文档介绍：Putnam and Beyond
Razvan˘ Gelca
Titu Andreescu
Putnam and Beyond
Razvan˘ Gelca Titu Andreescu
Texas Tech University University of Texas at Dallas
Department of Mathematics and Statistics School of Natural Sciences and Mathematics
MA 229 2601 North Floyd Road
Lubbock, TX 79409 Richardson, TX 75080
USA USA
rgelca@ titu.******@
Cover design by Mary Burgess.
Library of Congress Control Number: 2007923582
ISBN-13: 978-0-387-25765-5 e-ISBN-13: 978-0-387-68445-1
Printed on acid-free paper.
c 2007 Springer Science+Business Media, LLC
All rights reserved. This work may not be translated or copied in whole or in part without the written permission
of the publisher (Springer Science+Business Media LLC, 233 Spring Street, New York, NY 10013, USA) and the
author, except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of
information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology
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The use in this publication of trade names, trademarks, service marks and similar terms, even if they are not identified
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987654321
(JLS/HP)
Life is good for only two things, discovering
mathematics and teaching mathematics.
Siméon Poisson
Contents
Preface ............................................................ xi
A Study Guide ...................................................... xv
1 Methods of Proof ................................................ 1
Argument by Contradiction ...................................... 1
Mathematical Induction ......................................... 3
The Pigeonhole Principle ........................................ 11
Ordered Sets and Extremal Elements .............................. 14
Invariants and Semi-Invariants .