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\begin{center}\begin{large} Sample Latex File\\
\end{large}    Math Mode, Text Mode, and Using Labels\\
             Matchett, \today
\end{center}

The environments \emph{displaymath} and \emph{equation} are used 
for displayiong one-line mathematical expressions.  In these 
environments, LaTeX is in math mode.  This means that all kinds 
of symbols that are common in mathematics can be displayed.  But 
you may only display one line of material, and in the latex file 
there must not be any blank lines between the ``begin'' command 
and ``end'' command.  Here's the famous quadratic formula:
\begin{displaymath}
    x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}   
\end{displaymath}
If you want to display two lines of 
formulas, use two separate ``begin - end'' blocks. 

The only difference between \emph{displaymath} and 
\emph{equation} is that in the latter environment, whatever is 
displayed is given a number.  For example, I might want to 
display a trigonometric identity and have it be numbered: 
% Comment to reader: The \label command is explained further down.
\begin{equation}                \label{baddy}
    sin(\alpha + \beta) = sin \alpha cos\beta + sin \beta cos \alpha
\end{equation}
It improves readability if ``sin'' and ``cos'' are typset in 
ordinary text mode.  To that end, there are commands which are 
just ``sin'' and ``cos'' preceeded by a backslash.  
\begin{equation}                   
   \sin(\alpha + \beta) = \sin\alpha \cos\beta + \sin\beta \cos\alpha
\end{equation}
A further improvement comes from adding some spaces.
\begin{equation} 
   \sin(\alpha + \beta)\; = \; \sin\alpha \, \cos\beta \, + \, \sin\beta
       \, \cos\alpha       \label{goody}
\end{equation}
The space commands for math mode are as follows:
\begin{verbatim} 
           \,  thin space      \:  medium space     
           \;  thick space     \   very thick space
\end{verbatim} 
That fourth space is a backslash followed by a blank produced 
from the keyboard by pressing the space bar.  

To refer back to a numbered
expresion, use the \emph{label} and \emph{ref} commands.  You do 
this by sticking a ``label'' command like 
$\backslash$label$\{$baddy$\}$ inside the desired equation 
environment.  Then for ever after, you may refer to that 
expression with the ``ref'' command, as $\backslash 
\mbox{ref}\{\mbox{baddy}\}$. Using this feature of LaTeX, I can 
say ``Equation \ref{goody} is much nicer than Equation \ref{baddy}.''
without checking what number the equation has.  Latex figures out 
the number of the equation for me.

To embed short mathematical expressions in a paragraph, just 
surround the expression by dollar signs.  For example I might say 
that the equation $x = 12 - 2x$ has solution $ x = 4$.  If I 
write that last equation without dollar signs it gets typset as  
x = 4,  which is bad because the x is in the wrong font.  Also 
you cannot even access many math symbols if you stay in text 
mode.  So enclose math expressions in dollar signs whenever you 
embed them in a text paragraph.  

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