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Understanding Analysis【Stephen Abbott 】
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This book outlines an elementary, one-semester course which exposes students to both the process of rigor, and the rewards inherent in taking an axiomatic approach to the study of functions of a real variable. The aim of a course in real analysis should be to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on questions which give analysis its inherent fascination.
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Undergraduate Texts in Mathematics
StephenAbbott
Understanding
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
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 con-
cepts as well as exercises that strengthen understanding.
More information about this series at http://www.springer.com/series/666
Stephen Abbott
Understanding Analysis
Second Edition
123
Stephen Abbott
Department of Mathematics
Middlebury College
Middlebury, VT, USA
ISSN 0172-6056 ISSN 2197-5604 (electronic)
Undergraduate Texts in Mathematics
ISBN 978-1-4939-2711-1 ISBN 978-1-4939-2712-8 (eBook)
DOI 10.1007/978-1-4939-2712-8
Library of Congress Control Number: 2015937969
Mathematics Subject Classification (2010): 26-01
Springer New York Heidelberg Dordrecht London
© Springer Science+Business Media New York 2001, 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 Science+Business Media LLC New York is part of Springer Science+Business Media (www.
springer.com)
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