TAILIEUCHUNG - The William Lowell Putnam Mathematical Competition 1985–2000 Problems, Solutions, and Commentary

The William Lowell Putnam Mathematical Competition is the premier undergraduate mathematical competition in North America. This volume contains problems from the years 1985-2000, 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 | I I The William Lowell Putnam Mathematical Competition 1985-2000 Problems Solutions and Commentary i I I Reproduction. The work may be reproduced by any means for educational and scientific purposes without fee or permission with the exception of reproduction by services that collect fees for delivery of documents. In any reproduction the original publication by the Publisher must be credited in the following manner First published in The William Lowell Putnam Mathematical Competition 1985-2000 Problems Solutions and Commentary 2002 by the Mathematical Association of America and the copyright notice in proper form must be placed on all copies. Ravi Vakil s photo on p. 337 is courtesy of Gabrielle Vogel. 2002 by The Mathematical Association of America Incorporated Library of Congress Catalog Card Number 2002107972 ISBN 0-88385-807-X Printed in the United States of America Current Printing last digit 10 987654321 ii I I 1 The William Lowell Putnam Mathematical Competition 1985-2000 Problems Solutions and Commentary Kiran S. Kedlaya University of California Berkeley Bjorn Poonen University of California Berkeley Ravi Vakil Stanford University Published and distributed by The Mathematical Association of America .

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