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

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Discussion Overview

The discussion revolves around resources for learning contest-type mathematics, particularly for participants preparing for upcoming math competitions. The focus includes recommendations for books and materials that can aid in developing problem-solving skills relevant to contests.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant mentions their current experience with IB SL Math and expresses a desire for resources to prepare for contests, noting difficulties with a specific book due to vague solutions and lack of practice questions.
  • Another participant recommends "Art and Craft of Problem Solving" by Paul Zeitz, highlighting its effectiveness in teaching problem-solving techniques and providing a variety of problems.
  • A suggestion is made to consider "Problem-Solving Strategies" by Arthur Engel as a complementary resource, noted for its advanced content.
  • Concerns are raised about the nature of problems in the recommended books, indicating they require ingenuity rather than basic techniques, which may differ from typical math class exercises.
  • One participant emphasizes the importance of exposure to various problem types to develop the necessary skills for contest mathematics, particularly in number theory.

Areas of Agreement / Disagreement

Participants express differing views on the suitability of the recommended books for their learning style and needs. There is no consensus on the best approach or resources, as some find the suggested materials challenging while others advocate for their effectiveness.

Contextual Notes

Participants note limitations in the recommended books regarding the clarity of solutions and the types of problems presented, which may not align with typical classroom exercises.

Who May Find This Useful

Students preparing for math contests, educators seeking resources for teaching problem-solving, and individuals interested in enhancing their mathematical reasoning skills.

ultimatebusta
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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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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.
 
So in math class, we get a brief note, some examples, and some homework questions.

Anything like that in those 2 books/other materials?
 
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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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
 

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