William Lowell Putnam Mathematical Competition
The William Lowell Putnam Mathematical Competition, often abbreviated to the Putnam Competition, is an annual mathematics competition for under graduate college students enrolled at institutions of higher learning in the United States, Canada, and Tel-Aviv University (regardless of the students' nationalities). It awards scholarships with cash prizes ranging from $250 to $2,500 for the top students and $5,000 to $25,000 for the top schools, plus the top ten individual scores get tuition waived at Harvard, and the top 100 individual scores have their names mentioned by rank to leading universities. It is considered by many to be the most prestigious university-level mathematics examination in the world, and its difficulty is such that the median score is often zero or one (out of 120) despite being attempted by students specializing in mathematics.
Wikipedia
Official Website: William Lowell Putnam Mathematical Competition
Wikipedia
Official Website: William Lowell Putnam Mathematical Competition
Putnam Competition Problems, Solutions, Results
Exam problems, solutions, and results from the past Putnam exams. If you really want to test your math ability these are the problems to test on. Just click the title "Putnam Competition Problems, Solutions, Results"