How to Solve It: A New Aspect of Mathematical Method Paperback – 26 April 1990

Very interesting read and will be rereading in future to remind myself of its great ideas.

I thought I would buy this book after seeing it reviewed on a Japanese mathmatics program on TV . I found the contents difficult to read not being a higher maths candidate myself. How ever after trying to digest the words of wisdom in the theory of solving problems I had to admit it is only suitable for those amongst us who have a higher maths certificae than myself.very much higher ! The authur G.Polya was an aclaimed world wide mathematician, so if you are in his league then the book is worth reading ..TR

This is a very good book that takes a lot of time to digest. So, get it well before your exam or you start your job as a trainee mathematical modeller! What I mean by that is, I read it, cover to cover, then returned to my university studies with renewed excitement and found I still got stuck. Par for the course in mathematics, but disappointing nonetheless. However, once I had solved the problem (or given up and checked the solution), then reflected on why I got stuck, a heuristic from this book often jumped out at me. Ah... if only I'd thought to try this it would've made the way forward so obvious!And that is essentially what the book is. You will not get a list of algorithms to take the creativity and hard work out of mathematical problem solving (frankly, that'd no more be a good thing than taking the creativity and hard work out of sport). What you will get is a discussion of thought processes that professional mathematicians use, probably unconsciously at that stage of education, that may help you make headway on your problem. Essentially, 'What are fruitful questions to ask when I don't know how to proceed or even begin?' (Hint: don't just sit there and stare at it waiting for the muse to strike you.) In fact, you probably use some of these already but don't even realise you're using the same strategy over and over again. In this way, Polya has done what mathematicians do: he has abstracted, generalised and systematised a hitherto hodgepodge of problem-solving recipes used implicitly in particular situations.A simple example for when you get stuck: 'Can you rewrite the equation?' I cannot count how many times I have fallen into this trap, realising after I've given up on a problem that the way to proceed would've jumped out at me had I only thought to rewrite it in a different form. On one level, it might simply be that you, personally, are really quite uncomfortable with a particular form of notation. Rewriting things might well put you at psychological ease with more familiar forms, or forms you're much better practised at manipulating. Hate Leibniz notation for your calculus? Why not rewrite it as Newtonian to solve your problem, then translate back into Leibniz? This strategy, in fact, is what we do all the time - when you learn trig identities or to move between forms of vectors, say, you are implicitly learning the strategy: 'Rewrite the equation to make it easier to deal with.'The other reason might simply be that by rewriting it, the solution jumps out at you. This is what happens whenever you multiply out, factor, substitute into equations etc. Just because your question doesn't specify you need to do something, doesn't mean you aren't allowed to try it! But it has to occur to you first to rewrite your problem into an equivalent form, in order for the light at the end of the tunnel to reach you. And really this is something you do already: whenever you look up a word in a dictionary, you're essentially seeing the term which you don't understand rewritten as something you do understand. Then you can proceed with your paragraph, just like you can then proceed with your mathematical problem.

This book teaches you to dissociate yourself from the problem posed and ask yourself logical questions to decompose the problem before forming a plan.

Haven’t read it all yet. Good so far and fast delivery was much appreciated.

Enlightening ones mathematical mind and thinking out side of all boxes.

this book is not really worth buying, contains heuristics for problem solving. It is very dated, and states the obvious, very boring to read. May be useful for maths teachers.

An excellent approach to problem solving, one that has value far beyond just mathematics.