Introduction to Classical Mathematics I From the Quadratic Reciproci
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Mathematics and Its Applications
Managing Editor: M. HAZEWINKEL Centre for Mathematics and Computer Science, Amsterdam, The Netherlands
Editorial Board: F. CALOGERO, Universitä degli Studi di Roma, Italy Yu. I. MANIN, Steklov Institute of Mathematics, Moscow, U.S.S.R. M. NIVAT, Universite de Paris VII, Paris, France A. H. G. RINNOOY KAN, Erasmus University, Rotterdam, The Netherlands G. -C. ROTA, M.U., Cambridge, Mass., USA.
Volume 70
Introduction to Classical Mathematics I From the Quadratic Reciprocity Law to the Uniformization Theorem
by
Helmut Koch Karl-Weierstrass-Institut für Mathematik, Berlin, Germany
Translated by John Stillwell
SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.
Library of Congress Cataloging-in-Publication Data Koch, Helmut, 1932[Vom q u a d r a t i s c h e n R e z 1 p r o z 1 t ä t s g e s e t z b i s zum Uniformisierungssatz. English] From t h e q u a d r a t i c r e c i p r o c i t y law t o t h e u n i f o r m i z a t i o n t h e o r e m / by H e l m u t K o c h . p. cm. — ( M a t h e m a t i c s and i t s a p p l i c a t i o n s ; v. 7 0 ) R e z i p r o z i t ä t s g e s e t z b i s zum T r a n s l a t i o n o f : Vom q u a d r a t i s c h e ? Uniformisierungssatz. At head o f t i t l e : I n t r o d u c t i o n t o c l a s s i c a l m a t h e m a t i c s I . I n c l u d e s b i b l i o g r a p h i c a l r e f e r e n c e s and i n d e x e s . ISBN 978-0-7923-1238-3 ISBN 978-94-011-3218-3 (eBook) DOI 10.1007/978-94-011-3218-3 1. M a t h e m a t i c s . I.Title. I I . Title: Introduction to classical mathematics I . I I I .T i t l e : I n t r o d u c t i o n t o c l a s s i c a l mathematics 1. I V . S e r i e s : M a t h e m a t i c s and i t s a p p l i c a t i o n s (Kluwer Academic Publishers) v. 7 0 . Q A 3 7 . 2 . K 6 3 1 3 1991 510—dc20 91-12580 ;
ISBN 978-0-7923-1238-3
Printed on acid-free paper This edition is a revised edition of H. Koch, Einführing in die klassische Mathematik I © 1986 Akademie-Verlag Berlin, Germany
All Rights Reserved ©1991 Springer Seience+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 1991 Softcover reprint of the hardcover 1st edition 1991 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner.
SERIES EDITOR'S PREFACE
6Et moi, ..., si j'avait su comment en revenir, je n'y serais point alle.' Jules Verne
One service mathematics has rendered the human mce. It has put common sense back where it belongs, on the topmost shelf nCllt to the dusty canister labelled 'discarded non-
The series is divergent; therefore we may be able to do something with it. O. Heaviside
sense'.
Eric T. Bell
Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and nonlinearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other scien
