Let $X$ be the unit sphere of $\mathbb{R}^n$ with the sup norm, i.e. $X=\{x\in\mathbb{R}^n: \|x\|_{\infty}=1\}$. Let the metric $d$ on $X$ be the geodesic metric induced by the sup norm, i.e for any two points $x,y\in X$, $$d(x,y)=\inf \{\ell(\alpha): \alpha \mbox{ a continuous curve on }X \mbox...
I am a graduate PhD student and my topic is analytic number theory. I am also a mathematics teacher. I am planning to give a course to pupils in high school that motivates them to study arithmetic and see the beauty of numbers. For instance, I have enough informations about the golden ratio. I wa...
I was recent reading through Paul Erdos's classic elementary proof of Sylvester-Schur. It occurred me that there is a simple argument that when $x$ is sufficiently large and if $p_i$ represents the $i$th prime such that $p_i \le n < p_{i+1}$, then there are least $n - i$ numbers in the sequence...
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