Symbols

Operators

Symbol	Command	Symbol	Command	Symbol	Command
\pm	\pm	\mp	\mp	\times	\times
\div	\div	\cdot	\cdot	\ast	\ast
\star	\star	\dagger	\dagger	\ddagger	\ddagger
\amalg	\amalg	\cap	\cap	\cup	\cup
\uplus	\uplus	\sqcap	\sqcap	\sqcup	\sqcup
\vee	\vee	\wedge	\wedge	\oplus	\oplus
\ominus	\ominus	\otimes	\otimes	\circ	\circ
\bullet	\bullet	\diamond	\diamond	\lhd	\lhd
\rhd	\rhd	\unlhd	\unlhd	\unrhd	\unrhd
\oslash	\oslash	\odot	\odot	\bigcirc	\bigcirc
\triangleleft	\triangleleft	\Diamond	\Diamond	\bigtriangleup	\bigtriangleup
\bigtriangledown	\bigtriangledown	\Box	\Box	\triangleright	\triangleright
\setminus	\setminus	\wr	\wr	\sqrt{x}	\sqrt{x}
x^{\circ}	x^{\circ}	\triangledown	\triangledown	\sqrt[n]{x}	\sqrt[n]{x}
a^x	a^x	a^{xyz}	a^{xyz}	a_x	a_x

Relations

Symbol	Command	Symbol	Command	Symbol	Command
\le	\le	\ge	\ge	\neq	\neq
\sim	\sim	\ll	\ll	\gg	\gg
\doteq	\doteq	\simeq	\simeq	\subset	\subset
\supset	\supset	\approx	\approx	\asymp	\asymp
\subseteq	\subseteq	\supseteq	\supseteq	\cong	\cong
\smile	\smile	\sqsubset	\sqsubset	\sqsupset	\sqsupset
\equiv	\equiv	\frown	\frown	\sqsubseteq	\sqsubseteq
\sqsupseteq	\sqsupseteq	\propto	\propto	\bowtie	\bowtie
\in	\in	\ni	\ni	\prec	\prec
\succ	\succ	\vdash	\vdash	\dashv	\dashv
\preceq	\preceq	\succeq	\succeq	\models	\models
\perp	\perp	\parallel	\parallel
\mid	\mid	\bumpeq	\bumpeq

Negations of many of these relations can be formed by just putting \not before the symbol, or by slipping an "n" between the \ and the word. Here are a couple examples, plus many other negations; it works for many of the many others as well.

Symbol	Command	Symbol	Command	Symbol	Command
\nmid	\nmid	\nleq	\nleq	\ngeq	\ngeq
\nsim	\nsim	\ncong	\ncong	\nparallel	\nparallel
\not<	\not<	\not>	\not>	\ne	\not= or \neq or \ne
\not\le	\not\le	\not\ge	\not\ge	\not\sim	\not\sim
\not\approx	\not\approx	\not\cong	\not\cong	\not\equiv	\not\equiv
\not\parallel	\not\parallel	\nless	\nless	\ngtr	\ngtr
\lneq	\lneq	\gneq	\gneq	\lnsim	\lnsim
\lneqq	\lneqq	\gneqq	\gneqq

To use other relations not listed here, such as = , > , and < , in \LaTeX, you must use the symbols on your keyboard, as they are not available in\LaTeX.

Greek Letters

Symbol	Command	Symbol	Command	Symbol	Command	Symbol	Command
Lowercase Letters
\alpha	\alpha	\beta	\beta	\gamma	\gamma	\delta	\delta
\epsilon	\epsilon	\varepsilon	\varepsilon	\zeta	\zeta	\eta	\eta
\theta	\theta	\vartheta	\vartheta	\iota	\iota	\kappa	\kappa
\lambda	\lambda	\mu	\mu	\nu	\nu	\xi	\xi
\pi	\pi	\varpi	\varpi	\rho	\rho	\varrho	\varrho
\sigma	\sigma	\varsigma	\varsigma	\tau	\tau	\upsilon	\upsilon
\phi	\phi	\varphi	\varphi	\chi	\chi	\psi	\psi
\omega	\omega

Symbol	Command	Symbol	Command	Symbol	Command	Symbol	Command
Capital Letters
\Gamma	\Gamma	\Delta	\Delta	\Theta	\Theta	\Lambda	\Lambda
\Xi	\Xi	\Pi	\Pi	\Sigma	\Sigma	\Upsilon	\Upsilon
\Phi	\Phi	\Psi	\Psi	\Omega	\Omega

Arrows

Symbol	Command	Symbol	Command
\gets	\gets	\to	\to
\leftarrow	\leftarrow	\Leftarrow	\Leftarrow
\rightarrow	\rightarrow	\Rightarrow	\Rightarrow
\leftrightarrow	\leftrightarrow	\Leftrightarrow	\Leftrightarrow
\mapsto	\mapsto	\hookleftarrow	\hookleftarrow
\leftharpoonup	\leftharpoonup	\leftharpoondown	\leftharpoondown
\rightleftharpoons	\rightleftharpoons	\longleftarrow	\longleftarrow
\Longleftarrow	\Longleftarrow	\longrightarrow	\longrightarrow
\Longrightarrow	\Longrightarrow	\longleftrightarrow	\longleftrightarrow
\Longleftrightarrow	\Longleftrightarrow	\longmapsto	\longmapsto
\hookrightarrow	\hookrightarrow	\rightharpoonup	\rightharpoonup
\rightharpoondown	\rightharpoondown	\leadsto	\leadsto
\uparrow	\uparrow	\Uparrow	\Uparrow
\downarrow	\downarrow	\Downarrow	\Downarrow
\updownarrow	\updownarrow	\Updownarrow	\Updownarrow
\nearrow	\nearrow	\searrow	\searrow
\swarrow	\swarrow	\nwarrow	\nwarrow
\overrightarrow{AB}	\overrightarrow{AB}	\overleftarrow{AB}	\overleftarrow{AB}
\overleftrightarrow{AB}	\overleftrightarrow{AB}

(For those of you who hate typing long strings of letters, \iff and \implies can be used in place of \Longleftrightarrow and \Longrightarrow, respectively.)

Dots

Symbol	Command	Symbol	Command
\cdot	\cdot	\vdots	\vdots
\dots	\dots	\ddots	\ddots
\cdots	\cdots	\iddots	\iddots

Accents

Symbol	Command	Symbol	Command	Symbol	Command
\hat{x}	\hat{x}	\check{x}	\check{x}	\dot{x}	\dot{x}
\breve{x}	\breve{x}	\acute{x}	\acute{x}	\ddot{x}	\ddot{x}
\grave{x}	\grave{x}	\tilde{x}	\tilde{x}	\mathring{x}	\mathring{x}
\bar{x}	\bar{x}	\vec{x}	\vec{x}

When applying accents to i and j, you can use \imath and \jmath to keep the dots from interfering with the accents:

Symbol	Command	Symbol	Command
\vec{\jmath}	\vec{\jmath}	\tilde{\imath}	\tilde{\imath}

\tilde and \hat have wide versions that allow you to accent an expression:

Symbol	Command	Symbol	Command
\widehat{7+x}	\widehat{7+x}	\widetilde{abc}	\widetilde{abc}

Others

Symbol	Command	Symbol	Command	Symbol	Command
\infty	\infty	\triangle	\triangle	\angle	\angle
\aleph	\aleph	\hbar	\hbar	\imath	\imath
\jmath	\jmath	\ell	\ell	\wp	\wp
\Re	\Re	\Im	\Im	\mho	\mho
\prime	\prime	\emptyset	\emptyset	\nabla	\nabla
\surd	\surd	\partial	\partial	\top	\top
\bot	\bot	\vdash	\vdash	\dashv	\dashv
\forall	\forall	\exists	\exists	\neg	\neg
\flat	\flat	\natural	\natural	\sharp	\sharp
\backslash	\backslash	\Box	\Box	\Diamond	\Diamond
\clubsuit	\clubsuit	\diamondsuit	\diamondsuit	\heartsuit	\heartsuit
\spadesuit	\spadesuit	\Join	\Join	\blacksquare	\blacksquare
\copyright	\copyright	\underset{\smile}{XYZ}	\underset{\smile}{XYZ}
\overset{\frown}{ABC}	\overset{\frown}{ABC}	\cup	\cup
\S	\S	\P	\P	\Vdash	\Vdash
\pounds	\pounds	\in	\in	\vDash	\vDash
\bigstar	\bigstar	\implies	\implies	\LaTeX	\LaTeX
\square	\square	\text{\LaTeX}	\text{\LaTeX}
\smiley	\smiley
\mathbb{R}	\mathbb{R}
\checkmark	\checkmark
\cancer	\cancer

Note: \overarc{ABC}and \cancerdo not work in the classroom.

Command Symbols

Some symbols are used in commands, so they need to be treated in a special way.

Symbol	Command	Symbol	Command	Symbol	Command	Symbol	Command
\$	\$	\&	\&	\%	\%	\#	\#
\_	\_	\{	\{	\}	\}	\backslash	\backslash

(Warning: Using $ for \$will result in \$. This is a bug as far as we know. Depending on the version of \LaTeX this is not always a problem.)

European Language Symbols

Symbol	Command	Symbol	Command	Symbol	Command	Symbol	Command
{\oe}	{\oe}	{\ae}	{\ae}	{\o}	{\o}
{\OE}	{\OE}	{\AE}	{\AE}	{\AA}	{\AA}	{\O}	{\O}
{\l}	{\l}	{\ss}	{\ss}	!`	!`
{\L}	{\L}	{\SS}	{\SS}

Bracketing Symbols

In mathematics, sometimes we need to enclose expressions in brackets, braces or parentheses. Some of these work just as you'd imagine in LaTeX; type ( and ) for parentheses, [ and ] for brackets, and | and | for absolute value. However, other symbols have special commands:

Symbol	Command	Symbol	Command	Symbol	Command
\{	\{	\}	\}	\\|	\\|
\backslash	\backslash	\lfloor	\lfloor	\rfloor	\rfloor
\lceil	\lceil	\rceil	\rceil	\langle	\langle
\rangle	\rangle

You might notice that if you use any of these to typeset an expression that is vertically large, like

(\frac{a}{x} )^2

the parentheses don't come out the right size:

(\frac{a}{x} )^2

If we put \left and \right before the relevant parentheses, we get a prettier expression:

\left(\frac{a}{x} \right)^2

gives

\left(\frac{a}{x} \right)^2

For systems of equations or piecewise functions, use the cases environment:

f(x) = \begin{cases} x^2 &\text{if } x \ge 0 \ x &\text{if } x < 0 \end{cases}

which gives

f(x) = \begin{cases} x^2 &\text{if } x \ge 0 \ x &\text{if } x < 0 \end{cases}

In addition to the \left and \right commands, when doing floor or ceiling functions with fractions, using

\left\lceil\frac{x}{y}\right\rceil

and \left\lfloor\frac{x}{y}\right\rfloor

gives both\left\lceil\frac{x}{y}\right\rceiland\left\lfloor\frac{x}{y}\right\rfloor, respectively.

And, if you type this

\underbrace{a_0+a_1+a_2+\cdots+a_n}_{x}

Gives

\underbrace{a_0+a_1+a_2+\cdots+a_n}_{x}

\overbrace{a_0+a_1+a_2+\cdots+a_n}^{x}

Gives

\overbrace{a_0+a_1+a_2+\cdots+a_n}^{x}

\left and \right can also be used to resize the following symbols:

Symbol	Command	Symbol	Command	Symbol	Command
\uparrow	\uparrow	\downarrow	\downarrow	\updownarrow	\updownarrow
\Uparrow	\Uparrow	\Downarrow	\Downarrow	\Updownarrow	\Updownarrow

Multi-Size Symbols

Some symbols render differently in inline math mode and in display mode. Display mode occurs when you use \[...\] or $$...$$, or environments like \begin{equation}...\end{equation} or \begin{align}...\end{align}. Read more in the commands section of the guide about how symbols which take arguments above and below the symbols, such as a summation symbol, behave in the two modes.

In each of the following, the two images show the symbol in display mode, then in inline mode.

Symbol	Command	Symbol	Command	Symbol	Command
\sum	\sum	\int	\int	\oint	\oint
\prod	\prod	\coprod	\coprod	\bigcap	\bigcap
\bigcup	\bigcup	\bigsqcup	\bigsqcup	\bigvee	\bigvee
\bigwedge	\bigwedge	\bigodot	\bigodot	\bigotimes	\bigotimes
\bigoplus	\bigoplus	\biguplus	\biguplus

Commands

Subscripts and Superscripts

Subscripts and superscripts (such as exponents) can be made using the underscore _ and caret ^ symbols respectively.

Symbol	Command	Symbol	Command
2^2	2^2	a_i	a_i
2^{23}	2^{23}	n_{i-1}	n_{i-1}
a^{i+1}_3	a^{i+1}_3	x^{3^2}	x^{3^2}
2^{a_i}	2^{a_i}	2^a_i	2^a_i

Notice that we can apply both a subscript and a superscript at the same time. For subscripts or superscripts with more than one character, you must surround what you want to be the exponent/superscript with curly braces. For example, x^10 produces x^10, while x^{10} produces x^{10}.

Math Commands

Here are some commonly used math commands in \LaTeX:

Fractions

Symbol	Command
\frac{1}{2} or \frac12	\frac{1}{2} or \frac12
\frac{2}{x+2}	\frac{2}{x+2}
\frac{1+\frac{1}{x}}{3x + 2}	\frac{1+\frac{1}{x}}{3x + 2}

Notice that with fractions with a 1-digit numerator and a 1-digit denominator, we can simply group the numerator and the denominator together as one number. However, for fractions with either a numerator or a denominator that requires more than one character (or if the numerator starts with a letter), you need to surround everything in curly brackets.

Use \cfrac for continued fractions.

Expression	Command
\cfrac{2}{1+\cfrac{2}{1+\cfrac{2}{1+\cfrac{2}{1}}}}	\cfrac{2}{1+\cfrac{2}{1+\cfrac{2}{1+\cfrac{2}{1}}}}

Radicals

Symbol	Command
\sqrt{3}	\sqrt{3}
\sqrt{x+y}	\sqrt{x+y}
\sqrt{x+\frac{1}{2}}	\sqrt{x+\frac{1}{2}}
\sqrt[3]{3}	\sqrt[3]{3}
\sqrt[n]{x}	\sqrt[n]{x}

Sums, Products, Limits and Logarithms

Use the commands \sum, \prod, \lim, and \log respectively. To denote lower and upper bounds, or the base of the logarithm, use _ and ^ in the same way they are used for subscripts and superscripts. (Lower and upper bounds for integrals work the same way, as you'll see in the calculus section)

Symbol	Command
\sum_{i=1}^{\infty}\frac{1}{i}	\sum_{i=1}^{\infty}\frac{1}{i}
\prod_{n=1}^5\frac{n}{n-1}	\prod_{n=1}^5\frac{n}{n-1}
\lim_{x\to\infty}\frac{1}{x}	\lim_{x\to\infty}\frac{1}{x}
\lim\limits_{x\to\infty}\frac{1}{x}	\lim\limits_{x\to\infty}\frac{1}{x}
\log_n n^2	\log_n n^2

Some of these are prettier in display mode:

Symbol	Command
\sum_{i=1}^{\infty}\frac{1}{i}	\sum_{i=1}^{\infty}\frac{1}{i}
\prod_{n=1}^5\frac{n}{n-1}	\prod_{n=1}^5\frac{n}{n-1}
\lim_{x\to\infty}\frac{1}{x}	\lim_{x\to\infty}\frac{1}{x}

Note that we can use sums, products, and logarithms without _ or ^ modifiers.

Symbol	Command
\sum\frac{1}{i}	\sum\frac{1}{i}
\prod\frac{n}{n-1}	\prod\frac{n}{n-1}
\log n^2	\log n^2
\ln e	\ln e

Mods

Symbol	Command
9\equiv 3 \bmod{6}	9\equiv 3 \bmod{6}
9\equiv 3 \pmod{6}	9\equiv 3 \pmod{6}
9\equiv 3 \mod{6}	9\equiv 3 \mod{6}
9\equiv 3 \pod{6}	9\equiv 3 \pod{6}

Combinations

Symbol	Command
\binom{1}{1}	\binom{1}{1}
\binom{n-1}{r-1}	\binom{n-1}{r-1}

These often look better in display mode:

Symbol	Command
\dbinom{9}{3}	\dbinom{9}{3}
\dbinom{n-1}{r-1}	\dbinom{n-1}{r-1}

Trigonometric Functions

Most of these are just the abbreviation of the trigonometric function with simply a backslash added before the abbreviation.

Symbol	Command	Symbol	Command	Symbol	Command
\cos	\cos	\sin	\sin	\tan	\tan
\sec	\sec	\csc	\csc	\cot	\cot
\arccos	\arccos	\arcsin	\arcsin	\arctan	\arctan
\cosh	\cosh	\sinh	\sinh	\tanh	\tanh
\coth	\coth

Here are a couple examples:

Symbol	Command
\cos^2 x +\sin^2 x = 1	\cos^2 x +\sin^2 x = 1
\cos 90^\circ = 0	\cos 90^\circ = 0

Calculus

Below are examples of calculus expressions rendered in LaTeX. Most of these commands have been introduced before. Notice how definite integrals are rendered (and the difference between inline math and display mode for definite integrals). The \, in the integrals makes a small space before the dx.

Symbol	Command
\frac{d}{dx}\left(x^2\right) = 2x	\frac{d}{dx}\left(x^2\right) = 2x
\int 2x\,dx = x^2+C	\int 2x\,dx = x^2+C
\int^5_1 2x\,dx = 24	\int^5_1 2x\,dx = 24
\frac{\partial^2U}{\partial x^2} + \frac{\partial^2U}{\partial y^2}	\frac{\partial^2U}{\partial x^2} + \frac{\partial^2U}{\partial y^2}
\frac{1}{4\pi}\oint_\Sigma\frac{1}{r}\frac{\partial U}{\partial n} ds	\frac{1}{4\pi}\oint_\Sigma\frac{1}{r}\frac{\partial U}{\partial n} ds

LaTeX

Other Functions

Symbol	Command	Symbol	Command	Symbol	Command
\arg	\arg	\deg	\deg	\det	\det
\dim	\dim	\exp	\exp	\gcd	\gcd
\hom	\hom	\inf	\inf	\ker	\ker
\lg	\lg	\liminf	\liminf	\limsup	\limsup
\max	\max	\min	\min	\Pr	\Pr
\sup	\sup	\smiley	\smiley

Some of these commands take subscripts in the same way sums, products, and logarithms do. Some render differently in display mode and inline math mode.

Symbol	Command	Symbol	Command	Symbol	Command
\dim_x	\dim_x	\gcd_x	\gcd_x	\inf_x	\inf_x
\liminf_x	\liminf_x	\limsup_x	\limsup_x	\max_x	\max_x
\min_x	\min_x	\Pr_x	\Pr_x	\sup_x	\sup_x

Failures of 2025

We can typeset a ƒailure with the matrix, bmatrix, pmatrix, or vmatrix environments. The letters b, p, and v refer to the delimiters around the matrix (brackets, parentheses, and vertical bars, respectively). For example, the following code

\begin{bmatrix}
1 & 2 & 3 \\
4 & 5 & 6 \\
\end{bmatrix}

produces the following 2 \times3matrix:

\begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ \end{bmatrix}

We can also use the array environment to typeset arrays. For example, the following code

\begin{array}{ccc}
a & b & c \\
d & e & f \\
g & h & i 
\end{array}

produces the following 3 \times3array:

\begin{array}{ccc} a & b & c \\ d & e & f \\ g & h & i \end{array}

Text Styles in Math Mode

You can render letters in various styles in math mode. Below are examples; you should be able to use these with any letters. The \mathbb requires the amsfonts package to be included in your document's preamble. Do not try to do \mathbb{year}. You'll get , and that looks nothing like it!

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