This experience is optimized for Internet Explorer version 10 and above.

Please upgrade your browser

Send the Gift of Lifelong Learning!

Joy of Mathematics

Joy of Mathematics

Gifting Information


To send your gift, please complete the form below. An email will be sent immediately to notify the recipient of your gift and provide them with instructions to redeem it.

  • 500 characters remaining.

Frequently Asked Questions

With an eGift, you can instantly send a Great Course to a friend or loved one via email. It's simple:
1. Find the course you would like to eGift.
2. Under "Choose a Format", click on Video Download or Audio Download.
3. Click 'Send e-Gift'
4. Fill out the details on the next page. You will need to the email address of your friend or family member.
5. Proceed with the checkout process as usual.
Q: Why do I need to specify the email of the recipient?
A: We will send that person an email to notify them of your gift. If they are already a customer, they will be able to add the gift to their My Digital Library and mobile apps. If they are not yet a customer, we will help them set up a new account so they can enjoy their course in their My Digital Library or via our free mobile apps.
Q: How will my friend or family member know they have a gift?
A: They will receive an email from The Great Courses notifying them of your eGift. The email will direct them to If they are already a customer, they will be able to add the gift to their My Digital Library and mobile apps. If they are not yet a customer, we will help them set up a new account so they can enjoy their course in their My Digital Library or via our free mobile apps.
Q: What if my friend or family member does not receive the email?
A: If the email notification is missing, first check your Spam folder. Depending on your email provider, it may have mistakenly been flagged as spam. If it is not found, please email customer service at ( or call 1800 461 951 for assistance.
Q: How will I know they have received my eGift?
A: When the recipient clicks on their email and redeems their eGift, you will automatically receive an email notification.
Q: What if I do not receive the notification that the eGift has been redeemed?
A: If the email notification is missing, first check your Spam folder. Depending on your email provider, it may have mistakenly been flagged as spam. If it is not found, please email customer service at ( or call customer service at 1800 461 951 for assistance.
Q: I don't want to send downloads. How do I gift DVDs or CDs?
A: eGifting only covers digital products. To purchase a DVD or CD version of a course and mail it to a friend, please call customer service at 1800 461 951 for assistance.
Q: Oops! The recipient already owns the course I gifted. What now?
A: Great minds think alike! We can exchange the eGifted course for another course of equal value. Please call customer service at 1800 461 951 for assistance.
Q: Can I update or change my email address?
A: Yes, you can. Go to My Account to change your email address.
Q: Can I select a date in the future to send my eGift?
A: Sorry, this feature is not available yet. We are working on adding it in the future.
Q: What if the email associated with eGift is not for my regular Great Course account?
A: Please please email customer service at ( or call our customer service team at 1800 461 951 for assistance. They have the ability to update the email address so you can put in your correct account.
Q: When purchasing a gift for someone, why do I have to create an account?
A: This is done for two reasons. One is so you can track the purchase of the order in your ‘order history’ section as well as being able to let our customer service team track your purchase and the person who received it if the need arises.
Q: Can I return or Exchange a gift after I purchase it?
A: Because the gift is sent immediately, it cannot be returned or exchanged by the person giving the gift. The recipient can exchange the gift for another course of equal or lesser value, or pay the difference on a more expensive item

Priority Code


Joy of Mathematics

Course No. 1411
Professor Arthur T. Benjamin, Ph.D.
Harvey Mudd College
Share This Course
4.4 out of 5
152 Reviews
79% of reviewers would recommend this series
Course No. 1411
Video Streaming Included Free

What Will You Learn?

  • Reinvigorate your love of mathematics, and discover how the field can be enjoyed for its beauty and certainty.
  • Learn the beautiful and unexpected properties of Fibonacci numbers, which show up in art, nature, and even poetry.
  • Explore the bizarre concept of infinity, and deliberate over whether there are an infinite number of infinities.
  • Examine the concepts of imaginary and complex numbers, which play a surprisingly useful role in physics.
  • Study how mathematical proofs work, including proofs by deduction, proofs by induction, and proofs by existence.

Course Overview

Ready to exercise those brain cells? Humans have been having fun with mathematics for thousands of years. Along the way, they've discovered the amazing utility of this field—in science, engineering, finance, games of chance, and many other aspects of life. This course of 24 half-hour lectures celebrates the sheer joy of mathematics, taught by a mathematician who is literally a magician with numbers. Professor Arthur T. Benjamin of Harvey Mudd College is renowned for his feats of mental calculation performed before audiences at schools, theaters, museums, conferences, and other venues.

Although racing a calculator to solve a difficult problem may seem like a superhuman achievement, Professor Benjamin shows that there are simple tricks that allow anyone to look like a math magician. Professor Benjamin has another goal in this course: throughout these lectures, he shows how everything in mathematics is connected—how the beautiful and often imposing edifice that has given us algebra, geometry, trigonometry, calculus, probability, and so much else is based on nothing more than fooling around with numbers.

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.

Have You Forgotten Math? Worry Not!

Professor Benjamin gives his presentation on the number 9 in—where else?—Lecture 9. Other lectures are devoted to pi, the imaginary number i, the transcendental number e, and infinity. These numbers are gateways to intriguing realms of mathematics, which you explore under Dr. Benjamin's enthusiastic guidance.

He also introduces you to prime numbers, Fibonacci numbers, and infinite series. And you investigate the powerful techniques for manipulating numbers using algebra, geometry, trigonometry, calculus, and probability in lectures that may hark back to subjects you studied in high school and college. You will find Dr. Benjamin's introduction to these fields both a useful refresher and a bird's-eye view of the most important areas of mathematics. Intriguingly, he approaches these topics from the novel perspective of combinatorics and mathematical games, providing a fun entry into subjects that are often taught in a lackluster way.

In the next-to-last lecture, you look at the application of probability to games. And finally, you splurge on feats of mathematical magic: For instance, did you know that you don't have to be a genius to calculate cube roots in your head?

Throughout the course, Dr. Benjamin assumes that you may have no more than a distant memory of high school math. He believes that it is his job to fan those embers into a burning interest in the subject he loves so much—and in which he takes such exquisite joy.

A Math Course Designed for You

This course is especially well suited for:

  • Anyone attracted by Dr. Benjamin's promise of a joyful attitude to an often-imposing subject
  • Anyone for whom high school and college math courses are a distant memory who would like to revisit these subjects to explore topics they skipped the first time
  • Anyone now taking math who would like a big-picture perspective on the major areas of the field from a playful, joyous point of view
  • Budding math mavens who love numbers and the magic that can be done with them.

Be prepared to encounter strange equations, novel ways of thinking, and symbols and computational methods that may be new to you. But also prepare to sharpen your wits in ways you never thought possible. Math is a challenging subject, but it pays immense rewards. Few people understand everything the first time through an unfamiliar domain of math. "But that's OK," says Dr. Benjamin. "You can rewind me and have me explain it all over again! All of this material bears repeating, and I hope you get to enjoy it many times over."

Patterns, Patterns Everywhere

One of Dr. Benjamin's greatest loves is the Fibonacci sequence, which shows up in many spheres of mathematics, as well as in nature, art, computer science, and poetry. The distinctive meter of a limerick encodes Fibonacci numbers, and Dr. Benjamin has even composed his own limerick to show how the sequence begins:

I think Fibonacci is fun;
We start with a 1 and a 1.
Then 2, 3, 5, 8,
But don't stop there, mate!
The fun has just barely begun.

The series continues on: 13, 21, 34, 55, 89, … with each successive Fibonacci number being the sum of the previous two. This simple pattern is named for a 12th-century mathematician who described a problem involving imaginary rabbits that never die. Starting with a pair of baby rabbits, the animals take a month to mature, then mate and produce a male and a female; these mature after a month and mate, along with their parents. The total number of pairs after each month follows the Fibonacci sequence.

In our own day, Fibonacci numbers appear as a critical plot element in The Da Vinci Code, notably under the guise of the golden ratio, an ideal proportion favored by artists and architects that is intimately connected to the Fibonacci sequence. However, Dr. Benjamin cautions that the quest for instances of the golden ratio in nature can get out of hand.

A Feast for the Brain

Anyone who has ever witnessed a feat of mathematical prowess and chalked it up to unfathomable intellect will be interested to learn that there is often a simple shortcut at work. For example, the first 24 digits of pi, the famous ratio of the circumference of a circle to its diameter, can be memorized with the help of a silly sentence starting "My turtle Pancho …" Four more sentences take you to 100 digits, making you look like a prodigy indeed!

Similarly, if someone asked you to add up all the numbers from 1 to 100, you might take out a sheet of paper and start to work, little realizing that this difficult-looking problem can be done in your head in seconds by a method devised by the famous mathematician Carl Friedrich Gauss when he was a boy. The same goes for squaring and multiplying multidigit numbers in your head.

"Mathematics is food for the brain," says Dr. Benjamin. "It helps you think precisely, decisively, and creatively and helps you look at the world from multiple perspectives. Naturally, it comes in handy when you're shopping around for the best bargain or trying to understand the statistics you read in the newspaper.

"But I hope that you come away from this course with a new way to experience beauty—in the form of a surprising pattern or an elegant logical argument. Many people find joy in fine music, poetry, and other works of art—and mathematics offers joys that I hope you, too, will learn to experience. If Elizabeth Barrett Browning had been a mathematician, she might have said, ‘How do I count thee? Let me love the ways!'"

Hide Full Description
24 lectures
 |  30 minutes each
  • 1
    The Joy of Math—The Big Picture
    Professor Benjamin introduces the ABCs of math appreciation: The field can be loved for its applications, its beauty and structure, and its certainty. Most of all, mathematics is a source of endless delight through creative play with numbers. x
  • 2
    The Joy of Numbers
    How do you add all the numbers from 1 to 100—instantly? What makes a square number square and a triangular number triangular? Why do the rules of arithmetic really work, and how do you calculate in bases other than 10? x
  • 3
    The Joy of Primes
    A number is prime if it is evenly divisible by only itself and one: for example, 2, 3, 5, 7, 11. Professor Benjamin proves that there are an infinite number of primes and shows how they are the building blocks of our number system. x
  • 4
    The Joy of Counting
    Combinatorics is the study of counting questions such as: How many outfits are possible if you own 8 shirts, 5 pairs of pants, and 10 ties? A trickier question: How many ways are there to arrange 10 books on a shelf? Combinatorics can also be used to analyze numbering systems, such as ZIP Codes or license plates, as well as games of chance. x
  • 5
    The Joy of Fibonacci Numbers
    The Fibonacci numbers follow the simple pattern 1, 1, 2, 3, 5, 8, etc., in which each number is the sum of the two preceding numbers. Fibonacci numbers have many beautiful and unexpected properties, and show up in nature, art, and poetry. x
  • 6
    The Joy of Algebra
    Arguably the most important area of mathematics, algebra introduces the powerful idea of using an abstract variable to represent an unknown quantity. This lecture demonstrates algebra's golden rule: Do unto one side of an equation as you do unto the other. x
  • 7
    The Joy of Higher Algebra
    This lecture shows how to solve quadratic (second-degree) equations from the technique of completing the square and the quadratic formula. The quadratic formula reveals the connection between Fibonacci numbers and the golden ratio. x
  • 8
    The Joy of Algebra Made Visual
    Algebra can be used to solve geometrical problems, such as finding where two lines cross. The technique is useful in real-life problems, for example, in choosing a telephone plan. Graphs help us better understand everything from lines to equations with negative or fractional exponents. x
  • 9
    The Joy of 9
    Adding the digits of a multiple of 9 always gives a multiple of 9. For example: 9 x 4 = 36, and 3 + 6 = 9. In modular arithmetic, this property allows checking answers by "casting out nines." A related trick: mentally computing the day of the week for any date in history. x
  • 10
    The Joy of Proofs
    Professor Benjamin begins his discussion of mathematical proofs with intuitive cases like "even plus even is even" and "odd times odd is odd." He builds to more complex proofs by existence and induction, and ends with a checkerboard challenge. x
  • 11
    The Joy of Geometry
    Geometry is based on a handful of definitions and axioms involving points, lines, and angles. These lead to important conclusions about the properties of polygons. This lecture uses geometric reasoning to derive the Pythagorean theorem and other interesting results. x
  • 12
    The Joy of Pi
    Pi is the ratio of the circumference of a circle to its diameter. It starts 3.14 and continues in an infinite nonrepeating sequence. Professor Benjamin shows how to learn the first hundred digits of this celebrated number, making it look as easy as pie. x
  • 13
    The Joy of Trigonometry
    Trigonometry deals with the sides and angles of triangles. This lecture defines sine, cosine, and tangent, along with their reciprocals, the cosecant, secant, and cotangent. Extending these definitions to the unit circle allows a handy measure of angle: the radian. x
  • 14
    The Joy of the Imaginary Number i
    Could the apparently nonsensical number the square root of –1 be of any use? Very much so, as this lecture shows. Such imaginary and complex numbers play an indispensable role in physics and other fields, and are easier to understand than they appear. x
  • 15
    The Joy of the Number e
    Another indispensable number to learn is e = 2.71828 ... Defined as the base of the natural logarithm, e plays a central role in calculus, and it arises naturally in many spheres of mathematics, including calculations of compound interest. x
  • 16
    The Joy of Infinity
    What is the meaning of infinity? Are some infinite sets "more" infinite than others? Could there possibly be an infinite number of levels of infinity? This lecture explores some of the strange ideas associated with mathematical infinity. x
  • 17
    The Joy of Infinite Series
    Starting with the analysis of the proposition 0.999999999 ... = 1, this lecture ex­plores what it means to add up an infinite series of numbers. Some infinite series con­verge on a definite value, while others grow arbitrarily large. x
  • 18
    The Joy of Differential Calculus
    Calculus is the mathematics of change, and answers questions such as: How fast is a function growing? This lecture introduces the concepts of limits and derivatives, which allow the slope of a curve to be measured at any point. x
  • 19
    The Joy of Approximating with Calculus
    Exploiting the idea of the derivative, we can approximate just about any function using simple polynomials. This lecture also shows why a formula sometimes known as "God's equation" (involving e, i, p, 1, and 0) is true, and how to calculate square roots in your head. x
  • 20
    The Joy of Integral Calculus
    Geometry and trigonometry are used to determine the areas of simple figures such as triangles and circles. But how are more complex shapes measured? Calculus comes to the rescue with a technique called integration, which adds the simple areas of many tiny quantities. x
  • 21
    The Joy of Pascal's Triangle
    A geometric arrangement of binomial coefficients called Pascal's triangle is a treasure trove of beautiful number patterns. It even provides an answer to the song "The Twelve Days of Christmas": Exactly how many gifts did my true love give to me? x
  • 22
    The Joy of Probability
    Mathematics can draw detailed inferences about random events. This lecture covers major concepts in probability, such as the law of large numbers, the central limit theorem, and how to measure variance. x
  • 23
    The Joy of Mathematical Games
    This lecture applies the law of total probability and other concepts from the course to predict the long-term losses to be expected from playing games such as roulette and craps and understand what is known as the "Gambler's Ruin Problem." x
  • 24
    The Joy of Mathematical Magic
    Closing the course with a magician's flair, Professor Benjamin shows a trick for producing anyone's phone number, how to create a magic square based on your birthday, how to play "mathematical survivor," a technique for computing cube roots in your head, and a card trick to ponder. x

Lecture Titles

Clone Content from Your Professor tab

What's Included

What Does Each Format Include?

Video DVD
Video Download Includes:
  • Ability to download 24 video lectures from your digital library
  • Downloadable PDF of the course guidebook
  • FREE video streaming of the course from our website and mobile apps
Video DVD
DVD Includes:
  • 24 lectures on 4 DVDs
  • 184-page printed course guidebook
  • Downloadable PDF of the course guidebook
  • FREE video streaming of the course from our website and mobile apps

What Does The Course Guidebook Include?

Video DVD
Course Guidebook Details:
  • 184-page course synopsis
  • Equations, tables, & diagrams
  • Suggested readings
  • Questions to consider

Enjoy This Course On-the-Go with Our Mobile Apps!*

  • App store App store iPhone + iPad
  • Google Play Google Play Android Devices
  • Kindle Fire Kindle Fire Kindle Fire Tablet + Firephone
*Courses can be streamed from anywhere you have an internet connection. Standard carrier data rates may apply in areas that do not have wifi connections pursuant to your carrier contract.

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...
Learn More About This Professor
Also By This Professor


Joy of Mathematics is rated 4.4 out of 5 by 152.
Rated 5 out of 5 by from Very good indeed I enjoyed this course. The presenter comes over as very human, and makes great use of humour (see the bit about find c, and Harvey the horse who runs in the mud) The passionate presentation holds your attention through the more demanding bits; simple introductions do sometimes accelerate into a screen full of intimidating maths, but you can always re-run the disc, and to be fair, Dr Benjamin does explain this beforehand. Well worth the money.
Date published: 2017-11-06
Rated 1 out of 5 by from Turned out to be very expensive Had to pay for delivery and then a huge bill from FedEx as well.
Date published: 2017-08-26
Rated 5 out of 5 by from Wow I never thought I would like math ---much less love it but behold I have fallen in love!!! I am in my sixties and my idea of a good time is watching Dr Benjamin's Joy of Mathematics. Now" play time" is spent doing math problems and wanting to understand it. I have also fallen love with many other courses most of which I hope to buy. Thank you for creating this I think real joy is learning and exploring . Blessings Dee
Date published: 2017-04-08
Rated 3 out of 5 by from Not bad at all. But the arms!! I like the content of the course: It's a good walkthrough of what mathematics is all about. It is however very distracting to see the professor waving his arms all the times. It's pointless and does not bring any additional value to the training. Therefore, I give a poor rating for the presentation.
Date published: 2017-03-11
Rated 3 out of 5 by from Caution! A one-size-fits-all. Annoyingly-pleasant This is NOT a survey course, not a primer, not even a Joy of Math 101. Instead it is an annoyingly pleasant shutter-fast "spectrum of exposure" from the mundane, all the way to Calculus. As others have pointed out, the professor is very brainy, prone to shaggy dog stories and bad puns. BUT, they endear you to him as he is THE ONE saving grace for the audience-misidentified and far-ranging scope of this course. It is a course likely to completely please neither newbies nor rocket scientists. Brainiacs will be bored to death with the middle-school math of the initial lectures. Beginners or reviewers will be overly bedazzled by the fast-paced (yet moderately simple) linear and quadratic equations beginning with Algebra/Trigonometry and mercifully ending with "Probability Math". HOWEVER, at no point does the viewer need to take to pencil and paper or scientific calculator; for it is "exposure" to the concepts that is the real value in this know that certain mathematical concepts and constructs exist makes the course worthwhile. All along the way there are NUGGETS, take-aways and confections that will please the viewer. I found the lectures on Trigonometry and Geometry most rewarding. In the end, the Professor culminates with several examples of "Math Magic"; tricks to impress your friends and neighbors. The course is worthwhile, if you understand that it is best purchased at the occasional "Sale Price" offering. This course would benefit from being two separate courses: "The Joy of Mathematics" and "The Joy of Higher Mathematics". All this said, I recommend it for it's (among other things) warmly endearing entertainment value.
Date published: 2017-02-28
Rated 5 out of 5 by from Got my attention! Though never good at mathematics, I am finding the challenge interesting and stimulating. The presenter is animated and entertaining.
Date published: 2017-02-04
Rated 5 out of 5 by from Writing Sentences for Writer, Meditation, more I have these course incredible, I feel like I am back in collge. The lectures are presented in a clear professional manner. Do the homework, you win! Thomas Affatato
Date published: 2017-01-25
Rated 5 out of 5 by from Great Fun I wish I would have had an instructor that was so engaging when I was taking my mathematics courses. The course is presented in a straightforward format and makes the topics interesting and actually kind of fun. Highly recommended.
Date published: 2017-01-22
  • y_2018, m_1, d_15, h_8
  • bvseo_bulk, prod_bvrr, vn_bulk_2.0.6
  • cp_1, bvpage1
  • co_hasreviews, tv_13, tr_139
  • loc_en_US, sid_1411, prod, sort_[SortEntry(order=SUBMISSION_TIME, direction=DESCENDING)]
  • clientName_teachco
  • bvseo_sdk, p_sdk, 3.2.0
  • CLOUD, getContent, 8.32ms

Questions & Answers


1-10 of 11 Questions
1-10 of Questions

Customers Who Bought This Course Also Bought

Video title