Understanding some of the math Olympiad questions?

[Skynt]

I was looking at some of the questions from various competitions for high schools and colleges and their questions, and I couldn't begin to solve the majority of them.

I was looking at http://books.google.com/books?id=B3EYPeKViAwC&printsec=frontcover&dq=Problem+Solving and I couldn't follow it at all. I mean, the math only made sense in certain examples given, but much of the ideas escape me.

Are there any books out there that teach this sort of thing from the beginning?

 

[snipez90]

http://www.artofproblemsolving.com/Books/AoPS_B_Texts_FAQ.php#classics

These books will teach you about mathematical problem solving from the beginning. They cover the standard mathematics curriculum (before calculus) in content, but they will show you how to use the concepts to tackle hard problems.

But yeah, the only way to get better at this stuff is to do a lot of problems that do not appear trivial to you. So if you do decide to get these books, try to work on the problems first, because you can't learn this sort of thing just by reading text.

 

[gunch]

I was looking at some of the questions from various competitions for high schools and colleges and their questions, and I couldn't begin to solve the majority of them.

Remember that these are competitions so the problems are made sufficiently hard that many good students won't be able to solve them. Therefore you shouldn't feel bad about not being able to solve them. This is not to say that you shouldn't try though. Recreational/competition math is kind of fun and it's always cool if you get to a level where you get to go to competitions like the IMO or simply some training camps.

The book by Engel is sort of special. Personally I don't really like its style and feel that it is incredibly hard to learn from, but on the other hand it contains some tidbits that you simply won't find anywhere else. I think you should save Engel till you really need it. The art of problem solving books are of course quite good and thorough, but there are some alternatives if you are interested. I never used it myself, but I know some people at the IMO really liked The Art and Craft of Problem Solving by Zeitz as an introduction to contest math.

Terrence Tao also wrote a little introductory book called Solving Mathematical Problems. Personally I find it a little dull and without many real insights, but it could very well be helpful for a beginner with a slightly different taste than mine.

Another approach could be to consider the books by Titu Andresscu such as 104 number theory problems, x combinatorial problems, y trigonometry problems, etc. (just do a search for Titu Andreescu on a book site to see the books). These are however aimed at a somewhat experienced audience so perhaps these are good once you feel you have master The art and craft of problem solving or find the AoPS books too slow.

And of course I need to second what snipez90 said: you need to work on problems to become better.