I just came back from my Number Theory course, and during the lecture there was mention of the Collatz Conjecture. I'm sure that everyone here is familiar with it; it describes an operation on a natural number – $n/2$ if it is even, $3n+1$ if it is odd. The conjecture states that if this operat...

Not much time ago I saw an Instagram post about something called Borwein Integral, which is certainly such a "monster". This integral has the following form: $$\int_0^{\infty}\frac{\sin{x}}{x}\cdots\frac{\sin{\frac{x}{100n+1}}}{\frac{x}{100n+1}}$$ The most surprising thing about this result is t...

Let $p=p(x_1,...,x_N)$ be a non-zero polynomial in $N$ variables (real coefficients). Let $\mathscr{S}$ be the Schwartz space on $\mathbb{R}^N$ and let $\mathscr{S}'$ be its topological dual (i.e. the space of tempered distributions). I know that the map $\mathscr{S}'\to \mathscr{S}', \ \ \ T\map...

Here is the question I am trying to solve letter $(b)$ in it: Let $A$ be the matrix $\begin{pmatrix} 1 & 0 & 0 & 1 & 1 & 0\\ 0 & 1 & 0 & 1 & 0 & 1\\ 0 & 0 & 1 & 0 & 1 & 1 \end{pmatrix}$ For $q$ in $\{2,3\},$ let $M_q[A]$ be the vector matroid of $A$ when $A$ is viewed over $GF(q),$ the field of $...