LATEX Mathematical Symbols - Rutgers University

LATEX Mathematical Symbols

The more unusual symbols are not defined in base LATEX (NFSS) and require \usepackage{amssymb}

1

Greek and Hebrew letters α β χ δ  η γ ι

2

ψ ρ σ τ θ υ ξ ζ

\kappa \lambda \mu \nu o \omega \phi \pi

\psi \rho \sigma \tau \theta \upsilon \xi \zeta

z ε κ ϕ $ % ς ϑ

∆ Γ Λ Ω Φ Π Ψ Σ

\digamma \varepsilon \varkappa \varphi \varpi \varrho \varsigma \vartheta

\Delta \Gamma \Lambda \Omega \Phi \Pi \Psi \Sigma

Θ Υ Ξ

\Theta \Upsilon \Xi

ℵ i k ‫ג‬

\aleph \beth \daleth \gimel

LATEX math constructs abc xyz 0

f √ abc √ n abc

3

κ λ µ ν o ω φ π

\alpha \beta \chi \delta \epsilon \eta \gamma \iota

\frac{abc}{xyz}

abc

\overline{abc}

f’

abc

\underline{abc}

\sqrt{abc} \sqrt[n]{abc}

c abc f abc

\widehat{abc} \widetilde{abc}

−→ abc ←− abc z}|{ abc abc |{z}

\overrightarrow{abc} \overleftarrow{abc} \overbrace{abc} \underbrace{abc}

Delimiters | | k k

| \vert \| \Vert

{ } h i

\{ \} \langle \rangle

b c d e

/ \ [ ]

\lfloor \rfloor \lceil \rceil

/ \backslash [ ]

⇑ ↑ ⇓ ↓

\Uparrow \uparrow \Downarrow \downarrow

x y p q

\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) P Q `

5

\sum \prod \coprod

R H RR

\int \oint \iint

U T S

\biguplus \bigcap \bigcup

L N J

\bigoplus \bigotimes \bigodot

W V F

\bigvee \bigwedge \bigsqcup

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: Incorrect: arctan cot det hom lim log sec tan

\tan(at-n\pi) −→ tan(at − nπ) tan(at-n\pi) −→ tan(at − nπ)

\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

∗ ? · ◦ •

 × ÷  ~ }  u >

\ast \star \cdot \circ \bullet \bigcirc \diamond \times \div \centerdot \circledast \circledcirc \circleddash \dotplus \divideontimes

± ∓ q ⊕  ⊗ o 


≡ ∼ = 6 = ∼ ' ≈  . = ∝ |=



\pm \mp \amalg \odot \ominus \oplus \oslash \otimes \wr \Box \boxplus \boxminus \boxtimes \boxdot \square

∩ ∪ ] u t ∧ ∨ † ‡ Z f e ⊥ | [

\cap \cup \uplus \sqcap \sqcup \wedge \vee \dagger \ddagger \barwedge \curlywedge \Cap \bot \intercal \doublebarwedge

C B / . E D 5 4 \ Y g d > i h

\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

≤ ≺   ⊂ ⊆ @ v a ∈

\leq \prec \preceq \ll \subset \subseteq \sqsubset \sqsubseteq \dashv \in

≥    ⊃ ⊇ A w ` 3

\geq \succ \succeq \gg \supset \supseteq \sqsupset \sqsupseteq \vdash \ni

⊥ | k ./ o n n o ^ _ ∈ /

\perp \mid \parallel \bowtie \Join \ltimes \rtimes \smile \frown \notin

u ∼ v w , $ l m + ≈ ; : ∝ ∴ ∵ P 6 =

\approxeq \thicksim \backsim \backsimeq \triangleq \circeq \bumpeq \Bumpeq \doteqdot \thickapprox \fallingdotseq \risingdotseq \varpropto \therefore \because \eqcirc \neq

5 6 / ≪ l . 0 w b j @ 4 2 J E C

\leqq \leqslant \lessapprox \lll \lessdot \lesssim \eqslantless \precsim \precapprox \Subset \subseteqq \sqsubset \preccurlyeq \curlyeqprec \blacktriangleleft \trianglelefteq \vartriangleleft

= > ' ≫ m & 1 % v c k A < 3 I D B

\geqq \geqslant \gtrapprox \ggg \gtrdot \gtrsim \eqslantgtr \succsim \succapprox \Supset \supseteqq \sqsupset \succcurlyeq \curlyeqsucc \blacktriangleright \trianglerighteq \vartriangleright

≶ Q S T R ≷  G t p a `

  q /

\lessgtr \lesseqgtr \lesseqqgtr \gtreqqless \gtreqless \gtrless \backepsilon \between \pitchfork \shortmid \smallfrown \smallsmile \Vdash \vDash \Vvdash \shortparallel \nshortparallel

 ∦ . /  3 2 0 6 5 7 4

\ncong \nmid \nparallel \nshortmid \nshortparallel \nsim \nVDash \nvDash \nvdash \ntriangleleft \ntrianglelefteq \ntriangleright \ntrianglerighteq

 

≮ ⊀      

\nleq \nleqq \nleqslant \nless \nprec \npreceq \precnapprox \precnsim \lnapprox \lneq \lneqq \lnsim \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

8

Arrow symbols ← ⇐ → ⇒ ↔ ⇔

\leftarrow \Leftarrow \rightarrow \Rightarrow \leftrightarrow \Leftrightarrow

←− ⇐= −→ =⇒ ←→ ⇐⇒

\longleftarrow \Longleftarrow \longrightarrow \Longrightarrow \longleftrightarrow \Longleftrightarrow

↑ ⇑ ↓ ⇓ l m

\uparrow \Uparrow \downarrow \Downarrow \updownarrow \Updownarrow

7→ ←( )

\mapsto \hookleftarrow \leftharpoonup \leftharpoondown \rightleftharpoons

7−→ ,→ * +

\longmapsto \hookrightarrow \rightharpoonup \rightharpoondown \leadsto

% & . -

\nearrow \searrow \swarrow \nwarrow

99K   x  (  

 

\dashrightarrow \leftrightarrows \leftarrowtail \curvearrowleft \upuparrows \multimap \rightleftarrows \twoheadrightarrow \rightleftharpoons \Rsh \downharpoonright

L99 W "  ! ⇒  y 

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

⇔     ⇒  #  

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

8 ;

\nleftarrow \nRightarrow

9 =

\nrightarrow \nleftrightarrow

: <

\nLeftarrow \nLeftrightarrow

Miscellaneous symbols ∞ ∇ ∂ ð ♣ ♦ ♥ ♠ ··· .. . ... .. . = <

9

\infty \nabla \partial \eth \clubsuit \diamondsuit \heartsuit \spadesuit \cdots

∀ ∃ @ ∅ ∅ ı  ` RRRR

\forall \exists \nexists \emptyset \varnothing \imath \jmath \ell \iiiint

k F   ♦ ` a ~ }

\Bbbk \bigstar \diagdown \diagup \Diamond \Finv \Game \hbar \hslash

℘ ∠ ] ^ { O 4 M 

\wp \angle \measuredangle \sphericalangle \complement \triangledown \triangle \vartriangle \blacklozenge

\vdots \ldots

RRR RR

\iiint \iint

♦ f

\lozenge \mho

 N

\blacksquare \blacktriangle

\ddots \Im \Re

] [ \

\sharp \flat \natural

0  √

\prime \square \surd

H 8 s

\blacktrinagledown \backprime \circledS

A¯ Aˇ A˙˙

\Bar{\Bar{A}} \Check{\Check{A}}

ˆ Aˆ ~~ A

\Hat{\Hat{A}}

Math mode accents a ´

\acute{a}

a ¯

\bar{a}

a ˘

\breve{a}

a ˇ

\check{a}

a ¨

\ddot{a}

a˙

\dot{a}

a `

\grave{a}

a ˆ

\hat{a}

a ˜

\tilde{a}

~a

\vec{a}

´ A´ ˘ A˘ A¨¨ ` A` A˜˜

\Acute{\Acute{A}} \Breve{\Breve{A}} \Ddot{\Ddot{A}} \Grave{\Grave{A}} \Tilde{\Tilde{A}}

\Dot{\Dot{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]



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.

11

2τ 3ψ

7φ − π 8

5 12



x y



 and

5 3 4 1 3 729

  z 2 + cos z for |z| < 3 f (z) = 0 for 3 ≤ |z| ≤ 5  sin z for |z| > 5

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 Z R

Math Mode:

f −1 (x − xa ) dx

${\displaystyle \int f^{-1}(x-x_a)\,dx}$

f −1 (x − xa ) dx

${\textstyle \int f^{-1}(x-x_a)\,dx}$ ${\scriptstyle \int f^{-1}(x-x_a)\,dx}$ ${\scriptscriptstyle \int f^{-1}(x-x_a)\,dx}$

R R

Text Mode:

13

f −1 (x−xa ) dx f −1 (x−xa ) dx

\normalsize = normal \large = large \Large = Large

\tiny = smallest \scriptsize = very small \footnotesize = smaller \small = small

\LARGE =

LARGE

\huge =

huge

\Huge =

Huge

Text Mode: Accents and Symbols o´ o˙ o ¯ ø æ

\’{o} \.{o} \b{o} \o \ae

¨o o˘ ˚ A s Æ

\"{o} \u{o} \AA \t s \AE

o ˆ ˝ o ˚ a ˇs †

\^{o} \H{o} \aa \v s \dag

o ` o o ß Ø ‡

\‘{o} \t{oo} \ss \O \ddag

˜o o¸ ı ¶ c

\~{o} \c{o} \i \P \copyright

¯o o.  § £

\={o} \d{o} \j \S \pounds

s. ˚ s ˝s

\d s \r s \H s