Math in Your Head!

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Advanced Multiplication
Episode 11 of Secrets of Mental Math
Professor Benjamin shows you how to do enormous multiplication problems in your head, such as squaring three-digit and four-digit numbers; cubing two-digit numbers, and multiplying two-digit and three-digit numbers. While you may not frequently encounter these large problems, knowing how to mentally solve them cements your knowledge of basic mental…
Secrets of Mental Math
One key to expanding your math potential--whether you're a CEO or a high school student--lies in the power to perform mental calculations. Solving basic math problems in your head offers lifelong benefits including a competitive edge at work, a more active and sharper mind, and improved standardized test scores. Discover…
Introduction to Scale
Episode 24 of Geometry
If you double the side-lengths of a shape, what happens to its area? If the shape is three-dimensional, what happens to its volume? In this lecture, you explore the concept of scale. You use this idea to re-derive one of our fundamental assumptions of geometry, the Pythagorean theorem, using the…
Divide and Conquer
Episode 4 of Secrets of Mental Math
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,…
Go Forth and Multiply
Episode 3 of Secrets of Mental Math
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.
Mental Addition and Subtraction
Episode 2 of Secrets of Mental Math
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.
Mental Math and Paper
Episode 6 of Secrets of Mental Math
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.
The Joy of Numbers
Episode 2 of The Joy of Mathematics
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?
The Art of Guesstimation
Episode 5 of Secrets of Mental Math
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.
The Joy of Mathematical Magic
Episode 24 of The Joy of Mathematics
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.
The Joy of Approximating with Calculus
Episode 19 of The Joy of Mathematics
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.
The Geometry of Figurate Numbers
Episode 34 of Geometry
Ponder another surprising appearance of geometry--the mathematics of numbers and number theory. Look into the properties of square and triangular numbers, and use geometry to do some fancy arithmetic without a calculator.