For students interested in the Putnam exam, here are some self-study resources.
Basic strategies (from here): general/strategies.pdf
Recent Putnam exams and solutions: http://kskedlaya.org/putnam-archive/
AOPS Putnam Forum (very useful): https://artofproblemsolving.com/community/c7t441f7
30k IMO-level problems and solutions: https://mathnet.mit.edu/
Resources from other schools:
Collected challenges:
Other competitions:
For students at Emory, I also have physical books that I am willing to lend.
Good luck!