Formely: Northwestern University Math Problem Solving Group

Local links

• A few "old" problems (sporadically updated).
• "Easy" Problems from the Putnam Competition (periodically updated)

External links

• Putnam Archive (includes solutions from years 1995 and later.)

Mathematical Results

• Generating Functions
• Inequalities
• Mathematical Induction
• Modular Arithmetic
• Recurrence Relations
• Various Techniques - Summation by Parts, Euler-Maclaurin Summation Formula, Poisson Summation Formula.

Solved problems

• A binary operation on rationals
• Bijection between Two Sets
• Eventually constant modulo m
• Four squares theorem for rational numbers
• John's PIN
• Josephus problem
• Sorted random numbers
• Split squares
• Sums and products of tangents squared (MathJax version)
• Ternary Addition

Other Links

• The Art of Problem Solving - AoPS Putnam Forum
• Wolfram MathWorld PlanetMath
• William Lowell Putnam Mathematical Competition (MAA site)
• William Lowell Putnam Mathematical Competition (SCU site)
• IBM Research - Ponder this
• Problems of the Miklós Schweitzer Memorial Competition

Bibliography

• G. Alexanderson et al.: The William Lowell Putnam Mathematical Competition problems and solutions: 1965-1984, The Mathematical Association of America, Washington, D.C., 1985.
• W. W. Rouse Ball and H.S.M. Coxeter: Mathematical Recreations and Essays (13th edition), Dover Publications, 1987.
• Benjamin Bold: Famous Problems of Geometry and How to Solve Them, Dover Publications, 1969.
• Heinrich Dorrie: 100 Great Problems of Elementary Mathematics, Dover Publications, 1989.
• Arthur Engel: Problem-Solving Strategies, Springer, 1998.
• Gelfand, Gerver, Kirillov, Konstantinov and Kushnirenko: Sequences, Combinations, Limits, Dover Publications, 1969.
• A.M. Gleason et al.: The William Lowell Putnam Mathematical Competition problems and solutions: 1938-1964, The Mathematical Association of America, Washington, D.C., 1980.
• Kedlaya, Poonen and Vakil: The William Lowell Putnam Mathematical Competition 1985-2000: Problems, Solutions and Commentary, The Mathematical Association of America, Washington, D.C., 2002.
• Kenneth Hardy and Kenneth S. Williams: The Green Book of Mathematical Problems, Dover Publications, Inc., 1997.
• Kenneth Hardy and Kenneth S. Williams: The Red Book of Mathematical Problems, Dover Publications, Inc., 1996.
• Frederick Mosteller: Fifty Challenging Problems in Probability with Solutions, Dover Publications, 1965.
• Donald J. Newman: A Problem Seminar, Springer, problem books in mathematics, 1982.
• G. Polya: How to Solve It, 2nd ed., Princeton University Press, 1957.
• Alfred S. Posamentier, Charles T. Salkind: Challenging Problems in Algebra, Dover Publications, 1988.
• Alfred S. Posamentier, Charles T. Salkind: Challenging Problems in Geometry, Dover Publications, 1988.
• D. O. Shklarsky, N. N. Chentzov, I. M. Yaglom: The USSR Olympiad Problem Book: Selected Problems and Theorems of Elementary Mathematics, Dover Publications, 1993.
• Hugo Steinhaus: One Hundred Problems in Elementary Mathematics, Dover Publications, 1979.
• Wayne A. Wickelgren: How to Solve Mathematical Problems, Dover Publications, 1995.
• Herbert S. Wilf: Generatingfunctionology, online book, (download at http://www.math.upenn.edu/~wilf/DownldGF.html).
• Peter Winkler: Mathematical Puzzles: A Connoisseur's Collection, A K Peters, Ltd., 2004.
• A. M. Yaglom, I. M. Yaglom: Challenging Mathematical Problems with Elementary Solutions Vol. 1 & 2, Dover Publications, 1987.
• Paul Zeitz: The Art and Craft of Problem Solving, John Wiley & Sons, Inc., 1999.

Comments, suggestions...? email Miguel A. Lerma at: mlerma at math dot northwestern dot edu