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Problem Solving Through Recreational Mathematics (Dover Books on Mathematics)

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Bonnie Averbach (Author)
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Bonnie Averbach (Author), Orin Chein (Author), Mathematics (Author)
4.6 out of 5 stars 13 customer reviews
ISBN-13: 978-0486409177
ISBN-10: 0486409171
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Product Details

  • Series: Dover Books on Mathematics
  • Paperback: 480 pages
  • Publisher: Dover Publications (May 27, 1999)
  • Language: English
  • ISBN-10: 0486409171
  • ISBN-13: 978-0486409177
  • Product Dimensions: 9.2 x 6.5 x 0.9 inches
  • Shipping Weight: 1.6 pounds (View shipping rates and policies)
  • Average Customer Review: 4.6 out of 5 stars  See all reviews (13 customer reviews)
  • Amazon Best Sellers Rank: #110,043 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

32 of 32 people found the following review helpful
Recreational mathematics as course work
By Charles Ashbacher HALL OF FAMETOP 500 REVIEWERVINE VOICE on March 14, 2001
Format: Paperback
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.
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30 of 31 people found the following review helpful
Problem Solving Through Recreational Mathematics
By William Markel on March 28, 2000
Format: Paperback
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.
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21 of 21 people found the following review helpful
A gem and a steal
By Polymath-In-Training on April 3, 2006
Format: Paperback
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.
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14 of 14 people found the following review helpful
The Textbook for the Math Class of your Dreams
By Peter A. Farrell on April 23, 2009
Format: Paperback
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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5 of 5 people found the following review helpful
Very entertaining and educational book
By argsv on July 6, 2010
Format: Paperback Verified Purchase
I picked it up this book as I was looking for a fun way to refresh my math skills. I like the way this book written and organized. Also the problems in this books range from easy to very difficult and most of the are very interesting. Not all exercises have their solutions in the book. Some problems have full solutions in the back. Others have only hints and sometimes hints + the final answer. While other problems have the final answer only. Overall the book is very useful.
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Most Recent Customer Reviews

Five Stars

as described therefore fully meeting expectations
arrived well packaged and on time

my thanks

Published 9 months ago by Bob Kennedy
Four Stars

very helpful

Published 15 months ago by math teacher
Great collection of problems well explained

This book does a great job of presenting a variety of mathematical concepts in an engaging way. It could be enjoyed by mathematically inclined readers who would appreciate the... Read more

Published 15 months ago by Amazon Customer
One of my favorite books; rating is for the quality of the print which...

I own a hard copy of this book which I really like a lot. I bought many copies as gifts to a new generation of math-loving family members. Read more

Published 21 months ago by ksshopper
Good practice to keep the brain cells firing

This is a very good book for establishing multiple approaches for solving problems. I have enjoyed working the problems and find it good to tune up your analytical mind.

Published on April 3, 2013 by Amazon Customer
Excelente libro

Es un excelente apoyo para revisar muchos temas de matemáticas en clase desde la perspectiva del aprendizaje basado en problemas.

Published on March 11, 2012 by Edgar Sánchez Linares
Serious stuff from an entertaining point of view

This book is unusual in that it contains some pretty serious content, particularly in the areas of discrete mathematics that are of practical importance in computer science and... Read more

Published on February 27, 2012 by Just a Guy
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. Read more

Published on February 17, 2008 by C. Nirmal

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