In markdown notes, it’s easy to insert simple mathematical formulas with plain $\LaTeX$. However, I’m always forget some basic characters for equations. So, let’s take a short review basic on the note $\LaTeX$ math for undergrads¹. Note that the render engine is $\KaTeX$ on this web page.

Common constructs

Calligraphic letters

Use \mathcal{A}:

Greek

Sets and logic

Negate an operator, as in $\not\subset$, with \not\subset. Get the set complement $A^{\mathsf{c}}$ with A^{\mathsf{c}}, get $A^{\complement}$ with \A^{\complement}, or get $\bar{A}$ with \bar{A}.

Decorations

If the decorated letter is $i$ or $j$ then some decorations need \imath or \jmath, as in vec{\imath}. If you need boldface for vectors: \boldsymbol{x}.

Entering \overline{x+y} produces $\overline{x+y}$, and \widehat{x+y} gives $\widehat{x+y}$.

Dots

Use low dots in a list $\{0,1,2\,\ldots\}$, entered as \{0,1,2\,\ldots\}. Use entered dots in a su or product $1+\cdots+100$, entered as 1+\cdots+100. You can also get vertical dots \vdots and diagonal dots \ddots.

Roman names

Enter \tan{x}, with a backslash, instead of tan{x}. These get the same treatment:

Other symbols

Variable-sized operators

The summation $\sum_{j=0}^3 j^2$ using \sum_{j=0}^3 j^2 and the integral $\int_{x=0}^3 x^2\,dx$ with \int_{x=0}^3 x^2\,dx.

These do the same:

Arrows

The right arrows in the first column have matching left arrows, such as \nleftarrow, and there are some other matches for down arrows, etc.

Fences

They will grow with the enclosed formula using \left and \right.

\left\langle i, 2^{2^i} \right\rangle

Every \left must match a \right and they must end on the same line in the output. For a one-sided fence put a period \left. or \right. on the other side.

\left.\frac{df}{dx}\right|_{x_0}

Fix the size with \big, \Big, \bigg, or \Bigg.

\Big[\sum_{k=0}^n e^{k^2}\Big]

Array, matrices

Make an array of mathematical text as you make a table of plain text.

\begin{array}{rcl}
	0 &\leftrightarrow &0 \\
	1 &\leftrightarrow &1 \\
	2 &\leftrightarrow &4 \\
	\vdots &           &\vdots
\end{array}

Definition by cases is an array with two columns.

f_n=
\begin{cases}
    a   &\text{if \(n=0\)} \\
    r\cdot f_{n-1}  &\text{else}
\end{cases}

A matrix is another array variant. With this abbreviation you need not specify column alignments.

\begin{pmatrix}
    a   &b \\
    c   &d
\end{pmatrix}

For the determinant use |A| inline and vmatrix in display.

Spacing in mathematics

The left column spaces are in ratio $3:4:5$. The last in the right column is a negative space, opposite to \,. Get arbitrary spaces as in \hspace{0.5cm}.

Calculus examples

f\colon\mathbb{R}\to\mathbb{R}

9.8~\text{m}/\text{s}^2

\lim_{h\to 0}\frac{f(x+h)-f(x)}{h}

int x^2\,dx=x^3/3+C

\nabla=\boldsymbol{i}\frac{d}{dx}+\boldsymbol{j}\frac{d}{dy}+\boldsymbol{k}\frac{d}{dz}

Discrete mathematics examples

There are four modulo forms: $m\bmod n$ is from m\bmod n, and $a\equiv b\pmod m$ is from a\equiv b\pmod m, and $a\equiv b\mod m$ is from a\equiv b\mod m, and $a\equiv b\pod m$ is from a\equiv b\pod m.

For combinations the binomial symbol $\binom{n}{k}$ is from \binom{n}{k}. This resizes to be bigger in a display.

For permutations use $n^{\underline{r}}$ from n^{\underline{r}}.

Statistics examples

\sigma^2=\sqrt{\sum (x_i-\mu)^2/N}

E(x)=\mu_X=\sum (x_i-P(x_i))

The probability density of the normal distribution $\frac{1}{\sqrt{2\sigma^2\pi}}\,e^{-\frac{(x-\mu)^2}{2\sigma^2}}$ comes from this:

\frac{1}{\sqrt{2\sigma^2\pi}}\,e^{-\frac{(x-\mu)^2}{2\sigma^2}}

For more

See more comprehensive $\LaTeX$ symbols list at http://mirror.ctan.org/info/symbols/comprehensive.