Math Symbols Guide

User Manual:

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L
A
T
E
X Mathematical Symbols
The more unusual symbols are not defined in base L
A
T
E
X (NFSS) and require \usepackage{amssymb}
1 Greek and Hebrew letters
α\alpha κ\kappa ψ\psi \digamma ∆\Delta Θ\Theta
β\beta λ\lambda ρ\rho ε\varepsilon Γ\Gamma Υ\Upsilon
χ\chi µ\mu σ\sigma κ\varkappa Λ\Lambda Ξ\Xi
δ\delta ν\nu τ\tau ϕ\varphi Ω\Omega
\epsilon ooθ\theta \varpi Φ\Phi ℵ\aleph
η\eta ω\omega υ\upsilon \varrho Π\Pi \beth
γ\gamma φ\phi ξ\xi ς\varsigma Ψ\Psi \daleth
ι\iota π\pi ζ\zeta ϑ\vartheta Σ\Sigma ג\gimel
2 L
A
T
E
X math constructs
abc
xyz \frac{abc}{xyz}abc \overline{abc}−→
abc \overrightarrow{abc}
f0f’ abc \underline{abc}←−
abc \overleftarrow{abc}
√abc \sqrt{abc}c
abc \widehat{abc}z}|{
abc \overbrace{abc}
n
√abc \sqrt[n]{abc}f
abc \widetilde{abc}abc
|{z} \underbrace{abc}
3 Delimiters
| | { \{ b\lfloor //⇑\Uparrow x\llcorner
|\vert }\} c\rfloor \\backslash ↑\uparrow y\lrcorner
k\| h\langle d\lceil [[⇓\Downarrow p\ulcorner
k\Vert i\rangle e\rceil ]]↓\downarrow q\urcorner
Use the pair \lefts1and \rights2to match height of delimiters s1and s2to 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)
P\sum R\int U\biguplus L\bigoplus W\bigvee
Q\prod H\oint T\bigcap N\bigotimes V\bigwedge
`\coprod RR \iint S\bigcup J\bigodot F\bigsqcup
5 Standard Function Names
Function names should appear in Roman, not Italic, e.g., Correct: \tan(at-n\pi) −→ tan(at −nπ)
Incorrect: tan(at-n\pi) −→ tan(at −nπ)
arccos \arccos arcsin \arcsin arctan \arctan arg \arg
cos \cos cosh \cosh cot \cot coth \coth
csc \csc deg \deg det \det dim \dim
exp \exp gcd \gcd hom \hom inf \inf
ker \ker lg \lg lim \lim lim inf \liminf
lim sup \limsup ln \ln log \log max \max
min \min Pr \Pr sec \sec sin \sin
sinh \sinh sup \sup tan \tan tanh \tanh
6 Binary Operation/Relation Symbols
∗\ast ±\pm ∩\cap C\lhd
\star ∓\mp ∪\cup B\rhd
·\cdot q\amalg ]\uplus \triangleleft
◦\circ \odot u\sqcap \triangleright
•\bullet \ominus t\sqcup E\unlhd
\bigcirc ⊕\oplus ∧\wedge D\unrhd
\diamond \oslash ∨\vee 5\bigtriangledown
×\times ⊗\otimes †\dagger 4\bigtriangleup
÷\div o\wr ‡\ddagger \\setminus
\centerdot \Box Z\barwedge Y\veebar
~\circledast \boxplus f\curlywedge g\curlyvee
}\circledcirc \boxminus e\Cap d\Cup
\circleddash \boxtimes ⊥\bot >\top
u\dotplus \boxdot |\intercal i\rightthreetimes
\divideontimes \square [\doublebarwedge h\leftthreetimes
≡\equiv ≤\leq ≥\geq ⊥\perp
∼
=\cong ≺\prec \succ |\mid
6=\neq \preceq \succeq k\parallel
∼\sim \ll \gg \bowtie
'\simeq ⊂\subset ⊃\supset \Join
≈\approx ⊆\subseteq ⊇\supseteq \ltimes
\asymp @\sqsubset A\sqsupset \rtimes
.
=\doteq v\sqsubseteq w\sqsupseteq \smile
∝\propto a\dashv `\vdash \frown
|=\models ∈\in 3\ni /∈\notin
\approxeq 5\leqq =\geqq ≶\lessgtr
∼\thicksim 6\leqslant >\geqslant Q\lesseqgtr
v\backsim /\lessapprox '\gtrapprox S\lesseqqgtr
w\backsimeq ≪\lll ≫\ggg T\gtreqqless
,\triangleq \lessdot \gtrdot R\gtreqless
$\circeq .\lesssim &\gtrsim ≷\gtrless
l\bumpeq 0\eqslantless 1\eqslantgtr \backepsilon
m\Bumpeq -\precsim %\succsim G\between
+\doteqdot \precapprox \succapprox t\pitchfork
≈\thickapprox b\Subset c\Supset \shortmid
;\fallingdotseq j\subseteqq k\supseteqq a\smallfrown
:\risingdotseq @\sqsubset A\sqsupset `\smallsmile
∝\varpropto 4\preccurlyeq <\succcurlyeq \Vdash
∴\therefore 2\curlyeqprec 3\curlyeqsucc \vDash
∵\because J\blacktriangleleft I\blacktriangleright \Vvdash
P\eqcirc E\trianglelefteq D\trianglerighteq \shortparallel
6=\neq C\vartriangleleft B\vartriangleright \nshortparallel
\ncong \nleq \ngeq \nsubseteq
\nmid \nleqq \ngeqq \nsupseteq
∦\nparallel \nleqslant \ngeqslant \nsubseteqq
\nshortmid ≮\nless ≯\ngtr \nsupseteqq
\nshortparallel ⊀\nprec \nsucc \subsetneq
\nsim \npreceq \nsucceq \supsetneq
\nVDash \precnapprox \succnapprox \subsetneqq
\nvDash \precnsim \succnsim \supsetneqq
\nvdash \lnapprox \gnapprox \varsubsetneq
\ntriangleleft \lneq \gneq \varsupsetneq
\ntrianglelefteq \lneqq \gneqq \varsubsetneqq
\ntriangleright \lnsim \gnsim \varsupsetneqq
\ntrianglerighteq \lvertneqq \gvertneqq
7 Arrow symbols
←\leftarrow ←− \longleftarrow ↑\uparrow
⇐\Leftarrow ⇐=\Longleftarrow ⇑\Uparrow
→\rightarrow −→ \longrightarrow ↓\downarrow
⇒\Rightarrow =⇒\Longrightarrow ⇓\Downarrow
↔\leftrightarrow ←→ \longleftrightarrow l\updownarrow
⇔\Leftrightarrow ⇐⇒ \Longleftrightarrow m\Updownarrow
7→ \mapsto 7−→ \longmapsto %\nearrow
←\hookleftarrow →\hookrightarrow &\searrow
\leftharpoonup \rightharpoonup .\swarrow
\leftharpoondown \rightharpoondown -\nwarrow
\rightleftharpoons \leadsto
99K \dashrightarrow L99 \dashleftarrow ⇔\leftleftarrows
\leftrightarrows W\Lleftarrow \twoheadleftarrow
\leftarrowtail "\looparrowleft \leftrightharpoons
\curvearrowleft \circlearrowleft \Lsh
\upuparrows \upharpoonleft \downharpoonleft
(\multimap !\leftrightsquigarrow ⇒\rightrightarrows
\rightleftarrows ⇒\rightrightarrows \rightleftarrows
\twoheadrightarrow \rightarrowtail #\looparrowright
\rightleftharpoons \curvearrowright \circlearrowright
\Rsh \downdownarrows \upharpoonright
\downharpoonright \rightsquigarrow
\nleftarrow \nrightarrow \nLeftarrow
\nRightarrow \nleftrightarrow \nLeftrightarrow
8 Miscellaneous symbols
∞\infty ∀\forall k\Bbbk ℘\wp
∇\nabla ∃\exists F\bigstar ∠\angle
∂\partial \nexists \diagdown ]\measuredangle
ð\eth ∅\emptyset \diagup ^\sphericalangle
♣\clubsuit ∅\varnothing ♦\Diamond {\complement
♦\diamondsuit ı\imath \Finv O\triangledown
♥\heartsuit \jmath \Game 4\triangle
♠\spadesuit \ell \hbar M\vartriangle
··· \cdots RRRR \iiiint \hslash \blacklozenge
.
.
.\vdots RRR \iiint ♦\lozenge \blacksquare
. . . \ldots RR \iint \mho N\blacktriangle
...\ddots \sharp 0\prime H\blacktrinagledown
=\Im \flat \square 8\backprime
<\Re \natural √\surd s\circledS
9 Math mode accents
´a\acute{a}¯a\bar{a}´
´
A\Acute{\Acute{A}} ¯
¯
A\Bar{\Bar{A}}
˘a\breve{a}ˇa\check{a}˘
˘
A\Breve{\Breve{A}} ˇ
ˇ
A\Check{\Check{A}}
¨a\ddot{a}˙a\dot{a}¨
¨
A\Ddot{\Ddot{A}} ˙
˙
A\Dot{\Dot{A}}
`a\grave{a}ˆa\hat{a}`
`
A\Grave{\Grave{A}} ˆ
ˆ
A\Hat{\Hat{A}}
˜a\tilde{a}a \vec{a}˜
˜
A\Tilde{\Tilde{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 rowjincludes character &a total of (n−1) times to separate the nelements 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]
2τ7φ−5
12
3ψπ
8x
yand 3 4 5
1 3 729
f(z) = \left\{ \begin{array}{rcl}
\overline{\overline{z^2}+\cos z} & \mbox{for}
& |z|<3 \\ 0 & \mbox{for} & 3\leq|z|\leq5 \\
\sin\overline{z} & \mbox{for} & |z|>5
\end{array}\right.
f(z) =
z2+ cos zfor |z|<3
0 for 3 ≤ |z| ≤ 5
sin zfor |z|>5
11 Other Styles (math mode only)
Caligraphic letters:$\mathcal{A}$ etc.: ABCDE F G HI J KLMN OP QRS T U V W X Y Z
Mathbb letters:$\mathbb{A}$ etc.: ABCDEFGHIJKLMNOPQRSTUVWXYZ
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:
Zf−1(x−xa)dx ${\displaystyle \int f^{-1}(x-x_a)\,dx}$
Rf−1(x−xa)dx ${\textstyle \int f^{-1}(x-x_a)\,dx}$
Rf−1(x−xa)dx ${\scriptstyle \int f^{-1}(x-x_a)\,dx}$
Rf−1(x−xa)dx ${\scriptscriptstyle \int f^{-1}(x-x_a)\,dx}$
Text Mode:
\tiny =smallest
\scriptsize =very small
\footnotesize =smaller
\small =small
\normalsize = normal
\large =large
\Large =Large
\LARGE =LARGE
\huge =huge
\Huge =Huge
13 Text Mode: Accents and Symbols
´o \’{o} ¨o \"{o} ˆo \^{o} `o \‘{o} ˜o \~{o} ¯o \={o} s
.\d s
˙o \.{o} ˘o \u{o} ˝o \H{o} oo \t{oo} ¸o \c{o} o
.\d{o} ˚s \r s
o
¯\b{o} ˚
A\AA ˚a \aa ß\ss ı\i \j ˝s \H s
ø\o s\t s ˇs \v s Ø\O \P §\S
æ\ae Æ\AE †\dag ‡\ddag c
\copyright £\pounds

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