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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/.
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.
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 …
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 …