Working with LaTeX Equations

This site now supports LaTeX equations powered by KaTeX.

You can use both inline and display math directly in your Markdown files.

Inline Math

Use single dollar signs for inline equations:

The famous energy-mass equivalence is $E = mc^2$.

The logistic map, often used to study complex systems, is given by $x_{n+1} = r x_n (1 - x_n)$.

Display Equations

For larger, centered equations use double dollar signs:

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

More Examples

Sums and Products

$$\sum_{i=1}^{n} i = \frac{n(n+1)}{2}$$ $$\prod_{i=1}^{n} (1 + x_i)$$

Matrices

The covariance matrix in quantitative finance often looks like this:

$$\Sigma = \begin{pmatrix} \sigma_1^2 & \rho \sigma_1 \sigma_2 \\ \rho \sigma_1 \sigma_2 & \sigma_2^2 \end{pmatrix}$$

Black-Scholes (Simplified)

The price of a European call option $C$ under the Black-Scholes model:

$$C = S_0 N(d_1) - K e^{-rT} N(d_2)$$

where

$$d_1 = \frac{\ln(S_0 / K) + (r + \sigma^2 / 2)T}{\sigma \sqrt{T}}, \quad d_2 = d_1 - \sigma \sqrt{T}$$

Complex Systems: Lorenz Attractor

The Lorenz equations, a classic example of chaotic behavior:

$$\begin{aligned} \frac{dx}{dt} &= \sigma (y - x) \\ \frac{dy}{dt} &= x (\rho - z) - y \\ \frac{dz}{dt} &= x y - \beta z \end{aligned}$$

Usage Tips

• Inline: $ ... $
• Display: $$ ... $$ or \[ ... \]
• KaTeX supports most common LaTeX math commands, including \begin{align}, \begin{matrix}, and many more.
• For very advanced needs, you can also use the $$ syntax inside MDX files.

Happy writing!