Is there something like directed graph for mathematics domains that shows you how to learn any domain?
For example, you have to grasp basic arithmetic to be able to grasp basic algebra.
However, I'm interested in as completed graph as possible. I'd like to know, what I have to learn and in what order to grasp Markov Chain Monte Carlo, elliptic curve cryptography, bayesian statistics, mathematical foundation of artificial intelligence methods, etc.
Is there something like that for mathematics?
Is there something like that for... whole science?
Not a Complete Answer, but this does provide some related discussions, problems with this question, and a way to find out exactly what the graph is.
This was already discussed on the xkcd forums, and here is the farthest they got.
Math Dependencies http://forums.xkcd.com/download/file.php?id=29015&mode=view
The discussion died out when people brought up the fact that several fields of math intertwine at higher levels. The only suggestion I have to prevent any interdependencies is to separate the fields of math into distinct subjects, like separating Calculus I into limits, derivatives, and integrals. To find an answer to this, we need to build a tree by picking a random, but very specific topic, and then asking someone who knows what they are talking about what exactly we need to deal with this problem.
Another problem is that you can often use higher order math to prove simpler results, which often leads some people to group them together. Some people, for instance, say you need to know linear algebra to understand graph theory.
tl;dr: I would recommend focusing on specific subjects (limits) instead of domains (calculus/analysis).