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ISBN: 9781457514814
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Excerpt from the Book
Chapter 1 - Addition and Multiplication - 1.1 The decimal system for whole numbers

Numbers are the very core of mathematics, science, and economics. We are so accustomed to using numbers in our everyday lives that we seldom stop to think about what an amazing intellectual feat our current method of writing numbers really is. It wasn’t until the seventeenth century that the present “decimal” (i.e., base ten) system came into use. The Romans, in spite of their vast empire and the great organization that must have been required to conquer and maintain it, had developed only the unwieldy method of Roman numerals. How much is MCMLXXVIII? (In fact, it’s 1978.) How merchants in Roman times kept their accounts is hard to imagine (it seems they used counting devices, similar to the abacus still used today in China). Other early civilizations also had their own equally unwieldy systems for writing numbers.

The feature that makes the modern method of writing numbers so successful is positional significance of the digits. The expression 532 means five hundreds, three tens (thirty) and two ones. Once this simple way of writing numbers became known, it spread over the entire world, and is now used almost everywhere. The invention of positional notation ranks right up there with other great inventions, like the wheel and the transistor. Simple, but profound. ... 

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                                            1.9    How to learn mathematics

Most people find mathematics confusing, at times. This book tries to eliminate confusion as much as possible. Nevertheless, you the reader may still get confused occasionally. Everyone who studies mathematics experiences mental blocks once in a while, something that just doesn’t seem to make sense. This is not a sign of stupidity! The question is, what should you do to overcome a mental block? Here are three possible approaches:

1. Forget it, it’s probably not important anyway.

2. Forget about understanding the point, just memorize the result.

3. Take the time to identify the difficulty, and then try to resolve it.

One of the reasons, I think, that many people “drop out” of math is that they start adopting strategies 1 or 2. Either of these strategies is a sure-fire recipe for eventual failure. In learning mathematics, any point of confusion must be eliminated as soon as it occurs. If not, everything that follows on from the point of confusion will also be confusing. Pretty soon the whole subject becomes incomprehensible – and then hateful.

Suppose that you have encountered a difficulty, and that you wish to adopt strategy 3. How should you proceed? ….

For more excerpts, click on these links: 

(Speed and Distance)    http://www.MATHOVERBOARD.com/cms/uploads/pp129-132.pdf 

(Functions)   http://www.MATHOVERBOARD.com/cms/uploads/pp333-337.pdf