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AT X E SSENTIAL L E

A Mathematical symbols

\alpha \epsilon \theta \lambda o \varrho \upsilon \psi

\beta \varepsilon \vartheta \mu \pi \sigma \phi \omega

\gamma \zeta \iota \nu \varpi \varsigma \varphi

\delta \eta \kappa \xi \rho \tau \chi

\Gamma \Xi \Phi

\Delta \Pi \Psi

\Theta \Sigma \Omega

\Lambda \Upsilon

Table 1: Greek letters

9 

\pm \mp \times \div \ast \star \circ \bullet \cdot

\cap \cup \uplus \sqcap \sqcup \vee \wedge \setminus \wr

A Not predened in L TEX 2 . Use the packages latexsym or amssymb

\diamond \bigtriangleup \bigtriangledown \triangleleft \triangleright \lhd 9 \rhd 9 \unlhd 9 \unrhd 9

\oplus \ominus \otimes \oslash \odot \bigcirc \dagger \ddagger \amalg

Table 2: Binary operation symbols \leq \succ \simeq \parallel \subseteq \sqsupset \doteq =

\geq \sim \mid \subset \supseteq \neq \frown \vdash

\equiv \perp \ll \supset \cong \smile \in \dashv

\models \preceq \gg \approx \Join \sqsubseteq \ni <

\prec \succeq \asymp \bowtie \sqsubset \sqsupseteq \propto >

Table 3: Relation symbols

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21

\rmoustache \arrowvert

\lmoustache \Arrowvert

\rgroup \bracevert

\lgroup

Table 4: Large delimiters \uparrow \{ \lfloor \langle |

 

\Uparrow \} \rfloor \rangle \|

   

\downarrow \updownarrow \lceil /

   
  *  $ ' 

\Downarrow \Updownarrow \rceil \backslash

Table 5: Delimiters

    " # ( + !%

\leftarrow \Leftarrow \rightarrow \Rightarrow \leftrightarrow \Leftrightarrow \mapsto \hookleftarrow \leftharpoonup \leftharpoondown

   !  ! # & ) ,

\longleftarrow \Longleftarrow \longrightarrow \Longrightarrow \longleftrightarrow \Longleftrightarrow \longmapsto \hookrightarrow \rightharpoonup \rightharpoondown

\uparrow \Uparrow \downarrow \Downarrow \updownarrow \Updownarrow \nearrow \searrow \swarrow \nwarrow

Table 6: Arrow symbols

2 7 = K ; B

\ldots \prime \exists \Diamond \top \bot \mho

3 ; > G
A L T

./.0. 8 C L

\cdots \forall \nabla \imath \flat \clubsuit \Re

. . .

4 9 H M

\vdots \infty \surd \jmath \natural \diamondsuit \Im

5 @ E I N

..

\ddots \hbar \Box \ell \sharp \heartsuit \angle

6 A O J <

1 F

\aleph \emptyset \triangle \neg \wp \spadesuit \partial

Not predened in

EX 2 . Use the packages latexsym or amssymb

Table 7: Miscellaneous symbols

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AT X E SSENTIAL L E

\arccos \arcsin \arctan \arg

\cos \cosh \cot \coth

\csc \deg \det \dim

\exp \gcd \hom \inf

\ker \lg \lim \liminf

\limsup \ln \log \max

\min \Pr \sec \sin

\sinh \sup \tan \tanh

Table 8: Log-like symbols

QP [ ` e

QV

\hat{a} \check{a}

QR QW \ a f

\acute{a} \grave{a}

Q Q SX ] b g

\bar{a} \vec{a}

QT QY

\dot{a} \ddot{a}

QU QZ

\breve{a} \tilde{a}

Table 9: Math mode accents \sum \bigcap \bigodot \prod \bigcup \bigotimes \coprod \bigsqcup \bigoplus

^ c h

\int \bigvee \biguplus

_ d

\oint \bigwedge

Table 10: Variable-sized symbols

i jml Qo k Qkjm l Qkjml qsQx ruju twl v 9 { Qxjul z| 5 ;

\widetilde{abc} \overleftarrow{abc} \overline{abc} \overbrace{abc} \sqrt{abc} f

Qk l pn  jm Qk jml Qkjml tsQx vuju qwl r 9 y Qxjul ;mm }~ 0

\widehat{abc} \overrightarrow{abc} \underline{abc} \underbrace{abc} \sqrt[n]{abc} \frac{abc}{xyz}

A Table 11: L TEX math constructs

\hbar \triangledown \circledS \nexists \Game \varnothing \blacksquare \sphericalangle \diagup

KN

\hslash \square \angle \mho \Bbbk \blacktriangle \blacklozenge \complement \diagdown

\vartriangle \lozenge \measuredangle \Finv \backprime \blacktriangledown \bigstar \eth

A Not dened in style amssymb, dene using the L TEX 2 \DeclareMathSymbol command

Table 12: AMS miscellaneous symbols

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23

us

\digamma

\varkappa

\beth

\daleth

\gimel

Table 13: AMS Greek and Hebrew \ulcorner \urcorner \llcorner

\lrcorner

Table 14: AMS delimiters \dashrightarrow \leftrightarrows \leftarrowtail \curvearrowleft \upuparrows \multimap \rightleftarrows \twoheadrightarrow \rightleftharpoons \Rsh \downharpoonright

\dashleftarrow \Lleftarrow \looparrowleft \circlearrowleft \upharpoonleft \leftrightsquigarrow \rightrightarrows \rightarrowtail \curvearrowright \downdownarrows \rightsquigarrow

\leftleftarrows \twoheadleftarrow \leftrightharpoons \Lsh \downharpoonleft \rightrightarrows \rightleftarrows \looparrowright \circlearrowright \upharpoonright

Table 15: AMS arrows \nleftarrow \nRightarrow

\nrightarrow \nleftrightarrow

\nLeftarrow \nLeftrightarrow

Table 16: AMS negated arrows \dotplus \Cup \doublebarwedge \boxdot \ltimes \rightthreetimes \circleddash \centerdot

\smallsetminus \barwedge \boxminus \boxplus \rtimes \curlywedge \circledast \intercal

\Cap \veebar \boxtimes \divideontimes \leftthreetimes \curlyvee \circledcirc

Table 17: AMS binary operators

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AT X E SSENTIAL L E

    

\leqq \lesssim \lessdot \lesseqgtr \risingdotseq \backsimeq \sqsubset \precsim \trianglelefteq \smallsmile \Bumpeq \eqslantgtr \gtrdot \gtreqless \circeq \thickapprox \sqsupset \succsim \trianglerighteq \shortparallel \varpropto \backepsilon

     

\leqslant \lessapprox \lll \lesseqqgtr \fallingdotseq \subseteqq \preccurlyeq \precapprox \vDash \smallfrown \geqq \gtrsim \ggg \gtreqqless \triangleq \supseteqq \succcurlyeq \succapprox \Vdash \between \blacktriangleleft \blacktriangleright

       

\eqslantless \approxeq \lessgtr \doteqdot \backsim \Subset \curlyeqprec \vartriangleleft \Vvdash \bumpeq \geqslant \gtrapprox \gtrless \eqcirc \thicksim \Supset \curlyeqsucc \vartriangleright \shortmid \pitchfork \therefore \because

Table 18: AMS binary relations

# & / , 2 5 8 ; A I G D L O > )

\nless \nleqq \lvertneqq \nprec \precnapprox \nmid \ntriangleleft \subsetneq \varsubsetneqq \ngeqslant \gneqq \gnapprox \succnsim \nshortparallel \nVDash \nsupseteq \varsupsetneq

! ' 0 3 6 9 < ? H E J M P B * $

\nleq \lneq \lnsim \npreceq \nsim \nvdash \ntrianglelefteq \varsubsetneq \ngtr \ngeqq \gvertneqq \nsucc \succnapprox \nparallel \ntriangleright \nsupseteqq \supsetneqq

" ( 1 . + 4 7 : @ 1 F K N Q C = %

\nleqslant \lneqq \lnapprox \precnsim \nshortmid \nvDash \nsubseteq \subsetneqq \ngeq \gneq \gnsim \nsucceq \ncong \nvDash \ntrianglerighteq \supsetneq \varsupsetneqq

Table 19: AMS negated binary relations

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25

B Horrible Mathematical Examples to Study

]_^ f eXgihkjdl Y Z\[ `badc

(2)

\begin{equation} \phi(t)=\frac{1}{\sqrt{2\pi}} \intt_0 e{-x2/2} dx \end{equation}

m Q n vxw vzy{ n o `rsu p q vt o `

{ Q `x\` Q v y w | vt o ` d }qs ~X  t ~~ i   ~X

(3)

\begin{equation} \prod_{j\geq 0} \left(\sum_{k\geq 0}a_{jk} zk\right) = \sum_{k\geq 0} zn \left( \sum_{{k_0,k_1,\ldots\geq 0} \atop{k_0+k_1+\ldots=n} } a{_0k_0}a_{1k_1}\ldots \right) \end{equation}

[ SVW

c  V S vt t h |

  

c 0k

(4)

\begin{equation} \pi(n) = \sum_{m=2}{n} \left\lfloor \left(\sum_{k=1}{m-1} \lfloor(m/k)/\lceil m/k\rceil \rfloor \right){-1} \right\rfloor \end{equation}

v ; t Q } t v j v q jz ru q Q ru t vp vu q r 

(5)

\begin{equation} \{\underbrace{% \overbrace{\mathstrut a,\ldots,a}{k\ as}, \overbrace{\mathstrut b,\ldots,b}{l\ bs}} _{k+1\ \mathrm{elements}} \} \end{equation}

$ 

[  '

\ ` [ ` [

\begin{displaymath} \mbox{W}+\ \begin{array}{l} \nearrow\raise5pt\hbox{$\mu+ + \nu_{\mu}$}\\ \rightarrow \pi+ +\pi0 \\[5pt] \rightarrow \kappa+ +\pi0 \\ \searrow\lower5pt\hbox{$\mathrm{e}+ +\nu_{\scriptstyle\mathrm{e}}$} \end{array} \end{displaymath}

Sl W \

{{ {{ 0 m {

{{ {{ 0 m {

{{

\begin{displaymath} {F}(x,y)=0\quad\mathrm{and}\quad \left|\begin{array}{ccc} F_{xx} & F_{xy} & F_{x} \\ F_{yx} & F_{yy} & F_{y} \\ F_{x} & F_{y} & 0 \end{array} \right| =0 \end{displaymath}

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AT X E SSENTIAL L E

h h h

l h

h h

h h h h h

wh

\begin{displaymath} \frac{\pm \left|\begin{array}{ccc} x_1-x_2 & y_1-y_2 & z_1-z_2 \\ l_1 & m_1 & n_1 \\ l_2 & m_2 & n_2 \end{array}\right|}{ \sqrt{\left|\begin{array}{cc}l_1&m_1\\ l_2&m_2\end{array}\right|2 + \left|\begin{array}{cc}m_1&n_1\\ n_1&l_1\end{array}\right|2 + \left|\begin{array}{cc}m_2&n_2\\ n_2&l_2\end{array}\right|2}} \end{displaymath}

` S Xi W

[ h _

h  { S  x Z Z S _ h h h h  h  x Z S h h W h h  { h h S _ h h h h { h  x  Z

(6)

\newcommand{\CA}{C_{\rm A}} \newcommand{\CV}{C_{\rm V}} \newcommand{\CPA}{{C}_{\rm A}} \newcommand{\CPV}{{C}_{\rm V}} \newcommand{\GZ}{\Gamma2_{\rm Z}} \newcommand{\MZ}{M2_{\rm Z}} \newcommand{\MZs}{{(s-M2_{\rm Z})}} \newcommand{\BE}{\left\{\frac{\displaystyle 3-\beta2}{\displaystyle 2}\right\}} \begin{eqnarray} \sigmaf_0(Q,T_{3R},\beta,s) & = & \frac{4\pi\alpha2}{3s}\beta \times \left[ \frac{Q2 \BE - 2Q \CV \CPV s \MZs}{\MZs2 + \MZ \GZ \BE} \right. \nonumber \\[-3mm] & & \\[-3mm] & + & \left.\frac{(\CV2 + \CA2) s2}% {\MZs2+\MZ\GZ\left\{\CPV2 \BE+\CPA2 \{\beta2\}\right\}} \right] \nonumber \end{eqnarray}

Bibliography
A 1 Leslie Lamport. L TEXA Document Preparation SystemUsers Guide and Reference Manual. Addison-Wesley, Reading, MA, USA, 1985.

2 Donald E. Knuth. The TEXbook, volume A of Computers and Typesetting. Addison-Wesley, Reading, MA, USA, 1986.
A 3 Michel Goossens, Frank Mittelbach and Alexander Samarin. The L TEX Companion AddisonWesley, Reading, MA, USA, 1993.