Below are some useful links related to mathematical problem solving, including a link to the William Lowell Putnam Mathematical Competition, a nationwide mathematics contest for undergraduates. All students in the course are expected to participate in this competition.
William Lowell Putnam Mathematical Competition
International Mathematics Olympiad Problems
American Mathematics Competitions Internet Home Page
USA/International/Asian Pacific Olympiad Archive
My Putnam Problems: a list of problems I submitted for inclusion on the Putnam Exam when I was a member of the three-person committee to write the 1984-86 exams (PDF)