Real Analysis for the Undergraduate

With an Invitation to Functional Analysis

Authors: Pons, Matthew A.

  • Engaging style makes complex concepts accessible to a broad audience
  • Examples and illustrations accompany formal proofs
  • Over 450 exercises help readers develop connections between the concrete and abstract
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  • ISBN 978-1-4614-9638-0
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  • ISBN 978-1-4614-9637-3
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About this Textbook

This undergraduate textbook introduces students to the basics of real analysis, provides an introduction to more advanced topics including measure theory and Lebesgue integration, and offers an invitation to functional analysis. While these advanced topics are not typically encountered until graduate study, the text is designed for the beginner. The author’s engaging style makes advanced topics approachable without sacrificing rigor. The text also consistently encourages the reader to pick up a pencil and take an active part in the learning process. Key features include: - examples to reinforce theory; - thorough explanations preceding definitions, theorems and formal proofs; - illustrations to support intuition; - over 450 exercises designed to develop connections between the concrete and abstract. This text takes students on a journey through the basics of real analysis and provides those who wish to delve deeper the opportunity to experience mathematical ideas that are beyond the standard undergraduate curriculum.

About the authors

Matthew A. Pons is Associate Professor of Mathematics at North Central College.

Reviews

From the book reviews:

“This book is more than just an excellent introduction to real analysis at the undergraduate level. It also provides the basis for students to gain some experience in measure theory, Lebesgue integration, and functional analysis. … Summing Up: Highly recommended. Upper-division undergraduates and above.” (D. P. Turner, Choice, Vol. 52 (2), October, 2014)

“This book contains a reasonably complete exposition of real analysis theory which is needed for beginning undergraduate-level students. It includes basic material connected with this topic as well as more advanced problems. … All the topics are presented thoroughly. The book includes nice graphic illustrations of the problems considered.” (Ryszard J. Paẇlak, Mathematical Reviews, September, 2014)


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Table of contents (9 chapters)

  • The Real Numbers

    Pons, Matthew A.

    Pages 1-54

  • Sequences in ℝ

    Pons, Matthew A.

    Pages 55-98

  • Numerical Series

    Pons, Matthew A.

    Pages 99-135

  • Continuity

    Pons, Matthew A.

    Pages 137-182

  • The Derivative

    Pons, Matthew A.

    Pages 183-225

Buy this book

eBook n/a
  • ISBN 978-1-4614-9638-0
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
Hardcover n/a
  • ISBN 978-1-4614-9637-3
  • Free shipping for individuals worldwide
Softcover n/a
  • ISBN 978-1-4939-4649-5
  • Free shipping for individuals worldwide
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Real Analysis for the Undergraduate
Book Subtitle
With an Invitation to Functional Analysis
Authors
Copyright
2014
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
Distribution Rights
Distribution rights for India: Researchco Book Centre, New Delhi, India
eBook ISBN
978-1-4614-9638-0
DOI
10.1007/978-1-4614-9638-0
Hardcover ISBN
978-1-4614-9637-3
Softcover ISBN
978-1-4939-4649-5
Edition Number
1
Number of Pages
XVIII, 409
Number of Illustrations and Tables
43 b/w illustrations
Topics