Secrets of Mental Math

Course No. 1406
Professor Arthur T. Benjamin, Ph.D.
Harvey Mudd College
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4.7 out of 5
156 Reviews
92% of reviewers would recommend this product
Course No. 1406
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What Will You Learn?

  • Give yourself a competitive edge in school or at work and improve your performance on standardized tests.
  • Discover a simple trick that will let you mentally determine the day of the week of any date in history.
  • Quickly find squares and square roots.
  • Learn specific strategies for performing the nuts-and-bolts operations of mental mathematics.
  • Improve your memory for numbers (including phone and credit card numbers) by using a simple phonetic code.
  • Learn how to find approximate answers using the art of "guesstimation."

Course Overview

Quick: What's 25 × 45? How about 742 × 300? Or 4821 ÷ 9?

Most of us, when faced with math problems like these, immediately reach for a calculator or a pen. But imagine if you could perform these and other seemingly difficult—but surprisingly easy—calculations right in your head. Seems like an impossible feat? It's not.

One key to improving and expanding your math potential—whether you're a corporate executive or a high-school student—lies in the powerful ability to perform mental math calculations. Solving basic math problems in your head is a gateway to success in understanding and mastering higher mathematical fields such as algebra, statistics, and calculus. It's a skill that offers other lifelong benefits, including

  • giving you a competitive edge in school or at work;
  • keeping your mind active and sharp at any age;
  • improving your performance on standardized tests; and
  • learning to solve problems by using a variety of methods.

Mental mathematics also is valuable when you're 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 new 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—Made Simple

Mental math, as Professor Benjamin demonstrates, is not as daunting as it may seem. In fact, it's an ability you already have—you just may not know it. 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 other than what you learned in elementary school, Professor Benjamin has designed The Secrets of Mental Math to be accessible to anyone looking to tap into or strengthen his or her mental calculating skills.

In the first part of the course, you focus on specific strategies for performing the basic nuts-and-bolts operations of mental mathematics.

  • Adding any two numbers up to three digits
  • Subtracting any two numbers up to three digits
  • Multiplying any two numbers up to two digits
  • Dividing any number by a number up to two digits

Dr. Benjamin fills each lecture with a wealth of practice problems to follow along with and get you engaged in the joys of mentally solving math problems.

Once you've gotten these four fundamental operations down, you then branch out into some interesting directions that continue to hone your mental math skills. Among the exciting skills you'll develop are

  • how to find approximate answers using the art of "guesstimation";
  • how to quickly find squares and square roots;
  • how to improve your memory for numbers (including phone and credit card numbers) by using a simple phonetic code;
  • how to approach enormous calculations with increased confidence and accuracy;
  • how to mentally determine the day of the week of any date in history; and
  • how to do rapid pencil-and-paper mathematics in ways seldom taught in school.

And his accompanying course guidebook is filled with additional problems you can use to practice your newfound skills.

Discover Valuable Mathematical Tips and Techniques

Throughout The Secrets of Mental Math, Professor Benjamin leads you through some fun—and memorable—techniques for tackling specific mathematical calculations. Here's an example of one strategy he calls "Create a Zero, Kill the Zero," helpful for determining the divisibility of any odd number that doesn't end in 5.

Is 1232 a multiple of 7?

  • Start by adding or subtracting a multiple of 7 to create a 0 at the end (1232 + 28 = 1260).
  • Kill the 0 from the new number (1260 becomes 126).
  • Add or subtract a multiple of 7 to create another zero at the end (126 + 14 = 140), then kill the 0 at the end.
  • Determine whether the new number is a multiple of the original divisor (yes, it's 14).
  • Thus, 1232 is a multiple of 7.

An Encouraging, Rewarding Look at Numbers

But you'll get more than just fun strategies to help make mental math easier. Learning with Professor Benjamin is like having a supportive coach right by your side—someone to encourage you, challenge you, and instill mathematical confidence in you. It's this same teaching method that has won him a host of prestigious awards from the Mathematical Association of America, including the Deborah and Franklin Tepper Haimo Award for Distinguished College or University Teaching of Mathematics.

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. And it's a powerful way to take your first, more confident steps into the intriguing—and undeniably fun—world of numbers.

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12 lectures
 |  Average 33 minutes each
  • 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. x
  • 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. x
  • 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. x
  • 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. x
  • 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. x
  • 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. x
  • 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). x
  • 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. x
  • 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. x
  • 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. x
  • 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. x
  • 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. x

Lecture Titles

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What's Included

What Does Each Format Include?

Video DVD
Video Download Includes:
  • Download 12 video lectures to your computer or mobile app
  • Downloadable PDF of the course guidebook
  • FREE video streaming of the course from our website and mobile apps
Video DVD
Soundtrack Download Includes:
  • Ability to download 12 audio lectures from your digital library
  • Downloadable PDF of the course guidebook
  • FREE audio streaming of the course from our website and mobile apps
Video DVD
DVD Includes:
  • 12 lectures on 2 DVDs
  • 168-page printed course guidebook
  • Downloadable PDF of the course guidebook
  • FREE video streaming of the course from our website and mobile apps
Video DVD
CD Soundtrack Includes:
  • Audio tracks are taken directly from the video
  • Your 6 CDs include all 12 lectures of this course
  • 168-page printed course guidebook
  • Downloadable PDF of the course guidebook
  • FREE audio streaming of the course from our website and mobile apps

What Does The Course Guidebook Include?

Video DVD
Course Guidebook Details:
  • 168-page course synopsis
  • Charts & diagrams
  • Practice problems & solutions
  • Suggested readings

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Your professor

Arthur T. Benjamin

About Your Professor

Arthur T. Benjamin, Ph.D.
Harvey Mudd College
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...
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Secrets of Mental Math is rated 4.7 out of 5 by 156.
Rated 5 out of 5 by from Most Interesting I know "old" Math, i.e. right to left. I now know left to right. Fantastic how numbers fix together.
Date published: 2017-04-27
Rated 5 out of 5 by from Fun I watched this with The Great Courses plus app. Enjoyed it so much I brought it. The same thing happen with the previous purchase. Yes I have a list of classes I plan to buy but like most I live on a budget. It's wonderful to have the app I can test drive the classes buy what I most desire and have lots of great TV to watch! The 20 I spend each month is money I feel good about its an investment in me and supports a company that provides an excellent product what more can you want.
Date published: 2017-04-23
Rated 5 out of 5 by from A must for every home I would recommend every parent to buy this, learn the technics in the first instance, and then encourage their kids at their young age. My grand daughter would not pay much attention when I teach math. But she is following Prof Benjamin with interest ! Kranti Kadiyala
Date published: 2017-04-05
Rated 5 out of 5 by from Educational and entertaining! I was impressed by how fun he made math. I love the tricks for doing math in my head.
Date published: 2017-03-20
Rated 1 out of 5 by from A useless bag of tricks I went through 9 of the lectures and found I learned no new concepts. If you like new tricks to do simple operations, then maybe its ok. I only lasted 9 chapters and should have asked for a refund but since I paid less than $10, it wasn't worth the effort. Considering all the great courses I have purchased in the past this was a huge disappointment.
Date published: 2017-03-09
Rated 5 out of 5 by from Great way of rethinking the way we do math I have bought many courses from The Great Courses and this one has exceeded my expectations. The course provides many new ways of thinking that allow math to be easily accomplished without the aid of paper and pencil.
Date published: 2017-03-01
Rated 5 out of 5 by from Fascinating concepts I consider myself to be quite good at math, however, the techniques introduced in this series are very clever. They are not obvious but once explained are very intuitive. Highly recommend for anyone age level, but especially kids 8 and above
Date published: 2017-02-20
Rated 5 out of 5 by from Good host Really fast and easy to learn. Keep doing it and you will have mastered it.
Date published: 2017-02-14
Rated 5 out of 5 by from So far so good I brought this a week ago and so far I'am learning things i did not know.Loving it
Date published: 2017-02-02
Rated 5 out of 5 by from From five to sixty-five, we were all watching. It was difficult to get a 5, 7, 8 year old to start watching a program called Mental Math. The short segments made it possible for the little ones to have control over how much they watched. It was my objective to watch 1 segment a week with the little ones. They watched three segments, almost motionless, after which I asked if they wanted to watch more. 2 out of 3 said yes. I had to promise them they could watch it sometime in the future; tomorrow, or bedtime might have become a little sadder. A must for anyone who wants help in understanding and mastering the principles of Mental Math. Put down your electronics and grow your mind.
Date published: 2017-01-06
Rated 5 out of 5 by from Valuable resource Like most courses i choose it is interesting and i am learning so much. This presenter is one of my favorites and i only wish i had these courses available when i was in school.
Date published: 2016-12-28
Rated 1 out of 5 by from The idea is good, the course, not much I really tried to like this course, and Prof Benjamin must be terrific in class. However he shows how to do a certain multiplication for example, and then moves on to another one, without giving the viewer essentially any time to practice and learn the algorithm.
Date published: 2016-12-23
Rated 5 out of 5 by from Excellent Course Just in the first lesson there is a lot of great stuff. The key to the lessons is to practice and go through it slow so you don't get frustrated with all the information. The instructor tells you where to stop it and practice what you just learned.
Date published: 2016-12-04
Rated 5 out of 5 by from POWERFUL MIND I love this course I saw the DVD awhile ago. Now I have THE GREAT COURSES APP and the Mental Math video on my mobile device
Date published: 2016-12-03
Rated 5 out of 5 by from mental math Bought this as a gift for my grandson who was struggling with middle school math. He loves it and his math grades are rising. I couldn't ask for more from the course.
Date published: 2016-09-30
Rated 5 out of 5 by from How to Draw This course takes the student by the hand to understand the fundamentals of drawing...
Date published: 2016-09-27
Rated 5 out of 5 by from So far so good Only completed one lecture Covered an incredible amount of helpful techniques. Look forward to the remaining lectures. Will update when complete
Date published: 2016-09-27
Rated 5 out of 5 by from High impact course I teach fifth grade. After watching the first lesson I knew that this could change the lives of many students at our school. The Math Club is up and running, and struggling math students are finding reasons to embrace a subject they had nearly given up on. This course will provide the punch that common core seems to be missing. This is a must buy for anyone who is fascinated with the magic of numbers.
Date published: 2016-09-14
Rated 4 out of 5 by from Content fine, presentation a bit stereotyped Professor Benjamin presented his material in a well-organized way. As a self-taught mental calculator I found that many of the basic operations he showed were already known to me, but the more advanced ones built on them were new and will be helpful. His demonstrations of rapid calculation, performed at the start of lectures, were instructive. But I found his lecturing style annoying, with meaningless handwaving to emphasize points, overexpressive voice, and phony smiles. The video is filmed with two cameras and he's constantly turning from one to the other and pacing toward it. No doubt this device was intended to introduce physical action into the presentation, but I found it tiresome and stereotypical.
Date published: 2016-09-12
Rated 5 out of 5 by from Alot of fun Dr Benjamin is outstanding. He is obviously gifted not only in mathematics but has the ability to presents concept very simply. Definitely worth the money
Date published: 2016-09-11
Rated 5 out of 5 by from Good Value Although secrets might be questioned, the content of the course certainly brings good methods out of hiding. I would definitely recommend this course for students in high school and college.
Date published: 2016-09-11
Rated 5 out of 5 by from Fast Paced Lots and Lots of tricks to learn. We have only just started the program, however it is loaded with information. We purchased this course to supplement the Math curriculum of our Home School studies. Our only complaint is that it is VERY fast paced and we find ourselves having to pause the course to be able to take in all the information....or to even be able to "work" the problems, before he gives the solutions From day one we have been using the course tricks and having fun everywhere we go, Boring trips to the grocery store are now a fun learning experience.
Date published: 2016-08-26
Rated 5 out of 5 by from Awesome!! Very interesting and informative. More than what I hoped.
Date published: 2016-08-25
Rated 5 out of 5 by from Practice, practice,practice! Great big thank you for mental math! We watched it as a family with a couple of neighborhood kids. It really terned into a math party with competition after words, because we couldn't wait to practice the new and exciting methods of doing math! Boys went wild about math and couldn't wait for next lesson! Some lessons were a little harder when another, but we can go over after words as many times as we need ! Our kids were age 12-15, and it was our best summer time activity a long side whatever else we did!
Date published: 2016-08-10
Rated 5 out of 5 by from Great Course This is just one of those fun courses where you can take whatever you want out of it. While I sincerely doubt that I'll ever be able to do calculations in my head as quickly as Prof. Benjamin it's good exercise for your brain. The course is fun to take because of Prof Benjamin's enthusiastic delivery. I must admit that I couldn't stop myself from jumping ahead to lecture 10, Calendar Calculating. I practiced that one a bit and have already calculated the day of the week of friends and family's birthdays. Once again not as quickly as he does in the lecture, but within 30 seconds to a minute, but as long as I was careful I always came up with the correct answer. Also the history regarding the Gregorian calendar might be new to some people taking the course and is an interesting tidbit of history that has everyday ramifications. All in all it's a fun course that I would recommend to anyone of any age.
Date published: 2016-08-07
Rated 1 out of 5 by from Will not work on my computer works in fast motion.
Date published: 2016-08-03
Rated 4 out of 5 by from Solid Overview of a Useful Subject Matter Area The last Math course I took was in the 10th grade...and I have had a subsequent business career that involved substantial sophisticated financial concepts, but I never considered myself a mathematician. Professor Benjamin proved me wrong by simply and clearly demonstrating the fun to be had with numbers. As with any great course, some of the learning largely consists of the Professor merely confirming modes of operating that many of us have intuitively developed (e.g. "guesstimation techniques"). Whether dealing on that front or providing new approaches and concepts, Prof. Benjamin's superb pedagogy made this a truly "great course". I noticed (since I had downloaded the audio course version), that it is being advertised as a "soundtrack", rather than the "audio version" as had typically been the case for most courses which provide alternative modes for consumption. In this case, I suspect it was merely a function of the fact that occassional "paperwork" (non-mental) was suggested, as well as there being moments when a chryron would flash on the screen for those using a video version of the course with examples of math problems and processes that (obviously) can not be appreciated by audio listeners. This was not a serious impediment to total enjoyment of the course.
Date published: 2016-06-30
Rated 5 out of 5 by from Good content I've always considered myself fairly good at mental math, and in the first half of the program I've already learned quite a few clever methods to do calculations that I didn't know. Very good content. I bought the video download, and I think the visuals are helpful. The instructor is enthusiastic and lays it out in an understandable manner. Very good!
Date published: 2016-06-29
Rated 5 out of 5 by from I liked very much calendar calculating Wow, what a nice course. I am surprised that after completing the course (I did not become a math wizard) I was able to calculate dates in the past and in the future, among other useful things, such as: criss-cross multiplication, calculating change out several bill amounts. It is unbelievable what Professor Benjamin can accomplish in only 12 lectures.
Date published: 2016-06-02
Rated 5 out of 5 by from Spreading Mental math to others Dr. Benjamin, I am a retired physician, internal medicine geriatrics, who volunteers in the local elementary grade school. 5th and 6th grade students, three different groups each of about 3-5 kids, who are in the “study group” because they are behind or slow in their studies , or “hate math”. I was looking to try to make math interesting, 2 weeks on common denominators was going slow, and I was getting frustrated on trying to find interesting ways to make the case. Great Courses catalogue came to my wife in the mail. She also “hates math”, so I looked through the information and grabbed your “Secretes of Mental Math”. Just wanted you to know that I have burned through your lectures a number of times and have taken the lessons on Add, Subtract, Multiply and Dividing, and plan to at least introduce them to the “Golden rule of Algebra”, before they leave this school year. I am resentful that nobody taught me this stuff 65 years ago!, The “new math” is atrocious , at least to us old folks, but the kids really are excited about math, stuff their hands in the air to do the next problem. Fascinate their parents by multiplying any number by 11. Quickly catch on to multiplication problems, and are delighted to be able to “make change” in a flash. I think they have overcome their “fear of math”, and have increased their self confidence in general. The shy - speak up, the A.D.D. guy focuses better, ( is really quite good at math ) and the disgruntled , brighten up. The teacher informed me recently that one of “my “ kids got a 100% on a recent math test. I was no math whiz in my time, and do not recall using a quadratic equation in the last 50 years, but I have thoroughly enjoyed your lectures, feel more confident that I can help these kids with the basics of math, and show them a trick or two along the way. I am very thankful for your help. By the way, you make me look good. I received “volunteer of the year” last year.- another “certificate” to put on my wall next to the Mayo Clinic Certificate. With Best Regards David L. Fairbrook M.D.
Date published: 2016-04-17
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