Resources

Books and journal articles

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

• [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.
• [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.
• [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.
• [Intermediate-Advanced] Paul Zeitz, The Art and Craft of Problem Solving., An excellent book for self-study for more advanced students. Problems are grouped by technique and by subject.
• [Advanced] D.J. Newman, A problem seminar. A collection of 100+ carefully selected--and quite challenging--problems, with hints and solutions.
• [Advanced] R. Gelca and T. Andreescu, Putnam and Beyond. At 800 pages, with 1100 problems, all with complete solutions, this is by far the largest and most comprehensive Putnam training book. The level is fairly advanced and probably too much for all but the most experienced Putnam students.

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.
  NOTE (9/6/2013): The Putnam archive is currently unavailable as the website is in the process of being reorganized. Kiran Kedlaya has set up a temporary backup site, where the files will be available until the "official" Putnam Archive is back online.