I'll second this. "How to Prove It" gets recommended a lot, but I couldn't get through it. I found it terribly boring and unmotivated. Some people can power through dry material but I'm not one of them. I found it much easier to learn to write proofs when they were related to topics I was interested in.
I loved How to Prove It. Not for the proofs - which are interesting in a gazing-at-your-navel kinda way - but rather all the little _practical_ tidbits. "So THAT'S what a partially ordered set looks life in real life!"
And the last(?) chapter where he uses induction to determine how to place an L-shaped figure on a grid...I never knew how to even approach that kinda' problem.
So yeah, I want actual practical applications ("exercises" != "applications") for math.
