These examples show the LaTeX syntax supported in these notes. Write the source directly in a Markdown file; the site typesets it with MathJax.

Inline mathematics

Use \( ... \) for a formula inside a sentence. For example, \(f(x) = x^2\) produces \(f(x) = x^2\). The familiar $ ... $ syntax also works: $e^{i\pi}+1=0$.

Use a single backslash for commands such as \alpha, \frac, and \mathbb. Reserve \\ for line breaks inside a matrix or aligned calculation.

Display equations

Put a longer equation between $$ on separate lines, or between \[ and \].

$$
\int_0^1 x^2\,dx = \frac{1}{3}.
$$
$$ \int_0^1 x^2\,dx = \frac{1}{3}. $$

Aligned calculations and matrices

$$
\begin{aligned}
\nabla \cdot (\phi \mathbf{v})
  &= \nabla \phi \cdot \mathbf{v}
     + \phi \nabla \cdot \mathbf{v},\\
A &= \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}.
\end{aligned}
$$
$$ \begin{aligned} \nabla \cdot (\phi \mathbf{v}) &= \nabla \phi \cdot \mathbf{v} + \phi \nabla \cdot \mathbf{v},\\ A &= \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}. \end{aligned} $$

For automatic numbering, use an equation environment on its own, without surrounding $$. AMS environments and \label / \eqref are supported:

\begin{equation}
E = mc^2 \label{eq:energy}
\end{equation}

See equation \(\eqref{eq:energy}\).
\begin{equation} E = mc^2 \label{eq:energy} \end{equation}

See equation \(\eqref{eq:energy}\).

Commutative diagrams

Simple diagrams use the AMS CD environment:

$$
\begin{CD}
A @>f>> B\\
@VgVV @VVhV\\
C @>>k> D
\end{CD}
$$
$$ \begin{CD} A @>f>> B\\ @VgVV @VVhV\\ C @>>k> D \end{CD} $$

MathJax supports mathematical LaTeX, rather than compiling a complete .tex document. For TikZ or tikzcd, export the diagram as an SVG, PNG, or PDF and link it from the note.

Add a note

Create a new file with hugo new content blog/my-note.md, replace the title and description, and set draft: false when it is ready. Preview drafts with hugo server -D.

Keep source examples in fenced code blocks, as above, to display the LaTeX itself. For an ordinary dollar sign outside mathematics, write \\$.

MathJax loads from a public CDN, so an internet connection is needed to typeset equations. The Markdown and course downloads remain ordinary static files on GitHub Pages.