Formely: Northwestern University Math Problem Solving Group

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

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

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

- 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

- 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

- 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