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!