TypesettingWithLatex.tex

\documentclass{beamer}% Every LaTeX2e file starts with a \documentclass line so that TeX knows how to treat it.
%\documentclass[hyperref={colorlinks,linkcolor=white,urlcolor=blue}]{beamer}% Every LaTeX2e file starts with a \documentclass line so that TeX knows how to treat it.
% The beamer class makes PowerPoint-style slides; the [hyperref] part specifies a style for the hyperlinks in the slides.
% Notice that any text that appears between a "%" and the end of a line is treated as a comment: the TeX system ignores it.
% This part of the file is the preamble: it's the part where we load optional packages and do other setup-type stuff.

\usepackage{beamerthemesplit}% This package formats the slides nicely.
\usepackage[greek, english]{babel}% This package gives a Greek alphabet for text mode. Greek letters are available in math mode even without this package.
\usepackage{marvosym}% This loads several of the cool symbols, like \NoIroning.
\usepackage{esint}
\usepackage[export]{adjustbox}% This loads tools that stretch or shrink parts of the document, and tools that help with vertical alignment of images.

% Any string of letters preceded by "\" is a LaTeX command. Everything else is plain text.

\renewcommand*{\arraystretch}{1.3}% This redefines the \arraystretch value (previously = 1) so as to put 30% more space between the rows of each array.

\hypersetup{colorlinks,linkcolor=,urlcolor=blue}

\begin{document}% This is where TeX starts creating our slides.
\title{Typesetting with \LaTeX}
\author{James A. Swenson}
% \subtitle{MATH 4810 --- Fall 2012}
% \date{20 September 2012}
%\subtitle{Spring 2014}
%\date{28 January 2014}
\subtitle{\textsc{Math} 2610 --- Fall 2025}% \textsc makes `small caps,' and --- makes an em dash [use -- for en dash or - for hyphen]
\date{8 October 2025}

\begin{frame}% A "frame" is a single slide in beamer. This frame may be broken up into several "overlays."
\titlepage% This is the command that actually makes the title page; above, we were just entering the necessary data.
\end{frame}

\begin{frame}\frametitle{Plan}
\tableofcontents% This command automatically lists the section titles, with hyperlinks.
\end{frame}

\section{What is the problem?}% start of the first section

\begin{frame}\frametitle{Why not use the Microsoft Word Equation Editor?}

\begin{center}
\includegraphics[height=1.75in]{miktex}\quad{\tiny (Image: Marko Pinteric)}% You need the file "miktex.jpg" in the same folder as this file ("TypesettingWithLaTeX.tex").
% \quad inserts a small blank space. \tiny reduces the font size. Notice the curly braces {} around the \tiny; they restrict its scope.
% Image source: http://www.pinteric.com/miktex.html % I keep track of where I steal things from, using comments right in the file. It's important to give credit!
\end{center}

See also ``Word Processors: Stupid and Inefficient'' by Allin Cottrell
[\url{https://users.wfu.edu/cottrell/wp.html}].% \url starts a hyperlink, and helps LaTeX handle the special characters that might appear in a web address.
\end{frame}

\section{What is \TeX?}

\begin{frame}\frametitle{Portrait of the artist}
\begin{minipage}{0.6\textwidth}% start making a block of text; its width is 60% of the printable width of the frame.
\TeX\ % the last command on this line is "backslash-space," which is a blank space. TeX would ignore ordinary blank space directly after a command, as in \TeX .
is a typesetting system created by Prof. Donald E. Knuth.

\begin{itemize}% Start a list of "bullet items."
\item<2-> \TeX\ is free software.% Notice that this bullet is shown only on the 2nd and later "overlays" of this frame, because of the <2->.
\item<3-> \TeX\ is platform-independent.
\item<4-> \TeX\ is spelled {\greektext teq}, as in the Greek word {\greektext t'eqnh} ``art.''% This is where we're using the babel package.
\item<5-> \TeX\ produces beautiful documents!
\item<6-> The current, expanded edition is called \LaTeXe.
\end{itemize}
\end{minipage}
\hfill% This inserts a horizontal space between our blocks -- it expands to fill the space available.
\begin{minipage}{0.35\textwidth}% This block goes next to the one we just made.
\begin{center}% Start center-justifying everything in this minipage.
\includegraphics[width=\textwidth]{Knuth}\\% The \\ forces a line break.
% The width of the image is the full textwidth -- of this minipage!
{\scriptsize\textit{Donald Knuth (1938 -- )}}\\% \scriptsize is one step larger than \tiny.
\hbox{\tiny (image: \lower1pt\hbox{\includegraphics[height=\baselineskip]{CC80x15}}\ Jacob Appelbaum)}% \tiny is even smaller than \scriptsize.
%source URL = http://commons.wikimedia.org/wiki/File:KnuthAtOpenContentAlliance.jpg
\end{center}
\end{minipage}
\end{frame}

\begin{frame}[fragile]% This frame has to be created with the "fragile" option. If you don't, the verbatim environment inside breaks.
\frametitle{Markup langugage}
A \LaTeX\ document is not \textsc{wysiwyg}; % sc is for Small Caps.
you type a plain-text file, and then feed it to the \LaTeX\ system to get a PDF document.

For example, to produce:
\[\boxed{I(\lambda)=\iint_D g(x,y)e^{i\lambda h(x,y)}\,dx\,dy}\]% The \[ \] make a displayed equation: centered on its own line with space around it.
one types:
{\scriptsize
\begin{verbatim}
\[\boxed{I(\lambda)=\iint_D g(x,y)e^{i\lambda h(x,y)}\,dx\,dy}\]
\end{verbatim}} % The verbatim environment (below) keeps its input from being interpreted as LaTeX commands.

\uncover<2->{% \uncover<2-> reveals this part of the frame (between braces) on the 2nd "overlay" and all subsequent ones.
This presentation was designed using \texttt{beamer}, a \textit{package} that adds functionality to
\LaTeX. The \LaTeX\ file that produced these slides is on my \href{https://swensonj168.wixsite.com/notuwp/latex}{website}. I filled it with comments to explain how it works!}
\end{frame}

\begin{frame}[fragile]\frametitle{Another example}
The equation
\newcommand{\pd}[2]{\frac{\partial#1}{\partial#2}}
$% Remember, \( begins math mode.
\pd{(x,y)}{(u,v)}=
\left|
\begin{array}{cc}
\pd xu & \pd xv\\
\pd yu & \pd yv\\
\end{array}
\right|
$
was produced by typing:
{\scriptsize\begin{verbatim}
\newcommand{\pd}[2]{\frac{\partial#1}{\partial#2}}
$
\pd{(x,y)}{(u,v)}=
\left|
\begin{array}{cc}
\pd xu & \pd xv\\
\pd yu & \pd yv\\
\end{array}
\right|
$
\end{verbatim}}
%%% Without defining the new command, it looks like this:
% \frac{\partial(x,y)}{\partial(u,v)}=
% \left|
% \begin{array}{cc}
% \frac{\partial x}{\partial u} & \frac{\partial x}{\partial v}\\
% \frac{\partial y}{\partial u} & \frac{\partial y}{\partial v}\\
% \end{array}
% \right|
\end{frame}

\section{Using and learning \LaTeX}

\begin{frame}[fragile]\frametitle{Other \LaTeX\ commands}
You can make a whole variety of lovely symbols easily in \LaTeX:
\begin{center}
\begin{minipage}{0.40\textwidth}
\begin{tabular}{|p{3cm}|c|}% tabular is like array, but for use in text mode. p{3cm} is for a paragraph 3 centimeters wide: longer texts would be wrapped.
\hline
\verb=\in= & $\in$\\ % \verb is like a mini verbatim environment; the ='s are delimiters.
\hline
\verb=\infty= & $\infty$\\
\hline
\verb=\pi= & $\pi$\\
\hline
\verb=\forall= & $\forall$\\
\hline
\verb=\mathbb{Z}= & $\mathbb{Z}$\\
\hline
\verb=\NoIroning= & \NoIroning\\
\hline
\verb=\Capricorn= & \Capricorn\\
\hline
\end{tabular}
\end{minipage}
\begin{minipage}{0.40\textwidth}
\begin{tabular}{|p{3cm}|c|}
\hline
\verb=\ge= & $\ge$\\
\hline
\verb=\not\subseteq= & $\not\subseteq$\\
\hline
\verb=\xi= & $\xi$\\
\hline
\verb=\otimes= & $\otimes$\\
\hline
\verb=\aleph_0= & $\aleph_0$\\
\hline
\verb=\Coffeecup= & \Coffeecup\\
\hline
\verb=\Smiley= & \Smiley\\
\hline
\end{tabular}
\end{minipage}
\end{center}
You can find the 481-page ``Comprehensive \LaTeX\ Symbol List'' at:\\%
\adjustbox{width=\textwidth}{\hbox{[\url{https://ctan.math.illinois.edu/info/symbols/comprehensive/symbols-letter.pdf}]}}%
% \hbox groups the text into a chunk, and \adjustbox rescales it to make its width equal \textwidth, the width between the page margins.
\end{frame}

\begin{frame}\frametitle{Find that command!}

What command makes the symbol {\large$\oiint$}?

\bigskip% a little vertical space between paragraphs
\begin{minipage}[t]{0.4\textwidth}%
\begin{enumerate}
\item If there's an easy way to describe the symbol, Google it.
\item<2-> Draw it at \href{https://detexify.kirelabs.org/classify.html}{Detexify}.
\item<3-> Ask someone!
\item<4-> Hunt it down in the Comprehensive Symbol List.
\end{enumerate}
\end{minipage}
\quad
\only<1>{\includegraphics[width=0.55\textwidth,valign=t]{GoogleOiint}}% \only<1> makes the image appear only on the first overlay.
\only<2>{\includegraphics[width=0.55\textwidth,valign=t]{DetexifyOiint}}%
\only<3>{\hspace{0.15\textwidth}\includegraphics[width=0.25\textwidth,valign=t]{Swenson}}%
\only<4>{\includegraphics[width=0.55\textwidth,valign=t]{CompListOiint}}%

{\vskip 0pt plus 1filll} % stretchy vertical space, to push everything on this slide to the top. Otherwise it jumps around as we show taller/shorter images!
\end{frame}

\begin{frame}\frametitle{How do I get \LaTeX?}% all the text in this frame will be \small, which is one step bigger than \scriptsize.
Start by using Overleaf, at [\url{https://www.overleaf.com/}]. % \href inserts a hyperlink: its first argument is the URL and its second is the link text.
It works in your web browser, so there's nothing to install.
\begin{center}\includegraphics[width=0.6\textwidth]{Overleaf}\end{center}

\uncover<2->{If you become a \LaTeX\ fanatic, you can upgrade to installing your own system, customizing your text editor, creating your own commands, writing your own packages\dots.}
\end{frame}

\begin{frame}\frametitle{Have fun using \LaTeX!}
Steal what you need from the source file of this presentation! If you need to know how to type something in \LaTeX, you can certainly find out with Google. You could also ask me for advice!

\begin{center}
\fbox{\includegraphics[height=1.75in]{ConservativeVF}}
\end{center}
\end{frame}

\begin{frame}\frametitle{Time to experiment!}
\begin{center}
\includegraphics[height=2.5in]{OverleafExample}
\end{center}
\end{frame}

\begin{frame}\frametitle{Challenges}
\[
\begin{array}{|c|c|}
\hline
\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} &
\displaystyle \int_a^b F'(x)\,dx = F(b)-F(a)\\
\hline
\displaystyle \sum_{k=1}^\infty \frac{1}{k^6} = \frac{\pi^6}{945} &
\displaystyle\log\left(re^{i\theta}\right)=\ln r+i(\theta+2\pi n)\\
\hline
\displaystyle\sum_{i=r}^n \binom{i}{r} = \binom{n+1}{r+1} &
\displaystyle\oint_{\partial D} \vec{F}\cdot d\vec{r} = \iint_D \left(\frac{\partial Q}{\partial x}-\frac{\partial P}{\partial y}\right)\,dA\\
\hline
\displaystyle\frac{1}{\sqrt{2\pi\sigma^2}} e^{-\left(\frac{x-\mu}{\sigma}\right)^2/2}&
\displaystyle\lim_{x\to a} \frac{f(x)}{g(x)} \stackrel{\left(\frac00\right)}{=} \lim_{x\to a} \frac{f'(x)}{g'(x)} \\
\hline
\displaystyle\mathbb{C}\cong\left\{\left(\begin{array}{cc} a&-b\\b&a\end{array}\right)\colon a,b\in\mathbb{R}\right\} &
\displaystyle X\setminus\left(\bigcup_{A\in\mathcal{S}} A\right) = \bigcap_{A\in\mathcal{S}} \left(X\setminus A\right)\\
\hline
\end{array}
\]
\end{frame}

\end{document}% This is where \TeX stops reading

% I keep this bit down below the \end{document} to copy and paste when I create a new slide.
\begin{frame}\frametitle{}

\end{frame}