The William Lowell Putnam mathematical competition - 1985 - 2000

Problems, solutions and commentary

Kiran S. Kedlaya, Bjorn Poonen, Ravi Vakil

350 pages, parution le 01/01/2002

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Résumé

The William Lowell Putnam Mathematical Competition is the premier mathematical competition at the undergraduate level in North America. This volume, the third to cover the competition, contains the 192 problems from the years 1985-2000, as they appeared ir the competition, with solutions and extensive commentary.

It is unlike the first two Putnam volumes and unlike virtually every other problem-based book, in that it places the problems in the context of important mathematical themes. The authors highlight connections to other problems, to the curriculum, and to more advanced topics. The best problems contain kernels of sophisticated ideas related to important current research, and yet the problems are accessible to undergraduates.

The heart of the book is in the solutions, which have been compiled through extensive research. The authors present the best solutions from the American Mathematical Monthly, Mathematics Magazine, past competitors, and many problem enthusiasts. Often the authors have simplified these solutions, or have developed new solutions of their own. Multiple solutions are common. In editing the solutions, the authors have kept a student audience in mind, explaining techniques that have relevance to more than the problem at hand, suggesting references for further reading, and mentioning related problems, some of which are unsolved.

In addition to problems and solutions, the book contains :

a hint to each problem, separate from the full solution;
background information about the competition;
a list of winning individuals and teams, with current information about the career paths of winners;
a topic index;
Putnam Trivia for the Nineties, by Joseph A. Gallian; and
Some Thoughts on Writing for the Putnam, by Problems Committee member Bruce Reznick.

The authors of this volume are active research mathematicians who are renowned also for their expository skills. They were themselves winners of the Putnam Competition in most of the years covered by the volume: together they achieved the rank of Putnam Fellow eleven times.

This volume will appeal to students, teachers, and professors, or anyone interested in problem solving as an entree to beautiful and powerful ideas.

Introduction
- Structure of this book
- The Putnam Competition over the years
- Advice to the student reader
- Scoring
- Some basic notation
- Acknowledgements
Problems
Hints
Solutions
- The Forty-Sixth Competition (1985)
- The Forty-Seventh Competition (1986)
- The Forty-Eighth Competition (1987)
- The Forty-Ninth Competition (1988)
- The Fiftieth Competition (1989)
- The Fifty-First Competition (1990)
- The Fifty-Second Competition (1991)
- The Fifty-Third Competition (1992)
- The Fifty-Fourth Competition (1993)
- The Fifty-Fifth Competition (1994)
- The Fifty-Sixth Competition (1995)
- The Fifty-Seventli Competition (1996)
- The Fifty-Eighth Competition (1997)
- The Fifty-Ninth Competition (1998)
- The Sixtieth Competition (1999)
- The Sixty-First Competition (2000)
Results
- Individual Results
- Team Results
Putnam Trivia for the Nineties
Some Thoughts on Writing for the Putnam by Bruce Resmick
Bibliography
Index

L'auteur - Kiran S. Kedlaya

Kiran Kedlaya is from Silver Spring, MD. He received an BA. in mathematics and physics from Harvard (where he was a Putnam Fellow three times), an M.A. in mathematics from Princeton, and a Ph.D. in mathematics from M.I.T. He urrently holds a National Science Foundation postdoctoral fellowship at the University of California, Berkeley. Other affiliations have included the Clay Mathematics Institute and the Mathematical Sciences Research Institute.

L'auteur - Bjorn Poonen

Bjorn Poonen received his BA degree from Harvard in mathematics and physics, and the PhD degree in mathematics from the University of California, Berkeley, where he now holds the title of associate professor of mathematics. Other affiliations have included the Mathematical Sciences Research Institute, Princeton University, the Isaac Newton Institute, and Université de Paris-Sud.

L'auteur - Ravi Vakil

Ravi Vakil is from Toronto, Canada. He received his undergraduate degree at the University of Toronto. After completing a Ph.D. at Harvard, he taught at Princeton and M.I.T. before moving to Stanford, where he is a tenure-track assistant professor. He is currently an American Mathematical Society Centennial Fellow and an Alfred P. Sloan Research Fellow.

Caractéristiques techniques

	PAPIER
Éditeur(s)	The Mathematical Association of America (MAA)
Auteur(s)	Kiran S. Kedlaya, Bjorn Poonen, Ravi Vakil
Parution	01/01/2002
Nb. de pages	350
Format	18 x 26
Couverture	Relié
Poids	775g
Intérieur	Noir et Blanc
EAN13	9780883858073
ISBN13	978-0-88385-807-3