（一）数学符号列表

希腊字母

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

三角函数

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

关系符号

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

二元运算

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

集合逻辑

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

求和积分

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

自定义操作符

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

（二）上下标

上标^
下标_

• 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）分数与二项式

分数\frac{numerator}{denominator}
二项式\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
  
• 连分数

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

• 两数相乘

\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}{b}}
  
• 例子二
  \sqrt[n]{1+x+x^2+x^3+\dots+x^n}
  

（五）求和积分

求和\sum
积分\int

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

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

• 改变位置
  \int\limits_a^b
  

（六）括号分割符

• 自动调整大小
  \left，\right，\middle。
  \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
  
• 手动调整大小
  ( \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）矩阵

• 例子

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

• 矩阵类型与对齐（不支持对齐）

• 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}

• 增加间隔

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
  
• 字体

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

• 例子
  
• 强调

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）颜色

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

颜色	代码
	\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\, \mathrm{d}x

\int y\: \mathrm{d}x

\int y\; \mathrm{d}x

• 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)!}

• 定义新命令
  
• 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

• 其他位置标记
  \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，\underbrace。

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

• 对齐

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

• 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)\,\mathrm{d}x\\[6pt]
\begin{split}
a_n=\frac{1}{\pi}\int\limits_{-\pi}^{\pi}f(x)\cos nx\,\mathrm{d}x=\\
=\frac{1}{\pi}\int\limits_{-\pi}^{\pi}x^2\cos nx\,\mathrm{d}x
\end{split}\\[6pt]
\begin{split}
b_n=\frac{1}{\pi}\int\limits_{-\pi}^{\pi}f(x)\sin nx\,\mathrm{d}x=\\
=\frac{1}{\pi}\int\limits_{-\pi}^{\pi}x^2\sin nx\,\mathrm{d}x
\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  \mathrm{d} x
\end{equation}

\begin{equation}
  \int\limits_a^b x^2  \mathrm{d} 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}

• 字体大小

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}

$a \equiv b \pmod n$