Question

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:

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?

Answer 1

There is a good book, that I think would help you to get more out of computer science research papers and dissertations. It’s called “Concrete Mathematics: A foundation for Computer Science“, and it’s available on Amazon:

http://www.amazon.com/Concrete-Mathematics-Foundation-Computer-Science/dp/0201558025/ref=sr_1_1?s=books&ie=UTF8&qid=1341081763&sr=1-1&keywords=math+computer+science

I think this would help because it will all be relevant, and its consolidated which will help expedite the learning process.

Even if you don’t have any money, just Google it and take a look at the index to get an idea of what areas you might want to learn.

And here’s one more interesting book.