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Seasons

24. The Joy of Mathematical Magic

January 1, 1970

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.

23. The Joy of Mathematical Games

April 11, 2007

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."

22. The Joy of Probability

April 11, 2007

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.

21. The Joy of Pascal's Triangle

April 11, 2007

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?

20. The Joy of Integral Calculus

January 1, 1970

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.

19. The Joy of Approximating with Calculus

April 11, 2007

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.

18. The Joy of Differential Calculus

April 11, 2007

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.

17. The Joy of Infinite Series

January 1, 1970

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.

16. The Joy of Infinity

April 11, 2007

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.

15. The Joy of the Number e

January 1, 1970

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.

14. The Joy of the Imaginary Number i

April 11, 2007

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.

13. The Joy of Trigonometry

January 1, 1970

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.

12. The Joy of Pi

January 1, 1970

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.

11. The Joy of Geometry

April 11, 2007

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.

9. The Joy of 9

April 11, 2007

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.

8. The Joy of Algebra Made Visual

April 11, 2007

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.

7. The Joy of Higher Algebra

January 1, 1970

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.

6. The Joy of Algebra

April 11, 2007

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.

5. The Joy of Fibonacci Numbers

January 1, 1970

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.

4. The Joy of Counting

April 11, 2007

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.

3. The Joy of Primes

April 11, 2007

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.

2. The Joy of Numbers

April 11, 2007

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?

1. The Joy of Math - The Big Picture

April 11, 2007

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.#Science & Mathematics

Description

Where to Watch The Joy of Mathematics

The Joy of Mathematics is available for streaming on the The Great Courses Signature Collection website, both individual episodes and full seasons. You can also watch The Joy of Mathematics on demand at Apple TV Channels, Amazon Prime, Amazon, Kanopy and Hoopla.