Problem Solving and The Putnam Competition
The William Lowell Putnam Competition
The Putnam Exam
(officially known as the William Lowell Putnam Mathematical
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).
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
competitions. Two experimental competitions were held, one in English,
and one in mathematics, before the competition assumed its present
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
Questions and Solutions.
Harvey Mudd Putnam Links
Pizza and Problem Solving Sets from the Park City Math Institute
Online Mathematical Resources
- Math Fun Facts is
Francis Su’s website with many amusing math facts for students of all
- 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.
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
Putnam Preparation Web Sites
Here is just a selection of Putnam
Preparatory Seminars at various colleges. Note some of these sites move
Other Online Problem Competition and Sources
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
Horizons (MAA) is a magazine aimed at undergraduates with a
very accessible problem section.
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
- The American
Mathematical Monthly publishes articles about mathematics and the
profession. Its readers span a broad spectrum of mathematical
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.
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
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.
* Mathematics Department
* Harvey Mudd College
Maintained by Andrew J. Bernoff
Last Updated on 01-08-13