56

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?

Regards

Martin Sleziak
  • 50,316
  • 18
  • 169
  • 342
Amzoti
  • 55,120
  • 25
  • 75
  • 108

3 Answers3

46

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

Michael Greinecker
  • 29,902
  • 5
  • 71
  • 127
8

There is a new book on counterexamples in measure theory:

"Counterexamples in Measure and Integration" by René L. Schilling, Franziska Kühn. Cambridge University Press, 2021.

saz
  • 112,783
  • 10
  • 122
  • 213
0

No idea if it's any good, but here's a new one:

Counterexamples in Operator Theory - Mohammed Hichem Mortad

ajd138
  • 45
  • 1
  • 5
  • 1
    Your answer could be improved with additional supporting information. Please [edit] to add further details, such as citations or documentation, so that others can confirm that your answer is correct. You can find more information on how to write good answers [in the help center](/help/how-to-answer). – Community Jun 01 '22 at 02:49