MathJax is a very neat tool when it comes to writing math equations on Markdown (with a compatible note-taking app like Marktext, Logseq or Obsidian). I use it when taking notes for my college courses, instead of trying to write everything on pen and paper. However there’s a lot of syntax and functions baked into it, and It’s not really possible to remember it all. So I assembled this page to put down equations that I most commonly use, as well as some resources that have much more info than what this page provides.

Resources

Showing this first because it’s probably the first thing you’d want to check out before you scroll further.

  • MathJax Basic Tutorial and Quick Reference Sheet - The de-facto thread that contains almost everything you need to know, divided by topic. It’s extensive and very long.
  • Detexify - I found this site from the aforementioned thread, and it’s pretty neat. Lets you draw a symbol so that you can get the Mathjax operation for it.
  • LaTeX Mathematical Symbols - Contains most of the commonly used symbols and functions
  • Easy Copy MathJax - A list of common single & multi-line equations that you can easily copy & paste, based on topic. I found this useful especially with the matrix section.

Formatting

I provide source code, but you can also right click on an equation to get the functions as well.

$ a^2 = C_1cos(wt) \rightarrow sin(a)^2_5 $ is a^2 = C_1cos(wt) \rightarrow sin(a)^2_5

$\sum_{i=1}^{n} $ is \sum_{i=1}^{n}

$\frac{x}{y}$ is \frac{x}{y}

$\underrightarrow{R_1 \leftrightarrow R_2}$ for arrows under equations: $\underrightarrow{R_1 \leftrightarrow R_2}$

\\\\ starts a new line.

Putting square brackets after \\\\ adds spacing between lines: \\\\[10px]

\hspace{10px} adds spacing inside lines, useful for left/right aligning.

Here is all of it combined:

a^2 + b^2 \hspace{10cm}  \\[20px]
c^2 \hspace{5cm} +d^3

You can use \left and \right to put brackets to scale an equation:

\[S = \left\{ \begin{bmatrix} x\\ 2x+1 \end{bmatrix} \mid x \text{ is a real number} \right\}\] 
S = \left\{ \begin{bmatrix}
x\\
2x+1
\end{bmatrix} \mid x \text{ is a real number} \right\}

Common equations

Cases:

\[\begin{cases} x_1+2x_2-3x_3 = -4 \\ x_1+4x_2-2x_3 = 6 \\ 3x_1 -2x_2+2x_3=8 \end{cases} \begin{bmatrix} 3 & -2 & 4 \\ -2 & 5 & -6 \\ 0 & 2 & 7 \end{bmatrix}\] 
\begin{cases}
x_1+2x_2-3x_3 = -4 \\
x_1+4x_2-2x_3 = 6 \\
3x_1 -2x_2+2x_3=8
\end{cases}

Matrices:

\[\begin{bmatrix} 3 & -2 & 4 \\ -2 & 5 & -6 \\ 0 & 2 & 7 \end{bmatrix}\] 
\begin{bmatrix}
3 & -2 & 4 \\
-2 & 5 & -6 \\
0 & 2 & 7
\end{bmatrix}

Replace bmatrix with vmatrix for vertical matrices:

\[\begin{vmatrix} a_{21}&a_{22}\\ a_{31}&a_{32} \end{vmatrix}\]

You can also make this using the standard array, using left and right operators. This is useful if you want a formatting like an augmented matrix:

\[\left[ \begin{array}{cc|c} 1&2&3\\ 0&0&-6\\ 0&4&4\\ \end{array} \right|\] 
\left[
\begin{array}{cc|c}
  1&2&3\\
  0&0&-6\\
  0&4&4\\
\end{array}
\right|

Tables:

\[\begin{array}{r|lll} & x & y & \text{Available} \\ \hline \text{Time} & 12 & 3 & 120 \\ \text{Cost} & 0.2 & 0.4 & 4 \\ \text{Profit} & 2 & 1 & \end{array}\] 
\begin{array}{r|lll}
 & x & y & \text{Available} \\
\hline
\text{Time} & 12 & 3 & 120 \\
\text{Cost} & 0.2 & 0.4 & 4 \\
\text{Profit} & 2 & 1 & 
\end{array}