The Joy of Mathematics

Rated 5 out of 5 by from A Joy Indeed! Professor Benjamin's enthusiastic style of presentation of a wide variety of topics, and clever surprise endings to his lectures, make this series a delightful taste of mathematical adventure.
Date published: 2020-05-16
Rated 1 out of 5 by from Joy of mathematics everything in this video is really confusing, he dont give out easy explanations, do not buy this, there is literally no simple explanation, you will just be wasting time, this guy taught about bass 8, nobody will ever use that, totally wasted my time
Date published: 2020-04-27
Rated 5 out of 5 by from Entertaining and delivers as advertised This course more than met the expectations I had for it from the catalog description. Dr. Benjamin is an excellent instructor. His enthusiasm is infectious, his speech is cear and the cadence is just right. The visual aids are frequent and clear. I would have been ok if he had skipped one or two of the proofs, but overall the content is just what I hoped for. If you are like me, someone who enjoyed math in high school and college, but did not have much chance to practice it in their career, then you will find this to be an excellent and entertaining review of the most important topics and concepts you learned many years ago.
Date published: 2020-04-15
Rated 5 out of 5 by from Professor Benjamin's enthusiasm is great! I am enjoying the course taking me through all the mathematics I learned many years ago as a student from algebra through calculus and presenting it in a refreshing way.
Date published: 2020-04-08
Rated 4 out of 5 by from Great idea wish I was smart enough to understand. Love math but math does NOT love me
Date published: 2020-02-24
Rated 4 out of 5 by from Intriguing A very good introduction or refreshment of some of the beauty that makes mathematics so very interesting and intriguing. I am not a mathematician but I do have a love for the enticement the course offers to explore beyond the introduction.
Date published: 2020-02-16
Rated 5 out of 5 by from Fun and interesting I recently bought the Joy of Mathematics course and have watched the first 5 lessons. Professor Benjamin does a good job explaining the concepts and makes the course truly fun.
Date published: 2020-02-11
Rated 5 out of 5 by from I feel like a kid in Junior High on Pie Day! I’m enjoying learning with no stress. That is pure joy.
Date published: 2020-02-11
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The Joy of Mathematics
Course Trailer
The Joy of Math-The Big Picture
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....

31 min
The Joy of Numbers
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?

29 min
The Joy of Primes
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.

30 min
The Joy of Counting
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....

28 min
The Joy of Fibonacci Numbers
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....

30 min
The Joy of Algebra
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.

31 min
The Joy of Higher Algebra
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....

31 min
The Joy of Algebra Made Visual
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.

32 min
The Joy of 9
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....

32 min
The Joy of Proofs
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....

31 min
The Joy of Geometry
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....

31 min
The Joy of Pi
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.

31 min
The Joy of Trigonometry
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....

32 min
The Joy of the Imaginary Number i
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....

31 min
The Joy of the Number e
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....

30 min
The Joy of Infinity
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.

30 min
The Joy of Infinite Series
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.

31 min
The Joy of Differential Calculus
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....

32 min
The Joy of Approximating with Calculus
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....

31 min
The Joy of Integral Calculus
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....

32 min
The Joy of Pascal's Triangle
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?...

32 min
The Joy of Probability
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....

30 min
The Joy of Mathematical Games
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."

31 min
The Joy of Mathematical Magic
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.

31 min
Arthur T. Benjamin

As a professor, I have always wanted to bring math to the masses. The Great Courses has helped make that dream come true.


Johns Hopkins University


Harvey Mudd College

About Arthur T. Benjamin

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 Professor Benjamin the 2006-2008 George Pólya Lecturer. In 2012, Princeton Review profiled him in The Best 300 Professors. He is a professional magician, whose techniques are explained in his book Secrets of Mental Math: The Mathemagician's Guide to Lightning Calculation and Amazing Math Tricks. Professor Benjamin also served for five years as coeditor of Math Horizons magazine. An avid games player, Dr. Benjamin is a past winner of the American Backgammon Tour and has written more than 15 papers on the mathematics of games and puzzles. Professor Benjamin has appeared on dozens of television and radio programs and has been featured in publications, including Scientific American, People, and The New York Times. In 2005, Reader's Digest called him America's Best Math Whiz.

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