Problem Books in Mathematics

A Problem Book in Real Analysis

Authors: Aksoy, Asuman G., Khamsi, Mohamed

  • Helps instructors enhance lectures with problems beyond the classroom
  • Helps students prepare for examinations
  • Encourages students to find different solutions to problems than those presented in the text
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Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-1-4419-1296-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $29.99
$59.95 (listprice)
price for USA
valid through June 30, 2017
  • ISBN 978-1-4419-1295-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

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.

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)


Table of contents (11 chapters)

  • Elementary Logic and Set Theory

    Aksoy, Asuman G. (et al.)

    Pages 1-19

  • Real Numbers

    Aksoy, Asuman G. (et al.)

    Pages 21-39

  • Sequences

    Aksoy, Asuman G. (et al.)

    Pages 41-62

  • Limits of Functions

    Aksoy, Asuman G. (et al.)

    Pages 63-76

  • Continuity

    Aksoy, Asuman G. (et al.)

    Pages 77-96

Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-1-4419-1296-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $29.99
$59.95 (listprice)
price for USA
valid through June 30, 2017
  • ISBN 978-1-4419-1295-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
A Problem Book in Real Analysis
Authors
Series Title
Problem Books in Mathematics
Copyright
2010
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York
eBook ISBN
978-1-4419-1296-1
DOI
10.1007/978-1-4419-1296-1
Hardcover ISBN
978-1-4419-1295-4
Series ISSN
0941-3502
Edition Number
1
Number of Pages
X, 254
Topics