I am currently a junior in high school, interested in the Putnam exam.
I have access to number theory complex analysis, real analysis, any textbooks.
Spivak Calculus for one is a rigorous textbook, and I was thinking if that is good preparatory for the Putnam exam?
Also, a limit proofs important? I am not that good at those proofs, so just wondering!
What topics should I know?
Thanks
On
No, Spivak is not good training for putnam problems, I recommend you go to mathlinks and look at the actual problems. Also Engel's book on problem solving and Putnam and Beyond are good texts. I recommend you practice from actual contest exams. As for the theory, I think what you'll learn in college wil probably be enough. Also you should go to high school olympiads, that is probably the best preparation.
Spivak is a nice text of real analysis, so I recommend you to read it if you don't know much analysis.
Putnam is just an extension of USAMO and IMO, and it doesn't use much advanced mathematics like complex analysis. Solve as many questions of the above competitions as well as past Putnam questions, and use books like Putnam and Beyond.
I think linear algebra, combinatorics and number theory are the topics which most frequently appear on the exam. Geometry doesn't appear often.