The Real and the Complex: A History of Analysis in the 19th Century
This book contains a history of real and complex analysis in the nineteenth century, from the work of Lagrange and Fourier to the origins of set theory and the modern foundations of analysis. It studies the works of many contributors including Gauss, Cauc
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Jeremy Gray
The Real and the Complex: A History of Analysis in the 19th Century
Springer Undergraduate Mathematics Series Advisory Board M.A.J. Chaplain, University of St. Andrews, Dundee, UK K. Erdmann, University of Oxford, Oxford, England, UK A. MacIntyre, Queen Mary University of London, London, England, UK E. Süli, University of Oxford, Oxford, England, UK M.R. Tehranchi, University of Cambridge, Cambridge, England, UK J.F. Toland, University of Cambridge, Cambridge, England, UK
More information about this series at http://www.springer.com/series/3423
Jeremy Gray
The Real and the Complex: A History of Analysis in the 19th Century
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Jeremy Gray Department of Mathematics and Statistics The Open University Milton Keynes UK and University of Warwick Coventry UK
Whilst we have made considerable efforts to contact all holders of copyright material contained in this book we have failed to locate some of them. Should holders wish to contact the Publisher, we will make every effort to come to some arrangement with them. ISSN 1615-2085 ISSN 2197-4144 (electronic) Springer Undergraduate Mathematics Series ISBN 978-3-319-23714-5 ISBN 978-3-319-23715-2 (eBook) DOI 10.1007/978-3-319-23715-2 Library of Congress Control Number: 2015950876 Mathematics Subject Classification (2010): 01A55, 26-03, 30-03 Springer Cham Heidelberg New York Dordrecht London © Springer International Publishing Switzerland 2015 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer International Publishing AG Switzerland is part of Springer Science+Business Media (www.springer.com)
Preface
It is the task of the historian to give back to the past its sense of the future. —unattributed quote.
This book is based on a course on the history of mathematical analysis that I taught for four years to third- and fourth-year undergraduates at the University of Warwick from 2005 to 2008. It concentrates on the history of topics in analysis, starting with three topics that were act
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