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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.


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

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Could you be specific on which parts you want to see a visualization of? –  Ｊ. Ｍ. Sep 19 '11 at 2:11
For visualizing proofs, there are various types of natural deduction (deduction trees, flag notation=Fitch diagrams.) For visualizing links between theorems IMHO programs that visualize graphs (as rectangles connected with arrows) are suitable. –  beroal Sep 19 '11 at 9:30
Funny, I'm usually down with Visio for these sorts of things... :) –  Ｊ. Ｍ. Sep 19 '11 at 15:07
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2 Answers

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.

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+1, good link for software. –  Emmad Kareem Dec 18 '11 at 12:48
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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.

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