The Secrets of Mental Math
DVD 510 SEC, 2010
Secrets of Mental Math: The Mathemagician's Guide to Lightning Calculation and Amazing Math Tricks, 510 BEN, 2006
ARTHUR T. BENJAMIN, benjamin@hmc.edu
My comment: No mathematician bother explaining why. It is completely focusing on single-digit computation all the time. It is so ironic when I am watching this, youtube gives us this ad.
1: Math in Your Head!
adding from left to right, unlike what you do on paper and make using complement (the distance betwwen a number and a conveninent round number, typically, 100 or 1000. For example, the complemnt of 43 is 57, since 43 + 57 = 100. (Using zero's property, B^n- structure)
When adding numbers, it is easier to add largest to smallest, rather than smallest to largest. Again, doing calculation from left to right is easier because that's the way we read numbers. Also it gives you better estimation.
2: Mental Addition and Subtraction
3: Go Forth and Multiply
Proof of distributive law
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.
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.
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.
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).
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.
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.
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.
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.
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.
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