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% this is a comment -- it is a line starting in %
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% the pre-eamble is everything from \documentclass to \begin{document}
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\documentclass[12pt]{article} % the 12pt makes the font bigger
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\title{Math 152: Intro to Mathematical Software -- Lecture 7: LaTeX (part 2)}  % document title
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\author{Kiran Kedlaya (guest lecturer: Alina Bucur) \\ 
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(based on lectures by William Stein, University of Washington)}   % who wrote this
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\date{January 25, 2017}
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\usepackage{amssymb}
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\usepackage{hyperref}  % make it so there is a \url{} command and links work (in pdf!)
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% include support for putting pdf's and png's in our file
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\usepackage{graphicx}
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% Package for the "newtheorem" command
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\usepackage{amsthm}
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\newtheorem{exercise}{Exercise}[section]   % exercise environment
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\begin{document}
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% this is the body of the document
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% This is a command that says: "put the title block here".
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% Try copying this command and putting it somewhere else and get multiple titles
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\maketitle
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\tableofcontents
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% Use \section{...} to make a new section.
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% The * prevents it from being automatically numbered.
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\section{Announcements\label{announcements}}
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{\bf Some announcements:}  % md the {\bf ...} makes it bold
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\begin{enumerate}
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\item You should open {\tt lectures/2017-01-25/2017-01-25.tex} in your project to follow along.
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\item \label{reminder-homework} HW 2 peer grading due Thursday, January 26 at 8pm.
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\item HW 3 due Tuesday, January 31 at 8pm.
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\end{enumerate}
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\section{Math formulas}
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\LaTeX\ is massively different than a typical word processor (e.g., Microsoft Word).  You focus entirely on the content and structure of what you are
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writing, not on how it looks.  Also, the result is much more
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professional-looking.   And you can define functions, e.g.,
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\newcommand{\hello}[1]{Hello #1, hello #1 !! }
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\hello{World} - I say \hello{to you}!\\
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\hello{Kiran}
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\subsection{Some basics}
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Google ``latex symbols''\footnote{Look in the tex file for how I did those quotes and this footnote.} for tables\footnote{what is a table?} giving how to typeset
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interesting symbols, like this:
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$$
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\varphi, \Xi, \partial, \hookleftarrow, \bigoplus
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$$
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Consider $\varphi + \Xi^3$.
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Top hit (San Diego company interested in math education! Ask me about them later):\\ \url{https://www.artofproblemsolving.com/wiki/index.php/LaTeX:Symbols}
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This webpage explains a lot of math typesetting.  Here are some key things:
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\begin{itemize}
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\item Braces: $\{ x : x \in \mathbb{Q}\}$
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\item Powers: $x^{2+3}$,    $x^2+3$,  $x^(2+3)$
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\item Subscripts: $x_2, x_5, x_{2+3}$
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\item Both: $x^{2+3}_{5}$
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\item A fraction: $\frac{2+3 \hello{10}}{5}$
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\item An integral: $\int_0^{\pi+e^i} \sin(x) dx$
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\item A ``displayed'' integral: $$\int_0^{\pi} \sin(x) dx$$
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\end{itemize}
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\url{http://detexify.kirelabs.org/classify.html}
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\subsection{Using Sage}
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Given any object {\tt obj} in a Sage worksheet you
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can (try to) do {\tt latex(obj)} to see how to typeset
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obj.   You already learned about sagetex, which uses
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this under the hood, on Monday.
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$$
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x + \frac{1}{6} x^{3} + (-\frac{1}{40}) x^{5} + (-\frac{55}{1008}) x^{7} + \mathcal{O}\left(x^{8}\right)
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$$
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$$
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\displaystyle \left(\begin{array}{rrr}
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1 & -2 & \frac{1}{2} \\
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1 & 0 & 0 \\
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-2 & 0 & 1
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\end{array}\right)
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$$
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\begin{exercise}
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Use Sage to find a \LaTeX\ formula for the first few terms
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of the Taylor series of $\tan(x)$ about
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zero.\footnote{Hint: use {\tt latex(tan(x).series(x, 10))} in a worksheet, then copy/paste.}
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\end{exercise}
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$$
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your series here!
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$$
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\begin{exercise}
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Use Sage to find a \LaTeX\ formula for a matrix using Sage.  Use the command {\tt matrix} to make a matrix.
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\end{exercise}
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$$
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your matrix here!
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$$
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\subsection{Use Some random webpage}
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If you do a Google search for {\tt latex formula editor}
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you'll find (many) kind-of-ugly websites with
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various programs that
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let you graphically construct an equation, which show
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you the latex code.
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This is an unusual new demo, where they use machine learning
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to recognize handwriting (it is pretty impressive):\\
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\url{http://webdemo.myscript.com/#/demo/equation}
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$$
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\frac{\Omega +\alpha ^{3}} {2}
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$$
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\section{Sectioning and cross referencing\label{a-label}}
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This is Section \ref{a-label}.  The next section is Section \ref{graphics}.
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You can reference anything, e.g., reminder \ref{reminder-homework}
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from Section \ref{announcements}.
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%Fix the typo here!
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\begin{exercise}
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Try reordering the enumerate list above in some random way and or the sections
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(or adding new ones), then recompile and see all the cross reference numbers
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get updated.
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\end{exercise}
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\section{Including graphics\label{graphics}}
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You can take any pdf, png, or jpg file, put it in the
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same directory as your tex file (+New, drag and drop),
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and display them as follows. (Photo taken by William Stein.)
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\begin{center}  % this centers it
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\includegraphics[width=.6\textwidth]{svr.jpg}
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\end{center}
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\hello{\includegraphics[width=.1\textwidth]{svr.jpg}}
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% Newly added feature: if LaTeX encounters any errors while processing
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% your source file, the errors are marked in place. This isn't perfect,
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% but this example is spot on:
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$$x^{\includegraphics[width=.1\textwidth]{a.pdf}} + 1$$
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% Fix the typo and see what happens!
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\begin{exercise}
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Upload and insert an image of your choice below.  It must
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be png or pdf.
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\end{exercise}
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% Copy paste the includegraphics thing above here, change
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% the name from image to the name of your file:
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Sage can also produce pdf's of plots.
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E.g., if {\tt g = plot(sin) + plot(cos)}, then
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{\tt g.save('a.pdf')} will create a file {\tt a.pdf}
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that you can include.  This is a little more tedious
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than Sagetex, but you have more control.
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\begin{exercise}
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Create a plot and save it to a file
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as above in a Sage worksheet, then include it below. (Remember, you can use the ``Plots'' menu in a worksheet to see some examples of plotting syntax.)
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\end{exercise}
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% Copy paste the includegraphics thing above here, change
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% the name from image to the name of your file:
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\end{document}
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