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How To Solve It: A New Aspect of Mathematical Method Paperback – June 26, 2009
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- Publisher : Ishi Press (June 26, 2009)
- Language: : English
- Paperback : 280 pages
- ISBN-10 : 4871878309
- ISBN-13 : 978-4871878302
- Item Weight : 12.6 ounces
- Dimensions : 5.5 x 0.64 x 8.5 inches
- Best Sellers Rank: #637,791 in Books (See Top 100 in Books)
- Customer Reviews:
Top reviews from the United States
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Even though he explains the process in math terms, his insight on problem solving technique applies to anything.
High, HIGHLY recommended for anyone who wants to sharpen their analysis and problem solving skills!
Between them all, I see a real opportunity to improve the sharpness of one's thinking.
I'm glad I have discovered an excellent book on problem solving which would prove indispensable in my programming career. Other programming books mainly demonstrate features of an OS or a computer language but this book goes into the heart of the computer science which is problem solving.
It has two parts. One is the problem solving methodology itself with an excellent detail and options in every step. And another related for math problems.
As IT professional, it is useful for common issues, algorithm design , design alternatives. The chapters related to the methodology should be included in any course of algorithm design.
Top reviews from other countries
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.