1. LaTeX 数学公式基础知识

LaTeX的强大之处在于对数学符号和公式的排版，所以jupyter notebook采用LaTeX来进行数学符号和公式的显示排版。
首先，在jupyter notebook 里面，LaTeX数学公式用$$括起来。
数学模式和文本模式又很多的不同之处。例如在数学模式中：

1. 空格和分行都会被忽略，所有的空格或是由数学表达式逻辑的衍生，或是由特殊命令如\，\quad或\qquad来得到。空格可以用 或者 表示
2. 不允许有空行，每个公式中只能有一个段落。
3. 每个字符都将被看作是一个变量名并以此来排版。

2. 常用的排版命令

分式
命令\frac{a}{b}形式：$\frac{a}{b}$
命令\sum_{i=1}^n p_i形式：${\sum }_{i=1}^n{p}_i$

3. 常用的数学模式命令

1. 数学模式重音符

Symbol	Command	Symbol	Command	Symbol	Command
$\hat{a}$	\hat{a}	$\grave{a}$	\grave{a}	$\bar{a}$	\bar{a}
$\check{a}$	\check{a}	$\dot{a}$	\dot{a}	$\vec{a}$	\vec{a}
$\tilde{a}$	\tilde{a}	$\ddot{a}$	\ddot{a}	$\hat{A}$	\widehat{A}
$\acute{a}$	\acute{a}	$\breve{a}$	\breve{a}	$\tilde{A}$	\widetilde{A}

2. 小写希腊字母

Symbol	Command	Symbol	Command	Symbol	Command
$\alpha$	\alpha	$\theta$	\theta	$o$	o
$\beta$	\beta	$\vartheta$	\vartheta	$\pi$	\pi
$\gamma$	\gamma	$\iota$	\iota	$\varpi$	\varpi
$\delta$	\delta	$\kappa$	\kappa	$\rho$	\rho
$ϵ$	\epsilon	$\lambda$	\lambda	$\varrho$	\varrho
$\epsilon$	\varepsilon	$\mu$	\mu	$\sigma$	\sigma
$\zeta$	\zeta	$\nu$	\nu	$\varsigma$	\varsigma
$\eta$	\eta	$\xi$	\xi	$\tau$	\tau
$\upsilon$	\upsilon	$\varphi$	\phi	$\phi$	\varphi
$\chi$	\chi	$\psi$	\psi	$\omega$	\omega

3. 大写希腊字母

Symbol	Command	Symbol	Command	Symbol	Command
$\Gamma$	\Gamma	$\Lambda$	\Lambda	$\Sigma$	\Sigma
$\Delta$	\Delta	$\Xi$	\Xi	${\rm Y}$	\Upsilon
$\Theta$	\Theta	$\Pi$	\Pi	$\Phi$	\Phi
$\Psi$	\Psi	$\Omega$	\Omega

4. 二元关系符

Symbol	Command	Symbol	Command	Symbol	Command
$>$	>	$<$	<	$=$	=
$\le$	\leq or \le	$\ge$	\geq or \ge	$\equiv$	\equiv
$\ll$	\ll	$\gg$	\gg	$\doteq$	\doteq
$\prec$	\prec	$\succ$	\succ	$\sim$	\sim
$⪯$	\preceq	$⪰$	\succeq	$\simeq$	\simeq
$\subset$	\subset	$\supset$	\supset	$\approx$	\approx
$\subseteq$	\subseteq	$\supseteq$	\supseteq	$\cong$	\cong
$⊏$	\sqsubset	$⊐$	\sqsupset	$\bowtie$	\Join
$⊑$	\sqsubseteq	$⊒$	\sqsupseteq	$\bowtie$	\bowtie
$\in$	\in	$\ni$	\ni or \owns	$\propto$	\propto
$⊢$	\vdash	$⊣$	\dashv	$\models$	\models
$\mid$	\mid	$\parallel$	\parallel	$\perp$	\perp
$⌣$	\smile	$⌢$	\frown	$\asymp$	\asymp
$:$	:	$\notin$	\notin	$̸=$	\neq or \ne

5. 二元运算符

Symbol	Command	Symbol	Command	Symbol	Command
$+$	+	$-$	-
$\pm$	\pm	$\mp$	\mp	$◃$	\triangleleft
$\cdot$	\cdot	$÷$	\div	$▹$	\triangleright
$\times$	\times	$\setminus$	\setminus	$\star$	\star
$\cup$	\cup	$\cap$	\cap	$\ast$	\ast
$\bigsqcup$	\sqcup	$\sqcap$	\sqcap	$\circ$	\circ
$\vee$	\vee or \lor	$\wedge$	\wedge or \land	$\bullet$	\bullet
$\oplus$	\oplus	$\ominus$	\ominus	$\diamond$	\diamond
$\odot$	\odot	$\oslash$	\oslash	$\uplus$	\uplus
$\otimes$	\otimes	$◯$	\bigcirc	$⨿$	\amalg
$△$	\bigtriangleup	$▽$	\bigtriangledown	$†$	\dagger
$⊲$	\lhd	$⊳$	\rhd	$‡$	\ddagger
$⊴$	\unlhd	$⊵$	\unrhd	$\wr$	\wr

6. 大尺寸运算符

Symbol	Command	Symbol	Command	Symbol	Command
$\sum$	\sum	$\bigcup$	\bigcup	$\bigcap$	\bigcap
$\bigvee$	\bigvee	$⨁$	\bigoplus	$\prod$	\prod
$\bigwedge$	\bigwedge	$⨂$	\bigotimes	$\coprod$	\coprod
$⨆$	\bigsqcup	$⨀$	\bigodot	$\int$	\int
$\oint$	\oint	$⨄$	\biguplus

7. 箭头

Symbol	Command	Symbol	Command	Symbol	Command
$\leftarrow$	\leftarrow or \gets	$⟵$	\longleftarrow	$\uparrow$	\uparrow
$\to$	\rightarrow or \to	$⟶$	\longrightarrow	$\downarrow$	\downarrow
$\leftrightarrow$	\leftrightarrow	$⟷$	\longleftrightarrow	$\updownarrow$	\updownarrow
$\Leftarrow$	\Leftarrow	$⟸$	\Longleftarrow	$\Uparrow$	\Uparrow
$\Rightarrow$	\Rightarrow	$⟹$	\Longrightarrow	$\Downarrow$	\Downarrow
$\iff$	\Leftrightarrow	$⟺$	\Longleftrightarrow	$\Updownarrow$	\Updownarrow
$\mapsto$	\mapsto	$⟼$	\longmapsto	$\nearrow$	\nearrow
$\hookleftarrow$	\hookleftarrow	$\hookrightarrow$	\hookrightarrow	$\searrow$	\searrow
$\leftharpoonup$	\leftharpoonup	$\rightharpoonup$	\rightharpoonup	$\swarrow$	\swarrow
$\leftharpoondown$	\leftharpoondown	$\rightharpoondown$	\rightharpoondown	$\nwarrow$	\nwarrow
$\rightleftharpoons$	\rightleftharpoons	$⟺$	\iff	$⇝$	\leadsto

8. 定界符

Symbol	Command	Symbol	Command	Symbol	Command
$($	(	$)$	)	$\uparrow$	\uparrow
$[$	[ or \lbrack	$]$	] or \rbrack	$\downarrow$	\downarrow
{ \{ {	{ or \lbrace	$\}$	} or \rbrace	$\updownarrow$	\updownarrow
$⟨$	\langle	$⟩$	\rangle	$\Uparrow$	\Uparrow
$	$	\vert	$\Vert$	| or \Vert	$\Downarrow$
$\lfloor$	\lfloor	$\rfloor$	\rfloor	$\Updownarrow$	\Updownarrow
$\lceil$	\lceil	$\rceil$	\rceil	$/$	/
$\backslash$	\backslash

9. 大尺寸定界符

Symbol	Command	Symbol	Command	Symbol	Command
$⟮$	\lgroup	$⟯$	\rgroup	$⎰$	\lmoustache
$⎱$	\rmoustache	KaTeX parse error: Expected 'EOF', got '\arrowvert' at position 1: \̲a̲r̲r̲o̲w̲v̲e̲r̲t̲	\arrowvert	KaTeX parse error: Expected 'EOF', got '\Arrowvert' at position 1: \̲A̲r̲r̲o̲w̲v̲e̲r̲t̲	\Arrowvert
KaTeX parse error: Expected 'EOF', got '\bracevert' at position 1: \̲b̲r̲a̲c̲e̲v̲e̲r̲t̲	\bracevert

10. 其他符号

Symbol	Command	Symbol	Command	Symbol	Command
$\dots$	\dots	$\cdots$	\cdots	$⋮$	\vdots
$\ddots$	\ddots	$\hslash$	\hbar	$ı$	\imath
$ȷ$	\jmath	$\ell$	\ell	$\Re$	\Re
$\Im$	\Im	$\aleph$	\aleph	$\wp$	\wp
$\forall$	\forall	$\exists$	\exists	$\mho$	\mho
$\partial$	\partial	${}^{\prime }$	’	$\prime$	\prime
$\varnothing$	\emptyset	$\infty$	\infty	$\nabla$	\nabla
$△$	\triangle	$\square$	\Box	$◊$	\Diamond
$\perp$	\bot	$\top$	\top	$\angle$	\angle
$\surd$	\surd	$♢$	\diamondsuit	$♡$	\heartsuit
$♣$	\clubsuit	$♠$	\spadesuit	$\neg$	\neg or \lnot
$♭$	\flat	$♮$	\natural	$♯$	\sharp

11. 非数学符号

Symbol	Command
KaTeX parse error: Expected 'EOF', got '\S' at position 1: \̲S̲	\S

12. AMS定界符

Symbol	Command	Symbol	Command	Symbol	Command
$┌$	\ulcorner	$┐$	\urcorner	$└$	\llcorner
$┘$	\lrcorner	$|$	\lvert	$|$	\rvert
$\Vert$	\lVert	$\Vert$	\rVert

13. AMS希腊和希伯来字母

Symbol	Command	Symbol	Command	Symbol	Command
$ϝ$	\digamma	$\varkappa$	\varkappa	$\beth$	\beth
$\daleth$	\daleth	$\gimel$	\gimel

14. AMS二元关系符

Symbol	Command	Symbol	Command	Symbol	Command
$⋖$	\lessdot	$⋗$	\gtrdot	$\doteqdot$	\doteqdot or \Doteq
$⩽$	\leqslant	$⩾$	\geqslant	$\risingdotseq$	\risingdotseq
$⪕$	\eqslantless	$⪖$	\eqslantgtr	$\fallingdotseq$	\fallingdotseq
$\leqq$	\leqq	$\geqq$	\geqq	$\eqcirc$	\eqcirc
$⋘$	\lll or \llless	$⋙$	\ggg or \gggtr	$\circeq$	\circeq
$\lesssim$	\lesssim	$\gtrsim$	\gtrsim	$\triangleq$	\triangleq
$⪅$	\lessapprox	$⪆$	\gtrapprox	$\bumpeq$	\bumpeq
$\lessgtr$	\lessgtr	$\gtrless$	\gtrless	$\Bumpeq$	\Bumpeq
$⋚$	\lesseqgtr	$⋛$	\gtreqless	$\sim$	\thicksim
$⪋$	\lesseqqgtr	$⪌$	\gtreqqless	$\approx$	\thickapprox
$\preccurlyeq$	\preccurlyeq	$\succcurlyeq$	\succcurlyeq	$\approxeq$	\approxeq
$⋞$	\curlyeqprec	$⋟$	\curlyeqsucc	$\backsim$	\backsim
$\precsim$	\precsim	$\succsim$	\succsim	$\backsimeq$	\backsimeq
$⪷$	\precapprox	$⪸$	\succapprox	$\models$	\vDash
$⫅$	\subseteqq	$⫆$	\supseteqq	$⊩$	\Vdash
$⋐$	\Subset	$⋑$	\Supset	$\Vvdash$	\Vvdash
$⊏$	\sqsubset	$⊐$	\sqsupset	$∍$	\backepsilon
$\therefore$	\therefore	$\because$	\because	$\propto$	\varpropto
$ϝ$	\digamma	$\varkappa$	\varkappa	$\beth$	\beth
$ϝ$	\digamma	$\varkappa$	\varkappa	$\beth$	\beth

15. AMS箭头

Symbol	Command	Symbol	Command	Symbol	Command
$⇠$	\dashleftarrow	$⇢$	\dashrightarrow	$⊸$	\multimap
$\leftleftarrows$	\leftleftarrows	$\rightrightarrows$	\rightrightarrows	$\upuparrows$	\upuparrows
$\leftrightarrows$	\leftrightarrows	$\rightleftarrows$	\rightleftarrows	$\downdownarrows$	\downdownarrows
$\Lleftarrow$	\Lleftarrow	$\Rrightarrow$	\Rrightarrow	$\upharpoonleft$	\upharpoonleft
$\twoheadleftarrow$	\twoheadleftarrow	$\twoheadrightarrow$	\twoheadrightarrow	$\upharpoonright$	\upharpoonright
$\leftarrowtail$	\leftarrowtail	$\rightarrowtail$	\rightarrowtail	$\downharpoonleft$	\downharpoonleft
$\leftrightharpoons$	\leftrightharpoons	$\rightleftharpoons$	\rightleftharpoons	$\downharpoonright$	\downharpoonright
$\Lsh$	\Lsh	$\Rsh$	\Rsh	$⇝$	\rightsquigarrow
$\looparrowleft$	\looparrowleft	$\looparrowright$	\looparrowright	$\leftrightsquigarrow$	\leftrightsquigarrow
$\curvearrowleft$	\curvearrowleft	$\curvearrowright$	\curvearrowright	$\circlearrowleft$	\circlearrowleft
$\circlearrowright$	\circlearrowright

16. AMS二元否定关系符和箭头

Symbol	Command	Symbol	Command	Symbol	Command
$\nless$	\nless	$\ngtr$	\ngtr	$$	\varsubsetneqq
$⪇$	\lneq	$⪈$	\gneq	$$	\varsupsetneqq
$\nleqq$	\nleq	$\ngeqq$	\ngeq	$$	\nsubseteqq
$$	\nleqslant	$$	\ngeqslant	$$	\nsupseteqq
$\lneqq$	\lneqq	$\gneqq$	\gneqq	$\nmid$	\nmid
$$	\lvertneqq	$$	\gvertneqq	$\nparallel$	\nparallel
$$	\nleqq	$$	\ngeqq	$$	\nshortmid
$⋦$	\lnsim	$⋧$	\gnsim	$$	\nshortparallel
$⪉$	\lnapprox	$⪊$	\gnapprox	$\nsim$	\nsim
$\nprec$	\nprec	$\nsucc$	\nsucc	$≆$	\ncong
$⋠$	\npreceq	$⋡$	\nsucceq	$⊬$	\nvdash
$⪵$	\precneqq	$⪶$	\succneqq	$⊭$	\nvDash
$⋨$	\precnsim	$⋩$	\succnsim	$⊮$	\nVdash
$⪹$	\precnapprox	$⪺$	\succnapprox	$⊯$	\nVDash
$⊊$	\subsetneq	$⊋$	\supsetneq	$⋪$	\ntriangleleft
$$	\varsubsetneq	$$	\varsupsetneq	$⋫$	\ntriangleright
$⊈$	\nsubseteq	$⊉$	\nsupseteq	$⋬$	\ntrianglelefteq
$⫋$	\subsetneqq	$⫌$	\supsetneqq	$⋭$	\ntrianglerighteq
$\nleftarrow$	\nleftarrow	$\nrightarrow$	\nrightarrow	$\nleftrightarrow$	\nleftrightarrow
$\nLeftarrow$	\nLeftarrow	$\nRightarrow$	\nRightarrow	$\nLeftrightarrow$	\nLeftrightarrow

17. AMS二元运算符

Symbol	Command	Symbol	Command	Symbol	Command
$\dotplus$	\dotplus	$\cdot$	\centerdot	$⊺$	\intercal
$⋉$	\ltimes	$⋊$	\rtimes	$\divideontimes$	\divideontimes
$⋓$	\Cup or \doublecup	$⋒$	\Cap or \doublecap	$\setminus$	\smallsetminus
$⊻$	\veebar	$⊼$	\barwedge	$⩞$	\doublebarwedge
$⊞$	\boxplus	$\boxminus$	\boxminus	$⊝$	\circleddash
$⊠$	\boxtimes	$⊡$	\boxdot	$⊚$	\circledcirc
$⋋$	\leftthreetimes	$⋌$	\rightthreetimes	$⊛$	\circledast
$⋎$	\curlyvee	$⋏$	\curlywedge

18. AMS其它符号

Symbol	Command	Symbol	Command	Symbol	Command
$\hslash$	\hbar	$\hslash$	\hslash	$k$	\Bbbk
$\square$	\square	$■$	\blacksquare	$Ⓢ$	\circledS
$△$	\vartriangle	$▲$	\blacktriangle	$\complement$	\complement
$▽$	\triangledown	$▼$	\blacktriangledown	$⅁$	\Game
$◊$	\lozenge	$⧫$	\blacklozenge	$★$	\bigstar
$\angle$	\angle	$\measuredangle$	\measuredangle	$\sphericalangle$	\sphericalangle
$╱$	\diagup	$╲$	\diagdown	$‵$	\backprime
$\nexists$	\nexists	$Ⅎ$	\Finv	$\varnothing$	\varnothing
$ð$	\eth	$\mho$	\mho