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Preparing for a Math Olympiad


Date: 12/25/2000 at 14:59:16
From: Ryan Michaud
Subject: Generally improving at math

This question may be a little weird.

I'm fifteen years old and I'm in grade 10. I really like math and I do 
relatively well in school. But I want to be a candidate for the 
International Math Olympiad in grade 11 and/or grade 12. In order to 
do so, I have to push way past the subjects covered in class. I'm 
ready to work really hard and make sacrifices in order to reach my 
goal.

My question for you is: what is the best way to learn senior level 
math and beyond, and know how to do well on math contests? I can't 
just look over grade 12 math contests and learn the math. Do you have 
any ideas on how I could efficiently "reach the top"?

Thanks a lot,
Ryan


Date: 12/27/2000 at 12:30:35
From: Doctor Ian
Subject: Re: Generally improving at math

Hi Ryan,

I once had a neighbor once who was always trying different diets. We 
were talking about it one day, when she blurted out that she'd do 
anything to lose weight... except eat less, and exercise more.

Anyone who has become really good at math did it by reading books and 
practicing. I know that sounds too simple to be true, but there it is.

Here's how to choose a book: Look for one where the stuff in the first 
chapter is too easy, and the stuff in the last chapter is too hard. 
That means you need to learn the stuff that's in between.

When you've found a few like that, open each one up to a section that 
tries to explain something you don't understand, and see how well the 
author's style of teaching meshes with your style of learning. Choose 
the one that seems best suited for you.

As you go through the book you've selected, work the problems in each 
section until you can do them easily. If you get stuck, go back to the 
previous chapter, or the previous book, until you find what you failed 
to learn earlier.

When you reach the end of one book, select another one, using the same 
process described above. Keep selecting and reading books until you 
know everything.  :^D

If you haven't read anything by or about Richard Feynman, you should 
remedy that deficiency as soon as possible. (_Surely You're Joking, 
Mr. Feynman_ would be the natural place to start.) He was one of the 
great problem-solvers of all time, and his insights in that direction 
will be of great value to you.

You should also look at some of George Polya's classic works on 
problem-solving.

And work as many puzzles as you can. The value of puzzles is that they 
teach you alternative ways of thinking about problem solving by 
forcing you to learn to 'think outside the box', so to speak. As with 
textbooks, start with easy puzzles and work your way up to harder 
ones. When you've solved a puzzle, take some time to stop and think 
about what assumptions or habits of thought you had to work past in 
order to find the solution. (Why didn't you see it immediately? Where 
else might you be blinded by the same prejudices?) Write them down, 
and look over your notes from time to time.

One thing that you should keep in mind is that the people you'll be 
competing against have not, by and large, learned a lot of math in 
order to compete. They compete because they have learned a lot of 
math, and they have learned a lot of math because they love learning 
it.

I'll close with one of my favorite stories from a little book on Zen 
Buddhism that I've had for as long as I can remember:

   Matajura wanted to become a great swordsman, but his father wasn't
   quick enough and could never learn. So Matajura went to the famous
   dueller Banzo, and asked to become his pupil. "How long will it 
   take me to become a master?" he asked. "Suppose I become your 
   servant, to be with you every minute; how long?"

   "Ten years," said Banzo.

   "My father is getting old. Before ten years have passed I will have
   to return home to take care of him. Suppose I work twice as hard;
   how long will it take me?"

   "Thirty years," said Banzo.

   "How is that?" asked Matajura. "First you say ten years. Then when
   I offer to work twice as hard, you say it will take three times as
   long. Let me make myself clear: I will work unceasingly: no 
   hardship will be too much. How long will it take?"

   "Seventy years," said Banzo. "A pupil in such a hurry learns   
   slowly."

I hope this helps. Write back if you'd like to talk about this some 
more, or if you have any other questions.

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/   
    
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