A technical question that came up to mind as I was reading up on linear models today. Consider the $t$-distribution with $\nu$ degrees of freedom ($t_\nu$) for example. Let's say $T \sim t_{\nu}$; that is, the random variable $T$ follows this distribution. Does it mean that $T$ must equal $\dfr...

I am looking at the following exercise: Show that the following are equivalent conditions on a surface patch $\sigma (u, v)$ with first fundamental form $Edu^2 + 2F dudv + Gdv^2$ : $E_v = G_u = 0$. $σ_{uv}$ is parallel to the standard unit normal $N$. The opposite sides of any quadrilateral f...

I have just completed an introductory course on analysis, and have been looking over my notes for the year. For me, although it was certainly not the most powerful or important theorem which we covered, the most striking application was the Fourier analytic proof of the isoperimetric inequality....

I want to show that if a function $f:[a,b]\rightarrow \mathbb R$ satisfies a Hölder condition of order $\alpha > 1 $ then it is constant. The way I think of it is as follows: $$|f(x) - f(y)| < K|x-y|^\alpha$$ $$\frac{|f(x) - f(y)|} {|x-y]} < K|x-y|^{\alpha -1}$$ $$\lim_{y\rightarrow x} \frac...