 # Basic LaTeX for math

latex for equations

Tools

2020.10.28

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

plain $\LaTeX$ output
x^2 $x^2$
x_{i, j} $x_{i, j}$
\sqrt{2}, \sqrt[n]{3} $\sqrt{2}, \sqrt[n]{3}$
frac{2}{3}, 2/3 $\frac{2}{3}, 2/3$

## Calligraphic letters

Use \mathcal{A}:

$\mathcal{A} \mathcal{B} \mathcal{XYZ}$

## Greek

plain $\LaTeX$ output plain $\LaTeX$ output
\alpha $\alpha$ \xi, \Xi $\xi, \Xi$
\beta $\beta$ o $o$
\gamma, \Gamma $\gamma, \Gamma$ \pi, \Pi $\pi, \Pi$
\delta, \Delta $\delta, \Delta$ \varpi $\varpi$
\epsilon $\epsilon$ \rho $\rho$
\varepsilon $\varepsilon$ \varrho $\varrho$
\zeta $\zeta$ \sigma, \Sigma $\sigma, \Sigma$
\eta $\eta$ \varsigma $\varsigma$
\theta, \Theta $\theta, \Theta$ \tau $\tau$
\vartheta $\vartheta$ \upsilon, \Upsilon $\upsilon, \Upsilon$
\iota $\iota$ \phi, \Phi $\phi, \Phi$
\kappa $\kappa$ \varphi $\varphi$
\lambda, \Lambda $\lambda, \Lambda$ \chi $\chi$
\mu $\mu$ \psi, \Psi $\psi, \Psi$
\nu $\nu$ \omega, \Omega $\omega, \Omega$

## Sets and logic

plain $\LaTeX$ plain $\LaTeX$ plain $\LaTeX$
\cup $\cup$ \mathbb{R} $\mathbb{R}$ \forall $\forall$
\cap $\cap$ \mathbb{Z} $\mathbb{Z}$ \exists $\exists$
\subset $\subset$ \mathbb{Q} $\mathbb{Q}$ \neg $\neg$
\subseteq $\subseteq$ \mathbb{N} $\mathbb{N}$ \vee $\vee$
\supset $\supset$ \mathbb{C} $\mathbb{C}$ \wedge $\wedge$
\supseteq $\supseteq$ \varnothing $\varnothing$ \vdash $\vdash$
\in $\in$ \emptyset $\emptyset$ \models $\models$
\ni $\ni$ \aleph $\aleph$ \Rightarrow $\Rightarrow$
\notin $\notin$ \setminus $\setminus$ \nRightarrow $\nRightarrow$
\not\in $\not\in$ \equiv $\equiv$

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

plain $\LaTeX$ plain $\LaTeX$ plain $\LaTeX$
f' $f'$ \dot{a} $\dot{a}$ \tilde{x} $\tilde{x}$
f'' $f''$ \ddot{a} $\ddot{a}$ \bar{x} $\bar{x}$
\Sigma^{*} $\Sigma^{*}$ \hat{x} $\hat{x}$ \vec{x} $\vec{x}$

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:

plain $\LaTeX$ plain $\LaTeX$ plain $\LaTeX$
\sin $\sin$ \sinh $\sinh$ \arcsin $\arcsin$
\cos $\cos$ \cosh $\cosh$ \arccos $\arccos$
\tan $\tan$ \tanh $\tanh$ \arctan $\arctan$
\sec $\sec$ \coth $\coth$ \min $\min$
\csc $\csc$ \det $\det$ \max $\max$
\cot $\cot$ \dim $\dim$ \inf $\inf$
\exp $\exp$ \ker $\ker$ \sup $\sup$
\log $\log$ \deg $\deg$ \liminf $\liminf$
\ln $\ln$ \arg $\arg$ \limsup $\limsup$
\lg $\lg$ \gcd $\gcd$ \lim $\lim$

## Other symbols

plain $\LaTeX$ plain $\LaTeX$ plain $\LaTeX$
< $<$ \angle $\angle$ \cdot $\cdot$
\leq $\leq$ \measuredangle $\measuredangle$ \pm $\pm$
> $>$ \ell $\ell$ \mp $\mp$
\geq $\geq$ \parallel $\parallel$ \times $\times$
\neq $\neq$ 45^{\circ} $45^{\circ}$ \div $\div$
\ll $\ll$ \cong $\cong$ \ast $\ast$
\gg $\gg$ \ncong $\ncong$ \mid $\mid$
\approx $\approx$ \sim $\sim$ \nmid $\nmid$
\asymp $\asymp$ \simeq $\simeq$ n! $n!$
\equiv $\equiv$ \nsim $\nsim$ \partial $\partial$
\prec $\prec$ \oplus $\oplus$ \nabla $\nabla$
\preceq $\preceq$ \ominus $\ominus$ \hbar $\hbar$
\succ $\succ$ \odot $\odot$ \circ $\circ$
\succeq $\succeq$ \otimes $\otimes$ \star $\star$
\propto $\propto$ \oslash $\oslash$ \surd $\surd$
\doteq $\doteq$ \upharpoonright $\upharpoonright$ \checkmark $\checkmark$

## 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:

plain $\LaTeX$ plain $\LaTeX$ plain $\LaTeX$
\int $\int$ \iiint $\iiint$ \bigcup $\bigcup$
\iint $\iint$ \oint $\oint$ \bigcap $\bigcap$

## Arrows

plain $\LaTeX$ plain $\LaTeX$
\rightarrow, \to $\rightarrow, \to$ \mapsto $\mapsto$
\nrightarrow $\nrightarrow$ \longmapsto $\longmapsto$
\longrightarrow $\longrightarrow$ \leftarrow $\leftarrow$
\Rightarrow $\Rightarrow$ \leftrightarrow $\leftrightarrow$
\nRightarrow $\nRightarrow$ \downarrow $\downarrow$
\Longrightarrow $\Longrightarrow$ \uparrow $\uparrow$
\leadsto $\leadsto$ \updownarrow $\updownarrow$

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

plain $\LaTeX$ plain $\LaTeX$ plain $\LaTeX$
() $()$ \langle\rangle $\langle \rangle$ | | $| |$
[] $[]$ \lfloor\rfloor $\lfloor\rfloor$ \| \| $| |$
{} ${}$ \lceil\rceil $\lceil\rceil$

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

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

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

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}

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

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

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

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

## 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}

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

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}

$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}

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

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

## Spacing in mathematics

plain $\LaTeX$ plain $\LaTeX$
\rightarrow\,\leftarrow $\rightarrow\,\leftarrow$ \rightarrow\quad\leftarrow $\rightarrow\quad\leftarrow$
\rightarrow\:\leftarrow $\rightarrow\:\leftarrow$ \rightarrow\qquad\leftarrow $\rightarrow\qquad\leftarrow$
\rightarrow\;\leftarrow $\rightarrow\;\leftarrow$ \rightarrow\!\leftarrow $\rightarrow\!\leftarrow$

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}

$f\colon\mathbb{R}\to\mathbb{R}$
9.8~\text{m}/\text{s}^2

$9.8~\text{m}/\text{s}^2$
\lim_{h\to 0}\frac{f(x+h)-f(x)}{h}

$\lim_{h\to 0}\frac{f(x+h)-f(x)}{h}$
int x^2\,dx=x^3/3+C

$\int x^2\,dx=x^3/3+C$
\nabla=\boldsymbol{i}\frac{d}{dx}+\boldsymbol{j}\frac{d}{dy}+\boldsymbol{k}\frac{d}{dz}

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

## 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}

$\sigma^2=\sqrt{\sum (x_i-\mu)^2/N}$
E(x)=\mu_X=\sum (x_i-P(x_i))

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

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.

1. Jim Hefferon, Saint Michael’s College, VT USA 2017-Jan-10 ## 林宏

Frank Lin

Hey, there! This is Frank Lin (@flinhong), one of the 1.41 billion 🇨🇳. This 'inDev. Journal' site holds the exploration of my quirky thoughts and random adventures through life. Hope you enjoy reading and perusing my posts.

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