 # Watch The Joy of Mathematics

Humans have been having fun and games 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 math, taught by a mathematician who is literally a magician with numbers.

The Joy of Mathematics is a series that is currently running and has 1 seasons (15 episodes). The series first aired on April 11, 2007.

The Joy of Mathematics is available for streaming on the website, both individual episodes and full seasons. You can also watch The Joy of Mathematics on demand atAmazon Prime, Amazon online.

The Great Courses Signature Collection
1 Season, 15 Episodes
April 11, 2007
Cast: Arthur T. Benjamin
i Watch Episodes

## The Joy of Mathematics Full Episode Guide

• 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."

• 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.

• 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?

• 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.

• 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.

• 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.

• 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.

• 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.

• 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.

• 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.

• 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.

• 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.

• 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.

• 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?

• 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