\documentclass[10pt]{article}
\usepackage{color}
\definecolor{clr}{rgb}{0.1,0.2,0.8}
\addtolength{\textwidth}{120pt}
\addtolength{\evensidemargin}{-60pt}
\addtolength{\oddsidemargin}{-60pt}

\def\displayandname#1{\rlap{$\displaystyle\csname #1\endcsname$}%
                      \qquad\qquad \textcolor{clr}{\texttt{\char92 #1}}}
\def\mathlexicon#1{$$\vcenter{\halign{\displayandname{##}\hfil&&\qquad
                   \displayandname{##}\hfil\cr #1}}$$}
\begin{document}
\thispagestyle{empty}
\paragraph{\underline{A \LaTeX\ crash-course.}}
\begin{description}
\item[Special characters.] The following symbols have special meaning in \LaTeX:
{\color{clr}\verb"# $ % _ { } ~ ^ \"}\\
You can print the first seven of these by using {\color{clr}\verb"\# \$ \% \_ \{ \}"} .
\item[Paragraphs, Lines and Text.] A blank line starts a new paragraph, {\color{clr}\verb"\\"} starts a new line, {\color{clr}\verb"\ "} includes a space, {\color{clr}\verb"\mbox{...}"} includes text.
\item[Mathematics] You start (and end) 'math mode' by a
{\color{clr}\verb"$"} sign.

For instance
{\color{clr}\verb"the example $\frac{\sqrt{2}}{3}$ is finished."} produces the output: the example $\frac{\sqrt{2}}{3}$
is finished.

Alternatively you can enclose a displayed mathematics expression by {\color{clr}\verb"\[....\]"}.

{\color{clr}\verb"the example \[\frac{\sqrt{2}}{3}\] is finished."} produces the output: the example \[\frac{\sqrt{2}}{3}\]
is finished.
Replacing {\color{clr}\verb"\[....\]"} by {\color{clr}\verb"\begin{equation}....\end{equation}"} produces a numbered equation.

\item[Sub- and Superscripts.] {\color{clr}\verb"x^2"} produces $x^2$, {\color{clr}\verb"x_{2n}"} produces $x_{2n}$.
Here is another example: {\color{clr}\verb"\log_{5} 25=2"} gives $\log_{5} 25=2$.
\item[Fractions.] Use {\color{clr}\verb"\frac"} to display fractions.
Example: {\color{clr}\verb"\frac{\pi^2}{6}"} gives $\frac{\pi^2}{6}$.
\item[Roots.] Use {\color{clr}\verb"\sqrt"}. For instance, {\color{clr}\verb"\sqrt{a^2+b^2}"} produces $\sqrt{a^2+b^2}$.
You can also get ``other" roots: {\color{clr}\verb"\sqrt[3]{2}"} yields $\sqrt[3]{2}$.
\item[Delimiters.]The inputs {\color{clr}\verb"(  ) [ ] \{ \}"} yield the outputs  $(\ )\ [\ ]\ \{\ \}\ $.
\item[Greek letters.]
\begin{quotation}
\mathlexicon{alpha&beta&gamma&delta\cr
epsilon&zeta&eta&theta\cr
iota&kappa&lambda&mu\cr
nu&xi&pi&rho\cr
sigma&tau&upsilon&phi\cr
chi&psi&omega&varepsilon\cr
vartheta&varpi&varrho&varsigma\cr
varphi&Gamma&Delta&Theta\cr
Lambda&Xi&Pi&Sigma\cr
Upsilon&Phi&Psi&Omega\cr}
\end{quotation}
\item[Functions.]
\begin{quotation}
\mathlexicon{%
log&lg&ln&exp\cr
sin&cos&tan&cot\cr
sec&csc&arcsin&arccos\cr
arctan&deg&arg&inf\cr
sup&min&max&lim\cr
liminf&limsup&det&dim\cr
ker&gcd&bmod&\omit\cr}
\end{quotation}
\item[Miscellaneous Symbols.]
\begin{quotation}
\mathlexicon{aleph&prime&forall\cr
hbar&emptyset&exists\cr
imath&nabla&neg\cr
jmath&surd&flat\cr
ell&top&natural\cr
wp&bot&sharp\cr
Re&|&clubsuit\cr
Im&angle&diamondsuit\cr
partial&triangle&heartsuit\cr
infty&backslash&spadesuit\cr}
\end{quotation}
\item[``Large'' Operators.]
\begin{quotation}
\mathlexicon{sum&bigcap&bigodot\cr
prod&bigcup&bigotimes\cr
coprod&bigsqcup&bigoplus\cr
int&bigvee&biguplus\cr
oint&bigwedge&\omit\cr}
\end{quotation}
\item[Binary Operations.]
\begin{quotation}
\mathlexicon{pm&cap&vee\cr
mp&cup&wedge\cr
setminus&uplus&oplus\cr
cdot&sqcap&ominus\cr
times&sqcup&otimes\cr
ast&triangleleft&oslash\cr
star&triangleright&odot\cr
diamond&wr&dagger\cr
circ&bigcirc&ddagger\cr
bullet&bigtriangleup&amalg\cr
div&bigtriangledown&\omit\hfil\cr}
\end{quotation}
\item[Relations.]
\begin{quotation}
\mathlexicon{leq&geq&equiv\cr
prec&succ&sim\cr
preceq&succeq&simeq\cr
ll&gg&asymp\cr
subset&supset&approx\cr
subseteq&supseteq&cong\cr
sqsubseteq&sqsupseteq&bowtie\cr
in&ni&propto\cr
vdash&dashv&models\cr
smile&mid&doteq\cr
frown&parallel&perp\cr}
\end{quotation}
\item[Arrows.]
\begin{quotation}
\mathlexicon{%
leftarrow&rightarrow\cr
longleftarrow&longrightarrow\cr
Leftarrow&Rightarrow\cr
Longleftarrow&Longrightarrow\cr
leftrightarrow&Leftrightarrow\cr
longleftrightarrow&Longleftrightarrow\cr
hookleftarrow&hookrightarrow\cr
leftharpoonup&rightharpoonup\cr
leftharpoondown&rightharpoondown\cr
uparrow&downarrow\cr
Uparrow&Downarrow\cr
updownarrow&Updownarrow\cr
nearrow&nwarrow\cr
searrow&swarrow\cr
mapsto&longmapsto\cr
rightleftharpoons&\omit\hfil\cr}
\end{quotation}
\item[Lists, etc.] Lists are easy. A numbered list starts with {\color{clr}\verb"\begin{enumerate}"}
and ends with {\color{clr}\verb"\end{enumerate}"}. Items start
with {\color{clr}\verb"\item"}. There are also bullet item
lists---use "itemize" instead of "enumerate". Example:
{\color{clr}\verb"\begin{enumerate}\item one \item zwei \item $\sqrt{9}$\end{enumerate}"} produces
\begin{enumerate}\item one \item zwei \item $\sqrt{9}$\end{enumerate} Lists can be nested.
\item[Matrices, arrays, etc.]
{\color{clr}\verb"\begin{array}{cc}1&0\\0&1\end{array}"} produces
$\begin{array}{cc}1&0\\0&1\end{array}$. You can produce big
delimiters by prefacing with {\color{clr}\verb"\left"} and closing with
{\color{clr}\verb"\right"}. Example:
\begin{center}
{\color{clr}\verb"\left(\begin{array}{cc}1&0\\0&1\end{array}\right)"} produces
$\left(\begin{array}{cc}1&0\\0&1\end{array}\right)$.\end{center}

{\color{clr}\verb"\right."} matches a {\color{clr}\verb"\left..."} and is necessary to ``close" the {\color{clr}\verb"\left"}
tag, but does not produce any output. Example:
\begin{center}{\color{clr}\verb"f(x)=\left\{\begin{array}{cc}0,&\mbox{ if }"}
{\color{clr}\verb"x\leq 0\\1, & \mbox{ if } x>0\end{array}\right."}\end{center} produces
$f(x)=\left\{\begin{array}{cc}0,&\mbox{ if } x\leq 0\\1, & \mbox{
if } x>0\end{array}\right.$

{\color{clr}\verb"{cc}"} after the
{\color{clr}\verb"\begin{array}"} command means that the array
has two centered columns. Other alignment options are
{\color{clr}\verb"r"} and {\color{clr}\verb"l"}. Use
{\color{clr}\verb"|"} to insert a vertical line.
{\color{clr}\verb"\hline"} inserts a horizontal line. Example:
\begin{center}
{\color{clr}\verb"\begin{array}{l|cr|}4&1&2\\-4&-1&-2\\\hline\end{array}"}\end{center} yields $\begin{array}{l|cr|}4&1&2\\-4&-1&-2\\\hline\end{array}$
\item[Aligned Equations.]In a similar vein, you can produce aligned equations. Here is an example:
\begin{center}{\color{clr}\verb"\begin{eqnarray}y&=&(x-2)^2\\&=&x^2-4x+4\end{eqnarray}"} \end{center} yields
\begin{eqnarray}y&=&(x-2)^2\\&=&x^2-4x+4\end{eqnarray} There must be exactly two alignment characters {\color{clr}\verb"&"}
in each line. Note that the equations are automatically numbered.
Using {\color{clr}\verb"\begin{eqnarray*}....\end{eqnarray*}"} produces unnumbered equations instead.
\item[Over- and underlining.]
{\color{clr}\verb"\underline{\overline{x^2}+1}"} yields $\underline{\overline{x^2}+1}$,\\
{\color{clr}\verb"\underbrace{\overbrace{x^2}+1}"} produces $\underbrace{\overbrace{x^2}+1}$.
There are also {\color{clr}\verb"\hat, \tilde"} and {\color{clr}\verb"\widehat"} and {\color{clr}\verb"\widetilde"}. Example: $\tilde{x}, \widehat{\sqrt{x^2-1}}$.
Other accents: {\color{clr}\verb"\check, \bar, \vec, \dot, \ddot"}: $\check{a}, \bar{a}, \vec{a}, \dot{x}, \ddot{x}$.
\item[Font size.] Use {\color{clr}\verb"\displaystyle"} to make formulas bigger;\\
compare {\color{clr}\verb"\frac{1}{2}"} to
{\color{clr}\verb"\displaystyle{\frac{1}{2}}"}: $\frac{1}{2}$
versus $\displaystyle{\frac{1}{2}}$.
\item[Standard Template.]
{\color{clr}\verb"\documentclass[12pt]{article}\begin{document}"}....Text goes here....{\color{clr}\verb"\end{document}"}
\vfill\end{description}
{\tiny\copyright\ \today . Helmut Knaust}
\end{document}
