From 1678088b3d54bb6467925eb602c30d87fedda544 Mon Sep 17 00:00:00 2001 From: Karl Berry Date: Wed, 11 Jan 2017 23:07:17 +0000 Subject: undergradmath (11jan17) git-svn-id: svn://tug.org/texlive/trunk@42926 c570f23f-e606-0410-a88d-b1316a301751 --- .../doc/latex/undergradmath/undergradmath.tex | 649 +++++++++++++++++++++ 1 file changed, 649 insertions(+) create mode 100644 Master/texmf-dist/doc/latex/undergradmath/undergradmath.tex (limited to 'Master/texmf-dist/doc/latex/undergradmath/undergradmath.tex') diff --git a/Master/texmf-dist/doc/latex/undergradmath/undergradmath.tex b/Master/texmf-dist/doc/latex/undergradmath/undergradmath.tex new file mode 100644 index 00000000000..5d95b59e04b --- /dev/null +++ b/Master/texmf-dist/doc/latex/undergradmath/undergradmath.tex @@ -0,0 +1,649 @@ +\RequirePackage{mmap} % make PDF copy and paste-able +\documentclass[twocolumn]{article} +\usepackage{amsmath, amsthm, amssymb} +\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}{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, goes in 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{amsmath, amssymb, amsthm} +\usepackage[utf8]{inputenc} + +\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 \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} + + +\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! \\ + $\ni$\quad \lstinline[style=inline]!\ni! + &$\aleph$\quad \lstinline[style=inline]!\aleph! + &$\Rightarrow$\quad \lstinline[style=inline]!\Rightarrow! \\ + $\notin$\quad \lstinline[style=inline]!\notin! + &$\setminus$\quad \lstinline[style=inline]!\setminus! + &$\nRightarrow$\quad \lstinline[style=inline]!\nRightarrow! \\ + $\not\in$\quad \lstinline[style=inline]!\not\in! + &$\equiv$\quad \lstinline[style=inline]!\equiv! + & \\ + \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}}!, +get $A^{\complement}$ with \lstinline[style=inline]!A^{\complement}!, +or +get $\bar{A}$ with \lstinline[style=inline]!\bar{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}!. + +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 +\lstinline[style=inline]!London, Paris, \ldots{}\,.! 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} +Enter \lstinline[style=inline]!a|b! for the divides relation \( a|b \). +Use \lstinline[style=inline]!\mid! as in +\lstinline[style=inline]!\{a\in S\mid\text{\(a=0\) or \(a\) is odd}\}! +for the set \( \{a\in S \mid\text{\(a=0\) or \(a\) is odd}\} \). + +\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{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{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} +They will grow with the enclosed formula +using \lstinline[style=inline]!\left! and \lstinline[style=inline]!\right!. +\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 period +\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} +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} + + +\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 another array variant. +With this abbreviation 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} +\begin{center} + \begin{tabular}{@{}*{1}{l@{\hspace{2.25em}}}l@{}} + \(\rightarrow\,\leftarrow\)\quad\lstinline[style=inline]!\,! + &\(\rightarrow\quad\leftarrow\)\quad\lstinline[style=inline]!\quad! \\ + \(\rightarrow\:\leftarrow\)\quad\lstinline[style=inline]!\:! + &\(\rightarrow\qquad\leftarrow\)\quad\lstinline[style=inline]!\qquad! \\ + \(\rightarrow\;\leftarrow\)\quad\lstinline[style=inline]!\;! + &\(\rightarrow\!\leftarrow\)\quad\lstinline[style=inline]+\!+ + \end{tabular} +\end{center} +The left column spaces are in ratio \(3\mathbin{:}4\mathbin{:}5\). +The last in the right column is a negative space, +opposite to \lstinline[style=inline]!\,!. +Get arbitrary space as in +% \(\rightarrow\hspace*{0.5cm}\leftarrow\) +\lstinline[style=inline]!\hspace{0.5cm}!. + + +\section{Displayed equations} +Put equations on a separate line with the +\lstinline[style=inline]!equation*! environment. +\begin{center} +\vspace*{-\topsep} + \begin{minipage}{0.25\linewidth}\vspace*{-\abovedisplayskip} + \begin{equation*} + S=k\log W + \end{equation*} + \end{minipage} + \quad + \begin{minipage}{0.65\linewidth} +\begin{lstlisting}[xleftmargin=0ex] +\begin{equation*} + S=k\log 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 using the \lstinline[style=inline]!align*! environment +\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} +(you can have an empty left or right side of the alignment). +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}{@{}r@{\hspace{1em}}l@{}} + \( f\colon\mathbb{R}\to\mathbb{R} \) + &\lstinline[style=inline]!f\colon\mathbb{R}\to\mathbb{R}! \\ + \( 9.8~\text{m}/\text{s}^2 \) + &\lstinline[style=inline]!9.8~\text{m}/\text{s}^2! \\ + $\displaystyle + \lim_{h\to 0}\frac{f(x+h)-f(x)}{h} + $ + &\lstinline[style=inline]!\lim_{h\to 0}\frac{f(x+h)-f(x)}{h}! \\ + $\displaystyle + \int x^2\,dx=x^3/3+C + $ + &\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} + $ + &\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 for the inline version use \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}{@{}r@{\hspace{1em}}l@{}} + $ + \sigma^2=\sqrt{\sum (x_i-\mu)^2/N} + $ + &\lstinline[style=inline]!\sigma^2=\sqrt{\sum (x_i-\mu)^2/N}! \\ + $ + E(X)=\mu_X=\sum (x_i-P(x_i)) + $ + &\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 2017-Jan-10 +}} +\end{document} -- cgit v1.2.3