Secrets of Mental Math

Course No. 1406
Professor Arthur T. Benjamin, Ph.D.
Harvey Mudd College
Share This Course
4.7 out of 5
172 Reviews
92% of reviewers would recommend this product
Course No. 1406
Streaming Included Free

What Will You Learn?

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

Hide Full Description
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

Clone Content from Your Professor tab

What's Included

What Does Each Format Include?

Video DVD
Instant Video 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

What Does The Course Guidebook Include?

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

Enjoy This Course On-the-Go with Our Mobile Apps!*

  • App store App store iPhone + iPad
  • Google Play Google Play Android Devices
  • Kindle Fire Kindle Fire Kindle Fire Tablet + Firephone
*Courses can be streamed from anywhere you have an internet connection. Standard carrier data rates may apply in areas that do not have wifi connections pursuant to your carrier contract.

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...
Learn More About This Professor
Also By This Professor


Secrets of Mental Math is rated 4.7 out of 5 by 172.
Rated 5 out of 5 by from Great lesson structure I bought 5 download courses a few weeks ago & I have found these courses to be just amazing! The Instructors are extremely knowledgeable & enjoyable to learn from. The format is easy to follow, with on screen controls to move back or fwd in each lecture. I will order again when needed.
Date published: 2020-02-20
Rated 5 out of 5 by from More tricks in my bag of tricks I have always employed these types of tricks to do math in my head but this helps by adding even more. A few may not be useful in everyday math but you can amaze your friends at your next party. The presentation was interesting and kept me watching. Overall these are useful skills if you take the time to learn them.
Date published: 2020-02-08
Rated 1 out of 5 by from I bought this on 1/13 and did not receive it until 1/28. This shipping time is unacceptable. If there was a problem I should have been notified. Have not had a chance to check out the courses yet.
Date published: 2020-01-30
Rated 4 out of 5 by from Great tips for improving your math skills! Reinforced a few concepts I had discovered on my own but introduced me to many more. I'll need to do over it again and practice more but is time well spent. And his separate course on probability, odds and games is boffo!
Date published: 2019-07-22
Rated 4 out of 5 by from Good description of what it teaches As a middle school math teacher, I have found this course to be great for my students and for me. I actually have learned a lot.
Date published: 2019-05-12
Rated 5 out of 5 by from Impressive and Educational I bought this as I found the course description interesting. I was very pleased with the content although I don't see myself performing some of the advanced calculations mentally. Professor Benjamin enthusiastically presented the base concepts very clearly. I could see how easy handling basic arithmetic operations could be done. I liked seeing the various methods that I could employ to arrive at the correct answer. It was interesting to hear the Professor explain the difficulty with performing the mental calculations as the numbers used went to more than 3 digits being multiplied. However, he did repeat throughout the lectures that practice and the major system can overcome this difficulty. The course did not cover adding a lot of numbers other than a pair. At the start of one lecture when Professor Benjamin asked the crowd for several prices to sum, he did appear to take some time, but did arrive at the correct sum. I was extremely impressed with his demonstrations of multiplying 2 4 digit, and then 2 5 digit values.
Date published: 2019-05-06
Rated 5 out of 5 by from Fun I have not finished the courses, but I love math and this is entertainment for me. I am anxious for my 11 year old grandson to visit and let me watch too.
Date published: 2019-04-23
Rated 5 out of 5 by from One of the best At last I bought this course and it`s very helpful for all people
Date published: 2019-04-05
Rated 5 out of 5 by from Super Speed Math Course trains student to look at numbers in a different way to speed up mental math calculations. Extent of calculation ability will depend on incorporation of techniques into long term memory and short term memory capability. Course also provides various methods to aid short term memory (Major and peg systems). Recommend that course be repeated once per year to incorporate more procedures into long term memory and improve calculation performance. The mental exercises exercised in this course will definitely aid memory health much better than doing crossword puzzles. Professor Benjamin definitely has an amazing brain that is hard wired for short term memory and math.
Date published: 2019-03-13
Rated 5 out of 5 by from Fun Class - Great Professor I bought this over a month ago, finally got the chance to start it. Professor Arthur Benjamin is terrific - love his sense of humor & his joy for math. There is nothing better than having a professor who loves the subject! The subject is never boring with this kind of professor. Really enjoying math for first time. This should be taught in schools!
Date published: 2019-02-19
Rated 5 out of 5 by from Do the math in your head So far, I've only gone through the 1st lesson, but I think it's great. I've learned some neat math shortcuts. I'll be a math whiz in no time!
Date published: 2019-02-16
Rated 5 out of 5 by from What A Great Idea! Not sure why anyone would give this a negative review. While some of the easy problems were easy for me as I already use the same or similar mental math solutions, I am learning a great deal about the more difficult problems and enjoying every second. I enjoy a professor who enjoys teaching as much as I enjoy learning. Professor Benjamin doesn’t annoy me with his mannerisms, he makes me feel at home and if I actually know him. I also have his Math and Magic course and really like it also.
Date published: 2019-02-07
Rated 5 out of 5 by from Secrets of Mental Math Exciting & challenging. At my age (77), I am able to absorb a lecture & spend the rest of the week in repetitous review/practice. It has been amazing. Next summer, I plan to guide my 13 Year-old adopted daughter through the course, in preparation for 8th grade math.
Date published: 2019-02-04
Rated 5 out of 5 by from love this professor I love this professor and his teaching style. test test
Date published: 2019-01-14
Rated 5 out of 5 by from Great for Bright Kids I'm using this DVD with my academically gifted 4th and 5th graders and they love it!!
Date published: 2018-12-02
Rated 5 out of 5 by from Secrets of mental math Professors are well versed in the subject matter and their presentations are formatted and delivered effectively to excite the intellectual curiosity of the listeners.
Date published: 2018-11-08
Rated 5 out of 5 by from Love this course! The best $15.94 I ever spent!! Thanks for the free lectures.
Date published: 2018-11-08
Rated 5 out of 5 by from Secrets of Mental Math Too bad this course was not around when I was in school. They should be mandatory in all schools in North America, thank you.
Date published: 2018-09-30
Rated 5 out of 5 by from Absolutely loved it and thought it was fun! I originally purchased this for my grandchildren. I watched it before giving it to them and was totally blown away. I'm almost 66 yrs old and for the first time in my life I was not only doing it, but actually having fun doing math. Loved it so much I bought a copy just for me, one for my other grandchildren, one for our library, and one for my great nephews and nieces. I also bought the transcripts to go with them. Why isn't math taught this way to begin with?
Date published: 2018-09-09
Rated 5 out of 5 by from Very interesting - but pace is a bit slow I am a senior who has always liked to do mental math. The techniques I have learned in just the first three lectures are great. My goal is to teach the techniques to my 8 year old grandson who is excited by the idea. I have already spent many hours with him practicing simple mental math.
Date published: 2018-09-06
Rated 5 out of 5 by from Really cool and clever The Professor is brilliant, but arrgggh, stop with the puns already! They're really not funny. The algorithms presented are not merely clever, but solidly based on algebraic identities, theorems of modular arithmetic, and the nature of the base-10 number system. Overall, great stuff, and an invitation for further study and exploration.
Date published: 2018-08-31
Rated 5 out of 5 by from Good Title I have just reviewed the first 2 chapters, and am impressed with the instructors teaching methods and examples... I was a Math major in college, and this course is helping me exercise my memories.. My age is 80.
Date published: 2018-06-20
Rated 5 out of 5 by from Mental Math I am quite interested in any information that helps keep my brain active
Date published: 2018-06-20
Rated 3 out of 5 by from It piques interest I believe this material has substance but speaker keeps going back and forth which is distracting, and lectures gets tedious.
Date published: 2018-05-03
Rated 5 out of 5 by from Blew my mind, That's why I'm reading "the Aging Brain"!!!
Date published: 2018-05-03
Rated 5 out of 5 by from I'm Learning a Lot I'm doing this course with a friend, so it may take awhile for us to finish it. We both have to be available at the same time. So far, we are both enjoying ourselves. I have always liked to do math in my head. I wanted to improve that ability, and I am. As I'm 77 years old, I'm hoping it may stave off altzheimers disease.
Date published: 2018-04-28
Rated 5 out of 5 by from Absolutely love it. I think it has sharpened up my mind, I just love learning from a super instructor who loves his work. I highly recommend it to anyone who has the interest and desire. I love the course. I had a high school math teacher who made us learn the multiplication tables thru 20. She taught advanced math and I loved it. I am retired now but make money day by day with investments. A day without a profit is a disaster. So this is just up my alley.
Date published: 2018-04-19
Rated 5 out of 5 by from Become a mathemagician! This is a fantastic program. Just a little background about myself - I have a PhD in Biomedical Engineering and work as a University Professor. I have always been very good at math - calculus, differential equations, etc. In reading other reviews I was skeptical about purchasing this program. However, I am very glad that I did! The techniques that Dr. Benjamin teaches in his lectures are invaluable for quickly doing calculations without paper and pencil (or cellphone calculator!). One of the things I do during each lecture is look up math problems online and practice the techniques that he goes over. For this reason each lecture takes me about 1 hour instead of the 30 minute run time in the DVD. However, I find that pausing the lecture and doing 45-60 problems per technique really helps solidify my understanding of the concept and technique. Now, while that may seem like A LOT of math problems, when I employ Dr. Benjamins' techniques I am able to complete 20 problems in 1-2 minutes. One of the things I enjoy the most about this program is how Dr. Benjamin makes you look at mathematics differently. This may be because I always enjoyed mathematics but I love seeing the various ways we can combine numbers and "break" common rules and/or interchange techniques to arrive at answers more easily. He teaches with a lot of enthusiasm and you can tell that he enjoys what he is doing. That always helps as well.
Date published: 2018-04-09
Rated 5 out of 5 by from Perfect and fitting This is perfect little secrete of mental math. Some of it I have invoked over the years, but most I had no idea about. Just made life simpler. I recommend for any JR High, Senior or College kid. If you are out of school and get math problems thrown at you for quick answers this is the Holy Grail of mental math. You benefit from this course no matter who you are.
Date published: 2018-03-01
Rated 5 out of 5 by from The title is attractive. The course is fun and engaging and worth the investment.
Date published: 2018-02-26
  • y_2020, m_9, d_16, h_17
  • bvseo_bulk, prod_bvrr, vn_bulk_3.0.12
  • cp_2, bvpage2n
  • co_hasreviews, tv_17, tr_155
  • loc_en_US, sid_1406, prod, sort_[SortEntry(order=SUBMISSION_TIME, direction=DESCENDING)]
  • clientName_teachco
  • bvseo_sdk, p_sdk, 3.2.0
  • CLOUD, getContent, 62.31ms

Questions & Answers

Customers Who Bought This Course Also Bought

Buy together as a Set
Save Up To $12.00
Choose a Set Format