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Questions designed to generate a "big list" of certain results, examples, conjectures, etc. via many individual answers, each contributing one or a few instances. Such a question should typically be in Community Wiki mode (CW); after asking, please, flag for moderators attention requesting the question to be made CW.
1
vote
How should one present curl and divergence in an undergraduate multivariable calculus class?
Just another aproach. Even before talking about Stokes theorem, one can consider the problem of "detecting a gradient". If a vector field is a gradient, say
$$F=(F_1,F_2,F_3)=(\partial_x f,\partial_y …
22
votes
Short exact sequences every mathematician should know
I saw $0\to \mathbb Z_p\to \mathbb Z_{p^2}\to \mathbb Z_p\to 0$ as an answer, with $p$ prime, but I will add with $p$ not prime and the particular choice $p=10$,
$$0\to \mathbb Z_{10}\to \mathbb Z_{10 …