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I'm mainly a programmer, but I have a love for Mathematics that's been, well, insatiable. I've had my eye on learning Quantum Groups and Relativity, but I want to stay in something I can do with Computer Graphics. What do I need to know?

I have got a solid grasp of:

  1. Calc I,

  2. Clac II

  3. Some Calc III (basically 3D+ applications of single and multidimensional calculus).

  4. Linear Algebra (for graphics programming)

I have a decent grasp of:

  1. Abstract Algebra,

  2. Set Theory

  3. Binary Lattices (mostly from computer mathematics).

I do have a book on finite groups that is really interesting. However I have to admit, that other than knowing that in hyperbolic geometry sinx - cosx = 1 is nearly the extent of that subject.

So, what I think I'm asking is how to go from where I'm at, to get to the calculus of manifolds, riemannian geometry, so on.

EDIT: I think what I'm looking to do is mainly Theoretical/Mathematical Physics, specifically things that I can make into awesome graphics programs.

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2  
I heard good things about Michael Spivak's Calculus on Manifolds. Mainly that it's exceptionally difficult, but that it pays off greatly. Just throwing it out there. –  Adar Hefer May 2 '13 at 12:50
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What does Galois theory have to do with your problem? (Most of quantum mechanics and relativity do not require knowing Galois theory at all!) –  Willie Wong May 2 '13 at 12:58
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@Adar Hefer, I have that book, I just don't understand it when I do a read over of it yet, probably will take a bit more of a closer look. –  mathacka May 2 '13 at 13:04
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@mathacka check out the index of the Amazon textbooks that come up when you Google group theory and physics-no Galois theory. Galois theory is most directly related to number theory, which is getting more connections to physics but isn't central for that purpose. –  Kevin Carlson May 2 '13 at 13:14
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Your title also mentioned quantum groups. They are quite different from quantum mechanics. It will help if you clarified (edited the original question) a bit what exactly it is that you want to learn. –  Willie Wong May 2 '13 at 13:19
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