Combinatorics, number theory, and graph theory, in what order should they be learnt?
I would like to learn discrete math; these are the three main branches that compose it. I was wondering if there's a "best order" to learn them, or if they can be learnt in any order.
I have taken course on all of these subjects, and here is what I would recommend (since you are asking). First combinatorics, then graph theory, then number theory. Taking number theory at the same time as abstract/modern algebra is a very good idea, since there are lots of connections between group theory and number theory.
My justification for this particular ordering is the simple fact that combinatorics will teach you how to count, which will make you a better graph theorist. Graph theory will teach you how to represent mathematical structures graphically. In number theory and algebra, sometimes combinatorial arguments are handy proof mechanisms. Many properties in algebra and number theory have graph-theoretic representations, such as the Cayley digraph of a group.
You will find that graph theory is especially useful in almost every type of mathematics, computer science, etc...