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
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:
(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?