What are the Best Resources for Learning Contest-Type Mathematics?

In summary, the conversation discusses the need for resources to improve in contest-type mathematics, specifically for upcoming competitions. The suggested books are "Art and Craft of Problem Solving" by Paul Zeitz and "Problem-Solving Strategies" by Arthur Engel, which are highly recommended for developing techniques and skills for solving challenging problems. These books are not like typical math textbooks with brief notes and exercises, but rather contain a variety of problems ranging in difficulty, teaching the reader how to effectively approach and solve them. They also cover topics such as elementary geometry and number theory, requiring ingenuity and critical thinking.
  • #1
ultimatebusta
8
0
I'm currently in IB SL Math (No HL here unfortunately), and I wish to learn more about contest-type mathematics as I have 3-4 contest here this year. Is there any books/materials that's useful for me?

I have taken a look at this book: https://www.amazon.com/dp/0817645276/?tag=pfamazon01-20 Though i found it a little difficult as the solutions to examples are quite vague, and there's no extra practise questions after each example. Also it doesn't have too much about trigonometry and geometry.

Any ideas would be greatly appreciated. I have a contest coming up in 2 weeks exactly, and a couple in 2011.
 
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  • #2
Yes, try looking for "Art and craft of problem solving" by Paul Zeitz. Me and people I know find this an incredibly good and useful book for learning contest problem solving. It does not only contain a large amount of good problems, but it also teaches common techniques from general principles to very specific tricks which can be very useful. You could complement with the slightly more advanced "Problem-solving strategies" by Arthur Engel later on, but both are in themselves very good books.
 
  • #3
So in math class, we get a brief note, some examples, and some homework questions.

Anything like that in those 2 books/other materials?
 
  • #4
ultimatebusta said:
So in math class, we get a brief note, some examples, and some homework questions.

Anything like that in those 2 books/other materials?

Not at all, I suggest you read some reviews of them on them. The problems in them are ranging in difficulty from the first round of high-school competitions to the IMO. None are like high-school exercises where you apply some basic technique/formula. All problems require some ingenuity, and the book teaches you how to effectively search for solutions to such problems. Both contains material on elementary geometry.
 
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  • #5
I agree that applying things like number theory requires extensive insight, but I do believe that i have to see a fair amount of those questions (where i solved/attempted to solve) in order to develop the skills to see through the trickeries of those questions and apply the skills
 

1. What is contest math material?

Contest math material refers to the collection of topics and problems that are commonly encountered in math competitions. These may include algebra, geometry, number theory, combinatorics, and more. It is designed to challenge and test the problem-solving abilities of participants.

2. How is contest math material different from regular math?

Contest math material often involves more complex and abstract concepts than what is typically taught in a regular math curriculum. It also focuses on problem-solving techniques and strategies rather than simply solving equations or problems step-by-step.

3. What are some common types of contest math problems?

Some common types of contest math problems include geometry proofs, number theory equations, combinatorics counting problems, and algebraic manipulations. These problems often require creative thinking and multiple steps to arrive at the solution.

4. How can I improve my skills in contest math?

Practicing regularly with contest math material is the best way to improve your skills. You can also join a math club or take part in math competitions to gain more experience and exposure to different types of problems. Additionally, studying and learning from solutions to previous contest problems can also be helpful.

5. Is contest math material useful in real life?

While contest math material may not have direct applications in everyday life, the problem-solving skills and critical thinking developed through practicing it can be applied to various fields and situations. It also helps to develop a strong foundation in math, which is useful for many career paths.

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