I need a book for math competitions

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Discussion Overview

The discussion revolves around recommendations for math books suitable for high school students preparing for regional math competitions. Participants share their experiences and suggest resources that include competition-style problems and explanations.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant seeks a math book with competition-style problems and clear explanations, specifically for regional competitions.
  • Another suggests "My Best Mathematical and Logic Puzzles" by Martin Gardner as a potentially useful resource.
  • A participant proposes including additional examples to enhance understanding of problem-solving techniques.
  • Recommendations for books by Titu Andreescu are made for those looking for background knowledge and challenging problems.
  • Several participants mention "104 Number Theory Problems: From the Training of the USA IMO Team," "Schaum's 3,000 Solved Problems in Calculus," and "Challenging Problems in Algebra" as helpful resources.
  • One participant expresses satisfaction with "104 Number Theory Problems," noting its effectiveness for learning elementary number theory.
  • Another participant shares their interest in problem-solving and mentions ordering books on USSR Olympiad Math problems and a problems book from the MAA, while noting that their current problems are easier than Olympiad-level problems.

Areas of Agreement / Disagreement

Participants generally agree on the usefulness of specific books for math competitions, but there is no consensus on a single best resource. Some participants express differing levels of familiarity with the recommended books.

Contextual Notes

Some participants mention the varying difficulty levels of problems they are tackling, indicating a range of experience and expectations regarding competition preparation.

Who May Find This Useful

High school students preparing for regional math competitions, educators seeking resources for teaching problem-solving, and individuals interested in recreational mathematics.

Zeroth
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Hi
As the title suggests, I'm looking for a math book that has some competition-style problems in it, with explanations on how to solve them. I have found numerous of other competitions online but the explanations are very not understandable for me. I am NOT talking about international competitions, but regional. This is high school math.

Here is an example:

Find all prime numbers p and q and a natural number r such that they satisfy the equation.

p2 + q2+pq = r2
 
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You might find recreational mathematics books with a focus on puzzles useful. My Best Mathematical and Logic Puzzles by Martin Gardner, for example.
 
I checked the book and I think I should add another example for better understanding.

Determine a maximum and a minimum of the function:

f(x)=√(sin4(x)+4cos2(x)) - √(cos4(x) + 4sin2(x))
 
If you want to learn background knowledge, challenging problems along with good explanations, I recommend any book written by Titu Andreescu.
 
"104 Number Theory Problems: From the Training of the USA IMO Team," "Schaum's 3,000 Solved Problems in Calculus," and "Challenging Problems in Algebra" might help you, then.
 
The Bill said:
"104 Number Theory Problems: From the Training of the USA IMO Team," "Schaum's 3,000 Solved Problems in Calculus," and "Challenging Problems in Algebra" might help you, then.

Thumbs up for "104 NT Problems"; I used it to learn basics of elementary NT before studying analytics aspect. I think that book can be used as a first introduction to ENT too. Any book by Andreescu is extremely well-written.
 
The Bill said:
"104 Number Theory Problems: From the Training of the USA IMO Team," "Schaum's 3,000 Solved Problems in Calculus," and "Challenging Problems in Algebra" might help you, then.
I found the last book, and it is perfect, thank you
 
I have found an interest in problem solving myself. I ordered, but have yet to receive and view the contents of, two books. One is the USSR Olympiad Math problems book published by Dover and a problems book published by the MAA.
 
MidgetDwarf said:
I have found an interest in problem solving myself. I ordered, but have yet to receive and view the contents of, two books. One is the USSR Olympiad Math problems book published by Dover and a problems book published by the MAA.
Thank you but I think it should be said. The problems I am solving are much easier than any olympiad problems.
 

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