The Secrets of Mental Math

Learn how to do complex mathematical problems right in your head, with the aid of this fun and useful course that teaches you the secrets behind mental math.

Overview Course No. 1406

One key to expanding your math potential – whether you’re a corporate executive or a high school student – lies in the power to perform mental math calculations. Solving basic math problems in your head offers lifelong benefits, including a competitive edge at work, a sharper and more active mind, and improved performance on standardized tests. Mental mathematics is also valuable in your everyday life, such as when shopping for groceries or figuring out how much to tip at a restaurant.

And perhaps the best part? Learning how to do mental math can be fun – especially when you’re learning in the company of Professor Arthur T. Benjamin of Harvey Mudd College, one of the most engaging and entertaining members of The Great Courses faculty.

The Secrets of Mental Math, his exciting 12-lecture course, guides you through all the essential skills, tips, and tricks for improving and enhancing your ability to solve a range of mathematical problems right in your head. Mental math, according to Professor Benjamin, is not as daunting as it may seem. Performing calculations in your head is all just a process of breaking down a large problem into simpler and simpler problems until it’s finally reduced to a single answer.

Assuming no detailed knowledge of mathematics, Professor Benjamin has designed this course to be accessible to anyone looking to tap into or strengthen his or her mental calculating skills. So prepare yourself for an unforgettable adventure in mental mathematics. Enjoyable, eye-opening, and immensely rewarding, The Secrets of Mental Math makes basic math quicker and easier than ever before.

Course Structure

01: Math in Your Head!

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.
Duration: 34 min

02: Mental Addition and Subtraction

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.
Duration: 32 min

03: Go Forth and Multiply

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 toolkit.
Duration: 31 min

04: Divide and Conquer

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.
Duration: 34 min

05: The Art of Guesstimation

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.
Duration: 35 min

06: Mental Math and Paper

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.
Duration: 35 min

07: Intermediate Multiplication

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).
Duration: 33 min

08: The Speed of Vedic Division

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.
Duration: 35 min

09: Memorizing 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.
Duration: 33 min

10: Calendar Calculating

The fun continues in this lecture 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.
Duration: 34 min

11: Advanced Multiplication

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 math skills.
Duration: 34 min

12: Masters of Mental Math

Professor Benjamin concludes his exciting course by showing how you can use different methods to solve the same problem; how you can find the cube root of large perfect cubes; how you can use the techniques you’ve learned and mastered in the last 11 lectures; and more.
Duration: 32 min