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Real Analysis for the Undergraduate

With an Invitation to Functional Analysis

  • Matthew A. Pons

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Matthew A. Pons
    Pages 1-54
  3. Matthew A. Pons
    Pages 55-98
  4. Matthew A. Pons
    Pages 99-135
  5. Matthew A. Pons
    Pages 137-182
  6. Matthew A. Pons
    Pages 183-225
  7. Matthew A. Pons
    Pages 227-274
  8. Matthew A. Pons
    Pages 275-323
  9. Matthew A. Pons
    Pages 325-349
  10. Matthew A. Pons
    Pages 351-396
  11. Back Matter
    Pages 397-409

About this book

Introduction

This undergraduate textbook introduces students to the basics of real analysis, provides an introduction to more advanced topics including measure theory and Lebesgue integration, and offers an invitation to functional analysis. While these advanced topics are not typically encountered until graduate study, the text is designed for the beginner. The author’s engaging style makes advanced topics approachable without sacrificing rigor. The text also consistently encourages the reader to pick up a pencil and take an active part in the learning process. Key features include: - examples to reinforce theory; - thorough explanations preceding definitions, theorems and formal proofs; - illustrations to support intuition; - over 450 exercises designed to develop connections between the concrete and abstract. This text takes students on a journey through the basics of real analysis and provides those who wish to delve deeper the opportunity to experience mathematical ideas that are beyond the standard undergraduate curriculum.

Keywords

Functional Analysis Integrals Lebesgue Theory Limits Real Analysis

Authors and affiliations

  • Matthew A. Pons
    • 1
  1. 1.North Central CollegeNapervilleUSA

Bibliographic information