Saturday, July 25, 2009

Mathematics - the fun subject.
Recently, my college professor son mentioned that today's college students are flocking to the study of social sciences, largely to avoid mathematics.

What?

Why would anyone want to avoid math? Mathematics is a great subject - fun because it is full of interesting patterns. Easy because the answers are precise.

In that same conversation, he mentioned one interesting pattern. If you square a series of numbers, the difference between the squares of any two numbers is always two more than the difference between the squares of the two preceding numbers. In case you have forgotten, to square a number is to multiply it by itself, and is indicated in math with a small "2" written to the right of the number to be squared. The square of 2 is 2 X 2, and is written as 2². The square of 3 is 3 X 3, written 3².

Okay, as I was saying, 2² = 4. And, 3² = 9. The difference between 4 and 9 is 5. Continuing, 4² = 16. The difference between 16 and 9 (the square of 3) is 7. That is an increase of two over 5. Now if we square 5, we get 25, which is 9 more than 16, which is two more than 7. This pattern will continue as long as you want to square and subtract numbers. Now, if you don't find that at least a little bit interesting, your brain has been twittered - or tweeted - into terminal numbness.

But, this is only the beginning of the surprises in math. If you don't like multiplication or division, just fall back on addition and subtraction, You can, with logarithms. Every number has a logarithm. To get the logarithm (which is often shortened to just "log") of a number, you can go to a log table. When I was studying electronics, we used a slide rule to find the log of a number. Today there are calculators and computer programs to do the job. Anyway, to multiply two numbers, just find the log of each, add them together, and find the anti-log of the result. That result wil be the same as if you had multiplied the first two numbers. For division, just subtract the log of the second number from the log of the first, find the antilog of the result, and it is the same as if you had divided the first number by the second. Sure it is extra steps, but very helpful if you are multiplying or dividing complex numbers.

The study of mathematics can be one of wonder and joy. When I was studying mathematics, I found myself repeatedly saying, "Well, I'll be darned... that is amazing!" Sometimes I thought ahead of my then current level of study and wondered, "How do they know that?". When the answer was finally explained, it was a delight.

Knowledge of mathematics is core to many scientific disciplines. It is well to study math in college. How do you teach a child that mathematics is not a subject to be feared? Start early with simple number games. Make them fun. Learn shortcuts. Suppose you are watching a telecast of the Tour de France. The TV screen says the riders have 25 km to go. How far is that in mles?

Well, you could grab a calculator and multiply 25 by 0.62 and see that it is about 15.5 miles. But most people find that difficult to do "in their head" without calculator, or paper and pencil. Here's a shortcut you can easily do without calculator or pencil: divide the km (25) by 10, to get 2.5. Double that to 5.0. Multiply by 3 and you have 15. Actually, that is equal to multiplying the KM by 0.6, not 0.62. If you want a more accurate answer, multiply the 25 by 0.2 and add that to your original answer. But the shortcut is close enough, if you are only satisfying a moment of curiosity. And, certainly close enough to check your result if you go for the long, accurate computation. Your answer better be close to 15... not 150 or 1.5, either of which would mean you had misplaced a decimal point.

There are many such shortcuts in math, and just finding them is a great way to start making math a fun game.

1 comment:

Anonymous said...

I was "twittered"...long before there was such a thing.