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  • Textbook
  • © 2010

A Problem Book in Real Analysis

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  • Helps instructors enhance lectures with problems beyond the classroom

  • Helps prepare students for examinations

  • Text encourages students to find different solutions to problems than those presented

  • Includes supplementary material: sn.pub/extras

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

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USD 54.99
Price excludes VAT (USA)
  • ISBN: 978-1-4419-1296-1
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD 69.99
Price excludes VAT (USA)
Hardcover Book
USD 99.99
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Table of contents (11 chapters)

  1. Front Matter

    Pages i-vii
  2. Elementary Logic and Set Theory

    • Asuman G. Aksoy, Mohamed A. Khamsi
    Pages 1-19
  3. Real Numbers

    • Asuman G. Aksoy, Mohamed A. Khamsi
    Pages 21-39
  4. Sequences

    • Asuman G. Aksoy, Mohamed A. Khamsi
    Pages 41-62
  5. Limits of Functions

    • Asuman G. Aksoy, Mohamed A. Khamsi
    Pages 63-76
  6. Continuity

    • Asuman G. Aksoy, Mohamed A. Khamsi
    Pages 77-96
  7. Differentiability

    • Asuman G. Aksoy, Mohamed A. Khamsi
    Pages 97-126
  8. Integration

    • Asuman G. Aksoy, Mohamed A. Khamsi
    Pages 127-158
  9. Series

    • Asuman G. Aksoy, Mohamed A. Khamsi
    Pages 159-180
  10. Metric Spaces

    • Asuman G. Aksoy, Mohamed A. Khamsi
    Pages 181-195
  11. Fundamentals of Topology

    • Asuman G. Aksoy, Mohamed A. Khamsi
    Pages 197-221
  12. Sequences and Series of Functions

    • Asuman G. Aksoy, Mohamed A. Khamsi
    Pages 223-247
  13. Back Matter

    Pages 1-6

About this book

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

Reviews

From the reviews:

“Spread out over 11 chapters, this is a collection of 319 problems in what used to be called Advanced Calculus. … The authors see their book primarily as an aid to undergraduates … but I view it as being helpful to teachers in supplementing their courses or in preparing exams. … However, kept on a course reserve shelf of an academic library, the book under review might entice and benefit the more dedicated student. It certainly merits the attention of instructors of elementary analysis.” (Henry Ricardo, The Mathematical Association of America, June, 2010)

“A very readable collection of interesting problems of varying levels of difficulty. It is intended to build a bridge between ordinary high school or undergraduate exercises and more difficult and abstract concepts or problems. The book is so delightfully written that anyone who simply likes working on challenging problems could read it independently. … recommends this book to all students curious about elementary real analysis and how to learn it through solving problems. … a welcome resource for organizing their activities at a good level.” (Vicenţiu D. Rădulescu, Zentralblatt MATH, Vol. 1186, 2010)

Authors and Affiliations

  • Dept. Mathematics & Computer Science, Claremont McKenna College, Claremont, U.S.A.

    Asuman G. Aksoy

  • Dept. Mathematical Sciences, University of Texas, El Paso (UTEP), El Paso, U.S.A.

    Mohamed A. Khamsi

Bibliographic Information

  • Book Title: A Problem Book in Real Analysis

  • Authors: Asuman G. Aksoy, Mohamed A. Khamsi

  • Series Title: Problem Books in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4419-1296-1

  • Publisher: Springer New York, NY

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

  • Copyright Information: Springer-Verlag New York 2010

  • Hardcover ISBN: 978-1-4419-1295-4

  • Softcover ISBN: 978-1-4939-5109-3

  • eBook ISBN: 978-1-4419-1296-1

  • Series ISSN: 0941-3502

  • Series E-ISSN: 2197-8506

  • Edition Number: 1

  • Number of Pages: X, 254

  • Topics: Real Functions, Analysis

Buying options

eBook
USD 54.99
Price excludes VAT (USA)
  • ISBN: 978-1-4419-1296-1
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD 69.99
Price excludes VAT (USA)
Hardcover Book
USD 99.99
Price excludes VAT (USA)