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\centerline{{\Huge My First Latex Document}}

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\section{Tex versus Latex}\label{tex.vs.ltx}

This is a very simple document, intended to show
a few very basic commands.  To see how
Latex works, you should compare the source
file with the output document.

Latex is the most widely used ``flavor'' of
Tex --- it has largely displaced Plain Tex,
AMStex, and all the others.  Consequently,
the words ``Tex'' and ``Latex'' are used
interchangeably, more or less.  In our first
lesson we might not get to many
of the features that make Latex so
advantageous over those other flavors
of Tex.  We'll start with some features
that are
common to all versions of Tex.

Tex does
not follow the line breaks of your 
source file.
Also          Latex ignores extra       spaces
in your source file.
Compare this paragraph's source file and
output document
and you'll see what I       mean.



One or more blank lines begins a new paragraph.




\section{Doing math}\label{good.math}

Dollar signs are used to enter math mode
and then to exit math mode.  For instance,
here is an $\alpha$ and an $\Omega$.

Doubled dollar signs can be used to enter
or exit display math mode.  For instance,
here is a displayed equation (which illustrates
several of Tex's features:
$$ 1^2 + 2^2 + 3^2 + \ldots + n^2 =
\sum_{j=1}^n j^2 =
\frac 16 n(n+1)(2n+1).$$

One of Tex's biggest advantages is its
automatic use of spacing that suits the
mathematician's taste very well --- far
better than any WYSIWYG\footnote{``What
you see is what you get,'' an editor
such as Wordperfect or Microsoft Word.}.
Look at the spacing in these displays:
$$ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $$
$$ \left[ 
\begin{array}{cc}
  0 & 1 \\
  1 & 2 \\
\end{array}
\right] ^ n
= 
\left[\begin{array}{cc}
  f_{n-1} & f_n \\
  f_n & f_{n+1} \\
\end{array}\right]
\;\;
(n=1,2,3,\ldots)$$


\section{Lists, tables, and other formats}\label{lists}

The ``itemize'' environment in Latex is like
the ``unnumbered list'' (UL) of HTML:

\begin{itemize}

\item Its items are indicated by bullets

\item at least in the default setting

\item as shown here

\item but actually

\item[$\circ$] you can replace the bullets with whatever
you want.

\end{itemize}

The ``enumerate'' environment in Latex is like the
``ordered list'' (OL) of HTML:

\begin{enumerate}

\item Here is the first thing.

\item Here is the second thing.

\item Latex does the numbering automatically.

\item \label{numbered} And if I label an item in
an enumerated list (as I'm doing now), then
I can refer to the label elsewhere; see my
discussion of labels in section \ref{xrefs}.

\end{enumerate}

In addition to ``itemize'' and ``enumerate'',
advanced users can design their own customized
list environments.  (More about that in a
later lesson, perhaps.)

Another important environment is the \textit{table}.
Once you learn all the tricks, tables in Latex
are even more flexible and controllable
than those in HTML.

\begin{center}\begin{tabular}{r|ccc|c|}
 & a & b & x & total \\
\hline
more symbols & $\sqrt{3}$ & $\sqrt[5]{3}$  
& $f:A\to B$ & $\uparrow$ \\
\cline{1-2}\cline{4-5}
sizes of letters & {\Large Xy} & {\Huge Xy}
& {\tiny Xy} & ??? \\
\hline
\end{tabular}\end{center}

Tables and arrays can do essentially the
same things, though 
\begin{itemize}
\item 
tables are designed
primarily for text (with math thrown in
via extra commands), whereas 

\item arrays
are designed for math (with text thrown
in via extra commands).
\end{itemize}
Lately I have begun to prefer
tables because a slight adjustment in
``tabular'' turns it into ``supertabular'',
an environment that can go across page breaks
when desired.  I'm not aware of any
analogous variant for arrays.







\section{Cross-referencing}\label{xrefs}

Latex has lots of nice features built in for
cross-referencing.  For instance, I have
labeled the sections of this paper as
``tex.vs.ltx'', ``good.math'', etc.  Those
labels are not seen by the person who
eventually reads the paper; they are
only seen by me while I'm editing the
paper.  I can refer to a section of the
paper by citing its label; for instance,
right now the section labeled
``tex.vs.ltx'' is section \ref{tex.vs.ltx};
and in my example of an enumerated list,
the item in which I mentioned cross-referencing
was item number \ref{numbered}.
You can attach labels of this sort to
chapters, sections, subsections, equation numbers, 
and other subdivisions of the document.


\textbf{Why would you want to?}  Well, the
point is this:  If I rearrange my document,
changing the order in which the sections
(or equations, or whatever) appear, I
don't have to \textit{renumber} everything.
The numbering is done automatically by
Latex.  I keep the label with the content,
and Latex automatically recalculates what
number should go with that label.

If you're writing a book, Latex can automatically
keep track of the cross-references needed for
your table of contents and your index.
You don't have to rewrite those everytime
you change a page in the book; Latex rewrites
those automatically.  I can't imagine how
people wrote books before Latex was invented.

Another fancy bit of cross-referencing:
You can set up \textit{hyperlinks}, so that
(for instance) someone who clicks a mouse
on some reference to section 2 will automatically
be taken \textit{to} section 2.  That might
be nice for reading, but I find it even nicer
for \textit{writing} --- i.e., I can jump back and forth
easily between different parts of my document
while I'm writing and editing the document.



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