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I am new to this forum =)

I did physics and now I'm planning to apply for graduate studies in pure maths. I know it's relatively easier the other way (maths to physics).

I never had any proof-based mathematics courses but I've been reading pure maths books (such as books of Munkres, Spivak, Rudin, Lang, etc) and I've been trying to prove theorems as many as I can.

Now you might be wondering why I didn't register in pure maths courses and why I decided to switch. The reason is because my university in undergrad doesn't offer any pure math courses/program. I did my undergrad in non-research oriented university outside North America and Europe, and I didn't have any idea how to do proper mathematics nor how to be a scientist. Luckily, I got full scholarship for a 1 year master's program in Theoretical Physics in North America after my undergrad and there I experienced the real academia. But now I realized that I'm more into pure maths...I prefer to study things in rigorous way. I realized that I'm just interested in physics if it's only mathematical or very abstract, and I really enjoy proving than doing long calculations.

I'm primarily interested in mathematical physics or specifically in the interconnections of geometry, topology and high energy physics. I'm also very curious about analytic number theory and algebraic geometry but I barely know stuffs in those two fields.

Now my question is: Are there any good Mathematics departments which accept applicants who didn't acquire a strong background in pure mathematics (from university)? Or what is the best route for my case?

I know, I might be admitted first as qualifying student. Which universities does give enough financial support for students in qualifying year?

Just to give some points that might help: I have a high GPA and took advanced theoretical physics courses such as string theory, general relativity, conformal field theory, etc.

Responses will be greatly appreciated. Thanks in advance!!!