- 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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- About this Textbook
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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
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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)
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Rational Numbers
Pages 1-30
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Real Numbers
Pages 31-65
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Continuous Functions
Pages 67-86
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Differentiation
Pages 87-106
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Integration
Pages 107-131
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Table of contents (6 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Real Analysis: Foundations
- Authors
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- Sergei Ovchinnikov
- 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
