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Speaking of the lack of education in proofs and popularizing math, do you (or anyone else here) know of good resources to practice and learn more about proofs? I've asked several professors and TAs in my CS program and they say "practice," but they couldn't point to any good tools for self-teaching and I don't really feel confident evaluating the material I've found on my own.

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Velleman's "How to Prove It" is a nice textbook on how to develop mathematical proofs. You can apply the techniques to any other field you are interested in, and that is probably the best way to practice: by trying to prove things you already have some intuitive sense about.

Picked up a copy, thank you! And thanks for the suggestion on proving things in area I already have an intuition for, maybe I'll do that in conjunction with reading the book.

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