（一）數(shù)學符號列表

希臘字母

Symbol	Script	Symbol	Script
and	A and \alpha	and	N and \nu
and	B and \beta	and	\Xi and \xi
and	\Gamma and \gamma	and	O and o
and	\Delta and \delta	, and	\Pi, \pi and \varpi
, and	E, \epsilon and \varepsilon	, and	P, \rho and \varrho
and	Z and \zeta	, and	\Sigma, \sigma and \varsigma
and	H and \eta	and	T and \tau
, and	\Theta, \theta and \vartheta	and	\Upsilon and \upsilon
and	I and \iota	, and	\Phi, \phi and \varphi
, and	K, \kappa and \varkappa	and	X and \chi
and	\Lambda and \lambda	and	\Psi and \psi
and	M and \mu	and	\Omega and \omega

三角函數(shù)

Symbol	Script		Symbol	Script		Symbol	Script		Symbol	Script
	\sin			\arcsin			\sinh			\sec
	\cos			\arccos			\cosh			\csc
	\tan			\arctan			\tanh
	\cot						\coth

關(guān)系符號

Symbol	Script		Symbol	Script
	<			>
	\leq			\geq
	\ll			\gg
	\subset			\supset
	\subseteq			\supseteq
	\nsubseteq			\nsupseteq
	\sqsubset			\sqsupset
	\sqsubseteq			\sqsubseteq
	\preceq			\succeq
	\because			\therefore

Symbol	Script		Symbol	Script		Symbol	Script
	=			\parallel			\nparallel
	\doteq			\asymp			\bowtie
	\equiv			\vdash			\dashv
	\approx			\in			\ni
	\cong			\smile			\frown
	\simeq			\models			\notin
	\sim			\perp			\mid
	\propto			\prec			\succ
	\neq			\sphericalangle			\measuredangle

二元運算

Symbol	Script		Symbol	Script		Symbol	Script		Symbol	Script
	\pm			\cap			\diamond			\oplus
	\mp			\cup			\bigtriangleup			\ominus
	\times			\uplus			\bigtriangledown			\otimes
	\div			\sqcap			\triangleleft			\oslash
	\ast			\sqcup			\triangleright			\odot
	\star			\vee			\bigcirc			\circ
	\dagger			\wedge			\bullet			\setminus
	\ddager			\cdot			\wr			\amalg

集合邏輯

Symbol	Script		Symbol	Script
	\exists			\rightarrow
	\nexists			\leftarrow
	\forall			\mapsto
	\neg			\implies
	\subset			\Rightarrow
	\supset			\leftrightarrow
	\in			\iff
	\notin			\Leftrightarrow
	\ni			\top
	\land			\bot
	\lor		and	\emptyset and \varnothing
	\angle			\rightleftharpoons

界限

Symbol	Script		Symbol	Script		Symbol	Script		Symbol	Script
	\mid						/			\backslash
	{			}			\langle			\rangle
	\uparrow			\Uparrow			\lceil			\rceil
	\downarrow			\Downarrow			\lfloor			\rfloor

其他

Symbol	Script		Symbol	Script		Symbol	Script		Symbol	Script		Symbol	Script
	\partial			\imath			\Re			\nabla			\aleph
	\eth			\jmath			\Im			\Box			\beth
	\hbar			\ell			\wp			\infty			\gimel

求和積分

Symbol	Script		Symbol	Script		Symbol	Script
	\sum			\prod			\coprod
	\bigoplus			\bigotimes			\bigodot
	\bigcup			\bigcap			\biguplus
	\bigsqcup			\bigvee			\bigwedge
	\int			\oint			\iint
	\iiint			\iiiint			\idotsint

自定義操作符

$\operatorname{arg\,max}_a f(a)  = \operatorname*{arg\,max}_b f(b)$
$\DeclareMathOperator*{\argmax}{arg\,max}
\argmax_c f(c)$

（二）上下標

上標^
下標_

• 例子一
  k_{n+1} = n^2 + k_n^2 - k_{n-1}
  
• 例子二
  n^{22}
  
• 例子三
  f(n) = n^5 + 4n^2 + 2 |_{n=17}
  

（三）分數(shù)與二項式

分數(shù)\frac{numerator}{denominator}
二項式\binom{numerator}{numerator}

• 例子一
  \frac{n!}{k!(n-k)!} = \binom{n}{k}
  
• 例子二
  \frac{\frac{1}{x}+\frac{1}{y}}{y-z}
  
• 例子三
  ^3/_7
  
• 連分數(shù)

\begin{equation}
  x = a_0 + \cfrac{1}{a_1 
          + \cfrac{1}{a_2 
          + \cfrac{1}{a_3 + \cfrac{1}{a_4} } } }
\end{equation}

• 兩數(shù)相乘

\begin{equation}
\frac{
    \begin{array}[b]{r}
      \left( x_1 x_2 \right)\\
      \times \left( x'_1 x'_2 \right)
    \end{array}
  }{
    \left( y_1y_2y_3y_4 \right)
  }
\end{equation}

（四）根

根\sqrt

• 例子一
  \sqrt{\frac{a}侈离}
  
• 例子二
  \sqrt[n]{1+x+x^2+x^3+\dots+x^n}
  

（五）求和積分

求和\sum
積分\int

• 例子一
  \sum_{i=1}^{10} t_i
  
• 例子二
  \int_0^\infty \mathrm{e}^{-x}\,\mathrmmggcnlcx
  
• \substack用法

\sum_{\substack{
   0<i<m \\
   0<j<n
  }} 
 P(i,j)

• 改變位置
  \int\limits_a^b
  

（六）括號分割符

• 自動調(diào)整大小
  \left隧饼，\right巡李，\middle斟或。
  \left(\frac{x^2}{y^3}\right)

P\left(A=2\middle|\frac{A^2}{B}>4\right)

\left\{\frac{x^2}{y^3}\right\}

\left.\frac{x^3}{3}\right|_0^1
  
• 手動調(diào)整大小
  ( \big( \Big( \bigg( \Bigg(

\frac{\mathrm d}{\mathrm d x} \left( k g(x) \right)

\frac{\mathrm d}{\mathrm d x} \big( k g(x) \big)
  

（七）矩陣

• 例子

\begin{matrix}
  a & b & c \\
  d & e & f \\
  g & h & i
 \end{matrix}

• 矩陣類型與對齊（不支持對齊）

• 例子

A_{m,n} = 
 \begin{pmatrix}
  a_{1,1} & a_{1,2} & \cdots & a_{1,n} \\
  a_{2,1} & a_{2,2} & \cdots & a_{2,n} \\
  \vdots  & \vdots  & \ddots & \vdots  \\
  a_{m,1} & a_{m,2} & \cdots & a_{m,n} 
 \end{pmatrix}

\begin{array}{c|c}
  1 & 2 \\ 
  \hline
  3 & 4
 \end{array}

• 增加間隔

M = \begin{bmatrix}
       \frac{5}{6} & \frac{1}{6} & 0           \\[0.3em]
       \frac{5}{6} & 0           & \frac{1}{6} \\[0.3em]
       0           & \frac{5}{6} & \frac{1}{6}
     \end{bmatrix}

• smallmatrix

A matrix in text must be set smaller:
$\bigl(\begin{smallmatrix}
a&b \\ c&d
\end{smallmatrix} \bigr)$
to not increase leading in a portion of text.

A matrix in text must be set smaller:

to not increase leading in a portion of text.

（八）文本格式

• 文本
  
• 字體

公式	例子
\mathrm{…}
\mathit{…}
\mathbf{…}
\mathsf{…}
\mathtt{…}
\mathfrak{…}
\mathcal{…}
\mathbb{…}
\mathscr{…}

• 例子
  
• 強調(diào)

公式	例子		公式	例子
	a'			a''
	\hat{a}			\bar{a}
	\grave{a}			\acute{a}
	\dot{a}			\ddot{a}
	\not{a}			\mathring{a}
	\overrightarrow{a}			\overleftarrow{a}
	a'''			a''''
	\overline{aaa}			\check{a}
	\breve{a}			\vec{a}
	\dddot{a}			\ddddot{a}
	\widehat{AAA}			\widetilde{AAA}
	\stackrel\frown{AAA}
	\tilde{a}			\underline{a}

（九）顏色

k = {\color{red}x} \mathbin{\color{blue}-} 2

顏色	代碼
	\color{black}{text}
	\color{gray}{text}
	\color{silver}{text}
	\color{white}{text}
	\color{maroon}{text}
	\color{red}{text}
	\color{yellow}{text}
	\color{lime}{text}
	\color{olive}{text}
	\color{green}{text}
	\color{teal}{text}
	\color{aqua}{text}
	\color{blue}{text}
	\color{navy}{text}
	\color{purple}{text}
	\color{fuchsia}{text}

（十）控制

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

• 空格

\int y\, \mathrmr2dnc2kx

\int y\: \mathrmbt3jurjx

\int y\; \mathrmy8itacpx

• 例子

\left(
    \begin{array}{c}
      n \\
      r
    \end{array}
  \right) = \frac{n!}{r!(n-r)!}

\left(\!
    \begin{array}{c}
      n \\
      r
    \end{array}
  \!\right) = \frac{n!}{r!(n-r)!}

• 定義新命令
  
• 例子

\begin{equation}
   C^i_j = {\textstyle \sum_k} A^i_k B^k_j
\end{equation}

例子	公式
	\dots
	\ldots
	\cdots
	\vdots
	\ddots

• 例子

$A_1,A_2,\dotsc,$
$A_1+\dotsb+A_N$
$A_1 \dotsm A_N$
$\int_a^b \dotsi$
$A_1\dotso A_N$

（十一）特殊用法

• 其他位置標記
  \overset，\underset。

A \overset{!}{=} B; A \stackrel{!}{=} B

\lim_{x\to 0}{\frac{e^x-1}{2x}}
 \overset{\left[\frac{0}{0}\right]}{\underset{\mathrm{H}}{=}}
 \lim_{x\to 0}{\frac{e^x}{2}}={\frac{1}{2}}

\overbrace辛辨，\underbrace十气。

z = \overbrace{
   \underbrace{x}_\text{real} + i
   \underbrace{y}_\text{imaginary}
  }^\text{complex number}

y = a + f(\underbrace{b x}_{
                    \ge 0 \text{ by assumption}}) 

A \xleftarrow{\text{this way}} B 
  \xrightarrow[\text{or that way}]{ } C

• 對齊

$\begin{align*}
 f(x)  &= a x^2+b x +c   &   g(x)  &= d x^3 \\
 f'(x) &= 2 a x +b       &   g'(x) &= 3 d x^2
\end{align*}$

• case

f(x) = \left\{
  \begin{array}{lr}
    x^2 & : x < 0\\
    x^3 & : x \ge 0
  \end{array}
\right.

u(x) = 
  \begin{cases} 
   \exp{x} & \text{if } x \geq 0 \\
   1       & \text{if } x < 0
  \end{cases}

\begin{equation}
 \left.\begin{aligned}
        B'&=-\partial \times E,\\
        E'&=\partial \times B - 4\pi j,
       \end{aligned}
 \right\}
 \qquad \text{Maxwell's equations}
\end{equation}

\begin{alignat}{2}
 \sigma_1 &= x + y  &\quad \sigma_2 &= \frac{x}{y} \\   
 \sigma_1' &= \frac{\partial x + y}{\partial x} & \sigma_2' 
    &= \frac{\partial \frac{x}{y}}{\partial x}
\end{alignat}

\begin{gather*}
a_0=\frac{1}{\pi}\int\limits_{-\pi}^{\pi}f(x)\,\mathrma2krrmkx\\[6pt]
\begin{split}
a_n=\frac{1}{\pi}\int\limits_{-\pi}^{\pi}f(x)\cos nx\,\mathrmapalhu7x=\\
=\frac{1}{\pi}\int\limits_{-\pi}^{\pi}x^2\cos nx\,\mathrm2yfqeg3x
\end{split}\\[6pt]
\begin{split}
b_n=\frac{1}{\pi}\int\limits_{-\pi}^{\pi}f(x)\sin nx\,\mathrma7vozbgx=\\
=\frac{1}{\pi}\int\limits_{-\pi}^{\pi}x^2\sin nx\,\mathrm787al22x
\end{split}\\[6pt]
\end{gather*}

begin{equation}
 \boxed{x^2+y^2 = z^2}
\end{equation}

\begin{equation}
  \lim_{a\to \infty} \tfrac{1}{a}
\end{equation}

\begin{equation}
  \lim\nolimits_{a\to \infty} \tfrac{1}{a}
\end{equation}

\begin{equation}
  \int_a^b x^2  \mathrm3vrrr37 x
\end{equation}

\begin{equation}
  \int\limits_a^b x^2  \mathrm3hhlhuo x
\end{equation}

\begin{equation}
  \lim_{a \underset{>}{\to} 0} \frac{1}{a}
\end{equation}

\begin{equation}
  \sum\nolimits' C_n
\end{equation}

\begin{equation}
  \sum_{n=1}\nolimits' C_n
\end{equation}

\begin{equation}
  \sideset{}{'}\sum_{n=1}C_n
\end{equation}

\begin{equation}
  \sideset{_a^b}{_c^d}\sum
\end{equation}

\begin{equation}
  {\sum\limits_{n=1} }'C_n
\end{equation}

• 字體大小

命令	例子
\displaystyle {ABCDabcd1234}
\textstyle{ABCDabcd1234}
\scriptstyle{ABCDabcd1234}
\scriptscriptstyle{ABCDabcd1234}

\begin{equation}
  x = a_0 + \frac{1}{a_1 + \frac{1}{a_2 + \frac{1}{a_3 + a_4}}}
\end{equation}

\begin{equation}
  x = a_0 + \frac{1}{\displaystyle a_1 
          + \frac{1}{\displaystyle a_2 
          + \frac{1}{\displaystyle a_3 + a_4}}}
\end{equation}

$a \equiv b \pmod n$