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I am a graduating high school senior, and I will be starting college this September. During my middle and high school years, I have done introductory math competitions like Mathcounts, AMC, AIME, etc., but I have never gotten far (USA(J)MO, MOP, etc.). Now, since I am entering college, I am thinking of seriously preparing for the Putnam. Yes, I know that I have a lot to catch up, but I still want to try.

Thanks to some older students who gave their used books to me, besides my own materials, I have tons of high school competition math preparation books and resources. Just to mention a "few":

  • Art of Problem Solving books (volume 1, 2, introduction, intermediate, etc.)
  • "_ _ Problems" series (e.g. 104 Number Theory Problems, 105 Algebra Problems, 110 Geometry Problems)
  • Lemmas in Olympiad Geometry
  • Titu's Problems from the Book (and Straight from the Book)
  • Engel's Problem-Solving Strategies
  • Past AMC/AIME/USA(J)MO/IMO problems and solutions
  • Titu's Topics in Functional Equations
  • Titu's Mathematical Olympiad Challenges
  • Notes from summer programs like AMSP
  • The IMO Compendium
  • Evan Chen's EGMO

These are tons of unused resources, so I was just wondering if these books are useful in my preparation for the Putnam. Or, are the Putnam and the high school competitions too unrelated that it would likely be a waste of time to spend my time on these books? I guess it is possible that some of these books are relevant, while others aren't. If someone with experience in these resources and Putnam could answer this question, I would appreciate it. Thank you for any help that you are able to provide.

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    $\begingroup$ They involve very different topics, like the Putnam doesn't cover Euclidean geometry to the extent that the olympiads do, while requiring knowledge of abstract algebra and analysis. If are new to proof writing (esp if you didn't get far in USAJMO), then I'd recommend getting started with Engel's Problem solving strategies (or Paul's Art and Craft of problem solving). If you're confident (and know what it means to write a complete solution), then I'd suggest Titu's Putnam and Beyond. $\endgroup$ – Calvin Lin Apr 12 '20 at 6:02
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    $\begingroup$ It helps to 1) categorize problems and work on similar ones to learn about the various techniques/tricks/ideas, and when you've built up your knowledge/confidence then 2) take a 2000+ Putnam and start working through A/B 1/2(maybe 3) and solve them completely (write up your solution, then have a friend read it without you around). $\endgroup$ – Calvin Lin Apr 12 '20 at 6:03
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The USAMO and USAJMO questions will only help you with proof writing. You should focus more on calculus, abstract algebra, etc. The IMO focuses on high school material while the Putnam is more college material. You should focus on the basic of IMO prep such as basic euclidean geometry, basic combinatorics and more Putnam style questions such as matrices. Good luck and have fun!!

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