A good book for learning mathematical trickery

Question

I've seen several question here on what book to read to learn writing and reading proofs. This question is not about that. I've been doing that for a while, and I'm quite comfortable with proofs. I am looking for resources (books, ideally) that can teach not the concept of proofs, but rather some of the specific mathematical tricks that are commonly employed in proofs: those that mostly include clever number manipulation, ad-hoc integration techniques, numerical methods and other thing you are likely never to learn in theory-oriented books. I come mainly from applied math and engineering, and when I look at proofs from Stochastic Processes, Digital Signal Processing, Non-Linear Systems and other applied subjects, I feel like I need to learn a new method to understand every proof I read. Is there any good literature on such mathematical tricks?

Answer 1

The Tricki ("Trick Wiki") is an attempt to catalogue such things, although it is somewhat less successful than was initially hoped.

Answer 2

I don't know if you're interested in inequalities, but a very nice book which teaches lots of tricks is Steele's The Cauchy–Schwarz Master Class.

Answer 3

I enjoyed Mahajan's Street-Fighting Mathematics. It has a strongly "applied" bent, and is freely available.