A Problem Book in Real Analysis

  • Asuman G. Aksoy
  • Mohamed A. Khamsi

Part of the Problem Books in Mathematics book series (PBM)

Table of contents

  1. Front Matter
    Pages i-vii
  2. Asuman G. Aksoy, Mohamed A. Khamsi
    Pages 1-19
  3. Asuman G. Aksoy, Mohamed A. Khamsi
    Pages 21-39
  4. Asuman G. Aksoy, Mohamed A. Khamsi
    Pages 41-62
  5. Asuman G. Aksoy, Mohamed A. Khamsi
    Pages 63-76
  6. Asuman G. Aksoy, Mohamed A. Khamsi
    Pages 77-96
  7. Asuman G. Aksoy, Mohamed A. Khamsi
    Pages 97-126
  8. Asuman G. Aksoy, Mohamed A. Khamsi
    Pages 127-158
  9. Asuman G. Aksoy, Mohamed A. Khamsi
    Pages 159-180
  10. Asuman G. Aksoy, Mohamed A. Khamsi
    Pages 181-195
  11. Asuman G. Aksoy, Mohamed A. Khamsi
    Pages 197-221
  12. Asuman G. Aksoy, Mohamed A. Khamsi
    Pages 223-247
  13. Back Matter
    Pages 1-6

About this book

Introduction

Today, nearly every undergraduate mathematics program requires at least one semester of real analysis. Often, students consider this course to be the most challenging or even intimidating of all their mathematics major requirements. The primary goal of A Problem Book in Real Analysis is to alleviate those concerns by systematically solving the problems related to the core concepts of most analysis courses. In doing so, the authors hope that learning analysis becomes less taxing and more satisfying.

The wide variety of exercises presented in this book range from the computational to the more conceptual and varies in difficulty. They cover the following subjects: set theory; real numbers; sequences; limits of the functions; continuity; differentiability; integration; series; metric spaces; sequences; and series of functions and fundamentals of topology. Furthermore, the authors define the concepts and cite the theorems used at the beginning of each chapter. A Problem Book in Real Analysis is not simply a collection of problems; it will stimulate its readers to independent thinking in discovering analysis.

Prerequisites for the reader are a robust understanding of calculus and linear algebra.

Keywords

Riemann Taylor's theorem analysis elementary logic fundamentals topology improper integral intermediate value theorem limits functions linear algebra mean value theorem real analysis sequences functions series functions set theory upper sum

Authors and affiliations

  • Asuman G. Aksoy
    • 1
  • Mohamed A. Khamsi
    • 2
  1. 1.Dept. Mathematics & Computer ScienceClaremont McKenna CollegeClaremontU.S.A.
  2. 2.Dept. Mathematical SciencesUniversity of Texas, El Paso (UTEP)El PasoU.S.A.

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4419-1296-1
  • Copyright Information Springer Science+Business Media, LLC 2010
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4419-1295-4
  • Online ISBN 978-1-4419-1296-1
  • Series Print ISSN 0941-3502
  • About this book