Nonstandard analysis is a useful tool which can be used to prove a number of results in analysis. Question Can it also be used to prove results in computable or constructive …

Let $\mathfrak{M} = \langle R, +,\times,> \rangle$ be such that $R$ is the set of real numbers and $\mathfrak{M} \models RA^1$ (the first-order axioms for the reals). Do we have ch …

Which methods are available for computing a multidimensional integral with Delta distributions (in case one cannot sample them explicitly)? PS: This question correlates with this …

Can anyone give a simple example of a sequence that converges, but there's no computable function that gives $N$ as a function of $\epsilon$, i.e., the modulus of convergence is no …

On a mailing list (math-fun) that I subscribe to Dan Asimov asked what's the most efficient way to calculate the leading decimal digits (say 10 of them) of $(p/q)^n \bmod 1$ where …

Call a computable function a total function $\mathbb{R} \to \mathbb{R}$, for which there exists a Turing machine outputting arbitrary close approximation to $f(x)$ given arbitrary …

Let $f_{=}$ be a function from $\mathbb{R}^{2}$ be defined as follows: (1) if $x = y$ then $f_{=}(x,y) = 1$; (2) $f_{x,y} = 0$ otherwise. I would like to have a proof for / a ref …

Does anyone know of an easily-describable distribution on $[0,1]$ with a density $p$ (with respect to Lebesgue measure) that satisfies the following properties: $p$ is $C^\infty$ …