Tuesday, March 12, 2013

Secrets of Mental Math

 The Kieval Lecture Series (Cornell Mathematics Department) is funded through a bequest of the late Dr. Harry S. Kieval ’36, a longtime professor of mathematics at Humboldt State University in Arcata, California, who died in 1994.
Innaugural speaker in 1998 was John Milnor. The full list of speakers is here.

Today in 2013 Kieval lecture series Arthur Benjamin (Harvey Mudd) was speaking about Secrets of Mental Math.

Arthur Benjamin grew up in Cleveland, Ohio, and earned his B.S. at Carnegie Mellon University in 1983 and his Ph.D. in mathematical sciences at Johns Hopkins University in 1989. Since then he has been a professor of mathematics at Harvey Mudd College, in Claremont, California, where he has served as department chair. He has written three books and is co-editor of Math Horizonsmagazine, published by the Mathematical Association of America (MAA). In 2000, the MAA awarded him the Haimo Prize for Distinguished Teaching.
Arthur Benjamin is also a professional magician, and frequently performs at the Magic Castle in Hollywood. He has demonstrated and explained his calculating talents to audiences all over the world and has appeared on numerous 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, Los Angeles Times, and Reader's Digest. In 2005, Reader's Digest called him "America's Best Math Whiz."

While he clearly has an extraordinary gift in the realm of mathematics, Benjamin also considers a lot of his numerical talent (and prodigious talent in general) to be gained through hours of practice. He describes the some practical drills and techniques for left to right calculation. He also explores visual, auditory and mental imagery that can assist in holding and manipulating large numbers in your head. Certain tricks work better for some than others, depending on individual traits and learning styles.
Secrets of Mental Math are revealed to readers, hours of practice now should be done.

 TED talk: Arthur Benjamin does Mathmagic

 TED talk:    Teach Statistics before Calculus

Arthur Benjamin on Colbert Report

How to memorize Large Numbers

Bache Auditorium today was full with excited audience ages 3 to ... well, let us say, very mature (it means including professors-emeritus).
First calculators had to be checked, so four volunteers came forward. You may recognize that one of them is Steven Strogatz.
As expected, these four guys could not use their calculators as fast as Arthur Benjamin used his mental calculation skills.

One of audiences most liked tricks was creating "personalized" magic square - based on your birthdate. Since this was mostly "mathematical" audience one of the questions was - how did you do this? Arthur said that explaining magic tricks takes away that wow! moment but agreed to show how this trick works. Of course, the following question was - how did you come up with the idea of this trick? The answer was - very much like it happens with mathemathematics: you read about something, then start thinking how this can be used in other ways, then some new idea may appear. He said that he was reading some publication on magic tricks, then he decided to try to make these magic squares using person's birthdate and figured out how he could perform it. Important part of magic tricks is the performance. Magicians have to be also actors and psychologists.
Arthur Benjamin also explained how he has memorized digits of pi - this time paper sheet could hold only 60 of them but he can go up to 100.
How could this mental math can be useful? Arthur told us that he got interested in numbers after he learned as a child to multiply three digit numbers by two digit numbers. He figured out that there are many different ways how one can do it and amazingly - result is the same! This fact made him to be excited about mathematics and up to this day he always has the urge to try different ways how to prove or solve something. (Earlier today he gave a talk in Math Department how to prove trigonometric formulas with combinatorial tools. He call it "combinatorial proof" or shortly in Harvey Mudd it is called "cool proof".)
As the "grand finale" he sang us a song dedicated to "pi day" which will be in two days. Melody was borrowed but rhyms were original and cool.
It was fun day with Arthur Benjamin!

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