I am a rising college junior with major in the mathematics. I recently got interested to the contest mathematics through working with few Putnam problems in the real analysis and linear algebra, and I decided to prepare for Putnam Competition, which will be on this December.
I switched my major from the microbiology to mathematics on the last semester through my ongoing research in the theoretical computer science. Since then, I have been sharpening my proof skill. Unfortunately, Putnam Competition will be my first experience with the contest mathematics, and that means I do not have any experience with it.
I am currently self-studying Rudin-PMA, Apostol-Mathematical Analysis, Artin-Algebra (little bits per day), and Hoffman/Kunze-Linear Algebra. I will be taking the Analysis I (Rudin) and Linear Algebra with Introduction to Proofs (Friedberg) on the upcoming Fall. Since I also have to dedicate myself to the classes and undergraduate researches, I do not have enough time to read textbooks on other major topics of Putnam: number theory, combinatorics, probability theory, and mathematical statistics.
My preparation plan is to read and study the proof techniques and materials covering those topics (number theory, combinatorics, etc.) in the problem-solving books like Larson, Engel, and Andreescu (Putnam and Beyond). Then, I am going to jump directly to the past Putnam problems and pick up the additional materials on mathematical branches (such as combinatorics and number theory) embedded on Putnam problems. That way, I can sharpen my problem-solving tricks necessary for the Putnam Competition and acquire interesting knowledge in the mathematical branches like number theory in a discrete way of learning (by attempting the problems and learn the necessary concepts).
However, I am a rookie in the contest mathematics and my preparation plan for Putnam might be inefficient. I would like to take this chance to seek your advice and knowledge in the Putnam Competition, and to seek your comments in my preparation plan. Also I heard that Putnam problems generally do not require advanced mathematical branches like functional analysis and partial differential equations, and they instead require the deep understanding of basic mathematical concepts (such as limits, continuity, groups, etc.) and clever tricks. If my guess is correct, could you give me the advice what kind of mathematical branches and clever tricks I need to study and acquire, and elaborate more on them?
Thank you very much for your time, and I look forward to hear back from you!