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E.S.E advisers,

I am a college sophomore in US with a major in mathematics and an aspiring mathematician in the computation theory and cryptography. I apologize for this sudden interruption but I wrote this post to seek your recommendation on a problem-solving book (containing strategies and tricks) that can prepare me well for a competition mathematics, particularly the Putnam Competition (which I will take on this December). This is my first time preparing for a mathematical competition, and I am familiar with only the basic proof skills (direct, indirect, induction, etc.). I asked my Putnam coach and friends, and they all recommend the following books on below. My plan is to study one of them and tackle Putnam problems at the same time. What is your recommendation?

"Problem-Solving Trough Problems" Loren Larson "Problem-Solving Strategies" Arthur Engel "The Art and Craft of Problem Solving" Paul Zeitz "The Art of Problem Solving, Vol.1-2" Richard Rusczyk "Putnam and Beyond" Titu Andreescu "Thinking Mathematically" J. Mason "Mathematics and Plausible Reasoning: G. Polya

I am currently reading "How to Solve It" by G. Polya, and I will proceed to one of them (at your recommendation) along with Putnam problems. It is fairly natural to pick "Putnam and Beyond", but I heard that it is not a good introduction for the problem-solving skills and required knowledge for the Putnam Competition.

Thank you very much for your time, and I look forward to hear back from you!

Sincerely, PK

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    $\begingroup$ You need to state a clear goal to get a clear answer. Is the idea to become competitive? Is the idea to learn mathematics better? Do you think this will help with your classes/educational arc? If the goal is to do well on the competition, this is not a good forum. If the goal is to improve your process of education, I think you will need to refine your question some to make it apropos for this forum. Gerhard "Try Taking Last Year's Test" Paseman, 2015.07.17 $\endgroup$
    – Gerhard Paseman
    Jul 17, 2015 at 19:51
  • $\begingroup$ Dear Mr. Paseman: My goal is to become competitive in the contest mathematics and also enhance my mathematical maturity in the problem-solving. $\endgroup$
    – MathWanderer
    Jul 17, 2015 at 20:06
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    $\begingroup$ Look around at artofproblemsolving.com for helps and suggestions of study for Putnam (and many other competitions). $\endgroup$
    – Gerald Edgar
    Jul 17, 2015 at 21:34
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    $\begingroup$ Duplicate of math.stackexchange.com/q/1364883/18398. @MathWanderer, it is considered impolite to ask the same question at two different sites at the same time without referencing them. $\endgroup$
    – JRN
    Jul 18, 2015 at 0:56
  • $\begingroup$ Although the allure of competition in contest mathematics is often compelling for people your age, there is much more value in developing mathematical maturity in problem solving (even if that does not result in your highest possible score). $\endgroup$
    – Michael Joyce
    Nov 18, 2015 at 13:05

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