Any suggestions of books with cool, possibly nonrigorous math tricks?
For example, Joel Spencer "Asymptopia" has some really cool results in integral estimation using asymptotic ideas (e.g. estimating Stirling's Formula).
Another example would be Sanjoy Mahajan "Street-Fighting Mathematics" where he presents lots of fun techniques for guessing calculations.
Finally, another book I can remember is Steele "The Cauchy-Schwarz Master Class".
