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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 longterm 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?
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.
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.
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.
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 reallife problems, for example, in choosing a telephone plan. Graphs help us better understand everything from lines to equations with negative or fractional exponents.
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.
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
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 Amazon Prime, Amazon and Hoopla.

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Premiere DateApril 11, 2007