Mathematical Discovery on Understanding, Learning, and Teaching Problem Solving, Volume I

This book gives a good list of heuristics and the author is a famous person who popularised the heuristics approach to problem solving. Put in other words, you would have heard that International Math Olympiad, the toughest Math competition on the face of earth, is about learning learning tricks. While this is not true at all, there is a lot of usefulness in knowing the heuristics. I highly recommend this book to kids interested in preparing for Math contests.

This is a book that like many math books appears light, but is actually quite deep. It was a required course for an introductory grad level math class seminar that I had last year, so while the presentation is engaging enough for high school students, most who do not intend to be physicists, mathematicians or engineers will find it to be too difficult - at least the problem solving portions that is. On the other hand, the second volume (volume 2) has a couple of chapters on how to solve problems that a Geometry or Algebra II class would find helpful.As a note, constructions are quite difficult! I had no idea that they would be that difficult, otherwise I would not have taken the class, as it was an elective class in my MS in math program. Many beginning grad students found some of the proofs of the constructions to be too difficult, and needed the assistance of an experience professor and mathematician, and I count myself among them. Of course there were relatively easy ones, but the difficult ones were quite tough.The book is very readable and charming, helpful to students in understanding the problem solving process, and includes a variety of problems ranging from easy to quite difficult that should challenge all high school and college, as well as beginning grad students in math. I highly recommend it.

Este é o primeiro volume de um dos excelentes livros do matemático George Polya. Leitura altamente recomendada para quem tem interesse na resolução de problemas ou no seu ensino.