Basic Real Analysis

  • Houshang H. Sohrab

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Houshang H. Sohrab
    Pages 1-36
  3. Houshang H. Sohrab
    Pages 37-84
  4. Houshang H. Sohrab
    Pages 85-112
  5. Houshang H. Sohrab
    Pages 113-155
  6. Houshang H. Sohrab
    Pages 157-207
  7. Houshang H. Sohrab
    Pages 209-249
  8. Houshang H. Sohrab
    Pages 251-295
  9. Houshang H. Sohrab
    Pages 297-350
  10. Houshang H. Sohrab
    Pages 351-393
  11. Houshang H. Sohrab
    Pages 395-430
  12. Houshang H. Sohrab
    Pages 431-465
  13. Houshang H. Sohrab
    Pages 467-529
  14. Back Matter
    Pages 531-559

About this book

Introduction

One of the bedrocks of any mathematics education, the study of real analysis introduces students both to mathematical rigor and to the deep theorems and counterexamples that arise from such rigor: for instance, the construction of number systems, the Cantor Set, the Weierstrass nowhere differentiable function, and the Weierstrass approximation theorem. Basic Real Analysis is a modern, systematic text that presents the fundamentals and touchstone results of the subject in full rigor, but in a style that requires little prior familiarity with proofs or mathematical language.

Key features include:

* A broad view of mathematics throughout the book

* Treatment of all concepts for real numbers first, with extensions to metric spaces later, in a separate chapter

* Elegant proofs

* Excellent choice of topics

* Numerous examples and exercises to enforce methodology; exercises integrated into the main text, as well as at the end of each chapter

* Emphasis on monotone functions throughout

* Good development of integration theory

* Special topics on Banach and Hilbert spaces and Fourier series, often not included in many courses on real analysis

* Solid preparation for deeper study of functional analysis

* Chapter on elementary probability

* Comprehensive bibliography and index

* Solutions manual available to instructors upon request

By covering all the basics and developing rigor simultaneously, this introduction to real analysis is ideal for senior undergraduates and beginning graduate students, both as a classroom text or for self-study. With its wide range of topics and its view of real analysis in a larger context, the book will be appropriate for more advanced readers as well.

Keywords

Arithmetic Cardinal number Counting Equivalence calculus fundamental theorem ksa measure theory real analysis set theory

Authors and affiliations

  • Houshang H. Sohrab
    • 1
  1. 1.Mathematics DepartmentTowson UniversityTowsonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-8176-8232-3
  • Copyright Information Birkhäuser Boston 2003
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6503-0
  • Online ISBN 978-0-8176-8232-3
  • About this book