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Writing math with LaTeX in Markdown

#meta#math

This blog renders LaTeX math with MathJax. Posts opt in with math: true in the front matter, and then you can write mathematics inline with the rest of your prose. This post doubles as a reference: every rendered equation is shown next to the Markdown that produced it.

Kramdown (the Markdown engine GitHub Pages uses) treats $$...$$ as math. It’s smart about context: $$ in the middle of a sentence is rendered inline, while $$ in its own paragraph is rendered as a centered display block. Crucially, kramdown protects what’s inside from Markdown processing, so subscripts like x_i won’t get mangled into emphasis.

Inline math

You can drop symbols straight into a sentence. Euler’s identity, $$e^{i\pi} + 1 = 0$$, is hard to beat; merge sort runs in $$O(n \log n)$$; and a masked share might be written as $$x = x_1 \oplus x_2$$.

Euler's identity, $$e^{i\pi} + 1 = 0$$, is hard to beat; merge sort runs in
$$O(n \log n)$$; and a masked share might be written as $$x = x_1 \oplus x_2$$.

Display equations

Put the math in its own paragraph to center it. Average memory access time:

$$ \text{AMAT} = t_{\text{hit}} + r_{\text{miss}} \times t_{\text{penalty}} $$

$$
\text{AMAT} = t_{\text{hit}} + r_{\text{miss}} \times t_{\text{penalty}}
$$

Fractions, roots, sums, and integrals

The softmax used in a classifier’s output layer:

$$ \sigma(\mathbf{z})i = \frac{e^{z_i}}{\sum{j=1}^{K} e^{z_j}} $$

The continuous Fourier transform:

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

A classic limit and a root for good measure:

$$ \lim_{x \to 0} \frac{\sin x}{x} = 1 \qquad \lVert \mathbf{v} \rVert_2 = \sqrt{\sum_{k=1}^{n} v_k^2} $$

Aligned, multi-step derivations

Use \begin{aligned} to line equations up on the &. Closed form of a geometric series, the kind that shows up in amortized analysis:

$$ \begin{aligned} S &= \sum_{k=0}^{n-1} a r^k \ &= a \left( 1 + r + r^2 + \cdots + r^{n-1} \right) \ &= a , \frac{1 - r^n}{1 - r}, \qquad r \neq 1 \end{aligned} $$

$$
\begin{aligned}
S &= \sum_{k=0}^{n-1} a r^k \\
  &= a \, \frac{1 - r^n}{1 - r}, \qquad r \neq 1
\end{aligned}
$$

Matrices and vectors

A $$2 \times 2$$ matrix and a matrix-vector product:

$$ A = \begin{bmatrix} a_{11} & a_{12} \ a_{21} & a_{22} \end{bmatrix}, \qquad A\mathbf{x} = \begin{bmatrix} a_{11} x_1 + a_{12} x_2 \ a_{21} x_1 + a_{22} x_2 \end{bmatrix} $$

Piecewise definitions

The cases environment is perfect for recurrences. Factorial, written recursively:

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

Symbols, Greek, and operators

A quick sampler of the things you’ll reach for most:

$$ \alpha, \beta, \gamma, \delta, \quad \Delta, \Sigma, \Omega, \quad \nabla, \partial, \infty, \quad \forall x \in \mathbb{R}, \ \exists, \varepsilon > 0 $$

$$ \mathbb{Z} \subset \mathbb{Q} \subset \mathbb{R} \subset \mathbb{C}, \qquad a \equiv b \pmod{m}, \qquad \binom{n}{k} = \frac{n!}{k!,(n-k)!} $$

That’s the whole toolkit. Anything LaTeX’s math mode can express, MathJax will render here. To use it in your own post, add math: true to the front matter and write away.

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