The Secrets of Mental Math

Rated 5 out of 5 by from A Must Take Course! I was taking and enjoying Dr. Benjamin' course on "Discrete Mathematics". I highly recommended that course also. His engaging style and knowledge caught my interest. I surfed the web to learn more about him. I came across his TED talks, particularly his talk "Lightning calculation and other 'mathemagic'". To say the least, I was very impressed and wanted to learn the secrets of Mathemagic. Thank you for producing this course. I thoroughly enjoyed it and am using the techniques taught in the course.
Date published: 2021-04-12
Rated 5 out of 5 by from secrets of mental math fascinating and mind boggling, can envision many daily applications of this course, it will empower you!
Date published: 2020-10-31
Rated 5 out of 5 by from Very well spoken lecturer, some great techniques This is exactly what I was after. I need to improve my mental maths for an upcoming job application, and was looking for a step-by-step course to help me improve. The course textbook PDF also has loads of practice questions
Date published: 2020-10-13
Rated 5 out of 5 by from Excellent material I just wish this math is taught to children like the ones in the 4th grade. If any on in the audience would look at the core curriculum in schools, you will know what kind of skills these kids would have after graduation. I taught some of these addition techniques one night to my grandchild. When I picked her up, she told me that her teacher told her that what (Dr. Benjamin) told her last night is NOT what the teacher is teaching. Wow
Date published: 2020-06-20
Rated 4 out of 5 by from Simplified approach gives me hope I have always been in need of paper to solve a problem. I am actually making progress with instructor's approach!
Date published: 2020-06-16
Rated 4 out of 5 by from Fun Course! I am still working my way through this. I think the course is a lot of fun, though I have some doubt about the final utility of what I am learning. Admittedly, it might be fun to amaze your friends that you can multiply three digit numbers in your head, but the deserved response might be, "So what?" With today's world where everyone has a watch, phone, or calculator, doing the numbers in your head is hardly necessary, but it is good mental exercise and my wife is at times amazed.
Date published: 2020-06-04
Rated 5 out of 5 by from Rejuvenating Mental math was easy for me as a young man but I noticed some slippage as I got older. This course restored me by teaching me explicitly all the tricks I used to use implicitly. I’m definitely not as sharp as I was but Mental Math has rejuvenated me.
Date published: 2020-05-25
Rated 5 out of 5 by from Better than I expected With some extra time on my hands, I wanted to try something that would test and enhance my mental skills. Dr. Benjamin presents his material in an enthusiastic and entertaining manner. I'm only 1/3 through the course and am looking forward to future lectures. It's been over 50 years since I graduated from university. Who says you can't teach an old dog some new tricks.
Date published: 2020-04-28
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The Secrets of Mental Math
Course Trailer
Math in Your Head!
1: 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.

34 min
Mental Addition and Subtraction
2: 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.

32 min
Go Forth and Multiply
3: 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 tool kit.

31 min
Divide and Conquer
4: 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.

34 min
The Art of Guesstimation
5: 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.

35 min
Mental Math and Paper
6: 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.

35 min
Intermediate Multiplication
7: 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).

33 min
The Speed of Vedic Division
8: 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.

35 min
Memorizing Numbers
9: 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.

33 min
Calendar Calculating
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.

34 min
Advanced Multiplication
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.

34 min
Masters of Mental Math
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.

32 min
Arthur T. Benjamin

As a professor, I have always wanted to bring math to the masses. The Great Courses has helped make that dream come true.


Johns Hopkins University


Harvey Mudd College

About Arthur T. Benjamin

Dr. Arthur T. Benjamin is Professor of Mathematics at Harvey Mudd College. He earned a Ph.D. in Mathematical Sciences from Johns Hopkins University in 1989. Professor Benjamin's teaching has been honored repeatedly by the Mathematical Association of America (MAA). In 2000, he received the MAA Deborah and Franklin Tepper Haimo National Award for Distinguished College or University Teaching of Mathematics. The MAA also named Professor Benjamin the 2006-2008 George Pólya Lecturer. In 2012, Princeton Review profiled him in The Best 300 Professors. He is a professional magician, whose techniques are explained in his book Secrets of Mental Math: The Mathemagician's Guide to Lightning Calculation and Amazing Math Tricks. Professor Benjamin also served for five years as coeditor of Math Horizons magazine. An avid games player, Dr. Benjamin is a past winner of the American Backgammon Tour and has written more than 15 papers on the mathematics of games and puzzles. Professor Benjamin has appeared on dozens of television and radio programs and has been featured in publications, including Scientific American, People, and The New York Times. In 2005, Reader's Digest called him America's Best Math Whiz.

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