Let $f: A\to B$ and that $f$ is a bijection. Show that the inverse of $f$ is bijective. Surjectivity: Since $f^{-1} : B\to A$, I need to show that $\opera...

I started self-studying some differential geometry while using several different sources, but I'm confused about the notion of a one-form and how dif...

I would like to change $(3,4,12)$ in $xyz$ coordinate to spherical coordinate using the following relation It is from the this link. I do not understand t...

From wikipedia: Equivalently, a set P is a partition of X if, and only if, it does not contain the empty set and: The union of the elements of P is equal ...

Let $f: \mathbb{R} \to \mathbb{R} $ be a continuous function. I need to show that is a measurable function. I tried working with the definition: Let $f: X...

Rather than using mathematical libraries, how would you sample from a binomial random variable efficiently? Given the binomial random variable X, where $k...

Can anyone explain me what is the basic difference between a conforming finite element space and a non conforming finite element space. Say $\Omega\subset...

Let $H(x)$ be the cubic Hermite interpolation of $f(x)=x^4+1$ on the interval $[0,1]$ interpolating at $x=0$ and $x=1$. Then $\max_{x\in I} |f(x)-H(x)|=1/...

What's the difference between "balance laws" and "conservation laws" ? Can someone give me some examples?

This might seem like a basic question but I want a systematic way to factor the following polynomial: $$n^4+6n^3+11n^2+6n+1.$$ I know the answer but I am ...