I'm trying to map out how certain mathematical subjects depend on each other, i.e. which subjects could be described as prerequesites for which other subjects, in the sense that the former define needed or helpful concepts for the latter. In a crude ascii diagram, which might look messed up depending on the width of your spaces, what I've got so far is: A / \ B C |\ /| | D | |/|\| E | F | |\| | | G \|/ H where: A= set theory B= abstract algebra C= general topology D= real analysis E= Lie groups and algebras F= algebraic and geometric topology G= differential topology H= differential geometry Higher levels are prerequisites for lower levels, and connecting lines represent strong dependencies. As the ascii diagram might be illegible, the dependencies are: B depends on A C depends on A D depends on B and C E depends on B and D F depends on B, C, and D G depends on D and F H depends on D, E, and G Of course this partitioning of knowledge is rather arbitrary and subjective. To explain a couple choices: I've extracted "Lie groups and algebras" from "abstract algebra" because I'm considering the latter as strictly the general, elementary stuff. And both "Lie groups and algebras" and "algebraic and geometric topology" depend on "real analysis" for its rigorous notions about continuity, or so it seems to me. I'm interested in people's opinions about whether this particular organization seems reasonable, or whether some dependencies should be added or removed, etc.