Aha! Solutions (MAA Problem Book Series) [Hardcover]

Martin Erickson (Author)

Book Description

Publication Date: November 13, 2008 | Series: MAA Problem Book Series

Every mathematician (beginner, amateur, and professional alike) thrills to find simple, elegant solutions to seemingly difficult problems. Such happy resolutions are called ``aha! solutions,'' a phrase popularized by mathematics and science writer Martin Gardner. Aha! solutions are surprising, stunning, and scintillating: they reveal the beauty of mathematics.

This book is a collection of problems with aha! solutions. The problems are at the level of the college mathematics student, but there should be something of interest for the high school student, the teacher of mathematics, the ``math fan,'' and anyone else who loves mathematical challenges.

This collection includes one hundred problems in the areas of arithmetic, geometry, algebra, calculus, probability, number theory, and combinatorics. The problems start out easy and generally get more difficult as you progress through the book. A few solutions require the use of a computer. An important feature of the book is the bonus discussion of related mathematics that follows the solution of each problem. This material is there to entertain and inform you or point you to new questions. If you don't remember a mathematical definition or concept, there is a Toolkit in the back of the book that will help.

Editorial Reviews

Review

Erickson provides 100 exemplary problems to whet any problem-solver's appetite....A bonus is Erickson's detailed discussion of an AHA solution to each problem followed by discussion fo related problems and mathematics. --J. Johnson, CHOICE Magazine

Book Description

Mathematicians (beginner, amateur, and professional alike) thrill to find simple, elegant solutions to seemingly difficult problems. Such happy resolutions are called 'aha! solutions,' a phrase popularized by mathematics and science writer Martin Gardner. Aha! solutions reveal the beauty of mathematics. This book is a collection of problems with aha! solutions.

See all Editorial Reviews

Product Details

• Hardcover: 207 pages
• Publisher: The Mathematical Association of America (November 13, 2008)
• Language: English
• ISBN-10: 0883858290
• ISBN-13: 978-0883858295
• Product Dimensions: 10.1 x 7.1 x 0.7 inches
• Shipping Weight: 1.2 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #407,605 in Books (See Top 100 in Books)

More About the Author

I am a professor of mathematics. My main areas of interest are problem solving, combinatorics, discrete structures, geometry, and number theory. I especially like mathematical problems that have elegant solutions. I have written or co-written several mathematics books. The books are described at http://sites.google.com/site/martinjerickson/.

Customer Reviews

Most Helpful Customer Reviews

5.0 out of 5 stars None of the problems are hard, provided you apply the right insight, August 17, 2011

By 

Charles Ashbacher (Marion, Iowa United States) - See all my reviews
(TOP 500 REVIEWER)    (VINE VOICE)    (HALL OF FAME REVIEWER)   

This review is from: Aha! Solutions (MAA Problem Book Series) (Hardcover)

Mathematicians generally take second place to no other group in appreciating a mind-straining problem that can be solved with the right insight into the structure. In fact, one can argue that that is the primary way that progress is made in mathematics. Although they are split into the levels of elementary, intermediate and advanced, all the problems can be understood if read carefully by someone that has done well in a discrete mathematics course.

The elementary problems will be of special interest to teachers at nearly all levels of high school and college, most can be understood by people with a background in basic algebra with a little set theory and combinatorics included. They could serve as great primers for test and quiz questions as they are problems that appear much more difficult than they actually are.

My favorite in the elementary section is on page 8:

Which is greater sqrt(6) + sqrt(10) or sqrt(5) + sqrt(12)?

And the rules would be that a calculator is not allowed.

The solution is obvious if you simply square both numbers and then compare. Knowing the relative order of positive numbers and their squares gives you the answer immediately. Such problems are also easily altered to appear on exams.

Students in mathematics courses need to learn that there are many routes to an answer or a proof and sometimes, the route is a tedious one through many twists. However, there are times when the solution to a problem comes from somewhere in the mathematical equivalent of "A miracle happens!" This book demonstrates many of those problems in several areas of mathematics.

Published in Journal of Recreational Mathematics, reprinted with permission.