Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I have been able to find several counterexample books in some math areas. For example:

$\bullet$ Counterexamples in Analysis, Bernard R. Gelbaum, John M. H. Olmsted

$\bullet$ Counterexamples in Topology, Lynn Arthur Steen, J. Arthur Seebach Jr.

$\bullet$ Counterexamples in Probability and Statistics, Joseph P. Romano, A.F. Siegel

$\bullet$ Counterexamples in Probability and Real Analysis, Gary L. Wise and Eric B. Hall

$\bullet$ Counterexamples in Probability, Jordan M. Stoyanov

Why are there no other examples of books in other math topics (number theory, numerical analysis, DEQs, PDEs, Dynamical Systems, Discrete Math...)?

Is it that it is just not a rich enough area, examples are too trivial, the book wouldn't warrant publishing (low sales), someone just hasn't written one, I missed it or something else?


share|improve this question
Your list is not complete. –  Michael Greinecker Jan 15 '13 at 16:16
Nice question! Maybe, community wiki fits it? –  Ilya Jan 15 '13 at 16:16
@MichaelGreinecker: maybe we can append to the list and include missing items as I was just giving examples and probably missed many. Regards –  Amzoti Jan 15 '13 at 16:20
Great idea...I wish we'd have the opportunity to collect lists, even if Community Wiki, that people can update, modify, add...for many topics! +1 –  amWhy May 21 '13 at 0:14
@amWhy: Agreed, these are very valuable books! Regards –  Amzoti May 21 '13 at 5:46
add comment

1 Answer

up vote 18 down vote accepted

The following list of titles, all of which can be found on Amazon, may help to answer the question:

  • Counterexamples in Optimal Control Theory

  • Lectures on Counterexamples in Several Complex Variables

  • Counterexamples in Topological Vector Spaces

  • Theorems and Counterexamples in Mathematics

  • Counterexamples in Calculus

  • Convex Functions: Constructions, Characterizations and Counterexamples

  • Surprises and Counterexamples in Real Function Theory

  • Examples and Counterexamples in Graph Theory

  • Counter-Examples In Differential Equations And Related Topics

share|improve this answer
add comment

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.