 # Basic LaTeX for math

latex for equations

Tools

2020.10.28

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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$\LaTeX$ outputplain$\LaTeX$ 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

THE END ## 林宏

Frank Lin, PhD

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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