\documentstyle[a4]{article}
\setlength{\parindent}{0pt}

\let\latex=\LaTeX            % makes it easier to type...

\title{How to work with \latex}
\author{Armin Loerwald\\Kurze Straße 42\\33613 Bielefeld
\and
Sibylle Dürbaum\\Dieselstraße 23\\33613 Bielefeld}


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\begin{document}
\pagestyle{headings}
\maketitle
\newpage

\tableofcontents
\newpage

\pagestyle{headings}
\sloppy
\addtolength\topmargin{-27pt}
\addtolength\textheight{68pt}

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%%%%%% These are a definition  for the juxtapostion of LaTeX %%%%%%
%%%           Layout and and LaTeX-markup commands              %%%
 
\newcommand\exa{\nopagebreak \begin{flushleft}\smallskip \nopagebreak
                \begin{minipage}[t]{6cm}\sloppy}
\newcommand\exb{\end{minipage}\kern 1cm\begin{minipage}[t]{8cm}\sloppy }
\newcommand\exc{\end{minipage}\kern -3cm \smallskip\end{flushleft}}
 
\newcommand\oben[1]{\begin{center}\begin{minipage}{#1}\hrule\medskip}
\newcommand\unten  {\hrule \end{minipage}\end{center}}
 
\section{Introduction}

The document preparation system {\latex}, which contains about 900 commands,
 is based on the original {\TeX}
 or {\sl plain-\TeX} by Donald E.Knuth. This programm
 is especially helpful for the production of mathematical texts.
 Since {\TeX} is very difficult to deal with, {\latex} adds to
 this version a collection of commands that simplify typesetting and
 individual design of articles, books, letters or whatever.\\
 Your primary concern in working with {\latex} should be to concentrate on
 the description of the {\sl logical structure} of your text. While other
 text design programms mainly focus on the visual effect of the text,
 {\latex} approach to typesetting can be characterized as being mainly
 logical, not visual. Thus in {\latex} you must think first of how your
 text should be structured: you have to type in commands {\LaTeX} needs to
 format the text. On your input screen you don't see the final layout
 of your text.\\
 {\latex} encourages you to think of the logical structure:\\
 \hspace{2cm} You can put an equation like this...\\
For all {\it x}:\\
 \centerline{$f(x)= g(x+1)$}

...or like  this\\
\centerline{For all x: $f(x)= g(x+1)$}
\smallskip
\section{The structure of a {\LaTeX}-file}
Each {\latex} document consists of a {\it preamble} and a {\it body}. The {\bf preamble}
contains information about {\it papersize, textheight, design of the
text output, type of text} and all other sorts of commands which are valid for the whole document.
The {\bf body} contains your text in which you can use commands that are
locally valid. Thus the common syntax of a {\latex}-file looks like
this:
\begin{verse}
\verb|\documentstyle[options]{style}|\\
{\it commands and definitions that are valid for the whole document}\\
\bigskip
\verb|\begin{document}|\\
{\it your text and further commands which are valid only locally}\\
\verb|\end{document}|
\end{verse}
\vspace{1cm}
\verb|[options]|: you can use options like: {\bf 11pt,12pt...}{\it standard textheight is 11pt or 12pt
instead of 10pt}; {\bf twoside...}{\it the output is on two sides};
{\bf twocolumn...}{\it output is in two columns}; {\bf german...}{\it you can use
german umlaut like ö, ü, ä}.
\medskip
\verb|{style}:| depending on what your text is all about there's several
text styles available: {\bf book, report, article} or {\bf letter}.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{Commands}

\subsection{General structure of {\LaTeX}-commands}

In {\latex} can appear in an environment of
$\backslash${\it command},
$\{\backslash${\it command \hspace{1cm}}$\}$ or as well $\backslash${\it
command}$\{${\it specified command}$\}$ $\{${\it numeric addition}$\}$.      \\ %another way of doing it
If you use more complex structured commands, the structure appears like this:

\begin{verse}
\verb|\begin{|{\it command}\}\\
\smallskip
further commands or text\\
\smallskip

\verb|\end{|{\it command}\}
\end{verse}

\subsection {Page style and frontpage}
 
The layout of the paper {\em can\/} begin with the command
\begin{verse}
\verb|\pagestyle{|{\it style\/}\verb|}|
\end{verse}
With {\tt plain} (or simply by leaving \verb|\pagestyle| out)
the pagenumber is at the bottom of the paper.
With using {\tt headings} the headline of the chapter and the pagenumber
appear at the top of the paper.
{\tt Empty} of course keeps top and bottom of the page {\it empty}.
\smallskip

\verb|\maketitle| creates the frontpage and depends on your
document style. It can contain \verb|\title{text}|, \verb|\author{names}|,
\verb|\thanks{text}| to whomever you want -- and \verb|\date{text}|, of
course, creates the date. If you leave it out, the computer puts the
relevant time automatically.

\subsection{Headlines and table of contents}

There's many commands available to format your text.
The structure looks like this:\\
\verb|\part, \chapter, \section, \subsection, \subsubsection, \paragraph
and \subparagraph|; \verb| \part and \chapter| are not available
in the {\it article} style.
The command \verb|\tableofcontents| automatically makes the table of
contents. The headlines for the different levels must be in brackets after
the command, e.g.

\begin{verse}
\verb|\section{Two Roman fortresses in Gallia}|\\
\verb|\subsection{Laudanum}|\\
\verb|\subsection{Aquarium}|\\
\end{verse}

\subsection{Font size and font type}
 
\LaTeX\ actually chooses the right font and textheight itself due to the
surrounding commands and the logical structure of the document.
Tables ~\ref{fonts} and~\ref{sizes} show the commands for different types
and sizes.

\exa
{\small Die kleinen {\bf fetten} R"omer
beherrschten }{\large das ganze gro"se
{\it Italien\/}.} \\[6pt]
le $2^{\mbox{\scriptsize\`eme}}$
 r\'egime
\exb
\begin{verbatim}
{\small Die kleinen {\bf fetten}
R"omer beherrschten }{\large das
ganze gro"se {\it Italien\/}.}
\\
le $2^{\mbox{\scriptsize\`eme}}$
r\'egime
\end{verbatim}
\exc
 
\begin{table}[bp]
\caption{Font types} \label{fonts}
\oben{10cm}
\begin{tabbing}
 
{\tt xboldmathxx}\= und dann der Text \kill
\verb|\rm|       \> \rm  normale Schrift (roman) \\
\verb|\bf|       \> \bf  fette Schrift (boldface) \\
\verb|\it|       \> \it  kursive Schrift (italic) \\
\verb|\sl|       \> \sl  schr"age Schrift (slanted) \\
\verb|\sf|       \> \sf  "`sans serif"' Schrift  \\
\verb|\sc|       \> \sc  "`Caps and Small Caps"' Schrift \\
\verb|\tt|       \> \tt  Schreibmaschinenschrift (typewriter) \\
\verb|\boldmath| \> Fettdruck in mathematischen Formeln
\end{tabbing}
\unten
\end{table}
 
\begin{table}
\caption{font size} \label{sizes}
\oben{10cm}
\begin{tabbing}
 
{\tt xfootnotesizexx}\= und dann der Text \kill
\verb|\tiny|         \> \tiny        winzig kleine Schrift \\
\verb|\scriptsize|   \> \scriptsize  sehr kleine Schrift (wie Indizes)\\
\verb|\footnotesize| \> \footnotesize     kleine Schrift (wie Fu"snoten)\\
\verb|\small|        \> \small            kleine Schrift \\
\verb|\normalsize|   \> \normalsize  normale Schrift \\
\verb|\large|        \> \large       gro"se Schrift \\
\verb|\Large|        \> \Large       gr"o"sere Schrift \\
\verb|\LARGE|        \> \LARGE       sehr gro"se Schrift \\[3pt]
\verb|\huge|         \> \huge        riesig gro"s \\[3pt]
\verb|\Huge|         \> \Huge        riesig gro"s
\end{tabbing}
\unten
\end{table}
 
 
If you want to have a {\it large} and {\it bold} typeface you have to
put it into the right order: i.e.\ {\em not\/} with
\verb|\bf\large| but {\em only\/} with \verb|\large\bf|.\\
Remember: the more different font types you use in your document, the more
confusing it looks like!
 
 
 
\vspace{0pt plus 3cm}\pagebreak[2] % manual editing, may need changes!
 
\subsection{Line spacing}

If you want to change the line spacing of your document, i.e. from single
space to doublespace you have to increase the value of the command
\verb|\baselinestretch|
\begin{quote}
for "`line spacing 1.5"' output:\\*
\verb|\renewcommand{\baselinestretch}{1.3}|
 
for "`doublespace"' output:\\*
\verb|\renewcommand{\baselinestretch}{1.6}|
\end{quote}

\subsection{Enumerations}

There's two helpful commands which allow you to create lists very easily.
\verb|\enumerate| creates a numbered list and \verb|\itemize| a list with
dots instead of numbers. These commands are an example for a
\verb|\begin{| {\it command} \verb|}| \hspace{0.5cm} \verb|\end{|
{\it command} \verb|}|
environment. The listed items have to begin with \verb|\item|.

\exa
\begin{enumerate}
\item Troubadix {\bf is} a marvellous musician!
\item Obelix is {\bf not} fat!
\end{enumerate}
\begin{itemize}
\item Verleihnix
\item Raffnix
\item Idefix
\end{itemize}
\exb
\begin{verbatim}
\begin{enumerate}
\item Troubadix {\bf is} a marvellous musician!
\item Obelix is {\bf not} fat!
\end{enumerate}
\begin{itemize}
\item Verleihnix
\item Raffnix
\item Idefix
\end{itemize}
\end{verbatim}
\exc

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{How to use the mathematical style}
 
\subsection{General structure}
 
Mathematical terms have to be put either between
\verb|\(| and \verb|\)| or
between \verb|$| and \verb|$| or
between \verb|\begin{math}| and \verb|\end{math}|
. {\it Mathematical terms} are complete mathematical formula as well as single
variables correlated to formulas, Greek letters or special symbols. Since
{\LaTeX} is mainly created for mathematical texts, the following examples
gives an impression of how {\LaTeX} can look like when it's used in the right way.
\exa
Seien $a$ und $b$ die Katheten
und $c$ die Hypotenuse,
dann gilt $c^{2}=a^{2}+b^{2}$
(Pythagor"aischer Lehrsatz).
\exb
\begin{verbatim}
Seien $a$ und $b$ die Katheten
und $c$ die Hypotenuse,
dann gilt $c^{2}=a^{2}+b^{2}$
(Pythagor"aischer Lehrsatz).
\end{verbatim}
\exc
\exa
\TeX\ spricht man wie
 $\tau\epsilon\chi$ aus.\\[6pt]
100~m$^{2}$ Nutzfl"ache \\[6pt]
Mit $\heartsuit$-lichen
 Gr"u"sen
\exb
\begin{verbatim}
\TeX\ spricht man wie
 $\tau\epsilon\chi$ aus.\\
100~m$^{2}$ Nutzfl"ache \\
Mit $\heartsuit$-lichen
 Gr"u"sen
\end{verbatim}
\exc
 
Longer mathematical formulas or equations should be but in a separate
line. For this purpose one should pose them between
\verb|\[| und \verb|\]|
or between \verb|\begin{displaymath}| and \verb|\end{displaymath}|
or between \verb|\begin{equation}| and \verb|\end{equation}|,
if you want the equations to be enumerated.
\exa
Seien $a$ und $b$ die Katheten
und $c$ die Hypotenuse,
dann gilt
\begin{equation}
c = \sqrt{  a^{2}+b^{2}  }
\end{equation}
(Pythagor"aischer Lehrsatz).
\exb
\begin{verbatim}
Seien $a$ und $b$ die Katheten
und $c$ die Hypotenuse,
dann gilt
\begin{equation}
c = \sqrt{  a^{2}+b^{2}  }
\end{equation}
(Pythagor"aischer Lehrsatz).
\end{verbatim}
\exc

\subsection{Mathematical syntax}

 
\bigskip
 
Small
{\bf Greek letters}
are created like this: \verb|\alpha|, \verb|\beta|, \verb|\gamma|...\
if you want to use capitals you have to put it like this:
\verb|{\rm A}|, \verb|{\rm B}|,
\verb|\Gamma|, \verb|\Delta|...
\exa
$\lambda, \xi, \pi, \mu,
 \Phi, \Omega $
\exb
\begin{verbatim}
$\lambda, \xi, \pi, \mu,
 \Phi, \Omega $
\end{verbatim}
\exc
 
There's a great deal of {\bf mathematical symbols}:
like $\in$ or $\Rightarrow$ or $\infty$...
 
\bigskip
 
{\bf Exponents and indices} can be put high or low with help of
\verb|^| and \verb|_|
\exa
$a_{1}$ \qquad
$x^{2}$ \qquad
$e^{-\alpha t}$ \qquad
$a^{3}_{ij}$
\exb
\begin{verbatim}
$a_{1}$ \qquad
$x^{2}$ \qquad
$e^{-\alpha t}$ \qquad
$a^{3}_{ij}$
\end{verbatim}
\exc
 
{\bf Squareroots} are created like this: \verb|\sqrt| ,
{\it n\/}-th squareroot with \verb|\sqrt[|{\it n\/}\verb|]|.
The size of the squareroot is processed by \LaTeX\ automatically.
\exa
$\sqrt{x}$ \qquad
$\sqrt{ x^{2}+\sqrt{y} }$ 
\qquad $\sqrt[3]{2}$
\exb
\begin{verbatim}
$\sqrt{x}$ \qquad
$\sqrt{ x^{2}+\sqrt{y} }$
\qquad $\sqrt[3]{2}$
\end{verbatim}
\exc

\end{document}