Reddit reviews How to Solve It: A New Aspect of Mathematical Method (Penguin Science)

In the spirit of Halmos ( http://abstrusegoose.com/strips/saint_curious_george.png ) and in addition to the previous post, which is very helpful:

I think it's very helpful that you - when reading a proof - deliberately pay attention to the structure* of it, i.e. what is to be shown (a property, existence / non-existence of something, ...) and how it's done in general (i.e. construction of a solution, by assuming the opposite, ...). Especially for longer proofs (for me personally) it's helpful to cluster stuff together and write down something like a "table of contents" or sequence of (meta-)steps.

There is also a book "how to solve it" by George Polya; a link: http://www.amazon.co.uk/How-Solve-Mathematical-Penguin-Science/dp/0140124993/ref=sr_1_1?s=books&ie=UTF8&qid=1322784121&sr=1-1 It has the look-inside feature activated, so you can decide whether it is helpful to you.

Polya's How to Solve it is a classic.

You might prefer Housten's How to Think Like a Mathematician which is much more modern.

I found that they both had useful insights, though there was a fair bit of information which I didn't find helpful.

A) How to Solve it: A New Aspect of Mathematical Method (Penguin Science) https://www.amazon.co.uk/dp/0140124993/ref=cm_sw_r_cp_apa_i_jmYGDbXX07R9M

B) Mathematical Techniques: An Introduction for the Engineering, Physical, and Mathematical Sciences https://www.amazon.co.uk/dp/0199282013/ref=cm_sw_r_cp_apa_i_ZkYGDbWSX4JSP

These two.

Read Polya, then do the hard work of studying through the sections of Techniques you need to know.