Alexander Shen

Inline math works: Euler's identity $e^{i\pi} + 1 = 0$ , the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ , and sums like $\sum_{n=1}^\infty \frac{1}{n^2} = \frac{\pi^2}{6}$ should sit nicely in the text.

Display math, centered on its own line:

$f(x) = \int_{-\infty}^{\infty} \hat{f}(\xi)\, e^{2\pi i x \xi}\, d\xi$

Maxwell's equations, aligned:

\begin{aligned} \nabla \cdot \mathbf{E} &= \frac{\rho}{\varepsilon_0} \\ \nabla \cdot \mathbf{B} &= 0 \\ \nabla \times \mathbf{E} &= -\frac{\partial \mathbf{B}}{\partial t} \\ \nabla \times \mathbf{B} &= \mu_0 \mathbf{J} + \mu_0\varepsilon_0 \frac{\partial \mathbf{E}}{\partial t} \end{aligned}

A matrix determinant:

$\det\begin{pmatrix} a & b \\ c & d \end{pmatrix} = ad - bc$

And a piecewise definition:

f(n) = \begin{cases} 1 & \text{if } n = 0 \\ n f(n-1) & \text{otherwise} \end{cases}

More inline: $\binom{n}{k} = \frac{n!}{k!(n-k)!}$ , limits $\lim_{x \to 0} \frac{\sin x}{x} = 1$ , and a Greek mix $\alpha \beta \gamma \delta \epsilon \theta \lambda \mu \pi \sigma \omega$ .