Understanding some of the math Olympiad questions?

In summary, there are several books available that teach mathematical problem solving from the beginning, such as The Art of Problem Solving and The Art and Craft of Problem Solving. It is important to keep in mind that competition problems are designed to be challenging, so struggling with them is normal. Some other recommended books include Solving Mathematical Problems by Terrence Tao and various books by Titu Andresscu. However, it is important to also actively work on problems in order to improve in this area.
  • #1
Skynt
39
1
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?
 
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  • #2
http://www.artofproblemsolving.com/Books/AoPS_B_Texts_FAQ.php#classics [Broken]

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.
 
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  • #3
Skynt said:
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.
 

1. What is the purpose of math Olympiad questions?

The purpose of math Olympiad questions is to challenge and assess the problem-solving skills and mathematical knowledge of high-performing students. These competitions also aim to foster interest and passion for mathematics among students.

2. What topics are usually covered in math Olympiad questions?

Math Olympiad questions cover a wide range of topics including algebra, geometry, number theory, combinatorics, and logic. These questions are designed to test a student's understanding of fundamental concepts and their ability to apply them in problem-solving.

3. How can one prepare for math Olympiad questions?

To prepare for math Olympiad questions, one should have a strong foundation in basic mathematical concepts and problem-solving strategies. It is also beneficial to practice solving challenging and diverse mathematical problems, as well as participating in mock competitions.

4. How are math Olympiad questions graded?

Math Olympiad questions are typically graded based on the correctness of the solution, the logical reasoning used to arrive at the solution, and the clarity of presentation. Partial credit may also be given for partially correct answers.

5. Are there any tips for approaching math Olympiad questions?

Some tips for approaching math Olympiad questions include carefully reading and understanding the problem, breaking it down into smaller parts, using diagrams and visual aids if needed, and trying various problem-solving strategies such as working backwards or using trial and error. It is also important to check and verify the solution to ensure its accuracy.

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