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Understanding Analysis

  • Stephen Abbott

Part of the Undergraduate Texts in Mathematics book series (UTM)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Stephen Abbott
    Pages 1-34
  3. Stephen Abbott
    Pages 35-74
  4. Stephen Abbott
    Pages 75-97
  5. Stephen Abbott
    Pages 99-128
  6. Stephen Abbott
    Pages 129-149
  7. Stephen Abbott
    Pages 151-182
  8. Stephen Abbott
    Pages 183-212
  9. Stephen Abbott
    Pages 213-249
  10. Back Matter
    Pages 251-259

About this book

Introduction

Understanding Analysis outlines an elementary, one-semester course designed to expose students to the rich rewards inherent in taking a mathematically rigorous approach to the study of functions of a real variable. The aim of a course in real analysis should be to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on the questions that give analysis its inherent fascination. Does the Cantor set contain any irrational numbers? Can the set of points where a function is discontinuous be arbitrary? Are derivatives continuous? Are derivatives integrable? Is an infinitely differentiable function necessarily the limit of its Taylor series? In giving these topics center stage, the hard work of a rigorous study is justified by the fact that they are inaccessible without it.

Keywords

Taylor series algebra boundary element method convergence differentiable function function functional integral integration metric space real analysis real number set sets variable

Authors and affiliations

  • Stephen Abbott
    • 1
  1. 1.Mathematics DepartmentMiddlebury CollegeMiddleburyUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-387-21506-8
  • Copyright Information Springer-Verlag New York 2001
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-2866-5
  • Online ISBN 978-0-387-21506-8
  • Series Print ISSN 0172-6056
  • Buy this book on publisher's site
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