Problem Solving Through Recreational Mathematics

by Bonnie Averbach and Orin Chein

Book Overview

Historically, many of the most important mathematical concepts arose from problems that were recreational in origin. This book takes advantage of that fact, using recreational mathematics -- problems, puzzles and games -- to teach students how to think critically. Encouraging active participation rather than just observation, the book focuses less on mathematical results than on how these results can be applied to thinking about problems and solving...

• Format: Paperback
• Language: English
• ISBN: 0486409171
• ISBN13: 9780486409177
• Release Date: May 1999
• Publisher: Dover Publications
• Length: 480 Pages
• Weight: 1.55 lbs.
• Dimensions: 0.9" x 6.5" x 9.2"

Customer Reviews

The Textbook for the Math Class of your Dreams

Martin Gardner once asked why a whole math course couldn't be built around recreational math. If school districts ever allowed one to exist, this would be the textbook for the class. Recreational math gets a bad name, since most fear-conditioned parents react negatively to their kids "playing" anything in school after kindergarten, but a lot of real math can be learned efficiently and enjoyably through explorations like the ones in this book. Problem solving is the heart of mathematics, but not the "Do numbers 1 - 99 odd" kind of problem solving. A couple of substantial problems like "train problems" or "age problems" (both covered in Chapter 3) will give students better practice in algebra, arithmetic and logic than a chapter full of busy work. What I love about this book is the playful attitude it takes to some very involved math concepts. Some chapters are literally playful: solitaire games and games of strategy are explored in great depth in Chapters 7 and 8. Nim can be played with a child, but the richness of the math involved in the strategy could occupy a college student. Another thing I love is the sheer number of problems included to provide practice on a topic, and the progression of questions from the obvious to the very challenging (Questions are rated by difficulty). In-depth solutions to selected problems are included in each chapter, and many other problems have hints. Most are at least answered in the back of the book. I have taken Mr. Gardner's suggestion to heart, and am using this book to challenge my private students with real, substantial math. From logic and graph theory to cryptarithmetic and coin-weighing problems, all the classics of challenging but fun math are here. Also see Don Cohen's "Calculus By and For Young People" for what can be achieved using a non-traditional approach.

Full Brain Excersice

I bought this book for cracking interview tests. It has all the possible types of problems that can be asked in an aptitude test. The author explains the solutions in great detail and also explain how similar problems can be solved.

A gem and a steal

This is a fun puzzle-type book, but with a difference from most such books. In this book, you will really learn some interesting mathematics. The authors' way of presenting the material is very effective. First, they present a problem or puzzle for the reader to attempt to solve. Then they show the mathematics behind the problem. Then they lead the reader through the solution and show how the mathematics is used to make solving such a problem easier. I have an engineering degree and a minor in mathematics, but this book introduced me to some new areas of mathematics. It also helped me understand some areas that had been confusing before, such as applications of modular arithmetic and linear Diophantine equations. I bought this book in hardback a few years ago for $38. This new Dover edition in paperback at $14.95 list is a steal.

Recreational mathematics as course work

This book is the heavyweight champion of problems in recreational mathematics, containing a large number of very detailed problems in many areas. The presentation strategy is to develop the topic by using problems followed by an explanation followed by a detailed solution. The style is largely that of a textbook, which in fact is what it is designed to be. The authors developed the material as the main text for a course they teach in applied problem solving. The chapters are largely independent, so it is possible to pick and chose the topics for a course. Do not let the word recreational in the title lead you to believe that these problems are bunnies. I am a co-editor of Journal of Recreational Mathematics and I found myself thinking long and hard about some of these problems. Granted, many are straightforward, but there are enough of the head-scratching variety to satisfy every taste. The general topics are logic, basic number theory, graph theory and games, with a few other topics interspersed. With hundreds of problems, detailed solutions to the demonstrations and hints for most included, this is a resource unlike all others. If you teach a course in mathematical problem solving or beginning computer programming, you cannot help finding a problem in here that you can use to illustrate a topic or as a test question. I have already used a couple as the seeds for some programming exercises. Better yet, consider it as a textbook for your course in mathematical problem solving. Published in Journal of Recreational Mathematics, reprinted with permission.

Problem Solving Through Recreational Mathematics

I first became acquainted with this book about twenty years ago when it first appeared. Since it didn't fit into a standard niche in college mathematics curricula, it never really caught on and, before the Dover edition, was out of print for a number of years.This was a shame, as this is both a wonderful and remarkable book. It has a broad appeal; amateur mathematicians, professional mathematicians, and puzzle buffs should all find something in it to interest them. It is both fun and rewarding at the same time. One can learn a great deal of mathematics from it. It also contains a method for solving linear Diophantine equations that I have never seen anywhere else.The authors have added a chapter on probability which should further enhance this highly original work.