LaTeX test

What: LaTeX is a markup language for mathematical notation, uniquitous in academia and beyond.

Why: The examples below show how math can be readibly displayed using LaTeX, as opposed to awkwardly inserting images, or using English-alphabet characters to describe things.

How: I learned LaTeX notation in high school and University, as do most. And for this website, this blog post explains how:

Equality: a=ba = b

Integral: ex2=π\int_{-\infty}^{\infty} e^{-x^2} = \sqrt{\pi}

Shannon’s Entropy:

H(x)=EX P[I(x)]=EX P[logP(x)]H(x) = \mathbb{E}_{X ~ P}[I(x)] = -\mathbb{E}_{X ~ P}[log P(x)]

Sigmoid function:

11+expx\frac{1}{1 + \exp{-x}}

Euler’s identity:

eiπ=1e^{i\pi} = -1

Classic Greek alphabet:

α,β,γ,δ,ϵ\alpha, \beta, \gamma, \delta, \epsilon

Γ,Π,Σ\Gamma, \Pi, \Sigma