Most of the mathematics that we learn in school is taught to us on paper with the expectation that we will solve problems on paper. But there is joy and lifelong value in being able to do mathematics in your head. In school, learning how to do math in your head quickly and accurately can be empowering.
Modules 2-5 will focus on the nuts and bolts of mental math: addition, subtraction, multiplication, and division. Often, we will see that there is more than one way to solve a problem, and we will motivate many of the problems with real-world applications.
Once we have mastery of the basics of mental math, we will branch out in interesting directions. Module 6 offers techniques for easily finding approximate answers when we don’t need complete accuracy. Module 7 is devoted to pencil-and-paper mathematics but done in ways that are seldom taught in school; we’ll see that we can simply write down the answer to a multiplication, division, or square root problem without any intermediate results. This lecture also shows some interesting ways to verify an answer’s correctness.In Module 8, we go beyond the basics to explore advanced multiplication techniques that allow many large multiplication problems to be dramatically simplified.
In Module 9, we explore long division, short division, and Vedic division, a fascinating technique that can be used to generate answers faster than any method you may have seen before. Module 10 will teach you how to improve your memory for numbers using a phonetic code. Applying this code allows us to perform even larger mental calculations, but it can also be used for memorizing dates, phone numbers, and your favorite mathematical constants. Speaking of dates, one of my favorite feats of mental calculation is being able to determine the day of the week of any date in history. This is actually a very useful skill to possess. It’s not every day that someone asks you for the square root of a number, but you probably encounter dates every day of your life, and it is quite convenient to be able to figure out days of the week. You will learn how to do this in Module 11.
In Module 12, we venture into the world of advanced multiplication; here, we’ll see how to square 3- and 4-digit numbers, find approximate cubes of 2-digit numbers, and multiply 2- and 3-digit numbers together. In Module 13, you will learn how to do enormous calculations, such as multiplying two 5-digit numbers, and discuss the techniques used by other world- record lightning calculators. Even if you do not aspire to be a grandmaster mathemagician, you will still bene t tremendously by acquiring the skills taught in this course.