The Colorado Mathematical Olympiad and Further Explorations From the
This book presents the 20-year account of the Colorado Mathematical Olympiad — its dreams and rewards, hard work and conflict. It features more than just original wonderful problems and their ingenious solutions; it tells a compelling story involving the
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Alexander Soifer
The Colorado Mathematical Olympiad and Further Explorations From the Mountains of Colorado to the Peaks of Mathematics With over 185 Illustrations Forewords by Philip L. Engel Paul Erd˝os Martin Gardner Branko Gr¨unbaum Peter D. Johnson, Jr. and Cecil Rousseau
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Alexander Soifer College of Letters, Arts and Sciences University of Colorado at Colorado Springs 1420 Austin Bluffs Parkway Colorado Springs, CO 80918 USA [email protected]
ISBN: 978-0-387-75471-0 e-ISBN: 978-0-387-75472-7 DOI: 10.1007/978-0-387-75472-7 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2011925380 c Alexander Soifer 2011 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), 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 now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science +Business Media (www.springer.com)
To all those people throughout the world, who create Olympiads for new generations of mathematicians.
Forewords to The Colorado Mathematical Olympiad and Further Explorations
We live in an age of extreme specialization – in mathematics as well as in all other sciences, in engineering, in medicine. Hence, to say that probably 90% of mathematicians cannot understand 90% of mathematics currently published is, most likely, too optimistic. In contrast, even a pessimist would have to agree that at least 90% of the material in this book is readily accessible to, and understandable by 90% of students in middle and high schools. However, this does not mean that the topics are trivial – they are elementary in the sense that they do not require knowledge of lots of previously studied material, but are sophisticated in requiring attention, concentration, and thinking that is not fettered by preconceptions. The organization in groups of five problems for each of the “Olympiads”, for which the participants were allowed four hours, hints at the difficulty of finding complete solutions. I am convinced that most professional mathematicians would be hard pressed to solve a set of five problems in two hours, or even four. There are many collections of problems, for “Olympiads” of various levels, as well as problems in a variety of journals. What sets this book apart from the “competition” are several aspects that deserve to be noted. vi
Forewords
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• The serenity and enthusiasm with which the problems, and their solutions, are presented; • The absence of prerequ
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