How to solve it

[Spica99]

2013-12-30 (120min)

Title: How to solve it from Polya

Notes:

Solving problems is a fundamental human activity. Four steps:
1.The very first thing we must do for our problem is to understand it: Who understands ill, answer ill.
2.Devising a plan, conceiving the idea of an appropriate action, is the main achievement in the solution of a problem.
3.We should start carrying out our plan at the right moment, when it is ripe, but not before. We should not start rashly. Look before you leap. Try before you trust.
4.Look back at the completed solution is an important and instructive phase of the work. He thinks not well that thinks not again. Second thoughts are the best.

a)The intelligent problem-solver knows that the question is part of his mental attitude appropriate in such and such a phase of the work, and he summons up the right attitude by asking the right question. He has the gift of presenting just the germ of the proof, the main idea in its simplest form, and indicating the nature of the remaining details.
b)The open secret of real success is to throw your whole personality into your problem.
c)"Take counsel of your pillow" is an old piece of advice. Allowing an interval of rest to the problem and to ourselves, we may obtain more tomorrow with less effort.
d)Past ages regarded a sudden good idea as an inspiration, a gift of the gods. You must deserve such a gift by work, or at least by a fervent wish.
e)"A wise man will make more opportunities than he finds. A wise man turns chance into good fortune."
f)If you cannot solve the proposed problem, try to solve first some related problem. Could you imagine a more accessible related problem?
g)Always follow your inspiration-with a grain of doubt.