Skip to main content
SpringerLink
Log in
Birkhäuser
Book cover

From Classical to Modern Analysis

  • Textbook
  • © 2018

Overview

Authors:
  1. Rinaldo B. Schinazi

    1. Department of Mathematics, University of Colorado, Colorado Springs, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Guides undergraduate students from calculus to measure theory and the Lebesgue integral

  • Provides a self-contained presentation of metric spaces and their topology tailored for first-time students of real analysis

  • Includes cumulative exercises that prepare students for real analysis’s many applications

  • 17k Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 69.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (15 chapters)

  1. Front Matter

    Pages i-xii
    Download chapter PDF

  2. Number Systems

    • Rinaldo B. Schinazi
    Pages 1-17

  3. Sequences of Real Numbers

    • Rinaldo B. Schinazi
    Pages 19-38

  4. Limits Superior and Inferior of a Sequence

    • Rinaldo B. Schinazi
    Pages 39-53

  5. Numerical Series

    • Rinaldo B. Schinazi
    Pages 55-76

  6. Convergence of Functions

    • Rinaldo B. Schinazi
    Pages 77-98

  7. Power Series

    • Rinaldo B. Schinazi
    Pages 99-114

  8. Metric Spaces

    • Rinaldo B. Schinazi
    Pages 115-135

  9. Topology in a Metric Space

    • Rinaldo B. Schinazi
    Pages 137-153

  10. Continuity on Metric Spaces

    • Rinaldo B. Schinazi
    Pages 155-166

  11. Measurable Sets and Measurable Functions

    • Rinaldo B. Schinazi
    Pages 167-181

  12. Measures

    • Rinaldo B. Schinazi
    Pages 183-195

  13. The Lebesgue Integral

    • Rinaldo B. Schinazi
    Pages 197-228

  14. Integrals with Respect to Counting Measures

    • Rinaldo B. Schinazi
    Pages 229-234

  15. Riemann and Lebesgue Integrals

    • Rinaldo B. Schinazi
    Pages 235-241

  16. Modes of Convergence

    • Rinaldo B. Schinazi
    Pages 243-266

  17. Back Matter

    Pages 267-270
    Download chapter PDF
Back to top

Keywords

About this book

This innovative textbook bridges the gap between undergraduate analysis and graduate measure theory by guiding students from the classical foundations of analysis to more modern topics like metric spaces and Lebesgue integration. Designed for a two-semester introduction to real analysis, the text gives special attention to metric spaces and topology to familiarize students with the level of abstraction and mathematical rigor needed for graduate study in real analysis. Fitting in between analysis textbooks that are too formal or too casual, From Classical to Modern Analysis is a comprehensive, yet straightforward, resource for studying real analysis.


To build the foundational elements of real analysis, the first seven chapters cover number systems, convergence of sequences and series, as well as more advanced topics like superior and inferior limits, convergence of functions, and metric spaces. Chapters 8 through 12 explore topology in and continuity on metric spaces and introduce the Lebesgue integrals. The last chapters are largely independent and discuss various applications of the Lebesgue integral. 


Instructors who want to demonstrate the uses of measure theory and explore its advanced applications with their undergraduate students will find this textbook an invaluable resource. Advanced single-variable calculus and a familiarity with reading and writing mathematical proofs are all readers will need to follow the text. Graduate students can also use this self-contained and comprehensive introduction to real analysis for self-study and review. 

Reviews

“This textbook is designed for a two-semester introductory course on real analysis, and its unique feature is that it focuses on both elementary and advanced topics. … the book is written in an accessible and easy to follow style.” (Antonín Slavík, zbMATH 1408.26001, 2019)

Authors and Affiliations

  • Department of Mathematics, University of Colorado, Colorado Springs, USA

    Rinaldo B. Schinazi

About the author

Rinaldo Schinazi is a Professor of Mathematics at the University of Colorado, USA.

Bibliographic Information

  • Book Title: From Classical to Modern Analysis

  • Authors: Rinaldo B. Schinazi

  • DOI: https://doi.org/10.1007/978-3-319-94583-5

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing AG, part of Springer Nature 2018

  • Hardcover ISBN: 978-3-319-94582-8Published: 04 October 2018

  • Softcover ISBN: 978-3-030-06879-0Published: 03 January 2019

  • eBook ISBN: 978-3-319-94583-5Published: 21 September 2018

  • Edition Number: 1

  • Number of Pages: XII, 270

  • Number of Illustrations: 1 b/w illustrations

  • Topics: Functional Analysis, Real Functions, Measure and Integration

Publish with us

Policies and ethics

Back to top

Search

Navigation