Pizza and Problem Solving at PCMI

For 2012 Prof. Francis Su ran a problem session called Symmetry.
For 2011 Prof. Andrew Bernoff ran two problem session called The Sum of the Parts and Digits and Divisibility.
For 2010 Prof. Andrew Bernoff ran two problem session called Induction and Recursion and The Extreme Principle.
For 2009 Prof. Andrew Bernoff ran two problem session called The Pigeonhole Principle and Parity & Counting.
For 2008 Prof. Andrew Bernoff ran two problem session called Hidden Symmetries and Lattice Points & Polygons.
For 2007 Prof. Andrew Bernoff ran two problem session called Some Random Problems From Probability and Mathematical Games.
For 2006 Prof. Francis Su ran a problem session called Paths, Curves and Cycles. Prof. Andrew Bernoff ran a problem session called Digits and Divisibility.
For 2005 Prof. Andrew Bernoff ran a problem session called The Sum of the Parts on geometric dissection problems. Prof. Francis Su ran a problem session called The Extreme Principle on analyzing problems by considering extreme cases.
For 2004 Prof. Francis Su ran two seminars, the first on The Pigeonhole Principle and the second called Cubes and Other Geometric Objects.
For 2003 Prof. Andrew Bernoff ran two seminars one called Induction and Deduction and one called Parity and Invariants.

Problem Solving at Harvey Mudd College

At Harvey Mudd College we run a variety of seminars oriented towards problem solving:

The Harvey Mudd College Putnam Resource Page is a collection of links, pictures and resources skewed towards HMC's Putnam program
Putnam Classic - This is a seminar aimed at college underclassmen, and is certainly suitable for freshmen. Typically, I give a short lecture on a subject, such as induction, and then hand out a slate of problems. students work in small groups, and forty-five minutes later pizza arrives, and students present their problems. Here is a problem set on induction and the latex source file. Here are some pictures from the HMC Putnam Seminar.
Putnam TNG - This is a more advanced seminar ("TNG" stands for the "The Next Generation" -- a reference familiar to the trekkies among you) oriented around exclusively Putnam problems. Problems are handed out each week and the students are expected to have worked at least one problem and to be ready to present it in class. We again group problems by subject. Here is a sample problem set and the latex source file.
Problem Solving Seminar - In this seminar we solve problems out of the various college math journals (see below); students tend to work for multiple weeks on a problems, and learn to use online resources, library resources, and programs such as MAPLE and MATLAB. Here is a sample solution and the latex source file.

Math Horizons (MAA) is a magazine aimed at undergraduates with a very accessible problem section.
Mathematics Magazine (MAA) is an expository journal of undergraduate mathematics, with an a good problem section for the undergraduate.
The College Mathematics Journal (MAA) provides lively, well-motivated articles that can enrich undergraduate instruction and enhance classroom learning.
The American Mathematical Monthly publishes articles about mathematics and the profession. Its readers span a broad spectrum of mathematical interests, and include professional mathematicians as well as students of mathematics at all collegiate levels. The problem section is quite challenging, and often contains unsolved problems.

Math Fun Facts is Francis Su’s website with many amusing math facts for students of all abilities.
Math Forum is a good starting place for K-12 resources.
Eric Weisstein's World of Mathematics - An extensive encyclopedia of mathematics. Nearly anything that you might want to know about math can be found here.
The Inverse Symbolic Calculator - A program that attempts to find a symbolic expression for a given decimal approximation to a number.
Sloane's On-Line Encyclopedia of Integer Sequences - An encyclopedia of many interesting sequences of integers.
MathSciNet - The best site for doing key word searches on journal articles.

Macalester Problem of the Week - Great and offbeat problems due to Stan Wagon and friends !!!
Official Putnam Site - The official rules, regulations, and results of the competition.
AMC Putnam Archive- An extensive archive of recent Putnam problems, solutions, and statistics.
Information about and problems from other mathematics contests (USAMO,IMO, etc.) can be found here.