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So, I finished Computer Science study about 3 years ago (I'm 28 now) and lately I've been craving math.

As a daily job I work for a start up company building a web application. I mostly done web apps but previously I did some other things like RESTful web services, (Enterprise) Document/Content Management Systems, some frontend JavaScript, some Java byte code manipulation, various perl/ruby/bash scripts, ... You name it.

But I've started to realize most of the latest work I did was just bringin/glueing some premade components/services together. And this is not as fun. I remember programming being about problem solving. Hard problems we had to solve in college were really fun. So I started to learn a bit of Haskell.

Haskell is a pure functional programming language that has alot of constructs from category theory. Constructs like functors, monoids, monads and so on. Learning a bit about this was fun again. Then I started looking into category theory, and altough I did understand the basics I was missing some other fundemantls. So I started backtracking to see what I would have to learn to be able to understand it and then I realized, that maybe this side of programming is what I want to do. More on the theoretical/math side.

I really want to learn more math (and of course relearn what I don't remember anymore from college) so I would be able to use it well with my programming knowledge. Category theory is just one of many things I'd like to know.

So here goes the question...

How hard would it be to learn math on my own from sources like Khan Academy and online videos lectures from universities like MIT, Harvard and books and so on. Or should I consider pursuing another degree in mathematics? I don't have problems with time since I work when I want (no fixed hours).

Any suggestions?

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3  
Kahn category theory, sounds wrong somehow. –  James S. Cook May 4 at 22:49
    
Well I'll have to repeat the prerequisites. But yes, Khan academy was just one of the sources from the top of my head. –  Matjaz Muhic May 4 at 22:56
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If you have time and money, enroll again. That’s (probably/in my view) the best way for learning mathematics. Category theory is hard to learn if you know little algebra and other mathematics, as category theory abstracts the constructions needed in many fields of theoretical mathematics. So much of it only becomes meaningful after learning about these constructions. (One should also mention that one really needs time to learn mathematics, so it might hard to work parallely.) –  k.stm May 4 at 22:56
    
Lucky you, I really wish you go for it. I started BSc in maths at the age of 25 and graduated at 28...it is not too late and attending exams in the end gives you the proper education (I think). –  MattAllegro May 5 at 0:30
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If you are looking for a book on Calculus, I will recommend Apostol's Calculus vol.1 and Spivak's Calculus. –  Graduate May 6 at 18:05

1 Answer 1

up vote 3 down vote accepted

I'll answer some parts of your question. Sources like the Khan Academy, MIT OpenCourseWare, etc are I think, a really good starting point but they are basically more inclined towards engineering students. They are not exactly rigorous as one would expect a pure math course to be. If you really want to learn something like category theory, I think you need rigourous foundations. For that, you have to hit the books. I have now reduced your intial question to the following questions:

(1) Which subjects are important to begin with?

(2) Which are some good introductory texts on these subjects ?

To answer the first question, I think those subjects are real analysis and linear algebra. Absolutely no doubt about it. Answer to the second question can be found on this site. It has been asked several times. As you gain an understanding of these subjects, you will learn about other subjects in mathematics like topology, complex analysis, abstract algebra, functional analysis, differential geometry, etc but those come later. You can ask which books to read on those subjects later. Learn analysis and linear algebra really well. Without them you will be doomed to a life of mediocre mathematical understanding.

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That's a nice answer, more than I expected. Thank you! –  Matjaz Muhic May 4 at 23:06

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