\RequirePackage{mmap} % make PDF copy and paste-able \documentclass[twocolumn]{article} \usepackage{amsmath, amsthm, amssymb} \usepackage{mathrsfs} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} % \usepackage{lmodern} % from http://tex.stackexchange.com/a/115089/121234 \usepackage[margin=0.5in]{geometry} \setlength{\parskip}{0ex} \usepackage{ragged2e} \setlength{\RaggedRightParindent}{1em} \usepackage{url} \usepackage{listings} \lstset{% basicstyle=\scriptsize\ttfamily, % the size of the fonts columns=fixed, % anything else is horrifying showspaces=false, % show spaces using underscores? showstringspaces=false, % underline spaces within strings? showtabs=false, % show tabs within strings? xleftmargin=1.5em, % left margin space } \lstdefinestyle{inline}{basicstyle=\ttfamily} \usepackage[dvipsnames]{xcolor} \definecolor{headcolor}{HTML}{004225} % British racing green {E34234} % vermillion \usepackage{titlesec} % \titleformat{ command }[ shape ]{ format }{ label }{ sep }{ before-code }[ after-code ] % \titlespacing*{ command }{ left }{ before-sep }{ after-sep }[ right-sep ] \titleformat{\section}[runin]{\color{headcolor}\bf}{}{0em}{} \titlespacing*{\section}{0em}{0.65ex}{0.67em} % TODO \pagestyle{empty} \begin{document}\thispagestyle{empty} \RaggedRight \begin{center} {\large\color{headcolor}\textbf{\LaTeX{} Math for Undergrads}} \\ \end{center} \section{Rule One} Any mathematics at all, even a single character, gets a mathematical setting. Thus, for ``the value of $x$ is $7$\,'' enter \lstinline[style=inline]!the value of $x$ is $7$!. \section{Template} Your document should contain at least this. \begin{lstlisting} \documentclass{article} \usepackage{mathtools,amssymb,amsthm} % imports amsmath \begin{document} --document body here-- \end{document} \end{lstlisting} \section{Common constructs} \begin{center} \begin{tabular}{@{} *{1}{l@{\hspace{1.5em}}} l @{}} $x^2$\quad\lstinline[style=inline]!x^2! &$\sqrt{2}$, $\sqrt[n]{3}$\quad\lstinline[style=inline]!\sqrt{2}!, \lstinline[style=inline]!\sqrt[n]{3}! \\ $x_{i,j}$\quad\lstinline[style=inline]!x_{i,j}! &$\frac{2}{3}$, $2/3$\quad\lstinline[style=inline]!\frac{2}{3}!, \lstinline[style=inline]!2/3! \end{tabular} \end{center} \section{Calligraphic letters} Use as in \lstinline[style=inline]!$\mathcal{A}$!. \begin{center} $ \mathcal{A}\mathcal{B}\mathcal{C} \mathcal{D}\mathcal{E}\mathcal{F} \mathcal{G}\mathcal{H}\mathcal{I} \mathcal{J}\mathcal{K}\mathcal{L} \mathcal{M}\mathcal{N}\mathcal{O} \mathcal{P}\mathcal{Q}\mathcal{R} \mathcal{S}\mathcal{T}\mathcal{U} \mathcal{V}\mathcal{W}\mathcal{X} \mathcal{Y}\mathcal{Z} $ \end{center} Get script letters, such as $\mathscr{P}$ from \lstinline[style=inline]!$\mathscr{P}$!, by putting \lstinline[style=inline]!\usepackage{mathrsfs}! in the preamble. \section{Greek} \begin{center} \begin{tabular}{@{}l@{\hspace{1em}}l@{}} $\alpha$\quad\lstinline[style=inline]!\alpha! &$\xi$, $\Xi$\quad\lstinline[style=inline]!\xi!, \lstinline[style=inline]!\Xi! \\ $\beta$\quad\lstinline[style=inline]!\beta! &o\quad\lstinline[style=inline]!o! \\ $\gamma$, $\Gamma$\quad\lstinline[style=inline]!\gamma!, \lstinline[style=inline]!\Gamma! &$\pi$, $\Pi$\quad\lstinline[style=inline]!\pi!, \lstinline[style=inline]!\Pi! \\ $\delta$, $\Delta$\quad\lstinline[style=inline]!\delta!, \lstinline[style=inline]!\Delta! &$\varpi$\quad\lstinline[style=inline]!\varpi! \\ $\epsilon$\quad\lstinline[style=inline]!\epsilon! &$\rho$\quad\lstinline[style=inline]!\rho! \\ $\varepsilon$\quad\lstinline[style=inline]!\varepsilon! &$\varrho$\quad\lstinline[style=inline]!\varrho! \\ $\zeta$\quad\lstinline[style=inline]!\zeta! &$\sigma$, $\Sigma$\quad\lstinline[style=inline]!\sigma!, \lstinline[style=inline]!\Sigma! \\ $\eta$\quad\lstinline[style=inline]!\eta! &$\varsigma$\quad\lstinline[style=inline]!\varsigma! \\ $\theta$ $\Theta$\quad\lstinline[style=inline]!\theta!, \lstinline[style=inline]!\Theta! &$\tau$\quad \lstinline[style=inline]!\tau! \\ $\vartheta$\quad\lstinline[style=inline]!\vartheta! &$\upsilon$, $\Upsilon$\quad\lstinline[style=inline]!\upsilon!, \lstinline[style=inline]!\Upsilon! \\ $\iota$\quad\lstinline[style=inline]!\iota! &$\phi$, $\Phi$\quad\lstinline[style=inline]!\phi!, \lstinline[style=inline]!\Phi! \\ $\kappa$\quad\lstinline[style=inline]!\kappa! &$\varphi$\quad\lstinline[style=inline]!\varphi! \\ $\lambda$ $\Lambda$\quad\lstinline[style=inline]!\lambda!, \lstinline[style=inline]!\Lambda! &$\chi$\quad\lstinline[style=inline]!\chi! \\ $\mu$\quad\lstinline[style=inline]!\mu! &$\psi$, $\Psi$\quad\lstinline[style=inline]!\psi!, \lstinline[style=inline]!\Psi! \\ $\nu$\quad\lstinline[style=inline]!\nu! &$\omega$, $\Omega$\quad\lstinline[style=inline]!\omega!, \lstinline[style=inline]!\Omega! \end{tabular} \end{center} \section{Sets and logic} \begin{center} \begin{tabular}{@{}*{2}{l@{\hspace{1em}}}l@{}} $\cup$\quad \lstinline[style=inline]!\cup! &$\mathbb{R}$\quad\lstinline[style=inline]!\mathbb{R}! &$\forall$\quad \lstinline[style=inline]!\forall! \\ $\cap$\quad \lstinline[style=inline]!\cap! &$\mathbb{Z}$\quad\lstinline[style=inline]!\mathbb{Z}! &$\exists$\quad \lstinline[style=inline]!\exists! \\ $\subset$\quad\lstinline[style=inline]!\subset! &$\mathbb{Q}$\quad\lstinline[style=inline]!\mathbb{Q}! &$\neg$\quad \lstinline[style=inline]!\neg! \\ $\subseteq$\quad \lstinline[style=inline]!\subseteq! &$\mathbb{N}$\quad\lstinline[style=inline]!\mathbb{N}! &$\vee$\quad \lstinline[style=inline]!\vee! \\ $\supset$\quad \lstinline[style=inline]!\supset! &$\mathbb{C}$\quad\lstinline[style=inline]!\mathbb{C}! &$\wedge$\quad \lstinline[style=inline]!\wedge! \\ $\supseteq$\quad \lstinline[style=inline]!\supseteq! &$\varnothing$\quad \lstinline[style=inline]!\varnothing! &$\vdash$\quad \lstinline[style=inline]!\vdash! \\ $\in$\quad \lstinline[style=inline]!\in! &$\emptyset$\quad \lstinline[style=inline]!\emptyset! &$\models$\quad \lstinline[style=inline]!\models! \\ $\notin$\quad \lstinline[style=inline]!\notin! &$\aleph$\quad \lstinline[style=inline]!\aleph! &$\setminus$\quad \lstinline[style=inline]!\setminus! \\ % $\ni$\quad \lstinline[style=inline]!\ni! \end{tabular} \end{center} Negate an operator, as in $\not\subset$, with \lstinline[style=inline]!\not\subset!. Get the set complement $A^{\mathsf{c}}$ with \lstinline[style=inline]!A^{\mathsf{c}}! (or $A^{\complement}$ with \lstinline[style=inline]!A^{\complement}!, or $\overline{A}$ with \lstinline[style=inline]!\overline{A}!). \section{Decorations} \begin{center} \begin{tabular}{@{}*{2}{l@{\hspace{1em}}}l@{}} % $f^\prime$\quad\lstinline[style=inline]!f^\prime! $f'$\quad\lstinline[style=inline]!f'! &$\dot{a}$\quad\lstinline[style=inline]!\dot{a}! &$\tilde{x}$\quad\lstinline[style=inline]!\tilde{x}! \\ % $f^{\prime\prime}$\quad\lstinline[style=inline]!f^{\prime\prime}! $f''$\quad\lstinline[style=inline]!f''! &$\ddot{a}$\quad\lstinline[style=inline]!\ddot{a}! &$\bar{x}$\quad\lstinline[style=inline]!\bar{x}! \\ $\Sigma^{*}$\quad\lstinline[style=inline]!\Sigma^{*}! &$\hat{x}$\quad\lstinline[style=inline]!\hat{x}! &$\vec{x}$\quad\lstinline[style=inline]!\vec{x}! \end{tabular} \end{center} If the decorated letter is $i$ or~$j$ then some decorations need \lstinline[style=inline]!\imath! or \lstinline[style=inline]!\jmath!, as in \lstinline[style=inline]!\vec{\imath}!. Some authors use boldface for vectors: \lstinline[style=inline]!\boldsymbol{x}!. % Mention \bm? Entering \lstinline[style=inline]!\overline{x+y}! produces $\overline{x+y}$, and \lstinline[style=inline]!\widehat{x+y}! gives $\widehat{x+y}$. Comment on an expression as here (there is also \lstinline[style=inline]!\overbrace{..}!). \begin{center} $\underbrace{x+y}_{|A|}$\quad\lstinline[style=inline]!\underbrace{x+y}_{|A|}! \end{center} \section{Dots} Use low dots in a list $\{0,1,2,\,\ldots\}$, entered as \lstinline[style=inline]!\{0,1,2,\,\ldots\}!. (If you use \lstinline[style=inline]!\ldots! in plain text as with \lstinline[style=inline]!London, Paris, \ldots{}\,.! then note the thinspace \lstinline[style=inline]!\,! before the period.) Use centered dots in a sum or product $1+\cdots+100$, entered as \lstinline[style=inline]!1+\cdots+100!. You can also get vertical dots \lstinline[style=inline]!\vdots! and diagonal dots \lstinline[style=inline]!\ddots!. \section{Roman names} Enter \lstinline[style=inline]!\tan(x)!, with a backslash, instead of \lstinline[style=inline]!tan(x)!. These get the same treatment. \begin{center} \begin{tabular}{@{}*{3}{l@{\hspace{1.5em}}}l@{}} $\sin$\quad \lstinline[style=inline]!\sin! &$\sinh$\quad \lstinline[style=inline]!\sinh! &$\arcsin$\quad \lstinline[style=inline]!\arcsin! \\ $\cos$\quad \lstinline[style=inline]!\cos! &$\cosh$\quad \lstinline[style=inline]!\cosh! &$\arccos$\quad \lstinline[style=inline]!\arccos! \\ $\tan$\quad \lstinline[style=inline]!\tan! &$\tanh$\quad \lstinline[style=inline]!\tanh! &$\arctan$\quad \lstinline[style=inline]!\arctan! \\ $\sec$\quad \lstinline[style=inline]!\sec! &$\coth$\quad \lstinline[style=inline]!\coth! &$\min$\quad \lstinline[style=inline]!\min! \\ $\csc$\quad \lstinline[style=inline]!\csc! &$\det$\quad \lstinline[style=inline]!\det! &$\max$\quad \lstinline[style=inline]!\max! \\ $\cot$\quad \lstinline[style=inline]!\cot! &$\dim$\quad \lstinline[style=inline]!\dim! &$\inf$\quad \lstinline[style=inline]!\inf! \\ $\exp$\quad \lstinline[style=inline]!\exp! &$\ker$\quad \lstinline[style=inline]!\ker! &$\sup$\quad \lstinline[style=inline]!\sup! \\ $\log$\quad \lstinline[style=inline]!\log! &$\deg$\quad \lstinline[style=inline]!\deg! &$\liminf$\quad \lstinline[style=inline]!\liminf! \\ $\ln$\quad \lstinline[style=inline]!\ln! &$\arg$\quad \lstinline[style=inline]!\arg! &$\limsup$\quad \lstinline[style=inline]!\limsup! \\ $\lg$\quad \lstinline[style=inline]!\lg! &$\gcd$\quad \lstinline[style=inline]!\gcd! &$\lim$\quad \lstinline[style=inline]!\lim! \\ % &$\hom$\quad \lstinline[style=inline]!\hom! \\ \end{tabular} \end{center} \section{Other symbols} \begin{center} \begin{tabular}{@{}*{2}{l@{\hspace{1.2em}}}l@{}} $<$\quad \lstinline[style=inline]!$\quad \lstinline[style=inline]!>! &$\ell$\quad \lstinline[style=inline]!\ell! &$\mp$\quad \lstinline[style=inline]!\mp! \\ $\geq$\quad \lstinline[style=inline]!\geq! &$\parallel$\quad \lstinline[style=inline]!\parallel! &$\times$\quad \lstinline[style=inline]!\times! \\ $\neq$\quad \lstinline[style=inline]!\neq! &$45^{\circ}$\quad \lstinline[style=inline]!45^{\circ}! &$\div$\quad \lstinline[style=inline]!\div! \\ $\ll$\quad \lstinline[style=inline]!\ll! &$\cong$\quad \lstinline[style=inline]!\cong! &$\ast$\quad \lstinline[style=inline]!\ast! \\ $\gg$\quad \lstinline[style=inline]!\gg! &$\ncong$\quad \lstinline[style=inline]!\ncong! &$\mid$\quad \lstinline[style=inline]!\mid! \\ $\approx$\quad \lstinline[style=inline]!\approx! &$\sim$\quad \lstinline[style=inline]!\sim! &$\nmid$\quad \lstinline[style=inline]!\nmid! \\ $\asymp$\quad \lstinline[style=inline]!\asymp! &$\simeq$\quad \lstinline[style=inline]!\simeq! &$n!$\quad \lstinline[style=inline]+n!+ \\ $\equiv$\quad \lstinline[style=inline]!\equiv! &$\nsim$\quad \lstinline[style=inline]!\nsim! &$\partial$\quad \lstinline[style=inline]!\partial! \\ $\prec$\quad \lstinline[style=inline]!\prec! &$\oplus$\quad \lstinline[style=inline]!\oplus! &$\nabla$\quad \lstinline[style=inline]!\nabla! \\ $\preceq$\quad \lstinline[style=inline]!\preceq! &$\ominus$\quad \lstinline[style=inline]!\ominus! &$\hbar$\quad \lstinline[style=inline]!\hbar! \\ $\succ$\quad \lstinline[style=inline]!\succ! &$\odot$\quad \lstinline[style=inline]!\odot! &$\circ$\quad \lstinline[style=inline]!\circ! \\ $\succeq$\quad \lstinline[style=inline]!\succeq! &$\otimes$\quad \lstinline[style=inline]!\otimes! &$\star$\quad \lstinline[style=inline]!\star! \\ $\propto$\quad \lstinline[style=inline]!\propto! &$\oslash$\quad \lstinline[style=inline]!\oslash! &$\surd$\quad \lstinline[style=inline]!\surd! \\ $\doteq$\quad \lstinline[style=inline]!\doteq! &$\upharpoonright$\quad \lstinline[style=inline]!\upharpoonright! &$\checkmark$\quad \lstinline[style=inline]!\checkmark! \\ \end{tabular} \end{center} Use \lstinline[style=inline]!a\mid b! for the divides relation, \mbox{$a\mid b$}, and \lstinline[style=inline]!a\nmid b! for the negation, \mbox{$a\nmid b$}. Also use \lstinline[style=inline]!\mid! to get set builder notation \mbox{$\{a\in S \mid\text{$a$ is odd}\}$}, with \lstinline[style=inline]!\{a\in S\mid\text{$a$ is odd}\}!. \section{Arrows} \begin{center} \begin{tabular}{@{}l*{1}{@{\hspace{1.5em}}l}@{}} $\rightarrow$\quad \lstinline[style=inline]!\rightarrow!, \lstinline[style=inline]!\to! &$\mapsto$\quad \lstinline[style=inline]!\mapsto! \\ $\nrightarrow$\quad \lstinline[style=inline]!\nrightarrow! &$\longmapsto$\quad \lstinline[style=inline]!\longmapsto! \\ $\longrightarrow$\quad \lstinline[style=inline]!\longrightarrow! &$\leftarrow$\quad \lstinline[style=inline]!\leftarrow! \\ $\Rightarrow$\quad \lstinline[style=inline]!\Rightarrow! &$\leftrightarrow$\quad \lstinline[style=inline]!\leftrightarrow! \\ $\nRightarrow$\quad \lstinline[style=inline]!\nRightarrow! &$\downarrow$\quad \lstinline[style=inline]!\downarrow! \\ $\Longrightarrow$\quad \lstinline[style=inline]!\Longrightarrow! &$\uparrow$\quad \lstinline[style=inline]!\uparrow! \\ $\leadsto$\quad \lstinline[style=inline]!\leadsto! &$\updownarrow$\quad \lstinline[style=inline]!\updownarrow! \\ \end{tabular} \end{center} The right arrows in the first column have matching left arrows, such as \lstinline[style=inline]!\nleftarrow!, and there are some other matches for down arrows, etc. \section{Variable-sized operators} The summation $\sum_{j=0}^3j^2$\quad\lstinline[style=inline]!\sum_{j=0}^3 j^2! and the integral $\int_{x=0}^3x^2\,dx$ \lstinline[style=inline]!\int_{x=0}^3 x^2\,dx! expand when displayed. \begin{equation*} \sum_{j=0}^3j^2 \qquad \int_{x=0}^3x^2\,dx \end{equation*} These do the same. \begin{center} \begin{tabular}{@{}*{2}{l@{\hspace{.35in}}}l@{}} $\int$\quad\lstinline[style=inline]!\int! &$\iiint$\quad\lstinline[style=inline]!\iiint! &$\bigcup$\quad\lstinline[style=inline]!\bigcup! \\ $\iint$\quad\lstinline[style=inline]!\iint! &$\oint$\quad\lstinline[style=inline]!\oint! &$\bigcap$\quad\lstinline[style=inline]!\bigcap! \\ % &$\bigvee$\quad\lstinline[style=inline]!\bigvee! % &$\bigwedge$\quad\lstinline[style=inline]!\bigwedge! \\ \end{tabular} \end{center} \section{Fences} \begin{center} \begin{tabular}{@{}*{2}{l@{\hspace{1.5em}}}l@{}} $(\;)$\quad \lstinline[style=inline]!()! &$\langle\;\rangle$\quad\lstinline[style=inline]!\langle\rangle! &$|\; |$\quad\lstinline[style=inline]!| |! \\ $[\;]$\quad\lstinline[style=inline]![]! &$\lfloor\;\rfloor$\quad\lstinline[style=inline]!\lfloor\rfloor! &$\|\;\|$\quad\lstinline[style=inline]!\| \|! \\ $\{\;\}$\quad\lstinline[style=inline]!\{\}! &$\lceil\;\rceil$\quad\lstinline[style=inline]!\lceil\rceil! \end{tabular} \end{center} Fix the size with \lstinline[style=inline]!\big!, \lstinline[style=inline]!\Big!, \lstinline[style=inline]!\bigg!, or \lstinline[style=inline]!\Bigg!. \begin{center} $\displaystyle\Big[\sum_{k=0}^n e^{k^2}\Big]$\quad \lstinline[style=inline]!\Big[\sum_{k=0}^n e^{k^2}\Big]! \end{center} To have them grow with the enclosed formula, use \lstinline[style=inline]!\left! and \lstinline[style=inline]!\right! (although sometimes \lstinline[style=inline]!\big!, etc., are necessary). \begin{center} $\displaystyle\left\langle i,2^{2^i}\right\rangle$\quad \lstinline[style=inline]!\left\langle i,2^{2^i}\right\rangle! \end{center} Every \lstinline[style=inline]!\left! must match a \lstinline[style=inline]!\right! and they must end on the same line in the output. For a one-sided fence, put a \lstinline[style=inline]!\left.! or \lstinline[style=inline]!\right.! on the other side. \begin{center} $\displaystyle\left.\frac{df}{dx}\right|_{x_0}$\quad \lstinline[style=inline]!\left.\frac{df}{dx}\right|_{x_0}! \end{center} \section{Arrays, Matrices} Make an array of mathematical text as you make a table of plain text. \begin{center} \vspace*{-\topsep} \begin{minipage}{.2\columnwidth}\noindent $\displaystyle \begin{array}{@{}rcl@{}} 0 &\leftrightarrow &0 \\ 1 &\leftrightarrow &1 \\ 2 &\leftrightarrow &4 \\ \vdots & &\vdots \end{array} $ \end{minipage} \quad \begin{minipage}{.6\columnwidth}\noindent \begin{lstlisting}[xleftmargin=0em] \begin{array}{rcl} 0 &\leftrightarrow &0 \\ 1 &\leftrightarrow &1 \\ 2 &\leftrightarrow &4 \\ \vdots & &\vdots \end{array} \end{lstlisting} \end{minipage} \end{center} Definition by cases is an array with two columns. \begin{center} $\displaystyle f_n=\begin{cases} a &\text{if $n=0$} \\ r\cdot f_{n-1} &\text{else} \end{cases} $ \quad \begin{minipage}{.525\columnwidth}\noindent \begin{lstlisting}[xleftmargin=-1em] f_n= \begin{cases} a &\text{if $n=0$} \\ r\cdot f_{n-1} &\text{else} \end{cases} \end{lstlisting} \end{minipage} \end{center} A matrix is an array with fences. With a \lstinline[style=inline]!pmatrix! environment, you need not specify column alignments. \begin{center} $\displaystyle \begin{pmatrix} a &b \\ c &d \end{pmatrix} $ \quad \begin{minipage}{.525\columnwidth}\noindent \begin{lstlisting}[xleftmargin=0em] \begin{pmatrix} a &b \\ c &d \end{pmatrix} \end{lstlisting} \end{minipage} \end{center} For the determinant use \lstinline[style=inline]!|A|! inline and \lstinline[style=inline]!vmatrix! in display. \section{Spacing in mathematics} Improve $\sqrt{2}x$ to $\sqrt{2}\,x$ with a thin space, as in \lstinline[style=inline]!\sqrt{2}\,x!. Slightly wider are \lstinline[style=inline]!\:! and \lstinline[style=inline]!\;! (the three are in ratio $3\mathbin{:}4\mathbin{:}5$). Get the improvement of $n/\!\log n$ instead of $n/\log n$ by using a negative thin space, as in \lstinline[style=inline]+n/\!\log n+. Bigger spaces are: \lstinline[style=inline]!\quad! for $\rightarrow\quad\leftarrow$, and \lstinline[style=inline]!\qquad! for $\rightarrow\qquad\leftarrow$, which are useful between parts of a display. % \begin{center} % \begin{tabular}{@{}*{1}{l@{\hspace{2.25em}}}l@{}} % $\rightarrow\mkern3mu\leftarrow$\quad\lstinline[style=inline]!\,! % &$\rightarrow\quad\leftarrow$\quad\lstinline[style=inline]!\quad! \\ % $\rightarrow\mkern4mu\leftarrow$\quad\lstinline[style=inline]!\:! % &$\rightarrow\qquad\leftarrow$\quad\lstinline[style=inline]!\qquad! \\ % $\rightarrow\mkern5mu\leftarrow$\quad\lstinline[style=inline]!\;! % &$\rightarrow\!\leftarrow$\quad\lstinline[style=inline]+\!+ % \end{tabular} % \end{center} Get arbitrary space as in % $\rightarrow\hspace*{0.5cm}\leftarrow$ \lstinline[style=inline]!\hspace*{0.5cm}!. \section{Displayed equations} The \lstinline[style=inline]!equation*! environment puts an equation on a separate line. \begin{center} \vspace*{-\topsep} \begin{minipage}{0.25\linewidth}\vspace*{-\abovedisplayskip} \begin{equation*} S=k\cdot\lg W \end{equation*} \end{minipage} \quad \begin{minipage}{0.65\linewidth} \begin{lstlisting}[xleftmargin=0ex] \begin{equation*} S=k\cdot\lg W \end{equation*} \end{lstlisting} \end{minipage} \end{center} You can break into multiple lines. \begin{center} \vspace*{-\topsep} \begin{minipage}{0.35\linewidth}\vspace*{-\abovedisplayskip} \begin{multline*} \sin (x)=x-\frac{x^3}{3!} \\ +\frac{x^5}{5!}-\cdots \end{multline*} \end{minipage} \quad \begin{minipage}{0.55\linewidth} \begin{lstlisting}[xleftmargin=0ex] \begin{multline*} \sin (x)=x-\frac{x^3}{3!} \\ +\frac{x^5}{5!}-\cdots \end{multline*} \end{lstlisting} \end{minipage} \end{center} Align equations using \lstinline[style=inline]!align*! \vspace*{-\topsep} \begin{center} \begin{minipage}[c]{0.25\linewidth}\vspace*{-\abovedisplayskip} \begin{align*} \nabla\cdot\boldsymbol{D} &= \rho \\ \nabla\cdot\boldsymbol{B} &= 0 \end{align*} \end{minipage} \quad \begin{minipage}[c]{0.65\linewidth} \begin{lstlisting}[xleftmargin=0ex,boxpos=c] \begin{align*} \nabla\cdot\boldsymbol{D} &= \rho \\ \nabla\cdot\boldsymbol{B} &= 0 \end{align*} \end{lstlisting} \end{minipage} \end{center} (the left or right side of an alignment can be empty). For each environment, get a numbered version by dropping the asterisk from the name. \section{Calculus examples} The last three here are display style. \begin{center} \small \def\arraystretch{2} \vspace*{-\topsep}\vspace*{-0.25cm} \begin{tabular}{@{}l@{}} $ f\colon\mathbb{R}\to\mathbb{R} $ \quad\lstinline[style=inline]!f\colon\mathbb{R}\to\mathbb{R}! \\ $ 9.8~\text{m}/\text{s}^2 $ \quad\lstinline[style=inline]!9.8~\text{m}/\text{s}^2! \\ $\displaystyle \lim_{h\to 0}\frac{f(x+h)-f(x)}{h} $ \quad\lstinline[style=inline]!\lim_{h\to 0}\frac{f(x+h)-f(x)}{h}! \\ $\displaystyle \int x^2\,dx=x^3/3+C $ \quad\lstinline[style=inline]!\int x^2\,dx=x^3/3+C! \\ % $\displaystyle % \frac{dy}{dx}=\frac{dy}{du}\frac{du}{dx} % $ % &\lstinline[style=inline]!\frac{dy}{dx}=\frac{dy}{du}\frac{du}{dx}! \\ $\displaystyle \nabla=\boldsymbol{i}\frac{d}{dx} +\boldsymbol{j}\frac{d}{dy} +\boldsymbol{k}\frac{d}{dz} $ \quad\lstinline[style=inline]!\nabla=\boldsymbol{i}\frac{d}{dx}+!\,$\cdots$\\ \end{tabular} \end{center} \section{Discrete mathematics examples} There are four modulo forms: $m\bmod n$ is from \lstinline[style=inline]!m\bmod n!, and $a\equiv b\pmod m$ is from \lstinline[style=inline]!a\equiv b\pmod m!, and $a\equiv b\mod m$ is from \lstinline[style=inline]!a\equiv b\mod m!, and $a\equiv b\pod m$ is from \lstinline[style=inline]!a\equiv b\pod m!. For combinations the binomial symbol $\binom{n}{k}$ is from \lstinline[style=inline]!\binom{n}{k}!. This resizes to be bigger in a display (to require the display version use \lstinline[style=inline]!\dbinom{n}{k}! and require the inline version with \lstinline[style=inline]!\tbinom{n}{k}!). For permutations use $ n^{\underline{r}} $ from \lstinline[style=inline]!n^{\underline{r}}! (some authors use $ P(n,r) $, or $ {}_nP_r $ from \lstinline[style=inline]!{}_nP_r!). \section{Statistics examples} \begin{center} \small\def\arraystretch{1.5} \vspace*{-\topsep}\vspace*{-0.15cm} \begin{tabular}{@{}l@{}} $ \sigma^2=\sqrt{\,\sum (x_i-\mu)^2/N} $ \quad\lstinline[style=inline]!\sigma^2=\sqrt{\,\sum (x_i-\mu)^2/N}! \\ $ E(X)=\mu_X=\sum (x_i-P(x_i)) $ \quad\lstinline[style=inline]! E(X)=\mu_X=\sum (x_i-P(x_i))! \\ \end{tabular} \end{center} The probability density of the normal distribution \begin{equation*} \frac{1}{\sqrt{2\sigma^2\pi}}\,e^{-\frac{(x-\mu)^2}{2\sigma^2}} \end{equation*} comes from this. \begin{lstlisting} \frac{1}{sqrt{2\sigma^2\pi}} \,e^{-\frac{(x-\mu)^2}{2\sigma^2}}!. \end{lstlisting} \section{For more} See also the Comprehensive \LaTeX{} Symbols List at \url{mirror.ctan.org/info/symbols/comprehensive} and De\TeX ify at \url{detexify.kirelabs.org/classify.html}. \vfill \noindent\parbox{\columnwidth}{\small% {\color{headcolor}\hrulefill\\ \vspace*{0ex} Jim Hef{}feron, Saint Michael's College, VT USA\hfill 2020-Dec-30 }} \end{document}