How to prove that a compact set $K$ in a Hausdorff topological space $\mathbb{X}$ is closed? I seek a proof that is as self contained as possible. Thank you.

What is the relation between $A(G)$ and $A(G^2)$? Where $G^2$ is the square of a graph $G$ and $A(G^2),A(G)$ their respective adjacency matrix.

Here is an excerpt from what I am reading. One can similarly define right $A$-modules. A convenient way to give a formal definition of right module is as ...

I was just wondering what were the main/important uses of the Fibonacci sequence as well as any other generalized Fibonacci sequences in real life applica...

I know this may be really simple but here it is nonetheless. Let's say that I have a ring with a radius of $r$ and width of $dr$. I'm trying to ...

I am trying to learn about partitions and I would like to experiment a bit with a calculator. That's the only way I know how to teach myself somethin...

Is there a way to get an explicit formula for the sum after $n$ places of this summation: $$\frac{1}{4} + \frac{3}{16} + \frac{9}{64} + \frac{27}{256}... ...

I'm working through a question that I don't quite know how to get. It is: Find an inner product $\langle - , -\rangle$ on $\mathbb{R} ^3$, and a...

I have a practice problem on linear transformations that I'd like help on. I have to find the eigenvalues and eigenvectors of $$T(ax^2 + bx + c) = bx...

Why is the perpendicular vector on a plane always the vector of coefficients of the variables in the plane equation? e.g., for the plane $2x-y+3z=8$, the ...