Universitext

Real Analysis: Foundations

Authors: Ovchinnikov, Sergei

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  • Explores the foundations of real analysis using the framework of general ordered fields, demonstrating the multifaceted nature of the area
  • Illustrates the definitions and logical interrelations between core concepts of real analysis, using numerous examples and counterexamples
  • Presents the material in a self-contained manner, featuring three appendices and over 130 exercises
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eBook 37,44 €
price for Spain (gross)
  • ISBN 978-3-030-64701-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 46,79 €
price for Spain (gross)
  • ISBN 978-3-030-64700-1
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this Textbook

This textbook explores the foundations of real analysis using the framework of general ordered fields, demonstrating the multifaceted nature of the area. Focusing on the logical structure of real analysis, the definitions and interrelations between core concepts are illustrated with the use of numerous examples and counterexamples. Readers will learn of the equivalence between various theorems and the completeness property of the underlying ordered field. These equivalences emphasize the fundamental role of real numbers in analysis.

Comprising six chapters, the book opens with a rigorous presentation of the theories of rational and real numbers in the framework of ordered fields. This is followed by an accessible exploration of standard topics of elementary real analysis, including continuous functions, differentiation, integration, and infinite series. Readers will find this text conveniently self-contained, with three appendices included after the main text, covering an overview of natural numbers and integers, Dedekind's construction of real numbers, historical notes, and selected topics in algebra.

Real Analysis: Foundations is ideal for students at the upper-undergraduate or beginning graduate level who are interested in the logical underpinnings of real analysis. With over 130 exercises, it is suitable for a one-semester course on elementary real analysis, as well as independent study.

About the authors

​Sergei Ovchinnikov is Professor Emeritus of Mathematics at San Francisco State University. His other Universitext books are Functional Analysis (2018), Measure, Integral, Derivative (2013), and Graphs and Cubes (2011).

Table of contents (6 chapters)

Table of contents (6 chapters)

Buy this book

eBook 37,44 €
price for Spain (gross)
  • ISBN 978-3-030-64701-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 46,79 €
price for Spain (gross)
  • ISBN 978-3-030-64700-1
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Real Analysis: Foundations
Authors
Series Title
Universitext
Copyright
2021
Publisher
Springer International Publishing
Copyright Holder
The Author(s), under exclusive license to Springer Nature Switzerland AG
eBook ISBN
978-3-030-64701-8
DOI
10.1007/978-3-030-64701-8
Softcover ISBN
978-3-030-64700-1
Series ISSN
0172-5939
Edition Number
1
Number of Pages
XII, 178
Number of Illustrations
13 b/w illustrations
Topics