I'm doing some exercises on Khanacademy.org and I keep having trouble with one exercise. The questions are like this: how many $1/4$cm cubes does it ...

Is there a connexion between : 1) The monodromy group of a topological space. 2) The $\ell$-adic monodromy theorem of Grothendieck. 3) The $p$-adic monodr...

I have an exam in an hour and this one question is killing me! We enter our answers online so maybe I am just entering it wrong, but I can't for the ...

I know that the probability of tossing $r$ heads in a row is eventually $1$, but how about tossing $r$ heads in a row before $s$ tails in a row? What'...

Consider the integral $$I_n^{(a,b)} = \int_{-1}^1 (1-x)^a\,(1+x)^b\, P_n(x)\, dx,$$ where $P_n(x)$ is the $n$-th Legendre polynomial. Here's a plot o...

I have a problem, I am working with numerical approximations. Now I have $-1=x_0<x_1 <...<x_n=1$ with $x_i=x_{i-1}+h$ and $h=2/n$. Now given a fu...

Let be $D_n$ the group of symmetries of a regular n-sided polygon. Prove that $D_n$ is generated by a minimum rotation angle and a reflection (about a sym...

The cubic equation $x^3-5x^2+6x-3 = 0$ has solutions $\alpha$, $\beta$ and $\gamma$. Find the value of $$\frac{1}{\alpha^2}+\frac{1}{\beta^2}+\frac{1}{\ga...

We have an isosceles triangle, what is the theorem called that states that the sides opposite it's congruent angles will have congruent lengths? Coul...

Looking at a textbook of mine, I have noticed that there is a question I've been able to answer. Let f : $\mathbb{R}$ → $\mathbb{R}$ be bounded and c...