The Art and Craft of Problem Solving (Paul Zeitz; Wiley, 2nd edition, 2007)
How to get smart
Paul Zeitz had written an enlightening and entertaining book about mathematical problem-solving. The target audience of the book are students with some mathematical background, for example gifted high-schools students.
Paul Zeitz won in 1974 the USA Mathematical Olympiad, and he has edited problems for mathematics contests for several decades. Many examples and exercises arise from mathematics competitions, but the book has a wider scope. Zeitz encourages the reader towards a wide curiosity about mathematical problems. The tone of the book is playful, avoiding too much seriousness although going quite deeply into mathematics.
Zeitz' book can be compared with the classic books about mathematics and problem-solving, for example "How to Solve It" by Polya and "What is Mathematics?" by Courant, Robbins, and Stewart.
A lot of the motivation for Zeitz book stems from Polya's classic. But Zeitz targets a somewhat wider audience, young people interested in problems and perhaps not mathematics as such. The essence of mathematics is not quite so firmly discussed, and perhaps it is better to encourage curiosity first and provide sermons later.
Other recent books about problem-solving are "How to Solve It: Modern Heuristics" by Michalewicz and Fogel and "The Nature of Mathematical Modeling" by Gershenfeld. These books are targeted towards large-scale applications, not so much basic mathematical problem-solving. Real-world examples of using mathematics are somewhat lacking in Zeitz's book, but the author has made a clear choice which has to be respected.
Fostering curiosity abot a wide range of mathematical topics and techniques is not a small accomplishment. Here Zeitz succeeds admirably. I hope many young students get their hands on this book, and start trying out the examples and exercises.
Even though my student years are behind, I got interested in many of the questions and started to think about them. Just as Zeitz recommended the reader to do.