Proof Visualization

Question

I'm working through Apostol's 'Calculus, Vol 1', with a focus on learning the theory behind calculus. If you are not familiar, Apostol starts with analysis of the real line and works his way through some basic axiomatic geometry to integration and differentiation. As such, I'm constantly trying to track the relationships between various theorems and axioms.

I was wondering if anyone had any tips or tricks to help this. I have an idea for a visualization program, but I'm not skilled enough to pull it off, and I don't have the time to devote to learning programming just to learn to write it.

Best.

EDIT: I realized I was being silly and all I need is a flowchart.

Answer 1

Give a name to each theorem or concept that you find is important. Edit a file with the logical relationships among them, ie, what theorems are needed to prove a given theorem, or what concepts are needed to define a given concept. Use a format understood by Graphviz and you can draw nice dependency graphs.

Answer 2

Two programs that I (have) use(d) for this purpose are Personal Brain, and Mind Manager. PB is fairly unique, the MM paradigm is supported by many programs, i.e. E-Draw. I think that your use case is that you want to make re-usable notes of your reading work. Many people use a Wiki for that. You can create a Wikipedia clone on your own PC. And if you use Opera you can instantly share it with the world, no need to create a domain with a web-server.