Resources
Books and journal articles
Most of the books below have been placed on reserve in the
UI Math Library in Altgeld Hall, under course number Math 1000,
and can be checked out for up to two hours. (Just ask for the book by author.)
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 ProblemSolving 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.)

[BeginnerIntermediate]
E. Lozansky and C. Rousseau, Winning solutions,
A good introduction to some useful background material from number theory,
algebra, and combinatorics, and to problemsolving techniques.

[BeginnerAdvanced]
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.

[IntermediateAdvanced]
Loren Larson, Problem solving through problems,
A systematic treatment of problemsolving techniques, illustrated by
Putnam level problems.
Considerably more advanced than Lozansky/Rousseau, with the main focus on
techniques rather than theorems.

[IntermediateAdvanced]
Paul Zeitz, The Art and Craft of Problem Solving.,
An excellent book for selfstudy for more advanced students.
Problems are grouped by technique and by subject.

[Advanced] D.J. Newman, A problem seminar.
A collection of 100+ carefully selectedand quite challengingproblems,
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 19852000 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 sixtysix 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.
Back to the UI Math Contests page