Problem of the Week:

The Purdue University Math Department publishes a math problem every week to encourage interest in undergraduate mathematics. The problems can be found here.

If you are an undergraduate and think you can solve this week's problem, write up a solution and mail it to:

Problem of the Week
Department of Mathematics, Purdue University
150 North University Street
West Lafayette, IN 47907-2067

Art of Problem Solving Contest Archive:

A collection of math contests of varying difficulty for those interested in competition math.

The collection can be found here

Putnam Competition:

The William Lowell Putnam Mathematical Competition, often abbreviated to the Putnam Competition, is an annual mathematics competition for undergraduate college students enrolled at institutions of higher learning in the United States and Canada (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. The competition was founded in 1927 by Elizabeth Lowell Putnam in memory of her husband William Lowell Putnam, who was an advocate of intercollegiate intellectual competition. The exam has been offered annually since 1938 and is administered by the Mathematical Association of America.
Problems
A list of all problems from past Putnam competitions, can be found at the William Lowell Putnam Mathematics Competition Directory.
Prizes
Each competing university pre-selects a team of three students. Both team and individual performances are recognized. The first place team institution wins $25,000, and each member of the winning team wins $1000. Each of the top five individuals wins $2500.
How to participate
The Purdue Putnam supervisor is Professor Tzuong-Tsieng Moh. You can register for the Putnam Competition by contacting Professor Tzuong-Tsieng Moh by early October, or taking the course MA48100.
How to prepare
Here is a selection of Putnam Preparatory websites: Purdue offers a problem solving seminar each fall semester to help students prepare for the competition. You can join by registering for the course MA48100.