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

![enter image description here](https://i.stack.imgur.com/8WH0U.png)

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?