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Cover image for The William Lowell Putnam mathematical competition 1985-2000 : problems, solutions and commentary
Title:
The William Lowell Putnam mathematical competition 1985-2000 : problems, solutions and commentary
Series:
MAA problem books series
Publication Information:
Washington : The Mathematical Association of America, 2008
Physical Description:
xiv, 337 p. ill. 26 cm.
ISBN:
9780883858073
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30000010191203 QA43 K42 2008 Open Access Book Book
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Summary

Summary

This third volume of problems from the William Lowell Putnam Competition is unlike the previous two 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 solutions have been compiled from the American Mathematical Monthly, Mathematics Magazine and past competitors. Multiple solutions enhance the understanding of the audience, explaining techniques that have relevance to more than the problem at hand. In addition, the book contains suggestions for further reading, a hint to each problem, separate from the full solution, and background information about the competition. The book will appeal to students, teachers, professors and indeed anyone interested in problem solving as a gateway to a deep understanding of mathematics.


Reviews 1

Choice Review

Andreescu's 51 "introductory problems'' and 51 "advanced problems,'' all novel, would nicely supplement any university course in combinatorics or discrete mathematics. This volume contains detailed solutions, sometimes multiple solutions, for all the problems, and some solutions offer additional twists for further thought. Kedlaya, Poonen, and Vakil recognize that, just as mastering music means more than merely playing correct notes, mastering mathematics means more than just acquiring a knowledge of theorems and techniques. While most mathematics texts for students contain copious exercises, some easy, some harder, authors generally target their exercises toward the narrow goal of reinforcing of the material just exposited. As such, mathematics students seldom meet open-ended challenges, problems that force them to draw, potentially, on all the tools they have ever acquired, or else, perhaps, just on sheer cleverness. The William Lowell Putnam Mathematical Competition stands as the best-known competitive mathematics examination administered to American students, and every year a team of world-class research mathematicians compiles the questions. Surely every student who plans to sit for the exam should work these problems and study all the offered solutions. But all students will benefit from confronting problem-solving challenges of this difficulty.The USA and International Mathematical Olympiad aims to spotlight the most talented high school mathematics students in the world. Now considered from the vantage of a typical college mathematics student, the test questions which make up these competitions come out of only the most basic mathematics, primarily elementary algebra and plane geometry, but even so, they require a sort of decisive cleverness that few will find they can muster. And here lies their value: away from difficult concepts and new abstractions, the student has the opportunity to contemplate naked ingenuity. Though this slender volume follows on the heels of Istvan Reiman's treatment of all the Olympiads from 1959-99, the new book seems free of the occasional editorial lapses that mar the earlier book. Summing Up: Recommended. All three books--general readers; lower- and upper-division undergraduates; 102 Combinatorial Problems--two-year technical program students and professionals; USA and International Mathematical Olympiads--faculty also. D. V. Feldman University of New Hampshire


Table of Contents

Joseph A. GallianBruce Reznick
Introductionp. vii
1 Structure of this bookp. vii
2 The Putnam Competition over the yearsp. viii
3 Advice to the student readerp. ix
4 Scoringp. x
5 Some basic notationp. xi
6 Acknowledgementsp. xi
Problemsp. 1
Hintsp. 35
Solutionsp. 51
The Forty-Sixth Competition (1985)p. 53
The Forty-Seventh Competition (1986)p. 65
The Forty-Eighth Competition (1987)p. 76
The Forty-Ninth Competition (1988)p. 88
The Fiftieth Competition (1989)p. 101
The Fifty-First Competition (1990)p. 116
The Fifty-Second Competition (1991)p. 135
The Fifty-Third Competition (1992)p. 154
The Fifty-Fourth Competition (1993)p. 171
The Fifty-Fifth Competition (1994)p. 191
The Fifty-Sixth Competition (1995)p. 204
The Fifty-Seventh Competition (1996)p. 217
The Fifty-Eighth Competition (1997)p. 232
The Fifty-Ninth Competition (1998)p. 250
The Sixtieth Competition (1999)p. 262
The Sixty-First Competition (2000)p. 278
Resultsp. 295
Individual Resultsp. 295
Team Resultsp. 301
Putnam Trivia for the Ninetiesp. 307
Answersp. 321
Some Thoughts on Writing for the Putnamp. 311
Bibliographyp. 323
Indexp. 333
About the Authorsp. 337
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