I was helping my daughter with her physics homework. The problem had a bee flying back and forth between two bikes moving toward each other. The question ...

(1.) Not querying proofs or formality. I do this in my other question. Normal Subgroup Test says H is normal in G $\iff gH{g}^{-1}\subseteq H$ for all $g ...

The Problem Suppose I have an equation of the form $\nabla^2 \phi(x) = f(x)$ on the interval $A \le x \le B$, where $f(x)$ is known and $\phi(x)$ is unkno...

Question : Let $T$ be the centroid of a triangle $ABC$, and let $P$ be the midpoint of the side $\overline{AC}$. The line containing the point $T$ paralle...

Inadvertently, I find this interesting inequality. But this problem have nice solution? prove that $$\ln{2}>(\dfrac{2}{5})^{\frac{2}{5}}$$ This problem...

I'm trying to solve this system equations in matlab syms y z i x=[29.6,29.4,34.4,35.1,34.3,36.1,31.6,32.9,31.5,28.3,37.1,28.4,27.3,33.1,31.3,33.1] n ...

I have never taken a number theory course and so am only going off of the first few chapters in an introductory number theory book. The divisibility prope...

The fredholm determinant of an infinite matrix $A$ is defined by $$ \det(I+A) = \exp(\text{tr}(\log(I+A))). $$ I'm trying to understand the formula a...

I'm trying to understand the formula for the curl: $$\operatorname{Curl}(F) = \nabla \times F $$ Why the vector product? What means the vector produc...

I am having some difficulties understanding the difference between simplicial and singular homology. I am aware of the fact that they are isomorphic, i.e....