Prove that a $k$-regular bipartite graph has a perfect matching by using Hall's theorem. Let $S$ be any subset of the left side of the graph. The onl...

The answer I have which I'm sure is wrong is $(3x-2)\ln(\left \vert x+1 \right \vert + \text{constant}$ I let $x + 1$ be $u$ and $du$ would be $1$. B...

I had recently, just about a year ago, “discovered” that there are easy to see, clear patterns if you look at the Ulam spiral and just highlight the multi...

This might be a silly question, but is it possible at all for n.00000...[infinite zeros]...1 to be the next real number after n? If not, why not? Firstly,...

Apologies in advance, my math is very rusty. I'm slowly working my way through Schaum's Outline of Discrete Math for some self-study, occasional...

Recently I started thinking about how graphs relate to their functions. I took for granted that given a function I could plot a few points and get the gen...

I am given the equation: 5 * 3^x = 2 * 7^x The text book and everywhere online shows me how to do this when the variable is only on one side or when it ca...

$\frac{\partial^2 z}{\partial x^2}+z=0$, given that at $x=0, z=e^y$ and $\frac{\partial z}{\partial x}=1$ I am doing it in following way: Integrating w.r....

The regular dodecahedron has $20$ vertices, and $12$ faces which are (congruent) regular pentagons; three pentagons meet at a vertex. Fixing a vertex $v$ ...

Let $x_1> 1$ and let $x_{n+1} := 2 - \displaystyle\frac{1}{x{_n}}$ for $n \in \mathbb{ N}$. Show that $(x_n)$ is bounded and monotone. Find the limit. ...