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?

  • numbers Master card tricks and the mathematical principles behind them.
  • numbers Learn simple shortcuts for lightning-fast calculations in your head.
  • numbers 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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Math and Magic is rated 4.4 out of 5 by 49.
Rated 5 out of 5 by from Amaze your family and friends! Excellent course. Easy and thorough explanations of the tricks.
Date published: 2020-10-30
Rated 1 out of 5 by from Product was defective. I cannot say more as the disks would not run!!
Date published: 2020-06-13
Rated 3 out of 5 by from Very entertaining, a little short on math Dr. Benjamin is a treasure, and I could watch his videos all day. This is my second course featuring Dr. Benjamin. I was expecting to learn a bit more about the connections between math and magic. Too much emphasis on presentation. If that's what you are after, you will enjoy this a bit more than I did. Still, not sorry I purchased this one.
Date published: 2020-06-08
Rated 5 out of 5 by from Triple Amazing Professor Benjamin's "Math and Magic" course was very enjoyable three times over: the first time was watching him perform the tricks, the second time was understanding the secrets he explained, and the third time was being able to do the tricks myself. It would have been a grand slam if I had enough confidence in my own showmanship skills to do the tricks in front of an audience, but that's probably a matter of time and practice and is certainly no fault of the course. The guidebook was indispensable for me. There were only a handful of minor typographical errors (pages 1, 34, 49, 54....?) and maybe a couple in the "Exercise Solutions" section: 1. Lesson 1, exercise 2, step 1 (page 126): I think the last "b" in "bcdabcdab" should be omitted (there's only 8 cards in play), and 2. Lesson 9, exercise 1, paragraph e (page 132): I believe the second sentence (beginning with "Hence") should end with "8?9" rather than "8?8". Thanks for another great series of lectures from brilliant and talented Professor Benjamin!
Date published: 2020-05-29
Rated 5 out of 5 by from A fun course This is a good course for those who want to learn a few card (and other) tricks and is also great if you want to understand the fun side of mathematics. The professor is entertaining and easy to understand.
Date published: 2020-05-05
Rated 5 out of 5 by from Fascinating and fun! I've enjoyed Professor Benjamin's courses before. I've passed the lessons in this course on to my grandson with great success.
Date published: 2020-04-30
Rated 5 out of 5 by from Fun and Interesting I'm home schooling my grand-daughter. In addition to the normal school topics, I wanted something to entertain and educate her at the same time. This course is accomplishing that! The Professor teaches us the trick, then explains the math behind it. Couldn't be better. I sent a video to her teacher and whole class, with her performing a flawless 9 card trick. Everyone loved it. Her and I were both excited. BTW - she's in 2nd grade! Great course for everyone while staying home.
Date published: 2020-04-25
Rated 5 out of 5 by from Even for Non- Math Majors I was hoping to not need a degree in linear algebra to be able to understand how card tricks are done and this course did not disappoint.
Date published: 2020-04-20
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