Real Mathematical Analysis
Based on an honors course taught by the author at UC Berkeley, this introduction to undergraduate real analysis gives a different emphasis by stressing the importance of pictures and hard problems. Topics include: a natural construction of the real number
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Charles C. Pugh
Real Mathematical Analysis Second Edition
Undergraduate Texts in Mathematics
Undergraduate Texts in Mathematics Series Editors: Sheldon Axler San Francisco State University, San Francisco, CA, USA Kenneth Ribet University of California, Berkeley, CA, USA
Advisory Board: Colin Adams, Williams College David A. Cox, Amherst College Pamela Gorkin, Bucknell University Roger E. Howe, Yale University Michael Orrison, Harvey Mudd College Lisette G. de Pillis, Harvey Mudd College Jill Pipher, Brown University Fadil Santosa, University of Minnesota
Undergraduate Texts in Mathematics are generally aimed at third- and fourth-year undergraduate mathematics students at North American universities. These texts strive to provide students and teachers with new perspectives and novel approaches. The books include motivation that guides the reader to an appreciation of interrelations among different aspects of the subject. They feature examples that illustrate key concepts as well as exercises that strengthen understanding.
More information about this series at http://www.springer.com/series/666
Charles C. Pugh
Real Mathematical Analysis Second Edition
Charles C. Pugh Department of Mathematics University of California Berkeley, CA, USA
ISSN 0172-6056 ISSN 2197-5604 (electronic) Undergraduate Texts in Mathematics ISBN 978-3-319-17770-0 ISBN 978-3-319-17771-7 (eBook) DOI 10.1007/978-3-319-17771-7 Library of Congress Control Number: 2015940438 Mathematics Subject Classification (2010): 26-xx Springer Cham Heidelberg New York Dordrecht London © Springer International Publishing Switzerland 2002, 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)
To Candida and to the students who have encouraged me – – especially A.W., D.H., and M.B.
Preface Was plane geometry your favorite math course in high school? Did you like proving theo
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