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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 ≡ ∼ = 6 = ∼ ≃ ≈ . = ∝ |= ± ∓ q \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 ⩽ / ≪ 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 ` \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 ⊕ ⊗ o ≮ ⊀ ≯ q / * + " # ( ) $ % ! & ' \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 ( L99 W " \dashleftarrow \Lleftarrow \looparrowleft \circlearrowleft \upharpoonleft \leftrightsquigarrow \rightrightarrows \rightarrowtail \curvearrowright \downdownarrows \rightsquigarrow ⇔ \dashrightarrow \leftrightarrows \leftarrowtail \curvearrowleft \upuparrows \multimap \rightleftarrows \twoheadrightarrow \rightleftharpoons \Rsh \downharpoonright ⇒ # \leftleftarrows \twoheadleftarrow \leftrightharpoons \Lsh \downharpoonleft \rightrightarrows \rightleftarrows \looparrowright \circlearrowright \upharpoonright 8 ; \nleftarrow \nRightarrow 9 = \nrightarrow \nleftrightarrow : < \nLeftarrow \nLeftrightarrow Miscellaneous symbols ∞ ∇ ∂ ð ♣ ♦ ♥ ♠ ··· .. . ... .. . = < 9 ! ⇒ y \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 \Acute{\Acute{A}} Ā¯ Ǎˇ Ȧ˙ \Bar{\Bar{A}} \Check{\Check{A}} ˆ Â ~~ A \Hat{\Hat{A}} Math mode accents á \acute{a} ā \bar{a} ă \breve{a} ǎ \check{a} ä \ddot{a} ȧ \dot{a} à \grave{a} â \hat{a} ã \tilde{a} ~a \vec{a} ´ Á ˘ Ă Ä¨ ` À Ã˜ \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 5 7φ − 12 π 8 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: Text Mode: 13 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 f −1 (x−xa ) dx R f −1 (x−xa ) dx \normalsize = normal \large = large \Large = Large \tiny = smallest \scriptsize = very small \footnotesize = smaller \small = small \LARGE = \huge = huge LARGE \Huge = Huge õ o̧ ı ¶ c ō o.  § £ Text Mode: Accents and Symbols ó ȯ o ¯ ø æ \’{o} \.{o} \b{o} \o \ae ö ŏ Å s Æ \"{o} \u{o} \AA \t s \AE ô ő å š † \^{o} \H{o} \aa \v s \dag ò o o ß Ø ‡ \‘{o} \t{oo} \ss \O \ddag \~{o} \c{o} \i \P \copyright \={o} \d{o} \j \S \pounds s. s̊ s̋ \d s \r s \H s

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