LATEX Mathematical Symbols - Rice University
[Pages:4]LATEX Mathematical Symbols
The more unusual symbols are not defined in base LATEX (NFSS) and require \usepackage{amssymb}
1 Greek and Hebrew letters
\alpha \beta \chi \delta
\epsilon \eta \gamma \iota
\kappa \lambda ? \mu \nu oo \omega \phi \pi
\psi \rho \sigma \tau \theta \upsilon \xi \zeta
\digamma \varepsilon \varkappa \varphi
\varpi \varrho \varsigma \vartheta
\Delta \Gamma \Lambda \Omega \Phi \Pi \Psi \Sigma
\Theta \Upsilon \Xi
\aleph \beth \daleth
\gimel
2 LATEX math constructs
abc xyz
f abc n abc
\frac{abc}{xyz} f'
\sqrt{abc} \sqrt[n]{abc}
abc \overline{abc} abc \underline{abc}
abc \widehat{abc} abc \widetilde{abc}
- abc \overrightarrow{abc} - abc \overleftarrow{abc}
abc \overbrace{abc} abc \underbrace{abc}
3 Delimiters
|| | \vert
\| \Vert
{ \{ } \}
\langle \rangle
\lfloor / / \rfloor \ \backslash \lceil [ [ \rceil ] ]
\Uparrow \uparrow \Downarrow \downarrow
\llcorner \lrcorner \ulcorner \urcorner
Use the pair \lefts1 and \rights2 to match height of delimiters s1 and s2 to the height of their contents, e.g.,
\left| expr \right|
\left\{ expr \right\}
\left\Vert expr \right.
4 Variable-sized symbols (displayed formulae show larger version)
\sum \prod \coprod
\int \oint \iint
\biguplus \bigcap \bigcup
\bigoplus \bigotimes \bigodot
\bigvee \bigwedge \bigsqcup
5 Standard Function Names
Function names should appear in Roman, not Italic, e.g.,
arccos cos csc exp ker lim sup min sinh
\arccos \cos \csc \exp \ker \limsup \min \sinh
arcsin cosh deg gcd lg ln Pr sup
\arcsin \cosh \deg \gcd \lg \ln \Pr \sup
Correct: \tan(at-n\pi) - tan(at - n) Incorrect: tan(at-n\pi) - tan(at - n)
arctan cot det hom lim log sec tan
\arctan \cot \det \hom \lim \log \sec \tan
arg coth dim inf lim inf max sin tanh
\arg \coth \dim \inf \liminf \max \sin \tanh
6 Binary Operation/Relation Symbols
\ast \star
? \cdot \circ ? \bullet
\bigcirc \diamond ? \times ? \div \centerdot \circledast \circledcirc \circleddash \dotplus \divideontimes
? \pm \mp
\amalg \odot \ominus \oplus \oslash \otimes \wr \Box \boxplus \boxminus \boxtimes \boxdot \square
\cap \cup
\uplus \sqcap \sqcup \wedge \vee \dagger \ddagger \barwedge \curlywedge \Cap \bot \intercal \doublebarwedge
\lhd \rhd \triangleleft \triangleright \unlhd \unrhd \bigtriangledown \bigtriangleup \ \setminus \veebar \curlyvee \Cup \top \rightthreetimes \leftthreetimes
\equiv = \cong
= \neq
\sim
\simeq
\approx
=.
\asymp \doteq
\propto
|= \models
\leq \prec
\preceq \ll \subset \subseteq \sqsubset \sqsubseteq \dashv \in
\geq \succ \succeq \gg
\supset \supseteq
\sqsupset \sqsupseteq \vdash \ni
\perp | \mid
\parallel \bowtie \Join \ltimes \rtimes \smile \frown / \notin
\approxeq \thicksim
\backsim
\backsimeq
\triangleq \circeq \bumpeq \Bumpeq \doteqdot \thickapprox \fallingdotseq \risingdotseq \varpropto \therefore \because \eqcirc = \neq
\leqq \leqslant
\geqq \geqslant
\lessgtr \lesseqgtr
\lessapprox
\gtrapprox
\lesseqqgtr
\lll
\ggg
\gtreqqless
\lessdot \lesssim \eqslantless \precsim \precapprox \Subset \subseteqq \sqsubset \preccurlyeq \curlyeqprec \blacktriangleleft \trianglelefteq \vartriangleleft
\gtrdot
\gtreqless
\gtrsim
\gtrless
\eqslantgtr
\backepsilon
\succsim
\between
\succapprox
\pitchfork
\Supset
\shortmid
\supseteqq
\smallfrown
\sqsupset
\smallsmile
\succcurlyeq
\Vdash
\curlyeqsucc
\vDash
\blacktriangleright
\Vvdash
\trianglerighteq
\shortparallel
\vartriangleright
\nshortparallel
\ncong
\nleq
\nmid
\nleqq
\nparallel
\nleqslant
\nshortmid
\nless
\nshortparallel \nprec
\nsim
\npreceq
\nVDash
\precnapprox
\nvDash
\precnsim
\nvdash
\lnapprox
\ntriangleleft
\lneq
\ntrianglelefteq
\lneqq
\ntriangleright
\lnsim
\ntrianglerighteq
\lvertneqq
\ngeq \ngeqq \ngeqslant \ngtr \nsucc \nsucceq \succnapprox \succnsim \gnapprox \gneq \gneqq \gnsim \gvertneqq
\nsubseteq \nsupseteq \nsubseteqq \nsupseteqq \subsetneq \supsetneq \subsetneqq \supsetneqq \varsubsetneq \varsupsetneq \varsubsetneqq \varsupsetneqq
7 Arrow symbols
\leftarrow \Leftarrow \rightarrow \Rightarrow \leftrightarrow \Leftrightarrow
\mapsto \hookleftarrow
\leftharpoonup \leftharpoondown \rightleftharpoons
\dashrightarrow \leftrightarrows \leftarrowtail \curvearrowleft \upuparrows \multimap \rightleftarrows \twoheadrightarrow \rightleftharpoons \Rsh \downharpoonright
\nleftarrow \nRightarrow
- \longleftarrow = \Longleftarrow - \longrightarrow = \Longrightarrow \longleftrightarrow \Longleftrightarrow
- \longmapsto \hookrightarrow
\rightharpoonup \rightharpoondown \leadsto
\dashleftarrow \Lleftarrow \looparrowleft \circlearrowleft \upharpoonleft \leftrightsquigarrow \rightrightarrows \rightarrowtail \curvearrowright \downdownarrows \rightsquigarrow
\nrightarrow \nleftrightarrow
8 Miscellaneous symbols
\infty \nabla \partial ? \eth \clubsuit \diamondsuit \heartsuit \spadesuit ? ? ? \cdots ... \vdots . . . \ldots . . . \ddots
\Im \Re
\forall \exists
\nexists \emptyset \varnothing i \imath \jmath
\ell \iiiint
\iiint \iint
\sharp \flat \natural
k \Bbbk \bigstar \diagdown \diagup
\Diamond \Finv \Game \hbar \hslash
\lozenge \mho
\prime \square
\surd
9 Math mode accents
a? \acute{a} a \breve{a} a? \ddot{a} a` \grave{a} a~ \tilde{a}
a? \bar{a} a \check{a} a \dot{a} a^ \hat{a} a \vec{a}
A?? \Acute{\Acute{A}} A \Breve{\Breve{A}} A?? \Ddot{\Ddot{A}} A`` \Grave{\Grave{A}}
A~~ \Tilde{\Tilde{A}}
\uparrow \Uparrow \downarrow \Downarrow
\updownarrow \Updownarrow
\nearrow \searrow \swarrow \nwarrow
\leftleftarrows \twoheadleftarrow \leftrightharpoons \Lsh \downharpoonleft
\rightrightarrows \rightleftarrows \looparrowright \circlearrowright \upharpoonright
\nLeftarrow \nLeftrightarrow
\wp \angle
\measuredangle \sphericalangle \complement \triangledown \triangle \vartriangle \blacklozenge
\blacksquare \blacktriangle
\blacktrinagledown \backprime \circledS
A? \Bar{\Bar{A}} A \Check{\Check{A}} A \Dot{\Dot{A}} A^^ \Hat{\Hat{A}} A \Vec{\Vec{A}}
10 Array environment, examples
Simplest version:
\begin{array}{cols} row1 \\ row2 \\ . . . rowm \end{array}
where cols includes one character [lrc] for each column (with optional characters | inserted for vertical lines)
and rowj includes character & a total of (n - 1) times to separate the n elements in the row. Examples:
\left( \begin{array}{cc} 2\tau & 7\phi-frac5{12} \\ 3\psi & \frac{\pi}8 \end{array} \right)
\left( \begin{array}{c} x \\ y \end{array} \right) \mbox{~and~} \left[ \begin{array}{cc|r}
3 & 4 & 5 \\ 1 & 3 & 729 \end{array} \right]
2 3
7
-
5 12
8
x y
and
34 5 1 3 729
f(z) = \left\{ \begin{array}{rcl} \overline{\overline{z^2}+\cos z} & \mbox{for} & |z|5 \end{array}\right.
z2 + cos z for |z| < 3
f (z) =
0 for 3 |z| 5
sin z for |z| > 5
11 Other Styles (math mode only)
Caligraphic letters: $\mathcal{A}$ etc.: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Mathbb letters: $\mathbb{A}$ etc.: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Mathfrak letters: $\mathfrak{A}$ etc.: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z a b c 1 2 3 Math Sans serif letters: $\mathsf{A}$ etc.: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z a b c 1 2 3 Math bold letters: $\mathbf{A}$ etc.: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z a b c 1 2 3 Math bold italic letters: define \def\mathbi#1{\textbf{\em #1}} then use $\mathbi{A}$ etc.:
ABCDEFGHIJKLMNOPQRSTUVWXYZ abc 123
12 Font sizes
Math Mode:
f -1(x - xa) dx
f -1(x - xa) dx
f -1(x-xa) dx
f -1(x-xa ) dx
Text Mode:
\tiny = smallest \scriptsize = very small \footnotesize = smaller \small = small
${\displaystyle \int f^{-1}(x-x_a)\,dx}$
${\textstyle \int f^{-1}(x-x_a)\,dx}$ ${\scriptstyle \int f^{-1}(x-x_a)\,dx}$ ${\scriptscriptstyle \int f^{-1}(x-x_a)\,dx}$
\normalsize = normal
\large = large
\Large = Large
\LARGE = LARGE
\huge = huge
Huge \Huge =
13 Text Mode: Accents and Symbols
?o \'{o} ?o \"{o} ^o \^{o}
o \.{o} o \u{o} o \H{o}
o ??
\b{o} \o
?A s
\AA \t s
?a \aa s \v s
? \ae ? \AE \dag
`o \`{o} oo \t{oo} ? \ss ? \O \ddag
~o \~{o} o? \c{o} i \i ? \P c \copyright
?o \={o} o. \d{o}
s. \d s ?s \r s
\j
s \H s
? \S
? \pounds
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