Download Problem Solving Through Recreational Mathematics (Dover Books on Mathematics), by Bonnie Averbach, Orin Chein, Mathematics
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Problem Solving Through Recreational Mathematics (Dover Books on Mathematics), by Bonnie Averbach, Orin Chein, Mathematics
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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 them.
Each chapter contains a diverse array of problems in such areas as logic, number and graph theory, two-player games of strategy, solitaire games and puzzles, and much more. Sample problems (solved in the text) whet readers' appetites and motivate discussions; practice problems solidify their grasp of mathematical ideas; and exercises challenge them, fostering problem-solving ability. Appendixes contain information on basic algebraic techniques and mathematical inductions, and other helpful addenda include hints and solutions, plus answers to selected problems. An extensive appendix on probability is new to this Dover edition. Free solutions manual available for download at the Dover website.
- Sales Rank: #432162 in Books
- Brand: Averbach, Bonnie/ Chein, Orin
- Published on: 1999-05-27
- Released on: 1999-05-27
- Original language: English
- Number of items: 1
- Dimensions: 9.18" h x .92" w x 6.50" l, 1.50 pounds
- Binding: Paperback
- 480 pages
Most helpful customer reviews
30 of 31 people found the following review helpful.
Problem Solving Through Recreational Mathematics
By William Markel
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.
23 of 23 people found the following review helpful.
A gem and a steal
By Polymath-In-Training
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.
15 of 15 people found the following review helpful.
The Textbook for the Math Class of your Dreams
By Peter A. Farrell
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.
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