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I would like to know in which order I should learn different areas of maths so I can have a robust overview of all the theory in case I need something for a computer programming problem.

So I've created this mind map

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I do not intend to know all those small details about how to do a certain thing (e.g. "gauss-jordan reduction"), I would rather look over an example, but then do it with math software like sage-maths or mathematica.

I would like to know, for instance, how to get to a taylor series, given the analytical function (I know it already, I am merely illustrating the kind of knowledge depth I expect).

So all I all, I want to be able to read academic articles about maths which have applicability in computer science / programming, and actually understand something from those articles, so I can use that knowledge in solving actual programming problems.

The open question is:

  1. (a) In what order do you suggest to learn about these areas, on what areas should I insiste more?

    (b) Do you see any missing areas in the mind map?

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3  
What kind of programming problems? You can't possibly learn all the math you could need to solve any kind of problem. –  Qiaochu Yuan Jun 30 '12 at 18:51
    
That was not the question. Read carefully: to have a knowledge deep enough to be able to understand anything easier (within "reasonable time"). –  Flavius Jun 30 '12 at 18:54
2  
Linear algebra and some basic discrete mathematics (set theory, graph theory, combinatorics,..) would be a good way to start. From linear algebra you can branch off into numerical analysis/computational math, abstract algebra, functional analysis, etc. From discrete math, you can have a foundation for a lot of the more computersciency topics on there. –  Nick Alger Jun 30 '12 at 18:57
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