am 13. Januar 2000
Polya's brilliante Anleitung zum Lösen mathematischer Probleme vermittelt auch dem Laien ein überaus stimmiges und nützliches Bild vom täglichen Brot des Mathematikers. Gerade indem sie keine unfehlbare Beweismethode liefert, die einfach ohne kreativ nachdenken zu müssen nur abgearbeitet werden muss, sondern den intuitiven Aspekt mathematischen Denkens betont, vermittelt sie viel von der Schönheit eleganter Lösungen. Anders als beispielsweise ein Ingenieur ist der Mathematiker nicht zufrieden, sobald ein bestimmtes Problem irgendwie gelöst ist, sondern meist beginnt hier erst der interessante Teil der Arbeit: Kann die Lösung noch vereinfacht werden oder gar bei der Lösung anderer, verwandter Probleme helfen? Oft werden ganze Zweige der Mathematik geschaffen, um ein bestimmtes Problem wie z.B. die kürzlich bewiesene Fermat'sche Vermutung anzugehen. Polya's Büchlein hat auch ganz konkreten Nutzen: Wer seinen Kindern, Schülern oder Studenten einfache oder schwere Mathematik beibringen will, tut gut daran, sich mit Polya in den Prozess der Lösungsfindung einzufühlen statt fertige Lösungen zu präsentieren. (Dies ist eine Amazon.de an der Uni-Studentenrezension.)
am 14. Juli 2000
i must say that this is one of the most interesting books i've ever read. it is a must for teachers of mathematics and the sciences. polya exposes with an unmatched wit and cunning the art of breaking it down and analyzing parts of parts in order to arrive at a reliable and justifiable solution.
polya is the quintessential teacher and this teacher finds his writings both compelling as well as inspiring. this is NOT the last book by this great mathematician that i plan to read.
a word of advice for teachers: read it and REREAD it until you get the point. the teaching of mathematics is not a mere monkey-see-monkey-do regurgitation process. rather, it is the art of conveying to the student the problem-solving process. once the student has mastered this talent, the sky's the limit. and speaking of limits, the sky may just be a gross underexaggeration.
LOVE IT! got to say again, "BUY THE BOOK!" and this goes doubly for TEACHERS!
am 7. April 2000
In fact, do you want to be a robot? I talked to a woman who took a whole semester in computer science and came out learning nothing. She told me this. My love affair with Real Math started with this book in a library. I was reading a book which had a bunch of interviews with the most successful programmers in the world. One was Czech and I do not remember his name. But he was asked the following question. "What in your opinion is the biggest mistake that programmers are doing in their educations or their work today?" He answered, "It's simple. They don't know how to solve problems. At our company, we have some simple books that tell you how to do this. The best is Polya's 'How to Solve It'. It has a little diagram in the back that completely runs you through a series of questions on solving math problems. But even in schools, they don't take this approach. Everything is by rote and repetition! You solve a problem and YOU DON'T KNOW WHAT YOU SOLVED! We have a lot of these little books." The late Isaac Asimov wrote a beautiful little book called "The Realm of Algebra". It's out of print. But he explains the entire realm of algebra in something like 150 pages. The best book I've ever seen about math. Math can be fun. Programming can be fun. But only if you ask Polya's questions in the back of this book. "What do I have to do to make this problem complete?" "What is missing from this problem?" "What could I add to make this problem solved?" A two page diagram in the back. And everybody knows that programming is just "crummy mathematics". BUY THE BOOK! BUY THE BOOK! BUY THE BOOK!. 2 pages in the end of this book and at least 50% of your math/programming problems are down the drain. Buy the books for your son if you are a Betty Crocker. Or your daughter. Or they will end up in the "Valley of the Dead". Solving problems in school for years and years and simply not knowing what they did! Good luck. Oh yes. One last thing. BUY THE BOOK!
am 10. April 2011
"Schule des Denkens" means school of thought. The title of the original manuscript reveals the motivation for this book: to teach better. Polya wrote it as a guide on how to lecture mathematics. But only the publicized edition, after Polyas migration to the United States tells in plain English what its good for a broad audience: How to Solve It. I am not a teacher, the didactic musings of a lecturer would produce not more than a spark of curiosity in me. But "How to Solve It" describes a general procedure for problem solving. This freaks me out! Polya hides this endeavor in favor of the didactic justification, and only later in the book will reveal that its content is a Modern Heuristic to "understand the process of solving problems, especially the mental operations typically useful in this process" [p. 129]. The book is divided into four parts, I will discuss them briefly.
Part I: In the Classroom
This 32 pages are all you need to grasp his algorithm of problem solving. Good ideas are simple and the procedure proposed is nothing counterintuitive. You could easily come a similiar conclusion by your own: What is the first step of problem solving? (1) Understanding the problem. What is the next step? (2) Devise a plan. Then?(3) Execute the plan. And finally(4) Look back.
Mightily impressed? Then you are a lobotomized PowerPoint disciple! But follow Polya in a Socratic dialog with the classroom and look into the train of thoughts of an educated problem solver. There are many subtilities to discover.By reading this chapter, more than once I had moments of Heureka!, when Poly guides you to ask the so called right questions and instructs you how to take a different point of view of the problem.
Part II: How to Solve it - a Dialog
The second part compresses the problem solving procedure, the ars inveniendi, in a summary of two pages. I did not gain from this, but it might be helpful as a short rehearsal when time passes by.
Part III: Dictionary of Heuristic
This is a 200 pages collection of heuristics to use as a pattern language for problem solving. The autor advices to take your time read this piece by piece when you are struggling with problems. Which I do.
Part IV: Problems, Hints, Solutions
These 8 pages are filled with exercises and smart hints how to approach the individual problems.
Polya opens your mind for solutions. I will tackle future hard problems only with Polya's algorithm and benefit from the careful order he imposes to the confused mind. Albeit written for teaching mathematics, I suspect that Polyas work is useful not only for quantitativ problem solving, but for qualitative problems too. Here, I have no proof and only the application of it will tell. The book is easy to read, and you might master the first fundamental part "In the Classroom" in 3-5 hours. It is also a really cheap book, 13-something Euro, and if you are a problem solver you will need and enjoy it.
am 26. November 2013
Wer sich für die Kunst der Problemlösung interessiert sollte dieses Buch kennen. Es ist ein kleines Buch, aber mit einigen Wertvollen Ratschlägen. Die Essenz des Buches sind die vier Prinzipien (kann man in Wikipedia finden unter "How to Solve It") aber das Buch kann (und wie ich meine sollte) auch dann lesen wenn man die 4P kennt. Man sollte vom Buch keine Wunderlösungen erwarten ich fand es aber interessant weil das Thema schön strukturiert wurde. Man sieht, dass der Author sich damit länger beschäftigt hat und die wichtigen zentralen Punkte mit Sorgfalt ausgearbeitet hat.
am 24. Juli 1998
This is a book on problem solving, in its widest meaning, though mathematics dominates, given the author's education. It's a feast! Prepare yourself for many hours of fun and education. If you'll accept an advice, study every single book written by Polya.