14
$\begingroup$

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?

$\endgroup$
7
  • 4
    $\begingroup$ "numerical methods" - you'll pick up a whole lot of practical numerical advice/tricks of the trade from Acton's two books: Numerical Methods That (usually) Work and Real Computing Made Real. $\endgroup$ May 16, 2011 at 15:30
  • 2
    $\begingroup$ You might also be interested in The Art and Craft of Problem Solving. $\endgroup$ May 16, 2011 at 15:32
  • $\begingroup$ Wait until you see set theoretic proofs :-) $\endgroup$
    – Asaf Karagila
    May 16, 2011 at 15:36
  • $\begingroup$ Thanks, I'll definitely check them out. All of them look great. You should post these as answers, I'll upvote = ) $\endgroup$
    – Phonon
    May 16, 2011 at 15:36
  • 2
    $\begingroup$ @Phonon: can you be more specific about these examples you describe? I'm not really sure what "clever number manipulation" or "ad-hoc integration techniques" could be referring to. More generally, beyond a handful of very general things the "tricks" you're going to see will depend on the field (although not necessarily in an obvious way), so I wouldn't say that there are "proof tricks" so much as "tricks for certain kinds of proofs." $\endgroup$ May 16, 2011 at 16:35

3 Answers 3

13
$\begingroup$

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.

$\endgroup$
1
  • $\begingroup$ This looks very good. Much closer to what I'm looking for. $\endgroup$
    – Phonon
    May 16, 2011 at 20:17
11
$\begingroup$

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

$\endgroup$
10
$\begingroup$

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

$\endgroup$
1
  • $\begingroup$ This is great! = ) Thanks! Not exactly what I'm looking for, but indeed very promising. $\endgroup$
    – Phonon
    May 16, 2011 at 17:59

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .