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Secrets of Mental Math

Secrets of Mental Math

Course No.  1406
Course No.  1406
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Course Overview

About This Course

12 lectures  |  33 minutes per lecture

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

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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.

View Less
12 Lectures
  • 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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Arthur T. Benjamin
Ph.D. Arthur T. Benjamin
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 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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Reviews

Rated 4.7 out of 5 by 51 reviewers.
Rated 5 out of 5 by Loved This Course and Professor Professor Benjamin possesses both a love and a skill for teaching. He has structured this twelve lecture course to provide step-wise instruction to some advanced techniques for mental calculation and guesstimation. He progressively builds the skills of the learner to the point whereby one can multiply 3-digit by 2-digit numbers, and square 3 and even 4-digit numbers, all in your head. He also provides plenty of practice problems to review and master. This relatively complex business is presented in an energetic engaging fashion, demonstrating the Professor's true love of mathematics in the process. Mastering this material can be well worth the effort (and it takes some practice outside of the lecture time to do this). Although calendar calculating seems to be primarily a party trick the other calculation techniques have great practical benefits. Some may say that they have little reason to master these skills (that’s what calculators and computers are for). I suspect though that this may be the rationalization of one who has not yet put in the time to master the techniques. I found many opportunities to use the skills after I had grown comfortable with the methods. If these methods were taught in elementary school classrooms they would be methods of first choice when problems arose in the real world. I specifically enjoyed an introduction to Vedic division, a neat shortcut technique for “long” division. These techniques are not only important shortcuts, but are also very practical illustrative ways to demonstrate some of the basic laws (associative, distributive, etc.) laws of arithmetic. Professor Benjamin also emphasizes and illustrates a variety of alternate ways that one may conceive of and tackle any difficult-appearing arithmetic problem. In third grade our teacher asked us to add together all of the numbers from 1 to 100. Instead of trying to trudge through the long process of laboriously adding 1+2+3+4 and so on - I likely would have thought of the quick (and much easier) way of getting to the answer in seconds (if Professor Benjamin had been my third grade math teacher). October 19, 2013
Rated 5 out of 5 by What fun, how useful! This is an excellent course (requiring video). Professor Benjamin is an excellent lecturer: great pace, clear explanations, content rich, and a playful, likable style. The skills in mental math (and some tricks require paper) are so useful I wish I'd learned them decades ago. He gives you everything you need to know to divide, multiply, square large numbers, determine days of the week and more, solve things various ways and check your work. He also explains why these tricks work. This is a really fun and fast paced course, I have studied my notes and in about a week I have gotten pretty good! It is simply genius. Two more lectures to go --I just couldn't contain my enthusiasm. November 23, 2014
Rated 1 out of 5 by Disappointing Almost no full explanations of why the methods given work. A lot memorizing required. In many cases the methods require a significant amount short term memory to be applied successfully. I received a refund from The Great Courses on the same day that I requested it. I was dissatisfied with this particular course, but very satisfied with the customer service of The Great Courses and how they handled my refund request. November 9, 2014
Rated 3 out of 5 by Ask yourself: is mental math important for YOU? Almost halfway through the course, I stopped watching it. I love math, and was definitely interested in the course till I realized that knowing the mental math tricks wouldn't really help me in my life. The course seemed to be extremely informative at the beginning, and I was sure I'd enjoy it. Extremely informative about what? Easy math tricks that can help you work mentally. But once I began noticing how often the lecturer talked about how his mental math teachings can help do basic things like calculate bill totals and impress friends, I wasn't so keen about continuing. These basic things can be done with calculators, and I always keep a calculator in my pocket (a smartphone)----and soon enough, technology like Google Glasses will get commoner, and the Glasses will read and calculate problems before you can see them. In conclusion, before going ahead and watching it just 'cause it's got so many positive reviews, think about why you want to watch it. And hope this reason isn't to impress your friends. Straining your mind every two seconds is not going to help you! October 4, 2014
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