Numbers and Geometry
NUMBERS AND GEOMETRY is a beautiful and relatively elementary account of a part of mathematics where three main fields--algebra, analysis and geometry--meet. The aim of this book is to give a broad view of these subjects at the level of calculus, without
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S. Axler F.W. Gehring K.A. Ribet
Springer-Science+ Business Media, LLC
Graduate Texts in Mathematics Readings in Mathematics Ebbinghaus/Hennes/Hirzebruch/Koecher/Mainzer/NeukirchIPresteVRemmert: Numbers FultonIHarris: Representation Theory: A First Course Remmert: Theory of Complex Functions Walter: Ordinary Differential Equations
Undergraduate Texts in Mathematics Readings in Mathematics Anglin: Mathematics: A Concise History and Philosophy AngliniLambek: The Heritage of Thales Bressoud: Second Year Calculus Hairer/Wanner: Analysis by Its History HammerliniHoffmann: Numerical Mathematics Isaac: The Pleasures ofProbability Laubenbacher/Pengelley: Mathematical Expeditions: Chronicles by the Explorers Samuel: Projective Geometry Stillwell: Numbers and Geometry Toth: Glimpses ofAlgebra and Geometry
John Stillwell
Numbers and Geometry With 95 Illustrations
Springer
John Stillwell Monash University Department of Mathematics Clayton, Victoria 3168 Australia
Editorial Board S. Axler Department of Mathematics Michigan State University East Lansing, MI 48824 USA
F.w. Gehring
K.B. Ribet Department of Mathematics University ofCalifomia at Berkeley Berkeley, CA 94720
Department of Mathematics University of Michigan Ann Arbor; MI 48109 USA
USA
Cover illustration of the exponential map by Tristan Needham. Reprinted from Visual Complex Analysis by permission ofTristan Needham and Oxford University Press, 1997. Mathematics Subject Classification (2000): II-O 1, 51-01 Library of Congress Cataloging-in-Publication Data Stillwell, J ohn. Numbers and geometry p. cm. - (Undergraduate texts in mathematics. Readings in mathematics) Includes bibliographica1 references (p. ) and index. ISBN 978-1-4612-6867-3 ISBN 978-1-4612-0687-3 (eBook) DOI 10.1007/978-1-4612-0687-3 1. Mathematics. 1. Title. II. Series. QA39.2.S755 1997 510-dc21 97-22858 CIP Printed on acid-free paper.
© 1998 Springer Science+Business Media New York Originally published by Springer-Verlag New York Berlin Heidelberg in 1998 Softcover reprint of the hardcover lst edition 1998
Ali rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+ Bus.Îness Media, LLC) 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 here after developed is forbidden. The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the former are not especia1ly identified, is not to be taken as a sign that such names, as understood by the Thade Marks and Merchandise Marks Act, may accordinglybe used freelyby anyone. Production rnanaged by Lesley Poliner; manufacturing supervised by Joe Quatela. Photocomposed copy prepared from the author's 1EX files. 98765432 ISBN 978-1-4612-6867-3
SPIN 10764915
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Preface
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