20
E SSENTIAL LATEX
A
Mathematical symbols
"
&
\alpha
\epsilon
\theta
\lambda
o
\varrho
\upsilon
\psi
\beta
\varepsilon
\vartheta
\mu
\pi
\sigma
\phi
\omega
\Gamma
\Xi
\Phi
#
'
\Delta
\Pi
\Psi
\gamma
\zeta
\iota
\nu
\varpi
\varsigma
\varphi
$
(
\delta
\eta
\kappa
\xi
\rho
\tau
\chi
!
\Theta
\Sigma
\Omega
\Lambda
\Upsilon
%
Table 1: Greek letters
)
1
5
9
=
B
F
J
@
\pm
\mp
\times
\div
\ast
\star
\circ
\bullet
\cdot
*
\cap
\cup
\uplus
\sqcap
\sqcup
\vee
\wedge
\setminus
\wr
.
2
6
:
>
C
G
K
+
\diamond
\bigtriangleup
\bigtriangledown
\triangleleft
\triangleright
\lhd @
\rhd @
\unlhd @
\unrhd @
/
3
7
;
?
D
H
L
,
0
4
8
<
A
E
I
M
\oplus
\ominus
\otimes
\oslash
\odot
\bigcirc
\dagger
\ddagger
\amalg
Not predefined in LATEX 2N . Use the packages latexsym or amssymb
Table 2: Binary operation symbols
O
U
Z
^
c
g
l
S
S
\leq
\succ
\simeq
\parallel
\subseteq
\sqsupset
\doteq
=
P
V
R
_
q
m
hS
d
\geq
\sim
\mid
\subset
\supseteq
\neq
\frown
\vdash
Q
W
[
`
VS
i
n
r
\equiv
\perp
\ll
\supset
\cong
\smile
\in
\dashv
Table 3: Relation symbols
RS
X
\
a
e
s
o
j
\models
\preceq
\gg
\approx
\Join
\sqsubseteq
\ni
<
T
Y
]
;b7
f
k
p
t
\prec
\succeq
\asymp
\bowtie
\sqsubset
\sqsupseteq
\propto
>
E SSENTIAL LATEX
21
\rmoustache
\arrowvert
\lmoustache
\Arrowvert
\rgroup
\lgroup
\bracevert
Table 4: Large delimiters
R
\uparrow
\{
\lfloor
\langle
|
^
\Uparrow
\}
\rfloor
\rangle
\|
\downarrow
\updownarrow
\lceil
/
\Downarrow
\Updownarrow
\rceil
\backslash
G
Table 5: Delimiters
!
'
$#
*
\leftarrow
\Leftarrow
\rightarrow
\Rightarrow
\leftrightarrow
\Leftrightarrow
\mapsto
\hookleftarrow
\leftharpoonup
\leftharpoondown
!
%
(
+
S
S
\longleftarrow
\Longleftarrow
\longrightarrow
\Longrightarrow
\longleftrightarrow
\Longleftrightarrow
\longmapsto
\hookrightarrow
\rightharpoonup
\rightharpoondown
\uparrow
\Uparrow
\downarrow
\Downarrow
\updownarrow
\Updownarrow
\nearrow
\searrow
\swarrow
\nwarrow
)
&
"
,
Table 6: Arrow symbols
.
l l l
3
7
=
@
F
W
\ldots
\prime
\exists
\Diamond @
\top
\bot
\mho @
/
4
98
>
B
J J J
G
\cdots
\forall
\nabla
\imath
\flat
\clubsuit
\Re
..
.
0
5
:
?
H
C
\vdots
\infty
\surd
\jmath
\natural
\diamondsuit
\Im
Not predefined in LATEX 2N . Use the packages latexsym or amssymb
Table 7: Miscellaneous symbols
1
..
6
;
D
@
I
.
\ddots
\hbar
\Box @
\ell
\sharp
\heartsuit
\angle
2
/
J
<
E
A
\aleph
\emptyset
\triangle
\neg
\wp
\spadesuit
\partial
22
E SSENTIAL LATEX
\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
\hat{a}
\check{a}
\acute{a}
\grave{a}
\bar{a}
\vec{a}
\dot{a}
\ddot{a}
\breve{a}
\tilde{a}
Table 9: Math mode accents
\sum
\bigcap
\bigodot
\prod
\bigcup
\bigotimes
\coprod
\bigsqcup
\bigoplus
\int
\bigvee
\biguplus
Table 10: Variable-sized symbols
!"!#
5
%'&
\widetilde{abc}
\overleftarrow{abc}
\overline{abc}
\overbrace{abc}
\sqrt{abc}
f’
"!#!
5 $ ,.@)-0(+* /
\widehat{abc}
\overrightarrow{abc}
\underline{abc}
\underbrace{abc}
\sqrt[n]{abc}
\frac{abc}{xyz}
Table 11: LATEX math constructs
13
6
:
8
=
@
C
F
@
\hbar
\triangledown
\circledS
\nexists
\Game @
\varnothing
\blacksquare
\sphericalangle
\diagup @
1
4
FI
;
G
A
D
>
\hslash
\square
\angle
\mho
\Bbbk @
\blacktriangle
\blacklozenge
\complement
\diagdown @
2
5
9
<
E
B
7
?
\vartriangle
\lozenge
\measuredangle
\Finv @
\backprime
\blacktriangledown
\bigstar
\eth
Not defined in style amssymb, define using the LATEX 2N \DeclareMathSymbol command
Table 12: AMS miscellaneous symbols
\oint
\bigwedge
E SSENTIAL LATEX
\digamma
23
\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
0
Table 16: AMS negated arrows
1
4
7
:
@
=
F
C
\dotplus
\Cup
\doublebarwedge
\boxdot
\ltimes
\rightthreetimes
\circleddash
\centerdot
2
5
8
;
>
G
D
A
\smallsetminus
\barwedge
\boxminus
\boxplus
\rtimes
\curlywedge
\circledast
\intercal
Table 17: AMS binary operators
3
6
9
<
?
B
E
\Cap
\veebar
\boxtimes
\divideontimes
\leftthreetimes
\curlyvee
\circledcirc
24
E SSENTIAL LATEX
\leqq
\lesssim
\lessdot
\lesseqgtr
\risingdotseq
\backsimeq
\sqsubset
\precsim
\trianglelefteq
\smallsmile
\Bumpeq
\eqslantgtr
\gtrdot
\gtreqless
\circeq
\thickapprox
\sqsupset
\succsim
\trianglerighteq
\shortparallel
\varpropto
\backepsilon
f
#
&
)
,
g
1
4
7
:
=
!
$
'
*
-
/
2
5
8
;
>
\leqslant
\lessapprox
\lll
\lesseqqgtr
\fallingdotseq
\subseteqq
\preccurlyeq
\precapprox
\vDash
\smallfrown
\geqq
\gtrsim
\ggg
\gtreqqless
\triangleq
\supseteqq
\succcurlyeq
\succapprox
\Vdash
\between
\blacktriangleleft
\blacktriangleright
"
%
(
+
.
0
3
6
9
<
?
\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
@
C
F
I
L
O
R
U
X
[
^
a
d
g
i
o
l
\nless
\nleqq
\lvertneqq
\nprec
\precnapprox
\nmid
\ntriangleleft
\subsetneq
\varsubsetneqq
\ngeqslant
\gneqq
\gnapprox
\succnsim
\nshortparallel
\nVDash
\nsupseteq
\varsupsetneq
A
D
G
J
M
P
S
V
Y
\
_
b
e
h
p
m
j
\nleq
\lneq
\lnsim
\npreceq
\nsim
\nvdash
\ntrianglelefteq
\varsubsetneq
\ngtr
\ngeqq
\gvertneqq
\nsucc
\succnapprox
\nparallel
\ntriangleright
\nsupseteqq
\supsetneqq
B
E
H
K
N
Q
T
W
Z
]
`
c
f
Q
k
n
q
Table 19: AMS negated binary relations
\nleqslant
\lneqq
\lnapprox
\precnsim
\nshortmid
\nvDash
\nsubseteq
\subsetneqq
\ngeq
\gneq
\gnsim
\nsucceq
\ncong
\nvDash
\ntrianglerighteq
\supsetneq
\varsupsetneqq
E SSENTIAL LATEX
B
25
Horrible Mathematical Examples to Study
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#% 8
(3)
\begin{equation}
\prod_{j\geq 0}
\left(\sum_{k\geq 0}a_{jk} zˆk\right)
= \sum_{k\geq 0} zˆn
\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}
\begin{equation}
\pi(n) = \sum_{m=2}ˆ{n}
\left\lfloor \left(\sum_{k=1}ˆ{m-1}
\lfloor(m/k)/\lceil m/k\rceil
\rfloor \right)ˆ{-1}
\right\rfloor
\end{equation}
\begin{equation}
\{\underbrace{%
\overbrace{\mathstrut a,\ldots,a}ˆ{k\ a’s},
\overbrace{\mathstrut b,\ldots,b}ˆ{l\ b’s}}
_{k+1\ \mathrm{elements}}
\}
\end{equation}
\begin{displaymath}
\mbox{W}ˆ+\
\begin{array}{l}
\nearrow\raise5pt\hbox{$\muˆ+ + \nu_{\mu}$}\\
\rightarrow
\piˆ+ +\piˆ0
\\[5pt]
\rightarrow \kappaˆ+ +\piˆ0
\\
\searrow\lower5pt\hbox{$\mathrm{e}ˆ+
+\nu_{\scriptstyle\mathrm{e}}$}
\end{array}
\end{displaymath}
W
l l l
\begin{equation}
\phi(t)=\frac{1}{\sqrt{2\pi}}
\intˆt_0 eˆ{-xˆ2/2} dx
\end{equation}
` ,.& & ` -0& & ` -&
` ,&
` -&
b
ii
ii
ii c
S
b
\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}
26
E SSENTIAL LATEX
)
6
ii ii
6
ii
ii
6
a 6
i Z
Di 6
D 6
D ii
ii : 6
ii
ii
L
L L Z
S
D 6
D a
!6
Z
: 6
6 i
ii
i
: 6
: !
ii
ii
i
D i : i
ii : ii
ii
i
\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|ˆ2
+
\left|\begin{array}{cc}m_1&n_1\\
n_1&l_1\end{array}\right|ˆ2
+
\left|\begin{array}{cc}m_2&n_2\\
n_2&l_2\end{array}\right|ˆ2}}
\end{displaymath}
& Z Z Z
Z
& @@A1
& (6)
I
GG
\newcommand{\CA}{C_{\rm A}}
\newcommand{\CV}{C_{\rm V}}
\newcommand{\CPA}{{C’}_{\rm A}} \newcommand{\CPV}{{C’}_{\rm V}}
\newcommand{\GZ}{\Gammaˆ2_{\rm Z}}
\newcommand{\MZ}{Mˆ2_{\rm Z}}
\newcommand{\MZs}{{(s-Mˆ2_{\rm Z})}}
\newcommand{\BE}{\left\{\frac{\displaystyle 3-\betaˆ2}{\displaystyle 2}\right\}}
\begin{eqnarray}
\sigmaˆf_0(Q,T_{3R},\beta,s) & = &
\frac{4\pi\alphaˆ2}{3s}\beta \times
\left[ \frac{Qˆ2 \BE - 2Q \CV \CPV s \MZs}{\MZsˆ2 + \MZ \GZ \BE}
\right.
\nonumber \\[-3mm]
&
&
\\[-3mm]
& + &
\left.\frac{(\CVˆ2 + \CAˆ2) sˆ2}%
{\MZsˆ2+\MZ\GZ\left\{\CPVˆ2 \BE+\CPAˆ2 \{\betaˆ2\}\right\}}
\right]
\nonumber
\end{eqnarray}
Bibliography
1 Leslie Lamport. LATEX—A Document Preparation System—User’s 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.
3 Michel Goossens, Frank Mittelbach and Alexander Samarin. The LATEX Companion AddisonWesley, Reading, MA, USA, 1993.