Problem Solving and The Putnam Competition

The William Lowell Putnam Competition

The Putnam Exam (officially known as the William Lowell Putnam Mathematical Competition) is a very challenging, six-hour mathematics exam taken by about 3,600 undergraduates in the United States and Canada each year. It is given on the first Saturday in December, and is composed of two sessions, one in the morning and one in the afternoon, each with six questions. Each question is worth 10 points (for a total of 120). Typically, the median score for all contestants is approximately one (out of 120).

William Lowell Putnam, a graduate of Harvard in the class of 1882, believed strongly in the value of academic competitions. To this end, Mrs. Elizabeth Lowell Putnam, the wife of Mr. Putnam, created a trust fund for supporting such competitions. Two experimental competitions were held, one in English, and one in mathematics, before the competition assumed its present form.

Harvey Mudd College (HMC) has a long history of participation in the Putnam, and in recent years, the school has done very well. In 2003, we placed 5th in the country, and we are often the only undergraduate college to place in the top ten. We also regularly sport the highest participation rate in the country with roughly 10% of our students taking the exam!

Here are the 2006 Putnam Exam Questions and Solutions.

Harvey Mudd Putnam Links

The RIF Scholarship- A merit scholarship offered by the HMC Mathematics Department to students who demonstrate exceptional mathematical ability, possibly evidenced by strong performance in mathematical competitions.
The Putnam Problem Solving Seminar is offered every fall.
A Math Horizons article about the HMC Putnam Seminar.
Here are some pictures from the Putnam Seminar.
Mug Shots -- Pictures of the beautiful Putnam mugs given to all HMC Putnam participants.

Online Mathematical Resources

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 - A very extensive encyclopedia of mathematics. Anything that you might want to know about math can be found here.
MathSciNet - The best site for doing key word searches on journal articles.
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.
The Art of Problem Solving host a set of mathematical resources, publishes books, and runs courses aimed primarily at High School students.

Putnam Competition Sites

Official Putnam Site - The official rules, regulations, and results of the competition.
MAA/AMC Putnam Archive- An extensive archive of recent Putnam problems, solutions, and statistics.
John Scholes has put together an amazing site which includes worked Putnam Problems and Solutions.

Putnam Preparation Web Sites

Here is just a selection of Putnam Preparatory Seminars at various colleges. Note some of these sites move frequently.

MIT's Open Course Ware for Stanley & Rogers Problem Solving Seminar in 2004 (18.S34)
Stanley & Roger's MIT 18.S34 Problem Solving Seminar (2007)
Richard Stanley's Proposed Putnam Problems -- from when he was on the committee that wrote the exam.
Ravi Vakil's Stanford Putnam Webpage.
University of Waterloo.
Greg Lawler's Problems from Duke University.

Some Useful Problem Books

Putnam level and some easier problems grouped by subject:

Problem-Solving Strategies (Problem Books in Mathematics) by Arthur Engel
Problem Solving Through Problems by Loren C. Larson
The Art and Craft of Problem Solving by Paul Zeitz
Mathematical Olympiad Challenges by Titu Andreescu, Razvan Gelca
Winning Solutions (Problem Books in Mathematics) by Edward Lozansky, Cecil Rousseau

Collections of elementary problems appropriate for freshmen:

Five Hundred Mathematical Challenges by Edward J. Barbeau, Murray S. Klamkin, William O. J. Moser
Which Way Did the Bicycle Go? : And Other Intriguing Mathematical Mysteries -- Joseph D. E. Konhauser, Dan Velleman

Collection of Putnam probems:

The William Lowell Putnam Mathematical Competition 1985-2000 by Kiran S. Kedlaya et al.

Collections of Putnam level problems:

The Red Book of Mathematical Problems by Kenneth S. Williams, Kenneth Hardy
The Green Book of Mathematical Problems by Kenneth Hardy, Kenneth S. Williams

A classic on problem solving strategies:

How to Solve It by George Polya

College Mathematics Journals with Problem Sections

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.

Disclaimer: The sites listed here at the time of the composition of this page were available openly on the web. I expect these sites to move and migrate over time. Moreover, much of the material referenced may be protected by copyright and other intellectual property law. The user of these resources is encourage to acknowledge the source of problems used and to obtain permissions to copy problems, solutions, resources and other documents as appropriate.

Putnam Homepage * Mathematics Department * Harvey Mudd College

Maintained by Andrew J. Bernoff
Last Updated on 9-26-07