Math and Magic

Course No. 9202
Professor Arthur T. Benjamin, Ph.D.
Harvey Mudd College
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Course No. 9202
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What Will You Learn?

  • Master card tricks and the mathematical principles behind them.
  • Learn simple shortcuts for lightning-fast calculations in your head.
  • Understand how to create and solve geometric puzzles and magic squares.

Course Overview

Try this: Arrange an ordinary deck of cards so that the colors alternate red-black, red-black, all the way through. Now have someone cut the deck as many times as they like. Deal off a stack of cards, one card at a time, that roughly divides the pack in two. Invite someone to shuffle the two stacks together. Then deal cards from the top in pairs. Your audience will be astonished that every pair has a red card and a black card. How can that be?

Nothing can amaze quite like an expertly-executed magic trick. Ideally, only the magician knows how truly simple the deception is. After watching Math and Magic, you will know that this trick and its many variants rely on a remarkable property of patterned sequences called Gilbreath’s principle—named after an amateur magician who was also a mathematician. Magic is full of such wonders, as you discover in these 12 illuminating half-hour lessons presented by one of The Great Course’s most popular lecturers: award-winning Professor of Mathematics Arthur T. Benjamin of Harvey Mudd College, who is himself a professional magician.

Renowned in TED Talks, The Colbert Report, and other popular media as a “mathemagician,” Professor Benjamin teaches you the techniques and secrets behind dozens of great math-based tricks. Even if you are a numerical novice, you will look like a prodigy after mastering these math-inspired showpieces, which require no skills beyond basic algebra—and a bit of showmanship.

Learn the Fundamentals of the Magician’s Art

While magicians supposedly never reveal their tricks, when you learn the mathematical foundations behind how they work, you’re opening your eyes to one of the most fascinating and rewarding features of their craft and it gives you a crucial advantage in a number of areas, including:

•     Tricks are easier to remember if you understand how they work.

•     Knowing the “why” of a trick is the gateway to new effects as well as novel variations of the original.

•     Mathematical magic stimulates problem-solving skills, such as rapid mental calculation.

•     Magic can lead young people to fall in love with math—as happened with many professional mathematicians when they were young.

In Math and Magic, Professor Benjamin introduces you to magic, using tools like playing cards, numbers, and geometric figures. For each trick, he first runs through a demonstration. Then, he pulls back the curtain to show how the trick is done, explaining in detail the mathematical ideas underpinning the illusion. In this way, you learn such fundamentals of the magician’s art as:

•     Parity principle: Promoted by magician Bob Hummer, this idea has inspired a series of tricks in which the cards are treated in pairs according to a systematic procedure. Although the cards seem to be fairly mixed, an inherent order is preserved that, when revealed, astounds spectators.

•     Faro shuffle: Devised as a way to beat the popular 19th-century card game faro, this bit of trickery is also known as the perfect shuffle, in which cards from two equal halves of a deck are interlaced perfectly. A sequence of such shuffles can bring the top card to any desired position, creating a truly magical effect.

•     Lightning calculations: Dr. Benjamin is famous for his ability to solve problems in his head, often faster than someone punching numbers into a calculator. Naturally, he uses shortcuts, many of which are quite simple. For example, in this course you learn an easy method for determining cube roots that will make you look like a mathematical genius.

•     Magic squares: Popular for centuries, magic squares are grids of numbers where each row, column, and diagonal adds up to the same number. It might seem that only a few solutions are possible for a given grid, but that’s usually not true. You can impress your audience by building a magic square based on any number, or even based on someone’s birthday.

Astonish and Delight Your Friends

Throughout the lessons, Professor Benjamin teaches you how to astonish and delight your friends, family, and even yourself. In a bit of kitchen magic, he shows how to cut a bagel into two interlocking halves—a two-twist version of a Möbius strip. Among its advantages, this intriguing shape has a greater surface area than an ordinary sliced bagel and therefore holds more cream cheese!

Magic has held humans spellbound for a very long time. A few centuries ago, even simple card tricks like those in this course could have prompted accusations of witchcraft—with the result being persecution or even death. Fortunately, with Math and Magic, you don’t have that worry. Your only problem will be tearing yourself away from these “bewitching” lessons.

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12 lectures
 |  Average 32 minutes each
  • 1
    Mathematical Card Tricks
    Begin the course with card tricks in which mathematics is clearly being used, but the secret is not easy to figure out. Learn the invariant principle: Some qualities stay the same in a deck even though the order of cards is changing. End with what Professor Benjamin calls the tear-able" trick, being careful to use cards that you don't mind wrecking." x
  • 2
    What's Your Deal?
    Explore card tricks in which the cards are shuffled, dealt, and flipped over in interesting ways, leading to surprising outcomes. Discover Hummer's principle-an endless source of mystifying, crowd-pleasing tricks, based on random mixing of cards combined with a simple procedure that preserves a pattern that seems positively magical. x
  • 3
    Look like a Card Shark
    Professor Benjamin shows how to play cards like someone who would be thrown out of a casino. Learn the Jonah principle for always winning at poker. Get a feel" for counting cards and develop the knack for telepathically communicating a hidden card to an assistant. Finally, who could claim to be a card shark without a trick that turns up four aces every time?" x
  • 4
    The Deck Is Stacked
    Investigate tricks based on the cyclic method of card ordering, or stacking," popularized by magician Si Stebbins and tracing originally to one of the first books on magic, published in Italy in 1593. Learn how to seemingly weigh a deck of cards in your hands and other miraculous feats based on this simple principle." x
  • 5
    Perfect Shuffles
    Professor Benjamin introduces a special guest, mathematician and magician Brent Morris, master of the perfect shuffle (also known as the faro shuffle), in which two equal halves of the deck are interlaced perfectly. You will learn two versions of this virtuoso technique-the in-shuffle and out-shuffle-along with sequences of shuffles that lead to very interesting symmetries. x
  • 6
    Riffle Shuffles
    Explore results of an ordinary riffle shuffle, where the deck is cut roughly in half, and the cards are interlaced approximately-but usually not perfectly. Depending on how the cards are arranged beforehand, intriguing effects are possible, based on Gilbreath's principle of patterned sequences. Study several of these magic showpieces. x
  • 7
    Magic with Numbers
    Master an impressive medley of number-guessing tricks, involving the golden ratio, the Fibonacci series, and other notable numbers. In analyzing how the tricks work, discover how straightforward algebraic expressions are secretly pulling the strings. The feats include the very first mathematical magic trick that Professor Benjamin learned. x
  • 8
    Look like a Genius
    You don't have to be a genius to look like one. Drawing on young volunteers, Professor Benjamin shows easy strategies for mentally multiplying numbers by 11, dividing numbers by 91, multiplying any numbers near 100, squaring numbers ending in 5, and other seemingly fearless feats of arithmetic, without use of a calculator. x
  • 9
    The Magic of Nine
    Admire the magic of the number nine. An ancient technique called "casting out nines" lets you pick out the missing digit in a bewilderingly long series of operations. Then learn to determine two-digit cube roots and also find the age of a volunteer who has hidden the number in a complicated calculation-all with the help of the number nine. x
  • 10
    Look like a Psychic
    Hone your psychic powers by developing tricks such as these: Have someone scramble their birthday in a seemingly unbreakable code, which you decipher with ease. Calculate the hidden spots on a stack of dice. Use the parity principle to guess where your partner has landed in an alphabetic array. Also learn the magician's toxic" calculation principle." x
  • 11
    Geometric and Topological Magic
    Explore mathematical mysteries that seem geometrically or topologically odd. Consider a paper strip with a half twist, joined end-to-end, known as a Mobius band. What happens when there are more twists or if the shape is cut? Create an analogous shape by slicing a bagel. Also, solve puzzles with disappearing figures, including a rabbit. x
  • 12
    Magic Squares
    Since ancient times, magic squares have given endless hours of fun through designing grids of numbers where each row, column, and diagonal produces the same sum-as if by magic. In this last lesson, learn to create magic squares quickly from numbers provided by your amazed audience or based on your volunteer's birthday. Finally, end the course with a magic matrix based on the number pi. x

Lecture Titles

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What's Included

What Does Each Format Include?

Video DVD
Instant Video Includes:
  • Download 12 video lectures to your computer or mobile app
  • Downloadable PDF of the course guidebook
  • FREE video streaming of the course from our website and mobile apps
Video DVD
DVD Includes:
  • 12 lectures on 2 DVDs
  • 144-page printed course guidebook
  • Downloadable PDF of the course guidebook
  • FREE video streaming of the course from our website and mobile apps
  • Closed captioning available

What Does The Course Guidebook Include?

Video DVD
Course Guidebook Details:
  • 144-page printed course guidebook
  • Photos and illustrations
  • Exercises & Solutions
  • References

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Your professor

Arthur T. Benjamin

About Your Professor

Arthur T. Benjamin, Ph.D.
Harvey Mudd College
Dr. Arthur T. Benjamin is Professor of Mathematics at Harvey Mudd College. He earned a Ph.D. in Mathematical Sciences from Johns Hopkins University in 1989. Professor Benjamin's teaching has been honored repeatedly by the Mathematical Association of America (MAA). In 2000, he received the MAA Deborah and Franklin Tepper Haimo National Award for Distinguished College or University Teaching of Mathematics. The MAA also named...
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Reviews

Math and Magic is rated 4.7 out of 5 by 29.
Rated 5 out of 5 by from Magical!! I never stop being amazed at what this man can do. I use his tricks to get the attention of my reluctant students and to get the attention of students in a classroom that I am substituting in.
Date published: 2019-02-23
Rated 5 out of 5 by from Good I can’t say a lot as I only looked at the first chapter. I got it for a nephew who does some magic and is studying to be a clown and for his father who loves math and has an interest in magic. I think it can help both their skills and relationship. It seemed like it would be fun and interesting. I’ve always enjoyed math and I am a clown. Magic always adds to the fun.
Date published: 2019-02-06
Rated 5 out of 5 by from Grateful to learn so much! My grandkids were amazed I could do cube roots in my head! Priceless!! Math card tricks too.
Date published: 2019-01-31
Rated 5 out of 5 by from Fun Course but great brain building too Math has always been a necessity, but not fun for me. I look for classes that will challenge my mind while making the process of learning a pleasure. This course fits that balance very well. Dr. Benjamin describes the numeric sequences used in so many magic tricks. When you learn the math behind them, you just have to say "Wow!" Well done Dr. Benjamin. Top of the class!
Date published: 2019-01-25
Rated 5 out of 5 by from Fun, Well Done, and Enjoyable for Beginners! This was an enjoyable introduction to a variety of magic tricks based on elementary mathematics, primarily 9th-grade algebra. The first half explains many relatively simple card tricks, which anyone motivated can learn with a little practice, and the math is mostly an afterthought. The second half is more straightforwardly math-oriented. The algebra, which is used to explain the tricks, ranges from obvious to moderately involved, but it is all basic; the more complicated-appearing explanations just require a bit more time and effort to work through, not genius. And yes, you will learn some interesting math along the way. Of course it helps if you have a natural inclination to love magic and/or math. And Professor Benjamin is a natural performer, whose talent in this direction most of us will not be able to emulate. But don't let this stop you! - If the course description sounds interesting, you will likely be very pleased. I have no intention of getting up and performing any of the tricks, but I enjoyed seeing them so well performed and clearly explained. Thank you, professor!
Date published: 2019-01-17
Rated 5 out of 5 by from Perfect for me! I volunteer at church by reading to a group of kids who vary in age from about 4 to 10. Also I am a CASA for 2 teenage youths. While I would have preferred that this course would cover all age ranges I intend to use it for I am more than pleased with it. By utilizing a little creativity of your own and carefully choosing the card trick, even younger kids can be captivated. I highly recommend this course for anyone willing to invest a little time learning something both fun and educational.
Date published: 2019-01-14
Rated 5 out of 5 by from What fun! As usual, professor Benjamin continues to put out videos that are both instructive and entertaining while, at the same time, infused with some mathematical elements.
Date published: 2019-01-02
Rated 5 out of 5 by from Well presented, easy to learn I received this course for Christmas. It has been an immediate success for me and my grandkids, ages 6, 9, 9, 10. The card tricks are presented well and the math behind them explained so all can understand. I recommend highly!
Date published: 2018-12-30
Rated 4 out of 5 by from FUN AND INFORMATIVE I thoroughly enjoyed this course. I was pleased that it was not all about sleight of hand and tricks. Everything was done with logic and precision and it was all explained thoroughly. I think the teacher did an excellent job and I highly recommend this as an exercise is logical thinking
Date published: 2018-12-06
Rated 3 out of 5 by from Math and Magic It was good solid magic, but it was not the mathemagic I was looking for--I had hoped to find something to help kids get excited about magic. But this does well as adult magic.
Date published: 2018-11-25
Rated 5 out of 5 by from Excellent Outstanding course. Presenter is terrific. This is a fun course, the combination of the 'magic' and the math is very engaging.
Date published: 2018-11-11
Rated 5 out of 5 by from Fun AND informative! If you like magic tricks, this is one of my best Great Courses you can purchase! I love it. Examples are clear, concepts are easy to grasp, and tricks are "self working" so even unskilled folks like me can do them. My students love seeing the tricks, and it always spurs a great discussion of the mathematical principals behind. Also great for just showing card tricks in a casual crowd. HIGHLY RECOMMENDED.
Date published: 2018-11-11
Rated 5 out of 5 by from Math and Magic Professor Arthur Benjamin is such a great teacher. He makes learning so much fun and packs so much energy, into every lecture. His style really gave me the energy to keep going and practice. Everyone should have one or all his courses. I have all except one. This course is really neat - with all I learned, I could just about pass for a real Magician. He's the Best.
Date published: 2018-11-10
Rated 2 out of 5 by from Not for beginners I bought the "course" expecting to be able to perform some of the effects right away. I was wrong. While all the effects were completely explained (and some "over-explained"), a lot of it was just too technical for me. And I am no genius, because there were a lot of complicated formulas, and lots of "moves' to memorize. One of the things that bugged me the most was that the entire course had English subtitles and no way to shut that feature off. The subtitles and the complexity of the subject both prevented me from enjoying the course, and made me want to watch it only a little at a time.
Date published: 2018-11-09
Rated 5 out of 5 by from Great for math lovers Playing cards and card tricks have always been a mystery to me. I really enjoyed the math behind the tricks. If you like magic you'll like this course.
Date published: 2018-11-07
Rated 5 out of 5 by from Very Good Course! I have always enjoyed Magic, this course was enjoyable in that it not only taught me a few magic tricks but gave me a new attitude to math!
Date published: 2018-11-05
Rated 5 out of 5 by from Very impressive explanations Super easy to understand and makes math fun. I do appreciate math more now.
Date published: 2018-11-05
Rated 5 out of 5 by from Interesting subject, never thought of math/majic connection
Date published: 2018-10-28
Rated 5 out of 5 by from Excellent Course! I like magic and I like math, so this is a perfect course. There are fascinating card tricks to entertain friends. In addition, the math behind each trick is very clearly explained. The lecturer has an engaging and fun manner. I highly recommend this course.
Date published: 2018-10-24
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