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For questions related to teaching mathematics. For questions in Mathematics Education as a scientific discipline there is also the tag mathematics-education. Note you may also ask your question on http://matheducators.stackexchange.com/.

12 votes

Why do we need random variables?

Let $\Omega_n$ be the set of equivalence relations on $\{0,1,2,\dots,n-1\}$, each eq. rel. being equally likely. Let $X$ be the number of classes, and $Y$ the size of the largest class. Note that whe …
Bjørn Kjos-Hanssen's user avatar
25 votes
Accepted

Languages beyond enumerable

Yes, for starters there is the arithmetical hierarchy, where enumerable = $\Sigma^0_1$ and it continues $\Pi^0_1$, $\Delta^0_2$, $\Sigma^0_2$ etc. See also the Computability Menagerie.
Bjørn Kjos-Hanssen's user avatar
3 votes
Accepted

Which universities teach true infinitesimal calculus?

Since you mentioned University of Hawaii -- David Ross regularly teaches nonstandard analysis and infinitesimal calculus at University of Hawaii in various forms, for instance MATH 649K (a regular …
2 votes

Teaching stochastic calculus to students who know no measure theory (or PDE, or...)

In addition to Steve Shreve's "Stochastic Calculus for Finance II: Continuous time Models" you should definitely use Steve Shreve's "Stochastic Calculus for Finance I" about the binomial discrete time …
Bjørn Kjos-Hanssen's user avatar