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Math roadmap: Calculus and beyond

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This is sort of a sequal to http://www.gamedev.net/topic/645932-fastest-learning-path-to-spherical-harmonics/, but in a more general sense
So after I go trough the foundations(calc 1-3 and differential equations) what would you recommend as the next progression and what books would you recommend?I'm looking for all-around books that cover topics from analysis, but it's so broad, that I'm not sure where to branch to.Also about the books - are there any authors that are commonly accepted in the math community as "the best"?It would make it easier, because I'm not sure what learning sources to use.

http://mathworld.wolfram.com/topics/CalculusandAnalysis.html Should I just search for authors of books related to these categories?It's obviously impossible to cover them all, but I'm not sure where to go, maybe I should make a list and write a description for each category and see which one I feel I should branch to and which one would teach me skills that I might decide that will be most useful.

I'm most worried that I might end up learning a little bit of everything, but not ever gaining deep knowledge in one area.

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Finish learning calc and differential equations first.

Searching for what to do next before finishing the first step is an excellent way to never get there.

 

 

Once you know everything there it will be much easier to search out information and see for yourself what different directions there are and what interests you the most.

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Realistically, Calc III is going to help you tremendously with mostly everything you need to know about the math behind motion, vectors, projection, ray tracing, components, positioning, et cetera. So pay very close attention that course. Also, you could get some PDFs on Quaternion Algebra, and other texts about quaternions because of how cost effective toward memory using quaterions is. Hope this helps.

 

Regards,

 

Faraday

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