Graduate Mathematics Association

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% \usepackage{palatino} % I like this font family better than the standard

% for hyperlinks: use command \url{...}
\usepackage{hyperref}

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% \setlength{\textheight}{8in}

% OR just use the geometry package to set all margins
\usepackage[tmargin=1in,bmargin=2in,lmargin=1in,rmargin=1in]{geometry}
\setlength{\headheight}{1in}

% for doublespace, use linespread 1.6. for half space, 1.3
\linespread{1}

% headers and footers
\usepackage{fancyhdr} % gives greater control over headers/footers
\usepackage{graphicx} % allows insertion of graphics
%\lhead{\includegraphics[height=1.3cm]{icubedlogo}}
%\rhead{\includegraphics[height=1.2cm]{gmalogo}}
\cfoot{} % removes default page number from center footer
\pagestyle{fancy} % tells all pages to use the fancy style

% theorems and definitions
\usepackage{amsmath,amsthm,amssymb}
\newtheorem{thm}{Theorem}
\newtheorem{prop}{Proposition}
\newtheorem{defn}{Definition}

% extra commands to save on typing...
\newcommand{\Lt}{\LaTeX \ }
\newcommand{\bs}{\textbackslash}
% to create to commands which accept arguments, put the number
% of arguments in square brackets. This command centers text with
% \ct{this text will be centered}.
\newcommand{\ct}[1]{\begin{center} {#1} \end{center}}

% ================================================================= %
\begin{document}

\title{Spring 2013 \Lt Workshop}
\date{}
\author{}
\maketitle
\thispagestyle{fancy} % by default, TeX removes headers from first page

\section*{Getting Started}
\Lt, at its core, is a computer language which is used to specify
the layout of a page. Once the code is written, it can then be
compiled to produce a pdf, dvi, or ps document. There are a number
of applications which exist specifically to help write and compile
\Lt documents, but code can be written on any text editor and
compiled directly.

The first step to compiling your own code is installing a \Lt
distribution, which includes the actual programs used to compile
your code into a .pdf document (or a .dvi, or a .ps document).
With this is installed, you \Lt in any text editor
(such as notepad, vim, emacs, gedit, etc.), and build it into a
pdf with the command `pdflatex'. Even though all you need
is the distribution and a basic editor, it is typically
easier to learn on an editor specifically suited to \Lt.

The installation process can vary depending on your operating
system, but some of the more popular options are described below:

\subsection*{Windows}
Miktex is an excellent \Lt distrubution for the Microsoft
Windows operating systems, which is easily installed and manages
add-on packages for you as needed. It can be found here:
\url{http://miktex.org/}.

For the editor, TeXnic Center (\url{http://www.texniccenter.org/})
is a \Lt development suite which includes references, syntax
highlighing, and preview options. When starting up TeXnic Center
for the first time, it may ask you to tell it where your Miktex
files are. This will typically be C:\bs Program files\bs
MiKTeX\bs miktex\bs bin .

\subsection*{Mac OS X}
MacTeX (\url{http://www.tug.org/mactex/2011/}) is the most popular
\Lt distribution on OS X, and it includes an excellent editor
(TeXshop). MacTeX is a large program which is easy to set up and
full of useful features.

\subsection*{Linux}
The most popular distribution for Linux is TeXLive, which can be
installed in a variety of ways depending on your specific Linux
distribution (in Ubuntu: `sudo apt-get install
texlive').

TeXWorks is a popular and easy to set up \Lt editor which is
compatible with most popular Linux distributions. There are also a
number of plugins for editors such as vim or emacs.

Note that there are numerous online resources for learning \Lt (one
of the most comprehensive and well written can be found here:
\url{http://tobi.oetiker.ch/lshort/lshort.pdf}). If you run into
trouble while installing, visit your particular distribution's
website or try googling you're problem.

\section*{Compiling Your First Document}

Once you have a \Lt distribution installed, you're ready to compile
your first document. Fire up any text editor, and write the
following: % the verbatim environment prints text exactly as written
\begin{verbatim}
\documentclass{article}

\begin{document}

hello world! $e^{i \pi} + 1 = 0$

\end{document}
\end{verbatim}
Then save this file as hello.tex. If you're using an editor built
for \Lt, there should be a compile button, which will automatically
turn your code into a pdf. To compile manually, pull up a command
line, navigate to your file, and run the command `pdflatex
hello.tex'. Either way, you should end up with a pdf containing only
the line:

\vspace{.5cm}

hello world! $e^{i \pi} + 1 = 0$

\vspace{.5cm}

\section*{\Lt Syntax}

Looking at the above example, a few details stand out. The source
code is a mix of text and formatting commands, and the math is
written in between \$ signs. A command in \Lt typically is typically
begun with a backslash, and arguments are passed in brackets (with
options in square brackets) like so: \\
\verb+ \command[option]{argument1}{argument2}+.
For example, \verb+\frac{a}{b}+ produces $\frac{a}{b}$.

The commands before the \verb+\begin{document}+ statement are
known as the preamble and is where you place formatting
options to change the appearance of your document. For example, the
\verb+\documentclass{article}+ command tells \Lt that we want to use
the built in class `article'. A class sets basic formatting
options, such as fonts, margins, formatting for section headings,
additional packages, spacing, etc. The `article' class is very
flexible and easily extensible. Other options include `book',
`report', and `beamer' (for presentations).

The part of the document between the \verb+\begin{document}+ and
\verb+\end{document}+ lines is the body. This is where the actual
content goes which will make up the document. Text is divided up
into regular mode and math mode, and math can be either inline or in
display mode. By default, text is assumed to be non-math. To format a
mathematical expression, surround it by dollar signs or by
\verb+\( ... \)+ to fit it in the current line, or surround it by
double dollar signs or \verb+\[ ... \]+ to display it in its own
line. For example,

\verb+$ e^x = \sum_{k \geq 0} \frac{x^k}{k!}$+ will compile to $e^x =
\sum_{k \geq 0} \frac{x^k}{k!}$, while \\
\verb+$$ e^x = \sum_{k \geq 0} \frac{x^k}{k!}$$+ will come through as
$$ e^x = \sum_{k \geq 0} \frac{x^k}{k!}.$$

Another important aspect of \Lt is its handling of whitespace. The
code:
\begin{verbatim}\LaTeX treats multiple spaces
as just a single space, and
multiple blank lines as a single one .\end{verbatim}
is typeset as
\ct{\Lt treats multiple spaces as just a single space, and multiple
blank lines as a single one.}
A paragraph break is indicated either by a pair of backslashes or at
least one blank line between blocks of text.

\section*{Adding packages}
While the 'article' class is useful for most situations, and is
easily extended to fit many situations, there are other classes
specially suited for different tasks (notably: beamer, for
presentations). Changing the formatting of an entire document (for
example, for submission to a journal) is often as simple as changing
the class.

Where the class defines some of the global specifications for the
document, packages generally add functionality or environments to a
document. For example, this document (whose source code can be found
at \url{http://www.math.ufl.edu/gma/textalk}), uses the package
`fancyhdr' to make nice and customizable headers and footers, and
`hyperref' to embed hyperlinks.

For another example, the packages `amsmath', `amsthm', `amssymb' provide
additional mathematical symbols and theorem-like environments, which
can be specified in the preamble.
To see how this works, try compiling the following code.
Anything written after a $\%$ sign is a comment and
won't affect the code, which can be useful for explaining what your
code does (to youself or someone else).
\pagebreak

\begin{verbatim}
\documentclass{article}

\usepackage{amsmath,amssymb,amsthm}

\newtheorem{defn}{Definition} % I called them defn and thm
\newtheorem{thm}{Theorem} % for shorthand

\begin{document}

\begin{defn}
Let $n,k \in \mathbb{Z}^+$ with $n \geq k$. Then define
$$ \binom{n}{k} = \frac{n!}{k!(n-k)!}.$$
\end{defn}

\begin{thm}[Binomial Theorem] For all $x \in \mathbb{R}$ and $n \in \mathbb{Z}^+$,
$$ (x+1)^n = \sum_{k = 0}^n \binom{n}{k} x^k.$$
\end{thm}

\begin{proof}
Left as exercise.
\end{proof}

\end{document} \end{verbatim}

You should end up with something like:

\begin{defn}
Let $n,k \in \mathbb{Z}^+$ with $n \geq k$. Then define
$$\binom{n}{k} = \frac{n!}{k!(n-k)!}.$$
\end{defn}

\begin{thm}[Binomial Theorem] For all $x \in \mathbb{R}$ and $n \in \mathbb{Z}^+$,
$$ (x+1)^n = \sum_{k = 0}^n \binom{n}{k} x^k.$$
\end{thm}

\begin{proof}
Left as exercise.
\end{proof}

More information about various packages and useful tips can be found
at \url{http://en.wikibooks.org/wiki/LaTeX/}, and a more complete
(and better written) introduction can be found at
\url{http://tobi.oetiker.ch/lshort/lshort.pdf}.