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've often wondered if it would be feasible to have a searchable online database of worked out "first nontrivial examples". Users could upload their examples to the database and these could be community-refereed much like answers from this site or MathOverflow.

Certainly many textbooks contain such examples for undergrad material, but for research-level stuff this becomes more difficult to come by. It would be an efficient thing to crowdsource.

This question is a poor substitute for the above, but:

What are some hyperlinks to fully-worked "simplest nontrivial examples"?

In your answer, please indicate what your link will provide a basic nontrivial example of. If the example appears in a paper, please provide the page number and label for the example that is given in the paper.

share|improve this question

1 Answer 1

Similar questions have come up on MathOverflow. Here are some links.

http://mathoverflow.net/questions/16829/what-are-your-favorite-instructional-counterexamples has 46 answers.

http://mathoverflow.net/questions/29006/counterexamples-in-algebra has 39 answers.

http://mathoverflow.net/questions/68680/counterexamples-in-pde has 9 answers.

http://mathoverflow.net/questions/4994/fundamental-examples has 128 answers.

http://mathoverflow.net/questions/37525/what-is-your-favorite-isomorphism has 17 answers.

http://mathoverflow.net/questions/27357/what-are-your-favorite-finite-non-commutative-rings has 4 answers.

http://mathoverflow.net/questions/55365/counterexamples-in-algebraic-topology has 5 answers, but there are also a lot of examples in the question statement itself.

There are surely more, but that's a good start, I think.

share|improve this answer
There is also examples in arithmetic geometry (but there are only 3 answers at the moment) mathoverflow.net/questions/91546/arithmetic-geometry-examples –  Álvaro Lozano-Robledo Apr 21 '12 at 1:22
This is a good answer, Gerry. Exactly fits the purpose of the question...to consolidate. –  Jon Bannon Apr 21 '12 at 9:55

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.