I really, really
suck at proving things. Do you know of any free online resource one could use to master proving things?
I know enough math up to about one semester of calculus, a bit about sentential logic and a little bit of set theory, but even still, past finding a trig identity or something like that I couldn't prove to save my life. I can follow proofs well, even spot when one isn't complete, but I don't see how one thinks of the steps to prove something. I typically look at a neat proof and come across the third step or something and think "Wow! How the hell
did this guy think to do that! I would've never thought of that!" even on a lot of simple proofs involving elementary algebra.
For instance, I was reading this one website that, as an exercise, I was to try to prove that if a/4 is an integer, then a is the difference of two perfect squares. It seems like such a simple thing to prove! I struggled with it, tried 20 different things, ended up with a lot of crumpled paper, a headache, and no progress after quite awhile and gave up. And I bet anyone here could prove that statement after glancing at it once. In other words, I'm proof-challenged. Proof-tarded if you will. Durp.