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  • Counterexamples in Analysis

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Counterexamples in Analysis

4.8 out of 5 stars (143)

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These counterexamples deal mostly with the part of analysis known as "real variables." The 1st half of the book discusses the real number system, functions and limits, differentiation, Riemann integration, sequences, infinite series, more. The 2nd half examines functions of 2 variables, plane sets, area, metric and topological spaces, and function spaces. 1962 edition. Includes 12 figures.
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Product details

  • ASIN ‏ : ‎ 0486428753
  • Publisher ‏ : ‎ Dover Publications
  • Publication date ‏ : ‎ June 4, 2003
  • Edition ‏ : ‎ unknown
  • Language ‏ : ‎ English
  • Print length ‏ : ‎ 224 pages
  • ISBN-10 ‏ : ‎ 9780486428758
  • ISBN-13 ‏ : ‎ 978-0486428758
  • Item Weight ‏ : ‎ 2.31 pounds
  • Dimensions ‏ : ‎ 5.51 x 0.59 x 8.46 inches
  • Part of series ‏ : ‎ Dover Books on Mathematics
  • Best Sellers Rank: #387,199 in Books (See Top 100 in Books)
  • Customer Reviews:
    4.8 out of 5 stars (143)

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Bernard R. Gelbaum
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Customer reviews

4.8 out of 5 stars
143 global ratings
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Customers say

Customers find the book informative, with one mentioning it assists in understanding mathematical analysis, and several noting it's particularly useful for students. They also appreciate its value for money, noting it's available for around $10.
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15 customers mention informative, 15 positive, 0 negative
Customers find the book informative and useful for students, with one customer noting it serves as a handy reference and another mentioning it makes important points more clear.
Read this book as a graduate student. I think it is a very useful resource for mathematics teachers and students. Glad that they reprinted it.Read more
Very useful for students. I like to flip through it, and sometimes my professor mentioned examples/counterexamples that were in this book....Read more
Graduate student in Mathematics here. Great resource especially for the student looking for easy examples for qualifying examinations....Read more
This book is an incredible help to those trying to learn analysis....Read more
5 customers mention value for money, 5 positive, 0 negative
Customers find the book to be a good value, with several mentioning it costs only around $10.
...And unlike so many graduate level works this one is a bargain in a well made Dover edition. As one reviewer notes "Just get it".Read more
...When theorems seem too abstract the counterexamples in this incredibly cheap book come to the rescue....Read more
...thing, the explanations are crystal clear and, above all, this book is dirty cheap!...Read more
...The fact that it's only around $10 also makes it handier.Read more

Top reviews from the United States

  • 5 out of 5 stars
    This book helps unfold so many misters where the mind ...
    Reviewed in the United States on August 13, 2015
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    This book helps unfold so many misters where the mind has difficulties in producing examples that are not intuitive.

    What this book taught me later in my professional life: put a lot of effort to break things that are important: methods, software (yes! software), solution paths etc. For example, in software it is important to spend resources to break a code - we can see very well the merits, but it is hard to look under the hood.

    2 people found this helpful
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  • 5 out of 5 stars
    Awesome book!
    Reviewed in the United States on February 14, 2014
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    Ok this is among the best books in real analysis you can find around. The counterexamples are a big help in understanding the real thing, the explanations are crystal clear and, above all, this book is dirty cheap! It's difficult to find a better book for even a heftier sum, this book is a must have for anyone interested in real analysis!

    6 people found this helpful
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  • 5 out of 5 stars
    You can't understand something without counterexamples.
    Reviewed in the United States on September 24, 2009
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    Like the authors warned, I would've liked it if there were some counterexamples I thought of put in the book, but I realize this is technically infeasible.

    Really, this book acts as a handy reference. "Oh, is this true? (look for counterexample) Maybe it is/No it's not." It helps quicken the learning experience quite a bit. The fact that it's only around $10 also makes it handier.

    3 people found this helpful
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  • 4 out of 5 stars
    Minor Issue, but Invaluable
    Reviewed in the United States on March 2, 2017
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    I bought this to get help with limits of step functions. I've primarily looked at Example 24 of Chapter 2.

    Given the need to consider many examples, one can't quibble with a terse presentation. However, in the given example, it's difficult to see how the sequence converging to g_n(x) can be chosen to be "decreasing", as opposed to "non-increasing."

    Overall it's a great book and came to me in great condition!

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  • 5 out of 5 stars
    Genius.
    Reviewed in the United States on September 19, 2021
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    What a fantastic idea for a book. Every math undergrad needs this. Should be required.

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  • 5 out of 5 stars
    Helps real analysis exam using baby Rudin in undergrad
    Reviewed in the United States on April 21, 2018
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    One might question the taste of such a book but helpful in conjunction with baby Rudin to prepare for real analysis test in college on the first exposure.

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  • 5 out of 5 stars
    Classic book, now IN PRINT from Dover
    Reviewed in the United States on September 13, 2007
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    All the positive reviews here are true. This is an awesome book that every serious math student should own, especially graduate students preparing for qualification exams. And unlike so many graduate level works this one is a bargain in a well made Dover edition. As one reviewer notes "Just get it".

    5 people found this helpful
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  • 5 out of 5 stars
    I think it is a very useful resource for mathematics teachers and students
    Reviewed in the United States on September 12, 2016
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    Read this book as a graduate student. I think it is a very useful resource for mathematics teachers and students. Glad that they reprinted it.

    2 people found this helpful
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Top reviews from other countries

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  • 5 out of 5 stars
    Nice book
    Reviewed in Germany on June 5, 2023
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    Good for Students or teachers

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  • 5 out of 5 stars
    A must have reference
    Reviewed in Italy on August 20, 2019
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    Perfect for everytime that one risks to fall into ingenuos intuitions

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  • 5 out of 5 stars
    Una pequeña joya
    Reviewed in Spain on September 6, 2023
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    El libro me ha gustado mucho. Puede resultar muy útil para los estudiantes de Análisis Matemático, y también para los profesores, ya que pueden encontrar ejemplos y contraejemplos apropiados para las clases.

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  • 5 out of 5 stars
    good book for graduate students and teachers of Analysis
    Reviewed in India on April 10, 2021
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    good book for graduate students and teachers of Analysis

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  • 4 out of 5 stars
    Matemática Real
    Reviewed in Brazil on February 6, 2020
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    No estudo de análise real

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