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Discrete Mathematics
Arthur T. Benjamin, Ph.D.
PUBLISHED BY:
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Copyright © The Teaching Company, 2009
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The Teaching Company.
Arthur T. Benjamin, Ph.D.
Professor of Mathematics, Harvey Mudd College
Arthur T. Benjamin is a Professor of Mathematics at Harvey Mudd College.
He graduated from Carnegie Mellon University in 1983, where he earned a
B.S. in Applied Mathematics with university honors. He received his Ph.D.
in Mathematical Sciences in 1989 from Johns Hopkins University, where he
was supported by a National Science Foundation graduate fellowship and a
Rufus P. Isaacs fellowship. Since 1989, Professor Benjamin has been a
faculty member of the Mathematics Department at Harvey Mudd College,
where he has served as department chair. He has spent sabbatical visits at
Caltech, Brandeis University, and the University of New South Wales in
Sydney, Australia.
In 1999, Professor Benjamin received the Southern California Section of the
Mathematical Association of America (MAA) Award for Distinguished
College or University Teaching of Mathematics, and in 2000, he received
the MAA Deborah and Franklin Tepper Haimo National Award for
Distinguished College or University Teaching of Mathematics. He was
named the 2006–2008 George Pólya Lecturer by the MAA.
Professor Benjamin’s research interests include combinatorics, game
theory, and number theory, with a special fondness for Fibonacci numbers.
Many of these ideas appear in his book (coauthored with Jennifer Quinn)
Proofs That Really Count: The Art of Combinatorial Proof,
published by
the MAA. In 2006, that book received the MAA’s Beckenbach Book Prize.
From 2004 to 2008, Professors Benjamin and Quinn served as the coeditors
of
Math Horizons
magazine, published by the MAA and enjoyed by more
than 20,000 readers, mostly undergraduate math students and their teachers.
In 2009, the MAA published Professor Benjamin’s latest book,
Biscuits of
Number Theory,
coedited with Ezra Brown.
Professor Benjamin is also a professional magician. He has given more than
1000 “mathemagics” shows to audiences all over the world (from primary
schools to scientific conferences), where he demonstrates and explains his
calculating talents. His techniques are explained in his book
Secrets of
Mental Math: The Mathemagician’s Guide to Lightning Calculation and
Amazing Math Tricks.
Prolific math and science writer Martin Gardner calls
it “the clearest, simplest, most entertaining, and best book yet on the art of
calculating in your head.” An avid game player, Professor Benjamin was
winner of the American Backgammon Tour in 1997.
©2009 The Teaching Company.
i
Professor Benjamin has appeared on dozens of television and radio
programs, including the
Today
show, CNN, and National Public Radio. He
has been featured in
Scientific American, Omni, Discover, People, Esquire,
The New York Times,
the
Los Angeles Times,
and
Reader’s Digest.
In 2005,
Reader’s Digest
called him “America’s Best Math Whiz.”
ii
©2009 The Teaching Company.
Acknowledgments
It is a pleasure to thank the many people who helped me with
Discrete
Mathematics.
First I would like to thank the many students from Harvey
Mudd College and other Claremont Colleges who have taken discrete
mathematics from me over the last 20 years. I have learned a great deal
teaching and working with these highly motivated students. Special thanks
are due to Harvey Mudd College students Craig Burkhart, Jennifer Iglesias,
Jack Newhouse, Aaron Pribadi, and Elizabeth Reiland; Pitzer College
student Scott Garrabrant; and Harvey Mudd College Professor Geoff
Kuenning, all of whom offered valuable comments on the first draft of this
course. I was very fortunate to be able to present most of these lectures to
the students and faculty at Denison University and Roanoke College. I am
especially grateful to Professors Sarah Crown, Tom Wexler, Jan Minton,
and Roland Minton for their expertise, input, support, and hospitality.
It has been a pleasure working with the ultraprofessional staff of The
Teaching Company. Although I know there were many people working on
this course behind the scenes, I would especially like to thank Zach
Rhoades, Matt Costanza, John Levin, and most of all, Jay Tate.
Last, but not least, I thank my family for their patience and understanding
while this course was being created. I must especially thank my wife, Deena
Benjamin, who is my light, my inspiration, the love of my life, and my
typesetter. This course could not have been made without you!
Arthur T. Benjamin
©2009 The Teaching Company.
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