Resources

Books and journal articles

Most of the books below have been placed on reserve in the UIUC Math Library in Altgeld Hall, under course number Math 500, and can be checked out for up to two hours. You can make Xerox copies in the reading room, but you cannot take the books outside the library or check them out overnight.

Collections of Putnam Problems and Solutions

K. Kedlaya et al., The William Lowell Putnam Mathematical Competition problems and solutions: 1985 - 2000, Mathematical Association of America, Washington, D.C., 2003.
G. Alexanderson et al., The William Lowell Putnam Mathematical Competition problems and solutions: 1965 - 1984, Mathematical Association of America, Washington, D.C., 1985.
A.M. Gleason et al., The William Lowell Putnam Mathematical Competition problems and solutions: 1938 - 1964, Mathematical Association of America, Washington, D.C., 1980.
The American Mathematical Monthly. The flagship journal of the Mathematical Association of America (MAA). The October issue of this journal contains "official" problems and solutions from the previous year's Putnam competition, a list of top scorers, and various statistics about the contest.

Books on Problem-Solving Techniques

The following books, arranged in order of difficulty, are suitable for systematic study.

[Beginner] A. Gardiner, The Mathematical Olympiad Handbook. The first part of this book contains a brief, but very handy collection of useful tools from algebra, geometry, number theory, and other areas. (The "Beginner" rating applies to this part. The second part, containing problems from the British Mathematical Olympiad, is much more challenging.)
[Beginner-Intermediate] E. Lozansky and C. Rousseau, Winning solutions, A good introduction to some useful background material from number theory, algebra, and combinatorics, and to problem-solving techniques.
[Intermediate-Advanced] Loren Larson, Problem solving through problems, A systematic treatment of problem-solving techniques, illustrated by Putnam level problems. Considerably more advanced than Lozansky/Rousseau, with the main focus on techniques rather than theorems.
[Beginner-Advanced] Arthur Engel, Problem solving strategies, A huge (1300+) collection of problems, with solutions, grouped by subject and proof technique. The problems range from easy to extremely challenging.
[Advanced] D.J. Newman, A problem seminar. A collection of 100+ carefully selected--and quite challenging--problems, with hints and solutions.

Miscelleneous

Bruce Reznick, Some thoughts on writing for the Putnam. Originally published in 1993, this article by Professor Reznick has been reprinted in the the book "The William Lowell Putnam Competition 1985-2000 Problems, Solutions and Commentary" cited above. It provides a unique perspective on the Putnam from someone who has been on the committee that makes up the Putnam problems. A fascinating look at what goes on behind the scenes with many useful bits of information for those taking the Putnam.
Robert Beezer, 48 Hours of Putnam. This article, which appeared in the MAA publication "Math Horizons" (Sept. 2004), gives yet another perspective on the Putnam, that of a grader. (Incidentally, there is also a local connection: The author, now a Professor at the University of Puget Sound, is a UIUC alumn and received his PhD here in 1984.) The September 2004 Math Horizons issue contains several other Putnam articles that are worth checking out. You can find copies of Math Horizon (that are free for the taking while supplies last) in the Undergraduate Math Office in 223 Altgeld Hall.
Joseph A. Gallian, The first sixty-six years of the Putnam competition. American Math. Monthly 111 (2004), Number 8 (October 2004), p. 691 - 699. This article contains interesting historical tidbits and fascinating trivia and statistics about the Putnam.

Online resources

Archives of Putnam problems

Official Putnam web site. Contains general information about the Putnam exam, a list of winning teams since 1938, and a list of the top scorers in the most recent edition of the Putnam exam.
AMC (American Mathematical Competitions) web site. The AMC is an organization dedicated to the promotion of mathematical problem solving at all levels. Its web site contains an extensive collection of links to problem sites and other resources, including a Putnam Problem Archive, containing Putnam problems and solutions from the past few years.
David Rusin's Putnam page. Contains Putnam problems from recent years, along with solutions posted to the sci.math newsgroup.

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