For awhile I was under the impression that the rough asymptotic expression for the time to collect $m$ coupons from a set of $N$ unique elements was something like $E(T) \approx \T …

Let $M$ be a $n$-dimensional smooth connected not compact manifold s.t. groups (singular cohomology) $H^{k}(M,\mathbb{Z})$ are finitely generated for $k\geq 0$. Can we find …

I am looking for all finite groups $G$ such that for each subgroup $H$ of $G$ and each automorphism $\sigma$ of $H$ there exists an automorphism $\psi$ of $G$ whose restriction to …

if $f$ is a positive function such that $\int_0^\infty f$ converges, show that there is another function $g$ such that $\lim_{x \to \infty} \frac {g(x)} {f(x)} = \infty$ and $\int_ …

Describe your experiences with the Moore method. What are its advantages and disadvantages?

Let us consider a sequence of real valued functions of real variable $x$, defined as $f_n = g_n\;\;\;\;\;\;\;\;\;\;\;$ when $ a \leq x < b $ $f_n = g_n + \frac{1}{n}\;\;\;\;\;$ …

Hello Everyone, This might be a question people already asked or is obvious to experts, or is not appropriate for this forum, if so, I apologize. I am trying to calculate things l …

My vote would be Milnor's 7-page paper "On manifolds homeomorphic to the 7-sphere", in Vol. 64 of Annals of Math. For those who have not read it, he explicitly constructs smooth 7 …

I am trying to write a computer program which computes the action of the exponential of a differential operator on a function, for any given differential operator. Examples: $\ex …

I was asked this question during my interview recently and despite how much I think about it, I am yet to figure it out: Given $n$ balls which are painted by $k$ colors. Let $s_ …

The construction of a collage of two categories $\bf A,B$ along a profunctor $\phi\colon \bf A\mid\hspace{-2mm}\to B$ gives a new category $\bf A \uplus_\phi B$ having as objects t …

I need to know about this non-linear logarithmic fast diffusion equation for a function $u(x,t)$ of one space variable $x$ and time $t$: $$ u_t = (\ln u)_{xx}$$ which is to run on …

Let $j:\mathbb{A}^{n}\rightarrow\mathbb{A}^{n}$ an open immersion over a field $k$. Is it an isomorphism?

Given $ 0 < p < 1$, do there exist probability distributions for random variables $ X,Y $ such that all three of following are true: $$ P(X < Y) = p $$ $$ pdf (X) = f(x, …

This is a continuation of my question http://mathoverflow.net/questions/16261/. Let $G$ be a smooth, connected, reductive $k$-group over a field $k$ of characteristic $p>0$. Let $ …