\documentclass[12pt]{amsart}
%\pagestyle{plain}
\input 2emacros
%
\title{LaTeX and Friends}
\date{\today}
\author{V. Giambalvo}
%\address{UConn}
\begin{document}
\maketitle
%%%%%Start here%%%%%
{\Large
\section{Introduction}
\begin{enumerate}
\item Latex as a document processor: Global vs Local.
\item Bib-Tex to process your bibliography.
\item Bib-web to create the Bib-Tex database.
\item Ultra-TeX to aid in the typing.
\end{enumerate} }

\newpage

\section{Document Processor}\label{section:DocumentProccessing}
Latex is much more than a system to typeset mathematics formulas,
symbols and tables. It will automatically number your sections,
theorems, lemmas, equations in any manner you like, and keep track of
them through almost any changes. 

You set up the numbering scheme that you want usually in a macro
file. You might have different macro files in different directories
for different purposes. Here is a piece of one of mine:

\begin{verbatim}

%%% Macros for AMS-Latex
%page layout redefinition.  Makes margins wider
        \oddsidemargin 0in
        \evensidemargin 0in
        \topmargin -0.25in  \headsep 0.5in
        \textheight 8.5in  \textwidth 6.5in
%end of page layout redefinition.
%       Theorem environments
%% We want theorems in the introduction to have no associated
%% section. Just Theorem 1, etc.
\newtheorem{ithm}{Theorem}
\newtheorem{icor}[ithm]{Corollary}
%% For the rest of the Theorems, Lemmas, etc we want them
%% labeled as Theorem 2.1, etc.
\newtheorem{thm}{Theorem}[section]
\newtheorem{cor}[thm]{Corollary}
\newtheorem{lem}[thm]{Lemma}
\newtheorem{prop}[thm]{Proposition}
%%%%% We also want the equations to be numbered within sections.
\numberwithin{equation}{section}
%% We cannot number equations like theorems, if we want equations
%% numbered in sequence like theorems, we have to number the Theorems
%% like equations. This means chaging the above 4 lines to
%\newtheorem{thm}[equation]{Theorem}[section]
%\newtheorem{cor}[equation]{Corollary}
%\newtheorem{lem}[equation]{Lemma}
%\newtheorem{prop}[equation]{Proposition}
%
\end{verbatim}
\newpage

{\large
The two commands that link everything together are 

\begin{verbatim}
\label  and \ref 


Almost anything can and should be labelled. That is sections,
theorems, lemmas, equations, etc. If you label each section, theorem,
etc, then when you add a theorem in the start of section 4, delete
section 3 and add a new section 5, LaTeX will take care of the 
renumbering for you. It is advisable if you anticipate significant
changes to give names to sections and theorems, since after a few 
revisions you might forget that the theorem labeled 6 in section 4 is
really theorem 2 in section 5. 


To keep track of this through drafts I have defined a command 
\Label
as follows
\newcommand\Label[1]{{#1}\label{#1}}

which prints the label as in 
Theorem 4.2: thm::reducible-is-generator

It looks ugly, but for the final version I just change this to
\newcommand\Label[1]{\label{#1}}.

\end{verbatim}}
\end{document}
%%%%%%%%%%%%%%%%%Bibliography%%%%%%%%%%%%%%%%%

Now that you have everything internally linked, you will need external
references, which are called citations. 
Not surprisingly the command is 
\cite{bibliography-key}

The very old fashioned manual way to use this is to have 
for example

\cite{M-M}

and at the end of the paper to have a bibliography entries of the form:

\bibliographystyle{amsplain}
\begin{thebibliography}{10}

\bibitem{M-M} I. Madsen and J. Mil-gram, {\em The classifying spaces
for surgery and cobordism of manifolds}, Ann. of Math. Studies,
No. {\bf 92}, Princeton Univ. Press, 1979.

\bibitem{Arnon} D. Arnon, {\em Monomial Bases in the Steenrod
Algebra.} (to appear)

\end{thebibliography}

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

This has a few problems. One is that the formatting is mostly manual.
You can change a bit with the \bibliographstyle, but it is not very
flexible. Another problem is that many of the citations are used in
several papers, so you want to cut and paste. But you may need to
reorder a lot. The (relatively) modern answer is BibTeX, which
replaces the bibliography in the document with the following:

\bibliographystyle{amsplain}
\thebibliography{bibfile1, bibfile2,\dots bibfilek}

where bibfile1, etc, are database files with extension bib. The
entries in these files have a database format


@ARTICLE{lamport-gnats,
   author = {L[eslie] A. Lamport},
   title = {The Gnats and Gnus Document Preparation System},
   journal = {\mbox{G-Animal's} Journal},
   year = 1986,
   volume = 41,
   number = 7,
   pages = "73+",
   month = jul,
   note = "This is a full ARTICLE entry",
}

@BOOK{knuth-seminumerical,
   author = "Donald E. Knuth",
   title = "Seminumerical Algorithms",
   volume = 2,
   series = "The Art of Computer Programming",
   publisher = "Addison-Wesley",
   address = "Reading, Massachusetts",
   edition = "Second",
   month = "10~" # jan,
   year = "1981",
}


@INPROCEEDINGS{oaho-ullman;information-transfer-circuits,
   author = "Alfred V. Oaho and Jeffrey D. Ullman and Mihalis Yannakakis",
   title = "On Notions of Information Transfer in {VLSI} Circuits",
   editor = "Wizard V. Oz and Mihalis Yannakakis",
   booktitle = "Proc. Fifteenth Annual ACM" # STOC,
   number = 17,
   series = "All ACM Conferences",
   pages = "133--139",
   month = mar,
   year = 1983,
   address = "Boston",
   organization = ACM,
   publisher = "Academic Press",
}

@PHDTHESIS{baloney-thesis,
   author = "F. Phidias Phony-Baloney",
   title = "Fighting Fire with Fire: Festooning {F}rench Phrases",
   school = "Fanstord University",
   type = "{PhD} Dissertation",
   address = "Department of French",
   month = jun # "-" # aug,
   year = 1988,
}

@UNPUBLISHED{ulrich-unpublished,
   author = "Ulrich {\"{U}}nderwood and Ned {\~N}et and Paul {\={P}}ot",
   title = "Lower Bounds for Wishful Research Results",
   month = nov # ", " # dec,
   year = 1988,
   note = "Talk at Fanstord University (this is a full UNPUBLISHED entry)",
}

%%%%%%%%%%%%%% End of Bib File %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

This is often seen as more trouble than it is worth. But technology
comes to the rescue again. The program 

bibweb

will look at the files created when you latex your file, go out and 
search the web (mathscinet) and find the references, and update your 
bib file.

For example: 
Starting with ``bigopus.tex''
Running latex produces lots of files, including
``bigopus.log'', ``bigopus.dvi'' and ``bigopus.aux.''
Now you need a ``bigopus.bib'', (it can be empty, or it can contain old
stuff).
Running ``bibweb bigopus''
will search mathscinet and append to bibopus.bib entries for the
citations that are not already found. 

There are some limitiations. For example

\bibitem{Dickson} L. E. Dickson, {\em A Fundamental System of
Invariants of the General Modular Linear Group with a Solution of
the Form Problem}, Trans. Amer. Math. Soc., {\bf 12}(1911), 75--98.

will not be found, since it is before Math Reviews.

Also of course, unpublished items will need to be done by hand.

To make this work, you need to use a specific form of citation key in the
\cite{citation-key}. The format is as follows:

author-xxx-yyy-zzz-www 
or
author1-author2;title1-title2;journal

where xxx etc are anything relating to authors, titles, journals, etc.

{\bfseries This looks like too much typing for a citation. It is, but}

%%%%%%%%%%%%%%%%%%%%  Ultra TeX %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Ultra-TeX is a ``major mode'' for emacs. It configures emacs to 
do things to make typing easier. 

There are several major features:

\begin{enumerate}
\item Completions: It will finish a command, reference, citation,
after having only enough typing to decide. Also you can cycle through
possible completions with C-f or C-b.
\item Smart Keys: Dollar Signs, Braces, Sub and superscript.
\item Smart Return Key;
\item Symbol Keboard;
\end{enumerate}

To type $x_{\alpha }= y_{\beta -1}^{2}$ just do it. I typed
the following: 
 Dollar x _ ` a RET = y _ ` b - 1 RET ^ 2 RET RET 

\end{document}

$x_{\alpha }=1$ but  we can see from \cite{Arnon}