Our November 19, 2008 Special Presentation will be by Dr. Arthur Benjamin, who in addition to being a sought after speaker is also a successful author. Many people are familiar with Dr. Benjamin from the course that he authored for the Teaching Company entitled *Joy of Mathematics*. Following is an excerpt from the course description:

**Fun with Numbers**

Here is an example:

*Think of a number between 1 and 10. Triple it. Add 6. Then triple again. Now take your answer, probably a two-digit number, and add the digits of your answer. If you still have a two-digit number, add those digits again. You should now be thinking of the magical number 9. The reason this works is based on algebra and the fact that the digits of any multiple of 9 must sum to a multiple of 9.*

This is one of the many wonders of *modular arithmetic*, sometimes called clock arithmetic, where numbers wrap around in a circle. A useful application of this field is casting out nines, a simple and ancient technique for checking the answers to arithmetical problems.

Modular arithmetic also provides a very handy method for mentally computing the day of the week for any date in history.

This connection between entertaining number tricks and the deeper properties of mathematics reflects Dr. Benjamin’s specialty, which is *combinatorics*, the branch of mathematics that deals with the subtleties of counting. Some examples: How many different six-symbol license plates are possible? And for the book collector, how many ways are there of arranging 10 books on a shelf? (Would you believe more than 3 million?) These simple questions introduce concepts such as the *factorial function*.

Drawing on his dual fascination with combinatorics and games, Dr. Benjamin used his analytical skill to win first place in the American Backgammon Tour in 1997.

In addition to his scholarly articles, Dr. Benjamin has also written books that are highly accessible to the public. One such book is *Secrets of Mental Math: The Mathemagician’s Guide to Lightning Calculation and Amazing Math Tricks* co-written with Michael Shermer with a foreword by Bill Nye the Science Guy. Praise for this book includes:

“A great introduction to the wonder of numbers, from two superb teachers.”

— Brian Greene, author of The Elegant Universe

“A magical mystery tour of mental mathematics! Fascinating and fun.”

— Joseph Gallian, president of the Mathematical Association of America

“The clearest, simplest, most entertaining, and best book yet on the art of calculating in your head.”

— Martin Gardner, author of Mathematical Magic Show and hundreds of Mathematical Games columns for Scientific American.

“This book can teach you mental math skills that will surprise you and your friends. Better, you will have fun and have valuable practical tools inside your head.”

— Dr. Edward O. Thorp, mathematician and author of Beat the Dealer and “Beat the Market”

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