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Undergraduate Texts in Mathematics

Real Mathematical Analysis

Authors: Pugh, Charles Chapman

  • Elucidates abstract concepts and salient points in proofs with over 150 detailed illustrations
  • Treats the rigorous foundations of both single and multivariable Calculus
  • Gives an intuitive presentation of Lebesgue integration using the undergraph approach of Burkill
  • Includes over 500 exercises that are interesting and thought-provoking, not merely routine
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eBook $44.99
price for USA (gross)
  • ISBN 978-3-319-17771-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $59.99
price for USA
  • ISBN 978-3-319-17770-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $59.99
price for USA
  • ISBN 978-3-319-33042-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

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 numbers, four-dimensional visualization, basic point-set topology, function spaces, multivariable calculus via differential forms (leading to a simple proof of the Brouwer Fixed Point Theorem), and a pictorial treatment of Lebesgue theory. Over 150 detailed illustrations elucidate abstract concepts and salient points in proofs. The exposition is informal and relaxed, with many helpful asides, examples, some jokes, and occasional comments from mathematicians, such as Littlewood, Dieudonné, and Osserman. This book thus succeeds in being more comprehensive, more comprehensible, and more enjoyable, than standard introductions to analysis.

New to the second edition of Real Mathematical Analysis is a presentation of Lebesgue integration done almost entirely using the undergraph approach of Burkill. Payoffs include: concise picture proofs of the Monotone and Dominated Convergence Theorems, a one-line/one-picture proof of Fubini's theorem from Cavalieri’s Principle, and, in many cases, the ability to see an integral result from measure theory. The presentation includes Vitali’s Covering Lemma, density points — which are rarely treated in books at this level — and the almost everywhere differentiability of monotone functions. Several new exercises now join a collection of over 500 exercises that pose interesting challenges and introduce special topics to the student keen on mastering this beautiful subject.

About the authors

Charles C. Pugh is Professor Emeritus at the University of California, Berkeley. His research interests include geometry and topology, dynamical systems, and normal hyperbolicity.

Table of contents (6 chapters)

Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-3-319-17771-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $59.99
price for USA
  • ISBN 978-3-319-17770-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $59.99
price for USA
  • ISBN 978-3-319-33042-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Real Mathematical Analysis
Authors
Series Title
Undergraduate Texts in Mathematics
Copyright
2015
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-17771-7
DOI
10.1007/978-3-319-17771-7
Hardcover ISBN
978-3-319-17770-0
Softcover ISBN
978-3-319-33042-6
Series ISSN
0172-6056
Edition Number
2
Number of Pages
XI, 478
Number of Illustrations and Tables
1 illustrations in colour
Topics