilbert spaces etc.), and finally theory of Distributions (Dual spaces, Schwartz' spaces, etc). Hmm... Also Linear Analysis (+ intro to Abstract Alg.), ODEs, and a small intro to PDEs. All courses are proof based, of course.

Hopefully my bachelor thesis will be about Complex Manifolds, showing some properties, theorems, extensions, and finally some applications to Physics (for a Physics degree, the Bachelor needs to be minimally related to physics lol.)

P.S.2 ops, the post was way longer than I expected it to be.. sorry!