Mathematics

Dive right into the joys of mental math. First, learn the fundamental strategies of mental arithmetic (including the value of adding from left to right, unlike what you do on paper). Then, discover how a variety of shortcuts hold the keys to rapidly solving basic multiplication problems and finding squares.

Professor Benjamin demonstrates how easily you can mentally add and subtract one-, two-, and three-digit numbers. He also shows you shortcuts using the complement of a number (its distance from 100 or 1000) and demonstrates the uses of mental addition and subtraction for quickly counting calories and making change.

Delve into the secrets of easy mental multiplication: Professor Benjamin's favorite mathematical operation. Once you've mastered how to quickly multiply any two-digit or three-digit number by a one-digit number, you've mastered the most fundamental operations of mental multiplication and added a vital tool to your mental math tool kit.

Turn now to the last fundamental operation of arithmetic: division. Explore a variety of shortcuts for dividing by one- and two-digit numbers; learn how to convert fractions such as 1/7 and 3/16 into decimals; and discover methods for determining when a large number is divisible by numbers such as 3, 7, and 11.

In most real-world situations: such as figuring out sales tax or how much to tip: you don't need an exact answer but just a reasonable approximation. Here, develop skills for effectively estimating addition, subtraction, multiplication, division, and square roots.

Sometimes we encounter math problems on paper in our daily lives. Even so, there are some rarely taught techniques to help speed up your calculations and check your answers when you are adding tall columns of numbers, multiplying numbers of any length, and more.

Take mental multiplication to an even higher level. Professor Benjamin shows you five methods for accurately multiplying any two-digit numbers. Among these: the squaring method (when both numbers are equal), the close together method (when both numbers are near each other), and the subtraction method (when one number ends in 6, 7, 8, or 9).

Vedic mathematics, which has been around for centuries, is extremely helpful for solving division problems: much more efficiently than the methods you learned in school. Learn how Vedic division works for dividing numbers of any length by any two-digit numbers.

Think that memorizing long numbers sounds impossible? Think again. Investigate a fun: and effective: way to memorize numbers using a phonetic code in which every digit is given a consonant sound. Then practice your knowledge by trying to memorize the first 24 digits of pi, all of your credit card numbers, and more.

The fun continues in this episode with determining the day of the week of any date in the past or in the future. What day of the week was July 4, 2000? How about February 12, 1809? You'd be surprised at how easy it is for you to grasp the simple mathematics behind this handy skill.

Explore the origins of one of the oldest branches of mathematics. See how geometry not only deals with practical concerns such as mapping, navigation, architecture, and engineering, but also offers an intellectual journey in its own right--inviting big, deep questions.

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.