﻿ Problem Solving and the Putnam Competition

# 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 2011, we placed 6th in the country and in 2003, we placed 5th. 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 2011 Putnam Exam Questions and Solutions.

## 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.
• Wolfram Alpha is an amazingly smart cross between a calculator, a search engine and an encyclopedia.
• Wolfram's MathWorld - A very extensive encyclopedia of mathematics. Anythingthat 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 Preparation Web Sites

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

## Some Useful Problem Books

Putnam level and some easier problems grouped by subject:
Collections of elementary problems appropriate for freshmen:
Collection of Putnam probems:
Collections of Putnam level problems:
A classic on problem solving strategies:

## 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 01-08-13