Formula Placement

Inline formulas use $...$, while display mode uses $$...$$ for separate lines.

Superscripts and Subscripts

Superscript is denoted by ^, subscript by _. Example: C_n^2 renders as (C_n^2). Preceding sub/superscripts like {}_1^2\!X_3^4 render as ({}_1^2!X_3^4).

Grouping Expressions

Enclose expressions with {} to group them. For instance, e^{10} becomes (e^{10}), whereas e^10 renders as (e^10).

Font Styles

Display	Command	Style
(ABCabc)	$ABCabc$	Regular
(\text{ABCabc})	\text{ABCabc}	Text mode (can contain $)
(\mathbf{ABCabc})	\mathbf{ABCabc}	Bold
(\boldsymbol{\alpha})	\boldsymbol{\alpha}	Bold (other symbols)
(\mathit{ABCabc})	\mathit{ABCabc}	Italic
(\pmb{ABCabc})	\pmb{ABCabc}	Bold italic
(\mathbb{ABCabc})	\mathbb{ABCabc} or \Bbb{ABCabc}	Blackboard bold
(\mathtt{ABCabc})	\mathtt{ABCabc}	Typewriter
(\mathrm{ABCabc})	\mathrm{ABCabc}	Roman
(\mathsf{ABCabc})	\mathsf{ABCabc}	Sans serif
(\mathcal{ABCabc})	\mathcal{ABCabc}	Calligraphic
(\mathscr{ABCabc})	\mathscr{ABCabc}	Script
(\mathfrak{ABCabc})	\mathfrak{ABCabc}	Fraktur

Font Sizes

Display	Command
(ABCabc)	ABCabc
(\tiny ABCabc)	\tiny ABCabc
(\small ABCabc)	\small ABCabc
(\normalsize ABCabc)	\normalsize ABCabc
(\large ABCabc)	\large ABCabc
(\Large ABCabc)	\Large ABCabc
(\huge ABCabc)	\huge ABCabc
(\Huge ABCabc)	\Huge ABCabc

Grouping controls font size, e.g., ABC {\tiny ABC} {\large ABC} renders as (ABC {\tiny ABC} {\large ABC}).

Greek Letters

Lowercase	Command	Uppercase	Command
(\alpha)	\alpha	(\Alpha)	\Alpha
(\beta)	\beta	(\Beta)	\Beta
(\gamma)	\gamma	(\Gamma)	\Gamma
(\delta)	\delta	(\Delta)	\Delta
(\epsilon)	\epsilon	(\Epsilon)	\Epsilon
(\zeta)	\zeta	(\Zeta)	\Zeta
(\eta)	\eta	(\Eta)	\Eta
(\theta)	\theta	(\Theta)	\Theta
(\iota)	\iota	(\Iota)	\Iota
(\kappa)	\kappa	(\Kappa)	\Kappa
(\lambda)	\lambda	(\Lambda)	\Lambda
(\mu)	\mu	(\Mu)	\Mu
(\nu)	\nu	(\Nu)	\Nu
(\xi)	\xi	(\Xi)	\Xi
(\pi)	\pi	(\Pi)	\Pi
(\rho)	\rho	(\Rho)	\Rho
(\sigma)	\sigma	(\Sigma)	\Sigma
(\tau)	\tau	(\Tau)	\Tau
(\upsilon)	\upsilon	(\Upsilon)	\Upsilon
(\phi)	\phi	(\Phi)	\Phi
(\chi)	\chi	(\Chi)	\Chi
(\psi)	\psi	(\Psi)	\Psi
(\omega)	\omega	(\Omega)	\Omega
(\omicron)	\omicron	(\Omicron)	\Omicron

Italic Greek letters are prefixed with var, e.g., \varDelta renders as (\varDelta).

Arithmetic Operations

Display	Command
(\times)	\times
(\div)	\div
(\cdot)	\cdot
(\lt)	<
(\gt)	>
(\ll)	\ll
(\gg)	\gg
(\lll)	\lll
(\pm)	\pm
(\le)	\le or \leq
(\ge)	\ge or \geq
(\mp)	\mp
(\leqq)	\leqq
(\geqq)	\geqq
(\neq)	\neq
(\leqslant)	\leqslant
(\geqslant)	\geqslant
(\approx)	\approx

Set Theory

Display	Command
(\compliment)	\complement
(\in)	\in
(\notin)	\notin
(\subset)	\subset
(\subseteq)	\subseteq
(\subsetneq)	\subsetneq
(\cap)	\cap
(\cup)	\cup
(\varnothing)	\varnothing
(\emptyset)	\emptyset

Logical Operators

Display	Command
(\land)	\land or \wedge
(\lor)	\lor or \vee
(\lnot)	\lnot or \neg
(\forall)	\forall
(\exists)	\exists
(\top)	\top
(\vdash)	\vdash
(\vDash)	\vDash
(\bot)	\bot

Parentheses

Parenthesis	Command
((x))	(x)
({ x })	\{ x \} or \lbrace x \rbrace
([x])	[x]
(\vert x\vert)	\vert x \vert
(\Vert x \Vert)	\Vert x \Vert
(\langle x \rangle)	\langle x \rangle
(\lceil x \rceil)	\lceil x \rceil
(\lfloor x \rfloor)	\lfloor x \rfloor
(\left(\frac xy \right))	\left( \frac xy \right)
(\left. \frac 12 \right})	\left. \frac 12 \right\}
(\left{ \frac xy \middle y \neq 0 \right})	\left\{ \frac xy \middle y \neq 0 \right\}
(\Bigg(\bigg(\Big(\big((x) \big)\Big)\bigg)\Bigg))	\Bigg(\bigg(\Big(\big((x) \big)\Big)\bigg)\Bigg)
(\dbinom nr)	\dbinom nr
(\binom nr)	\binom nr or {n \choose r}

Spacing

Display	Command
(a b)	a b
(a \qquad b)	a \qquad b
(a \quad b)	a \quad b
(a\ b)	a\ b
(a;b)	a\;b
(a,b)	a\,b
(a!b)	a\!b

Summation, Integrals, and Derivatives

Display	Command
(\sum_1^n)	\sum_1^n
(\sum_{i=0}^\infty x^2)	\sum_{i=0}^\infty x^2
(\int)	\int
(\iint)	\iint
(\iiint)	\iiint
(\idotsint)	\idotsint
(\oint)	\oint
(\prod)	\prod
(\coprod)	\coprod
(\bigcap)	\bigcap
(\bigcup)	\bigcup
(\bigvee)	\bigvee
(\bigwedge)	\bigwedge
(\infty)	\infty
(\nabla)	\nabla
(\partial x)	\partial x
(\mathrm{d}x)	\mathrm{d}x
(\dot x)	\dot x
(\ddot y)	\ddot y

Fractions, Roots, and Functions

Display	Command	Description
(\frac 12)	\frac 12
(\dfrac 12)	\dfrac 12	Force display style
(\tfrac 12)	\tfrac 12	Force text style
(\cfrac 12)	\cfrac 12	For continued fractions
(\frac {x^2}{1+x})	\frac {x^2}{1+x}
({x^2 \over 1+x})	{x^2 \over 1+x}	For complex fractions
(\sqrt{x^3})	\sqrt{x^3}
(\sqrt[3]{\frac xy})	\sqrt[3]{\frac xy}
(\sin x)	\sin x	Most functions use \ + function name
(\operatorname{arcsec}x)	\operatorname{arcsec}x	For custom functions
(\lim_{x \to 0})	\lim_{x \to 0}
(\varinjlim)	\varinjlim
(\varprojlim)	\varprojlim
(\varliminf)	\varliminf
(\varlimsup)	\varlimsup

Arrow Symbols

Display	Command
(\Rightarrow)	\Rightarrow
(\Leftarrow)	\Leftarrow
(a \rightarrow b)	a \rightarrow b
(a \leftarrow b)	a \leftarrow b
(a \to b)	a \to b
(a \gets b)	a \gets b
(a \Longrightarrow b)	a \Longrightarrow b
(a \Longleftarrow b)	a \Longleftarrow b
(a \implies b)	a \implies b
(a \impliedby b)	a \impliedby b
(\longrightarrow)	\longrightarrow
(\longleftarrow)	\longleftarrow
(\Leftrightarrow)	\Leftrightarrow
(\leftrightarrow)	\leftrightarrow
(\Longleftrightarrow)	\Longleftrightarrow or \iff
(\longleftrightarrow)	\longleftrightarrow
(\xrightarrow[y>0]{x+y})	\xrightarrow[y>0]{x+y}
(\xleftarrow{x+y})	\xleftarrow{x+y}
(\longmapsto)	\longmapsto
(\mapsto)	\mapsto
(\hookleftarrow)	\hookleftarrow
(\hookrightarrow)	\hookrightarrow
(\searrow)	\searrow
(\nearrow)	\nearrow
(\nwarrow)	\nwarrow
(\swarrow)	\swarrow
(\downarrow)	\downarrow
(\uparrow)	\uparrow
(\upuparrows)	\upuparrows
(\updownarrow)	\updownarrow
(\Uparrow)	\Uparrow
(\downdownarrows)	\downdownarrows
(\Updownarrow)	\Updownarrow
(\Downarrow)	\Downarrow
(\rightharpoonup)	\rightharpoonup
(\leftharpoonup)	\leftharpoonup
(\rightharpoondown)	\rightharpoondown
(\leftharpoondown)	\leftharpoondown
(\upharpoonleft)	\upharpoonleft
(\downharpoonleft)	\downharpoonleft
(\upharpoonright)	\upharpoonright
(\downharpoonright)	\downharpoonright
(\rightleftharpoons)	\rightleftharpoons
(\leftrightharpoons)	\leftrightharpoons
(\rightrightarrows)	\rightrightarrows
(\leftleftarrows)	\leftleftarrows
(\Rrightarrow)	\Rrightarrow
(\Lleftarrow)	\Lleftarrow
(\rightleftarrows)	\rightleftarrows
(\leftrightarrows)	\leftrightarrows
(\nrightarrow)	\nrightarrow
(\nleftarrow)	\nleftarrow
(\nLeftarrow)	\nLeftarrow
(\nRightarrow)	\nRightarrow
(\nleftrightarrow)	\nleftrightarrow
(\curvearrowleft)	\curvearrowleft
(\circlearrowleft)	\circlearrowleft
(\curvearrowright)	\curvearrowright
(\circlearrowright)	\circlearrowright
(\looparrowleft)	\looparrowleft
(\rightarrowtail)	\rightarrowtail
(\looparrowright)	\looparrowright
(\leftarrowtail)	\leftarrowtail
(\Lsh)	\Lsh
(\twoheadleftarrow)	\twoheadleftarrow
(\Rsh)	\Rsh
(\twoheadrightarrow)	\twoheadrightarrow
(\rightsquigarrow)	\rightsquigarrow
(\leftrightsquigarrow)	\leftrightsquigarrow

Geometry and Vectors

Display	Command
(\triangle)	\triangle
(\Diamond)	\Diamond
(\Box)	\Box
(\odot)	\odot
(\angle ABC)	\angle ABC
(30^\circ)	30^\circ
(\perp)	\perp
(\sim)	\sim
(\cong)	\cong
(\hat{a})	\hat{a}
(\vec{a})	\vec{a}
(\overrightarrow{AB})	\overrightarrow{AB}
(\overleftarrow{AB})	\overleftarrow{AB}
(\overleftrightarrow{AB})	\overleftrightarrow{AB}
(\widehat{e f g})	\widehat{e f g}

Diacritical Marks

Display	Command
(\bar a)	\bar a
(\acute{a})	\acute{a}
(\check{a})	\check{a}
(\grave{a})	\grave{a}
(\breve{a})	\breve{a}
(\dot{a})	\dot{a}
(\ddot{a})	\ddot{a}
(\dddot{a})	\dddot{a}
(\hat a)	\hat{a}
(\tilde{a})	\tilde{a}

Overlines, Underlines, and Braces

Display	Command
(\overline{h i j})	\overline{h i j}
(\underline{h i j})	\underline{h i j}
(\underbrace{a+b+\cdots+z}_{10})	\underbrace{a+b+\cdots+z}_{10}
(\overbrace{a+b+\cdots+z}^{10})	\overbrace{a+b+\cdots+z}^{10}

Special Characters

Symbol	Display	Symbol	Display	Symbol	Display
(\eth)	\eth	(\S)	\S	(\P)	\P
(%)	\%	(\dagger)	\dagger	(\ddagger)	\ddagger
(\star)	\star	(\ast)	\ast or *	(\circ)	\circ
(\bullet)	\bullet	(\ldots)	\ldots	(\cdots)	\cdots
(\vdots)	\vdots	(\ddots)	\ddots	(\smile)	\smile
(\frown)	\frown	(\wr)	\wr	(\oplus)	\oplus
(\bigoplus)	\bigoplus	(\otimes)	\otimes	(\bigotimes)	\bigotimes
(\bigodot)	\bigodot	(\boxtimes)	\boxtimes	(\boxplus)	\boxplus
(\triangleleft)	\triangleleft	(\triangleright)	\triangleright	(\bot)	\bot
(\top)	\top	(\vdash)	\vdash	(\Vdash)	\Vdash
(\vDash)	\vDash	(\models)	\models	(\infty)	\infty
(\imath)	\imath	(\hbar)	\hbar	(\ell)	\ell
(\mho)	\mho	(\Finv)	\Finv	(\Re)	\Re
(\Im)	\Im	(\wp)	\wp	(\diamondsuit)	\diamondsuit
(\heartsuit)	\heartsuit	(\clubsuit)	\clubsuit	(\spadesuit)	\spadesuit
(\Game)	\Game	(\flat)	\flat	(\natural)	\natural
(\sharp)	\sharp	(\because)	\because	(\therefore)	\therefore

Arrays

Syntax: $$\begin{array}…\end{array}$$, where r aligns right, l left, c center, | vertical line, \hline horizontal line, \\ for new line, and & separates elements.

Example:

$$
  \begin{array}{c|lcr}
    n & \text{Left} & \text{Center} & \text{Right} \\\hline
    1 & 0.24 & 1 & 125 \\
    2 & -1 & 189 & -8 \\
    3 & -20 & 2000 & 1+10i
  \end{array}
$$

Matrices

Syntax: $$\begin{matrix}…\end{matrix}$$, each row ends with \\, and elements separated by &.

Example:

$$
  \begin{matrix}
    1 & x & x^2 \\
    1 & y & y^2 \\
    1 & z & z^2 \\
  \end{matrix}
$$

Add parentheses:

• pmatrix (())
• bmatrix ([\ ])
• Bmatrix ({\ })
• vmatrix (\vert\ \vert)
• Vmatrix (\Vert\ \Vert)

Add ellipses:

\begin{pmatrix}
  1 & a_1^2 & a_1^2 & \cdots & a_1^2 \\
  1 & a_2^2 & a_2^2 & \cdots & a_2^2 \\
  \vdots & \vdots & \vdots & \ddots & \vdots \\
  1 & a_n^2 & a_n^2 & \cdots & a_n^2 \\
\end{pmatrix}

Horizontal augmented matrix:

$$
  \left[
    \begin{array}{cc|c}
      1&2&3\\
      4&5&6
    \end{array}
  \right]
$$

Vertical augmented matrix:

$$
  \begin{pmatrix}
    a & b\\
    c & d\\
    \hline
    1 & 0\\
    0 & 1
  \end{pmatrix}
$$

Inline matrices:

(\big( \begin{smallmatrix} a & b \ c & d \end{smallmatrix} \big)) using $\big( \begin{smallmatrix} a & b \\ c & d \end{smallmatrix} \big)$

Equation Alignment

Syntax: \begin{align}…\end{align}, rows end with \\, elements separated by &.

Example:

$$
  \begin{align}
    \sqrt{37} & = \sqrt{\frac{73^2-1}{12^2}} \\\n     & = \sqrt{\frac{73^2}{12^2}\cdot\frac{73^2-1}{73^2}} \\
     & = \sqrt{\frac{73^2}{12^2}}\sqrt{\frac{73^2-1}{73^2}} \\
     & = \frac{73}{12}\sqrt{1 - \frac{1}{73^2}} \\
     & \approx \frac{73}{12}\left(1 - \frac{1}{2\cdot73^2}\right)
  \end{align}
$$

Piecewise Functions

Syntax: \begin{cases}…\end{cases}, rows end with \\, elements separated by &.

Example:

$$
  f(n) =
    \begin{cases}
      n/2,  & \text{if $n$ is even} \\\n      3n+1, & \text{if $n$ is odd}
    \end{cases}
$$

Alternative form:

$$
  \left.
    \begin{array}{l}
    \text{if $n$ is even:}&n/2\\
    \text{if $n$ is odd:}&3n+1
    \end{array}
  \right\}
  =f(n)
$$

Equation Numbering

Syntax: \tag.

Example:

$$
  y=x^2        \tag{1.5a}
$$