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What are some interesting, but less popular, math topics that are useful for physics that can be self-studied? Specifically, topics that might ultimately be useful in high energy theory (even if it is a while down the road).

My background is: real analysis, differential equations, advanced linear algebra, complex analysis, and some functional analysis.

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Why do you ask? –  Mew Dec 19 '12 at 6:41
    
"interesting, but less popular" The specific math topic is either required or not. As for your question, for a start you should know algebra and differential geometry, that's the basic requirement for every field in physics. –  Yrogirg Dec 19 '12 at 6:51
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Hi Alex - sorry to keep harping on you about these sorts of things, but questions like this which are just asking for a list of things aren't really appropriate for this site. Like the FAQ says, we're looking for specific questions that have specific, definite answers. –  David Z Dec 19 '12 at 6:54
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Hi @Alex, maybe you can have a look at what Gerard 't Hooft says what is needed to become a good theoretical physicist here. Maybe you can restate the question at Math SE too, there seem to be a number of people interested in advanced mathematics and high energy theoretical physics too. I've seen questions there of people seeking advice about what is needed to study theoretical physics from a mathematical point of view, that get answered. I'm sorry to see that you get closed here and wish you good luck and success for your studies. –  Dilaton Dec 19 '12 at 10:59
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closed as not constructive by David Z Dec 19 '12 at 6:52

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