We propose a game that is quite simple: You choose a house to start (the starting house). From this square you must move to the adjacent square (left, rig...

Having known about what axioms are, I want to know whether there are some "fundamental axioms of mathematics" on which every branch of mathematics depends...

Grinberg's theorem is a condition used to prove the existence of an Hamilton cycle on a planar graph. It is formulated in this way: Let $G$ be a fini...

This may seem like an overly trivial question, but I've just recently become confused about Langrange's 'prime' notation for derivativ...

Boltzmann’s Transformation is used (among other things) to convert Fick's second law into an easily solvable ordinary differential equation. It uses ...

$$\log\sqrt [ 3 ]{ \frac { x+2 }{ x^{ 4 }(x^{ 2 }+4) } } $$ How is this answer incorrect? $$\frac { 1 }{ 3 } [\log(x+2)-(4\log x+\log(x^ 2+4))]$$

The distribution of the number of words in text messages between employees at a large company is skewed right with a mean of $8.6$ words and a standard de...

Prove that every positive integer is congruent to the sum of its digits modulo 3.So I start with rewrite as $n = c_r 10^r + c_{r-1} 10^{r-1}...$?

From what I understand, taking the inverse of a matrix is used when solving a system of linear equations. When we perform second order optimization, we ta...

I struggle with following problem. A two-dimensional Gaussian function $f(x,y) = \frac{1}{2 \pi s^2} e^{-(x^2+y^2)/(2s^2)}$ is given and shall be integrat...