Web page for the Northwestern University Math Problem Solving Group.

Goals

1. Acquire basic math problem solving skills.
2. Help in training future candidates for the yearly Putnam Competition.

Activities

1. Solve math problems proposed in magazines like Math Horizons, College Mathematics Journal and the Mathematics Magazine. Ideally we should solve at least one problem from each issue.
2. Discuss solutions to problems and study mathematical subjects related to problem solving.

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