## Sekai 🌐 🗺

Sekai is the kanji for 世界, meaning “the world”. That’s a great word because of the scale it designates.

## Interactive Blog on Static Web Host

Vision gain autonomy: freedom is the basis of moral actions. No freedom, no morality. transcend ourselves: change/improve our lives through free thoughts Goal Convert our free thoughts into free code. Free code allows users around the world to run and/or improve them. This would bring real enhancement to our tools. For example, beautiful math writing used to be a complicated process. A decade ago, this required the installation of a typesetting engine called $\LaTeX$. [Read More]

## Simplex Calculations for Stokes' Theorem

Oriented affine $k$-simplex $\sigma = [{\bf p}_0,{\bf p}_1,\dots,{\bf p}_k]$ A $k$-surface given by the affine function $$\sigma\left(\sum_{i=1}^k a_i {\bf e}_i \right) := {\bf p}_0 + \sum_{i=1}^k a_i ({\bf p}_i - {\bf p}_0) \tag{1},$$ where ${\bf p}_i \in \R^n$ for all $i \in \{1,\dots,k\}$. In particular, $\sigma({\bf 0})={\bf p}_0$ and for each $i\in\{1,\dots,k\}$, $\sigma({\bf e}_i)={\bf p}_i$. Standard simplex $Q^k := [{\bf 0}, {\bf e}_1, \dots, {\bf e}_k]$ A particular type of oriented affine $k$-simplex with the standard basis $\{{\bf e}_1, \dots, {\bf e}_k\}$ of $\R^k$. [Read More]

## Filters and Nets

### Some basic examples

Motivation $\gdef\vois#1#2{\mathcal{V}_{#1}(#2)}$ Nets and filters are used for describing convergence in a non-metric space $X$. Denote the collection of (open) neighbourhoods of $x \in X$ by $\vois{X}{x}$. Definitions and examples Directed set A partially ordered set $I$ such that $$\forall i, j \in I: i \le j, \exists k \in I: k \ge j.$$ Net A function in $X^I$, where $I$ is a directed set. example: any sequence in $X^\N$ Convergence of nets to a point $x_i \to x$ if \forall A \in \vois{X}{x}, \exists j \in I: \forall k \ge j, x_k \in A. [Read More]

## Cover Letter Organisation

### A simple summary

I keep sentences below short and minimal for memory.

1. Sender’s contact info at top-right hand corner, followed by receipent’s contact info left-aligned.
2. “I’m …”, “apply for …, as advertised in …”
3. Why apply? Link with the company(’s employee)
4. Pastimes (all-rounded person), continual learning (for useful skills)
5. Friendly, polite and to-the-point sign-off
6. Signature followed by sender’s name