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motion: TOC for Knowledge Concepts, Exercises, and Solutions

Mathematics is, in many important ways, a language like English or French or 
Chinese.  It has a vocabulary (numbers and symbols), grammar (operations and 
rules), and sentences (equations).  It tells us about the universe around us, just 
as story or a poem might - but in a different and powerful way.

Five year old children speak Russian fluently, but I do not; does this mean that I 
am unintelligent compared with five year old Russian children?  Or that I am "bad" 
at Russian?  Or that "my father was no good at Russian, so it makes sense that I'm 
no good at it either?"  Obviously not.  I just have too little exposure to Russian 
at this point in my life.  If I went to Russia and did nothing but speak, read and 
write Russian, there's a very good chance I'd be fluent in Russian after five 
years.  I have nothing to fear from Russian - I just need either to get used to 
it, or have a good translator.

So if we approach mathematics with the same attitude as we might approach a 
foreign language, there's no need ever to be afraid of it.  The key is to realize 
that if we don't speak it often, we might get a phrase wrong once in a while.  
It's no big deal; as long as we communicate the main ideas, we'll be all right.

You'll be happy to know that, whether you realize it or not, you use math all the 
time - and well.  If you live in a reasonably large city and you want to get 
across town by noon, would you leave your home at 11:59 A.M., 11:00 A.M., or 6 
A.M.?  You use math to figure that out.  If you want to buy a medium-priced house, 
should you plan to spend $100, $100,000 or $100,000,000? Of course, you probably 
won't compute beforehand that you need to leave at precisely 11:06 A.M. to arrive 
precisely at noon, or that you'll spend $123,692.00 for your house.  Rather, you 
find an answer that "feels right" or "makes sense."

Using that "common sense" is the most important part of using mathematics as a 
language to help translate the universe.  Having some general idea of what numbers 
are appropriate to answering a question or solving a problem is 90% of the battle.  
Use that common sense!