summaryrefslogtreecommitdiff
path: root/info/maltby-intro.tex
diff options
context:
space:
mode:
authorNorbert Preining <norbert@preining.info>2019-09-02 13:46:59 +0900
committerNorbert Preining <norbert@preining.info>2019-09-02 13:46:59 +0900
commite0c6872cf40896c7be36b11dcc744620f10adf1d (patch)
tree60335e10d2f4354b0674ec22d7b53f0f8abee672 /info/maltby-intro.tex
Initial commit
Diffstat (limited to 'info/maltby-intro.tex')
-rw-r--r--info/maltby-intro.tex3590
1 files changed, 3590 insertions, 0 deletions
diff --git a/info/maltby-intro.tex b/info/maltby-intro.tex
new file mode 100644
index 0000000000..d492d9f5f0
--- /dev/null
+++ b/info/maltby-intro.tex
@@ -0,0 +1,3590 @@
+% introduction to \TeX
+% written for course at unp, november 1992
+% written in \LaTeX
+% with the NFSS, but should work with normal \LaTeX
+
+\documentstyle[12pt]{report}
+
+\begin{document}
+\pagenumbering{roman}
+
+\newcommand{\contact}{Gavin Maltby (Maths Department, UNP)}
+
+\newcommand{\AmSLaTeX}{{\protect\the\textfont2 A}\kern-.1667em\lower.5ex\hbox
+{\protect\the\textfont2 M}\kern-.125em{\protect\the\textfont2 S}-\LaTeX}
+
+
+\newcommand{\AmSTeX}{{\protect\the\textfont2 A}\kern-.1667em\lower.5ex\hbox
+{\protect\the\textfont2 M}\kern-.125em{\protect\the\textfont2 S}-\TeX}
+
+\newcommand{\usertype}[1]{\vspace{3pt plus 3pt}\centerline{%
+#1}\vspace{3pt plus 3pt}}
+
+\newcommand{\BibTeX}{{\rm B\kern-.05em{\sc i\kern-.025em b}\kern-.08em
+T\kern-.1667em\lower.7ex\hbox{E}\kern-.125emX}}
+
+\newcommand\bs{\char '134 } % A backslash character for \tt font
+\newcommand{\lb}{\char '173 } % A left brace character for \tt font
+\newcommand{\rb}{\char '175 } % A right brace character for \tt font
+
+\newenvironment{syntax}[1]{\smallskip\hspace{1.3cm}\tt\bs#1}{\smallskip}
+\newcommand{\opt}[1]{[{\em #1\/}]}
+\newcommand{\man}[1]{\{{\em #1\/}\}}
+
+\long\def\result#1{{\smallskip\moveright0.1\textwidth\vbox{\hsize 0.8\textwidth\footnotesize#1}}\smallskip}
+
+%\newcommand{\nsubsubsection}[1]{\subsubsection{#1}\addcontentsline{toc}
+%{subsection}{\quad\quad#1}}
+\newcommand{\nsubsubsection}[1]{\subsection{#1}}
+
+\newenvironment{mathegs}%
+{\medskip\footnotesize\begin{center}%
+\renewcommand{\arraystretch}{1.3}
+\begin{tabular}{ll}%
+\it \makebox[190pt][l]{Type} & \it To produce\\}
+{\end{tabular}\end{center}\medskip}
+
+\title{An introduction to \TeX\ and friends}
+\author{Gavin Maltby}
+\date{November 1992}
+
+\maketitle
+\tableofcontents
+\listoftables
+\newpage
+\pagenumbering{arabic}
+
+\chapter{Getting acquainted with \TeX}
+\TeX\ is well known to be {\em the\/} typesetting package,
+and a vast cult of \TeX\ lovers has evolved. But to the beginning
+\TeX\ user, or to someone wondering if they should bother changing
+to \TeX, it is often not clear what all the fuss is about. After all,
+are not both WordPerfect and Ventura Publisher capable of
+high quality output? Newcomers have often already seen what \TeX\
+is capable of (many books, journals, letters are now prepared with \TeX)
+and so expect to find a tremendously powerful and friendly package.
+In fact they {\em do}, but that fact is well hidden in one's initial
+\TeX\ experiences. In this chapter we describe a little of what
+makes \TeX\ great, and why other packages cannot even begin
+to compete. Be warned that a little patience is required---\TeX's
+virtues are rather subtle to begin with. But when the penny drops,
+you will wonder how you ever put up with anything different.
+
+\section{The spirit of \TeX}
+In order to really appreciate \TeX\ one needs to get a feel
+for what I call the ``spirit'' of \TeX. When \TeX\
+appears to be making me work overtime to achieve something
+that I think ought to be perfectly straightforward, consultation
+with the \TeX\ spirit shows me the error of my ways.
+
+\subsection{\TeX\ is a typesetter, not a word-processor}
+% we chat about the pros and cons of this;
+% talk about compilation, previewing, printing
+% start to convince of the essential power of this
+% a few examples
+% macro packages & style files
+\TeX\ was designed with no limiting application in mind.
+It was intended to be able to prepare practically any document---from
+a single page all-text letter to a full blown book with huge numbers
+of formulae, tables, figures etc. The size and the complexity of a
+{\TeX}able document is limited only by hardware considerations.
+Furthermore, \TeX\ seeks to achieve all this whilst setting
+typesetting standards of the highest order for itself. The expertise
+of generations of professional printers has been captured in
+\TeX, and it has been taught all the tricks of the trade.
+
+Historically, printers prepared a document by placing metal
+characters in a large tray and arranging and binding them
+to form a page. This was very precisely done, but the ultimate
+precision was limited because of the mechanical nature of
+things and by time considerations. \TeX\ prepares a page
+in an analogous manner (putting your characters and
+formulae into ``boxes'' which are then ``glued'' together
+to form the page), but has the advantage of enormous
+precision because placement calculations are performed
+by computer. Indeed, \TeX's internal unit (the ``scaled
+point'') is about one-hundredth of the wavelength of
+natural light!
+
+``But conventional word processors run on computers , too'',
+you object. Yes, but their fundamental limitation is that
+they try to ``keep up'' with you and ``typeset'' your document
+as you type. This means that it can only make decisions at
+a local level (eg, it decides where to break a line just as you
+type the end of the line). \TeX's secret is that it waits until
+you have typed the {\em whole\/} document before it typesets
+a single thing! This means that \TeX\ can make decisions of
+a global nature in order to optimise the aesthetic appeal of
+your document. It has been taught what looks good and what
+looks bad (having been given a measure of the ``badness'' of
+various possibilities) and makes choices for your document that
+are designed to make it ``minimally bad''.
+
+But \TeX's virtues run much deeper than that, which is just as well
+because it is possible to get satisfactory, though imperfect, results from
+some word processors. One of \TeX's strongest points is its ability
+to typeset complicated formulae with ease. Not only does \TeX\
+make hundreds of special symbols easily accessible, it will lay them
+out for you in your formulae. It has been taught all the spacing,
+size, font, \ldots conventions that printers have decided look
+best in typeset formulae. Although, of course, it doesn't understand
+any mathematics it knows the grammar of mathematics---it
+recognises binary relations, binary operators, unary operators, etc.\
+and has been taught how these parts should be set. It is consequently
+rather difficult to get an equation to look bad in \TeX.
+
+Another advantage of compiling a document after it is typed is that
+cross-referencing can be done. You can label and refer back to
+chapters, sections, tables etc.\ by {\em name\/} rather than absolute
+number, and \TeX\ will number and cross-reference these for you.
+Similarly, it will compile a table of contents, glossary, index and bibliography
+for you.
+
+Essential to the spirit of \TeX\ is that {\em it formats the document whilst
+you just take care of the content}, making for increased productivity.
+The cross-referencing just mentioned is just part of this. Many more
+labour-saving mechanisms are provided for through {\em style files}.
+These are generic descriptions of classes of documents, teaching \TeX\
+just how each class likes to be formatted. This is taught in terms
+of font preferences, default page sizes, placement of title, author, date,
+etc. For instance, a {\tt paper} style file could teach \TeX\ that
+when typesetting a theorem it should embolden the part that states
+the theorem number and typeset the text of the theorem statement
+in slanted Roman typeface (as in many journals). The typist simply
+provides and indication that a theorem is being stated, and then
+types the text of the theorem {\em without\/} bothering to choose
+any fonts or do any formatting---all that is done by the style
+file. Style files exist for all manner of document---letters,
+articles, papers, books, proceedings, review articles, and so on.
+
+In addition to style files, there are {\em macro packages}. A
+{\em macro\/} is just a definition of a new \TeX\ command
+in terms of existing ones. Don't think small when you think of
+macros! When typing a document that has a lot of repetition
+in it, say the same expression is used again and again in different
+different equations, you can define a macro in your document
+to abbreviate that expression. But macros can teach \TeX\
+how to typeset all sorts of complicated structures, not just
+parts of an equation. Many macro packages (files that are
+just collections of definitions) have been written to teach \TeX\
+all sorts of applications. There are specialist maths packages
+(\AmSTeX, \AmSLaTeX), general purpose packages (\LaTeX),
+packages for setting tree diagrams, Feynmann diagrams,
+languages like Chinese, Arabic and Ancient Greek,
+orchestral scores, and many, many more. All these are
+freely available, a spin-off of the giant \TeX\ cult.
+
+Another facet of the design of \TeX\ allows it to use
+practically {\em any\/} output device. In fact, \TeX\
+doesn't talk to any printers, screens, phototypesetters
+at all! Instead, when a document is compiled a
+{\em device independent\/} ({\tt .dvi}) is produced---%
+\TeX\ does not compile with any particular output
+device in mind. Printer drivers are then invoked on
+this {\tt .dvi} file and, in consultation with the font
+data for that printer, produce output suitable for the
+particular device. You can choose an HP Laserjet
+driver, or an Apple LaserWriter driver, or a dot matrix
+driver etc. All use the same {\tt .dvi} file as input (and
+remember the material in there is set to enormous
+accuracy) and attempt to image that file on the particular
+device as faithfully as possible. If you are using a top of the
+line laser printer or phototypesetter, then \TeX's
+massive internal precision will not be wasted. Alternatively,
+a dot matrix printer
+will give a coarse approximation of the ideal image that is
+suitable only for proof-reading. In addition to portability,
+these {\tt .dvi} files help ensure that there are very few printing
+surprises when you move from one device to another: how many times
+has your favourite word-processor made you reformat a document when
+you wish to change printers?
+
+There are many other motivations one could cite for the
+superiority of \TeX. But it is time that we started to get
+our hands dirty. One last comment: \TeX\ was not designed
+to supplant secretaries and professional printers---it was designed
+to aid them in their work and, in the words of the \TeX\ designer
+Donald Knuth, allow them to ``go forward and create masterpieces
+of the publishing art''.% or was that typesetting art?
+It also allows those who generate the material
+to be typeset---mathematicians, physicists, computer scientists, etc---to
+prepare their own documents in a language that is intimately linked
+to the language we use for writing such material.
+
+The novice reader will still have no idea of what a \TeX\ source file
+looks like. Indeed, why do we keep referring to it as a {\em source
+file}? The fact of the matter is that \TeX\ is essentially a
+{\em programming language}. Just as in any compiled language
+(e.g.,\ Pascal, C) one prepares a source file and submits it to the
+compiler which attempts to produce an object file ({\tt .dvi} file
+in the \TeX\ case). To learn \TeX\ is to learn the command syntax
+of the commands that can be used in the source file.
+
+\subsection{Typical \TeX\ interfaces}
+% multicompter setting
+% device independence
+% command line level and script files
+% \TeX\ shells
+\TeX\ was designed to run on a multitude of computers. It is therefore
+the case that the documentation for \TeX\ and its ``friends''
+\LaTeX, \AmSTeX, etc.\ is not computer specific. Only
+command syntax is described---i.e., the content of your source file---but
+few details of how to get from there to a printout are given. Those details
+are left to site-specific documents.
+
+The average user loses little in using \TeX\ on, say, a PC rather than
+on a bigger machine. Indeed, compilation times on the
+new PCs begin to rival those on a Sun Sparc
+Station 2 (no slouch). Running on top of DOS can cause memory problems
+when very large documents are being prepared. That aside, the quality
+of the document is not affected because of the careful design of \TeX---%
+whether you work on a a machine with massive floating point precision or
+a modest XT the {\tt .dvi} files produced on compilation will be
+identical; and when those files are submitted to printer equivalent
+printer drivers (say for an HP LaserJet III attached to a Sun in one case
+and a PC in the other) the output will be identical because the font
+information they draw on is identical.
+
+By the nature of \TeX\ most time is spent editing the source document
+(before submitting it for compilation). No special interface is necessary
+here, you just use your favourite text editor (perhaps customising it
+to enhance {\TeX}nical typing. Thus \TeX\ user interfaces are usually
+small and simple, often even missing. One frequently uses \TeX\ at
+command line level, just running the editor, compiler etc.\ as you need them.
+Sometimes a {\TeX}shell program is present, which runs these for you
+when you choose various menu options.
+
+Whatever the interface, there are just a few basic steps to preparing
+a document:
+\begin{enumerate}
+\item Choose a document style to base your document on (e.g., letter, article).
+\item Glance through the material you have to type, and decide what
+ definitions might be made to save you a lot of time. Also, decide on
+ the overall structure of the prospective document (e.g., will the largest
+ sectional unit be a chapter or a part?). If you are going to compose as
+ you type, then pause a moment to think ahead and plan the structure
+ of your document. The importance of this step cannot be overstressed,
+ for it makes clear in {\em your\/} mind what you want from \TeX.
+\item Prepare your input file, specifying only the content and the logical
+ structure (parts, sections, theorems,...) thereof and forgetting about formatting details.
+\item Submit your input, or source, file to the \TeX\ compiler for compilation
+ of a {\tt .dvi} file.
+\item If the compiler finds anything in your source file strongly objectionable,
+ say incorrect command syntax, then return to editing.
+\item Run a {\em previewer\/} to preview your compiled document on the
+ screen. Resolution is only limited by your screen, and can be very
+ good indeed on some modern monitors.
+\item Go back to editing your document until glaring errors have been taken
+ care of.
+\item Make a printout of your compiled document, and check for those errors that
+ you failed to notice on the screen.
+\end{enumerate}
+Performing these steps may be effected through typing at the system prompt
+(barebones technique) or through choosing menu options in a {\TeX}shell program.
+The latter will probably provide some conveniences to make your life easier.
+
+If you think this sounds like a lot of work, it is time that you consult with the
+\TeX\ spirit! Sure your first couple of tries may be hesitant, but before long
+you'll find that you can take {\em less\/} time to prepare a document on \TeX\
+than on any other package.
+
+
+\chapter{Getting started with \LaTeX}
+\section{Why start with \LaTeX?}
+To answer this question we must say a little more about
+some of the macro packages we mentioned earlier.
+
+The \TeX\ typesetting system was designed by the eminent Stanford
+computer scientist Donald Knuth, on commission from the American
+Mathematical Society. It was designed with enormous care, to be
+ultimately powerful and maximally flexible. The enormous success
+of Knuth's design is apparent from the vast number of diverse applications
+\TeX\ has found. In reading the following you must keep one thing clearly
+in mind: {\em there is only \TeX\ language, and all the other packages whose
+names end in the suffix \mbox{-\TeX} simply harness it's power via a whole
+lot of complicated macro definitions}.
+
+\TeX\ proper is a collection of around 300 so called {\em primitive\/}
+typesetting commands. These work at the very lowest level, affording
+enormous power. But to make this raw power manageable, some macros
+must be defined to tame raw \TeX\ somewhat. The standard set
+of macros is called Plain \TeX, and consists of about 600 macro definitions.
+It is clear that these definitions must be made in terms of \TeX\ primitives,
+or in terms of previously made definitions. Plain \TeX, however, is still
+no place for the timid. A strong working knowledge of \TeX\ is still required
+to understand the ins and outs of Plain \TeX.
+
+In the few years after the initial \TeX\ release (1982), the macro packages
+\AmSTeX\ and \LaTeX\ were born. \AmSTeX\ was written by Michael
+Spivak, also on commission from the AMS. This package was designed to
+facilitate the preparation of the numerous books, journals, and review
+indices that fall under the auspices of the AMS and its affiliates.
+Married to the macro package was a style file---the AMS preprint style.
+This was distributed along with the macro package, so that authors
+submitting to journals could use it in the preparation of their articles.
+The given style was based on the style used by the {\em Journal of the
+American Mathematical Society}, i.e., it conformed to their page sizes
+and typographical conventions. This meant that people around the world
+produced papers that were all based on the same style. The clever part
+is this: when a source file is submitted to a journal {\em other\/} than
+the {\em Journal of the AMS}, the journal staff simply substitute their
+style file for the AMS preprint style and the paper will appear completely
+different {\em with no other changes to the source code\/}! To create
+their style file, a journal just needed to tweak the standard AMS prepint
+style: for instance, the original preprint style places author addresses
+at the very end of a paper; If a journal wishes this to appear on the first
+page then they just modify their in-house version of the style file, and
+the change will be effected without having to change the file submitted
+by the author.
+
+\LaTeX\ was written for more general usage. It lacks some of the
+mathematical finesse inherited by \AmSTeX\ from the vast experience of the AMS
+technical staff, but more than makes up for this in its ability to enhance
+the typesetting of letters, books, poetry, etc. \LaTeX\ also scores high
+points for its enhanced command syntax.
+
+With \AmSTeX\ and \LaTeX\ being released at around the same time (1984--1985),
+there were born many \AmSTeX\ literate but \LaTeX\ illiterate users,
+and conversely. \LaTeX\ was easier to learn because of its more friendly
+syntax, and also provided powerful cross-referencing commands that
+\AmSTeX\ did not. So the AMS commissioned another project to
+furnish \LaTeX\ users with the additional power of \AmSTeX\
+while not compromising the \LaTeX\ command syntax or
+cross-referencing commands. This resulted in the \AmSLaTeX\
+macro package and associated style file for submission to journals.
+
+{\em That\/} is why we will kick off our \TeX\ careers with \LaTeX!
+It is easier to learn and provides many conveniences, and the user
+who requires additional mathematical typesetting prowess can
+easily move on to \AmSLaTeX. Much of what we say will be true
+for \TeX\ itself, but we shall regard \LaTeX\ as the lowest
+common-denominator. By far the majority of \LaTeX\ and
+\AmSLaTeX\ users will never have to learn ``raw'' \TeX, for they will
+be shielded from direct exposure by the numerous powerful macro packages.
+In the rare case that something way out of the ordinary is required,
+the local \TeX\ guru can be consulted.
+
+\section{\LaTeX\ formats, and we compose}
+% free form nature of input file
+The {\em free form nature\/} of the input file is essential to the
+spirit of \TeX. As we type, we do not concern ourselves with linebreaks
+and pagebreaks so much as the content of what we are typing. In fact,
+we'll see that \TeX\ will choose nice line breaks even for bizarre looking
+input. This is just part of the concept of only having to describe the
+{\em logical\/} structure of the document to \LaTeX, and not worry
+about nuisance-value formatting details. We inform \LaTeX\
+of the logical structure of our document by telling it when to begin
+a new paragraph, subsection, section, chapter, theorem, definition,
+remark, poem, list etc. When typing a particular element of the logical
+structure, we need pay little attention to how we lay our source file out.
+
+A consequence of this is that we have to go to a bit of effort to mess things
+up. Starting a new line, for instance, entails more than just pressing
+Return because \LaTeX\ will just regard the next word you type
+as exactly that---the next word in the paragraph. You have to specifically
+ask for a line to be terminated. Things like this may seem to be a bit of a
+nuisance, but it is a small price to pay for the automatic formatting that
+necessitated it. Further, such small inconveniences have been localised
+to rare events. I have, for instance, not once forced a new line up until
+this point in the present document.
+
+\section{Document styles}
+We have explained the concept of a document style during our discussion
+of the virtues of \TeX\ and the discussion of \AmSTeX. It remains to
+name a few, and indicate where they would be used. One {\em always\/}
+has to choose a document style when preparing a document with \LaTeX.
+
+The basic document styles in \LaTeX\ are {\tt letter}, {\tt article}, {\tt report},
+and {\tt book}. Many more are available, but these few cover the majority
+of straightforward applications. This is because styles are not rigid---you
+can impose your own parameter choices if you want. So one chooses the
+style that most closely approximates the document you have in mind, and
+performs some minor tweaks here and there. The {\tt article} style is
+used for documents that are to have the appearance of a journal or
+magazine article. The {\tt report} style is usually used
+for larger documents than the {\tt article} style. These styles really only
+differ in their choice of default page size, font, placement of title and author,
+sectional units, etc.\ and on how they format certain \LaTeX\ constructs.
+You use the same \LaTeX\ commands in each. Since the
+examples here will be small, we will choose to use the {\tt article} document
+style.
+
+There are a number of possible options with each document style. The syntax
+for choosing a document style follows. Don't worry if this leaves you with no idea
+of how to choose a document style, for we will soon be seeing some examples. Also,
+remember that an argument in square brackets is optional, and can omitted
+altogether (including the brackets).
+\begin{syntax}{documentstyle}
+\opt{options}\man{style}
+\end{syntax}
+where {\em style\/} is the main document style (eg {\tt report})
+and the optional argument {\em options\/} is a list of document style options chosen
+from the following list:
+\begin{itemize}
+\item[\tt 11pt] chooses 11-point as the default font size for the document, instead
+ of the default 10-point.
+\item[\tt 12pt] chooses 12-point as the default font size.
+\item[\tt twoside] formats output as left and right pages, as in a book.
+\item[\tt twocolumn] produces two-column magazine like output.
+\item[\tt titlepage] applies to the {\tt article} style only, causing the
+ title and abstract to appear on a page each.
+\end{itemize}
+
+In fact there are many, many more document style options but we
+won't mention any more here.
+
+\section{Preparing a non-mathematical document}
+We assume that you have read the local guides to \TeX\ at your site and have
+decided which system environment you want to work in. There you have been
+shown how to perform the steps required to produce a printed document from a
+\LaTeX\ source file.
+
+\subsection{Sentences and paragraphs}
+Let's create our very first \LaTeX\ document, which will consist
+of just a few paragraphs.
+
+As mentioned above, paragraph input is free-form. You type the words
+and separate them by spaces so that \LaTeX\ can distinguish between
+words. For these purposes, pressing Return is equivalent to inserting
+a space---it does not indicate the end of a line, but the end of a word.
+You tell \LaTeX\ that a sentence has ended by typing a period followed
+by a space. \LaTeX\ ignores extra spaces; typing three or three thousand will
+get you no more space between the words that these spaces separate than
+typing just one space. Finally, you tell \LaTeX\ that a paragraph has
+ended by leaving one or more blank lines.
+In summary: \LaTeX\ concerns itself only with the
+logical concepts end-of-word, end-of-sentence, and end-of-paragraph.
+Sounds complicated? An example should clear things up:
+
+\moveright0.1\textwidth\vbox{%
+\footnotesize\begin{verbatim}
+\documentstyle{article}
+\begin{document}
+Words within a sentence are ended by spaces. One space
+between words is equivalent to any number. We are only
+interested in separating one word from the
+next, not in formatting the space between them.
+For these purposes, pressing Return
+at the end of a line
+and starting a new word on the next line
+just serves to separate
+words, not to cut a line short.
+The end of a sentence is indicated by a period
+followed by one or more spaces.
+
+The end of a paragraph is indicated by leaving a blank line.
+All this
+means that we can type without too much regard for layout, and
+the typesetter will sort things out for us.
+\end{document}
+\end{verbatim}
+}
+\noindent produces the result
+
+\result{%
+Words within a sentence are ended by spaces. One space
+between words is equivalent to any number. We are only
+interested in separating one word from the
+next, not in formatting the space between them.
+For these purposes, pressing Return
+at the end of a line
+and starting a new word on the next line
+just serves to separate
+words, not to cut a line short.
+The end of a sentence is indicated by a period
+followed by one or more spaces.
+
+The end of a paragraph is indicated by leaving a blank line. All this
+means that we can type without too much regard for layout, and
+the typesetter will sort things out for us.
+}
+
+Perhaps you would like to try running \LaTeX\ on the above input.
+Consult your local guide for details.
+
+Note that we have learned more than just how \LaTeX\ recognises words,
+sentences and paragraphs. We've also seen how to specify our choice
+of document style and how to tell \LaTeX\ where our document begins
+and ends. Any material that is to be printed must lie somewhere between
+the declaration of \verb@\begin{document}@ and that of \verb@\end{document}@.
+Definitions that are to apply to the entire document can be made before
+the declaration of the document beginning. The specification of
+document style must precede all other material.
+
+In future examples we won't explicitly display the commands that
+select document style and delimit the start and end of the document.
+But if you wish to try any of the examples, don't forget to include those
+commands. The {\tt article} document style will do for most of our examples.
+Of course, the preceding example looks not at all like an article because
+it is so short and because we specified no title or author information.
+
+Most of what you need to know to type regular text is contained in the
+example above. When you consider that by far the majority of any document
+consists of straight text, it is obvious that \LaTeX\ makes this fabulously straightforward.
+\LaTeX\ will do all the routine work of formatting, and we simply get on with the
+business of composing.
+
+\LaTeX\ does more than simply choose pleasing line breaks and
+provide natural spacing when setting a paragraph. Remember we
+said that \TeX\ has inherited the knowledge of generations of
+professional printers---well part of that knowledge includes
+being on the look-out for {\em ligatures}. These are combinations
+of letters within words which should be typeset as a single special
+symbol because they will ``clash'' with each if this is not done.
+Have a look at these words
+\begin{center}
+flight, flagstaff, chaff, fixation
+\end{center}
+and compare them with these
+\begin{center}
+f{l}ight, f{l}agstaf{f}, chaf{f}, f{i}xation
+\end{center}
+See the difference? In the first set I let \LaTeX\ run as it usually does.
+In the second I overruled it somewhat, and stopped it from creating
+ligatures. Notice how the `fl', `ff', and `fi' combinations are different
+in the two sets---in the former they form a single symbol (a ligature)
+and in the latter they are comprised of two disjoint symbols. There
+are other combinations that yields ligatures, but we don't have to bother
+remembering any of them because \LaTeX\ will take care of these, too.
+
+Notice, too, that \LaTeX\ has been taught how to hyphenate the
+majority of words. It will hyphenate a word if it feels that the overall
+quality of the paragraph will be improved. For long words it has been
+taught several potential hyphenation positions.
+
+\LaTeX\ also goes to a lot of trouble to try to choose pleasing page
+breaks. It avoids ``widows'', which are single lines of a paragraph
+occurring by themselves at either the bottom of a page (where
+it would have to be the first line of a paragraph) or at the top
+of a page (where it would have to be the last). It also
+``vertically justifies'' your page so that all pages have exactly
+the same height, no matter what appears on them. As testimony
+to the success of the pagebreaking algorithm, I have (to
+this point) not once chosen a page break in this document.
+
+\subsection{Punctuation}
+Typists have a convention whereby a single space is left after a
+mid-sentence comma, and two spaces are left after a sentence-ending
+period. How do we enforce this if \LaTeX\ treats a string of spaces just like
+a single one? The answer, unsurprisingly, is that we {\em don't}.
+
+\moveright0.1\textwidth\vbox{%
+\footnotesize\begin{verbatim}
+To have a comma followed by the appropriate space, we simply
+type a comma follows by at least one space. To end a sentence
+we type a period with at least one following space. No space will
+be inserted if we type a comma or period followed straight away
+by something other than a space, because there are times when
+we won't require any space, i.e., we do what comes narurally.
+\end{verbatim}
+}
+\noindent will produce
+
+\result{%
+To have a comma followed by the appropriate space, we simply
+type a comma follows by at least one space. To end a sentence
+we type a period with at least one following space. No space will
+be inserted if we type a comma or period followed straight away
+by something other than a space, because there are times when
+we won't require any space, i.e., we do what comes naturally.
+}
+
+\LaTeX\ will produce suitable space after commas, periods,
+semi-colons and colons, exclamation marks, question marks etc.\
+if they are followed by a space.
+In stretching a line to justify to the
+right margin, it also knows that space after a punctuation
+character should be more ``stretchable'' than normal inter-word
+space and that space after a sentence-ending period should be stretched
+more than space after a mid-sentence comma. \TeX\ knows the nature of
+punctuation if you stick to the simple rules outlined here. As we've already
+said, those rules tell \LaTeX\ how to distinguish consecutive words,
+sentences, phrases, etc.
+
+Actually, there is more to ending sentences than mentioned above.
+Since \LaTeX\ cannot speak English, it works on the assumption
+that {\em a period followed by a space ends a sentence unless the period
+follows a capital
+letter}. This works most of the time, but can fail. To get a normal
+inter-word space after a period that doesn't end a sentence,
+follow the period by a {\em control space}---a \verb*@\ @
+(a {\tt \bs} character followed by a space or return). Very
+rarely, you will have to force a sentence to end after a
+period that follows a capital letter (remember that \LaTeX\
+assumes this doesn't end a sentence). This is done by preceding
+the period with a \verb!\@! command (you can guess from the odd
+syntax that this is rarely needed).
+
+It's time we saw some examples of this. After all, this is our first
+experience of {\em control symbols} (don't worry, there are many
+more to come).
+
+\moveright0.1\textwidth\vbox{%
+\footnotesize\begin{verbatim}
+We must be careful not to confuse intra-sentence periods
+with periods that end a sentence, i.e.\ we must remember
+that our task is to describe the sentence structure. Periods
+that the typesetter requires a little help with typically result
+from abbreviations, as in etc.\ and others. We have to work
+somewhat harder to break a sentence after a capital letter,
+but that shouldn't bother us to much if we keep up our intake
+of vitamin E\@. All this goes for other sentence-ending
+punctuation characters, so I could have said vitamin E\@!
+Fortunately, these are rare occurrences.
+\end{verbatim}
+}
+\noindent results in
+
+\result{%
+We must be careful not to confuse intra-sentence periods
+with periods that end a sentence, i.e.\ we must remember
+that our task is to describe the sentence structure. Periods
+that the typesetter requires a little help with typically result
+from abbreviations, as in etc.\ and others. We have to work
+somewhat harder to break a sentence after a capital letter,
+but that shouldn't bother us to much if we keep up our intake
+of vitamin E\@. All this goes for other sentence-ending
+punctuation characters, so I could have said vitamin E\@!
+Fortunately, these are rare occurrences.
+}
+
+Quotation marks is another area where \LaTeX\ will do some
+work for us. Keyboards have the characters \verb@`@, \verb@`@, and \verb@"@ but we
+want to to have access to each of `, ', ``, and ''. So we proceed like this:
+
+\moveright0.1\textwidth\vbox{%
+\footnotesize\begin{verbatim}
+`\LaTeX' is no conventional word-processor, and
+to to get quotes, like ``this'', we type repeated
+` and ' characters. Note that modern
+convention is that ``punctuation comes after
+the closing quote character''.
+\end{verbatim}
+}
+\noindent which gives just what we want
+
+\result{%
+`\LaTeX' is no conventional word-processor, and
+to to get quotes, like ``this'', we type repeated
+{\tt `} and {\tt '} characters. Note that modern
+convention is that ``punctuation comes after
+the closing quote character''.
+}
+
+Very rarely, you have three quote characters together.
+Merely typing those three quote characters one-after-the-other
+is ambiguous---how should they be grouped? You tell
+\LaTeX\ how you want them grouped by inserting a
+very small space called \verb@\,@.
+
+\moveright0.1\textwidth\vbox{%
+\footnotesize\begin{verbatim}
+``\,`Green ham' or `Eggs?'\,'' is the question.
+\end{verbatim}
+}
+\noindent gives the desired result
+
+\result{%
+``\,`Green ham' or `Eggs?'\,'' is the question.
+}
+
+Since we have a typesetter at our disposal, we might as
+well use the correct dashes where we need them. There
+are three types of dash: the hyphen, the endash, and
+the emdash. A minus sign is not a dash.
+
+Hyphens are typed as you'd hope, just by typing a \verb@-@
+at the point in the word that you want a hyphen. Don't
+forget that \LaTeX\ takes care of hyphenation that is
+required to produce pretty linebreaks. You only type
+a hyphen when you explicitly want one to appear,
+as in a combination like ``inter-college''.
+
+An endash is the correct dash to use in indicating
+number ranges, as in ``questions~1--3''. To
+specify an endash you type two consecutive
+dashes on the keyboard, as in \verb@1--3@.
+
+An emdash is a punctuation dash, used at the end
+of a sentence---I tend to use them too much.
+To specify an emdash you type three consecutive
+dashes on the keyboard, as in ``\ldots\verb@a sentence---I tend to@\ldots''.
+
+\moveright0.1\textwidth\vbox{%
+\footnotesize\begin{verbatim}
+Theorems 1--3 concern the semi-completeness
+of our new construct---in the case that it
+satisfies the first axiom.
+\end{verbatim}
+}
+\noindent yields
+
+\result{%
+Theorems 1--3 concern the semi-completeness
+of our new construct---in the case that it
+satisfies the first axiom.
+}
+
+\subsection{Ties}
+When you always remember to use {\em ties\/}, you know
+that you are becoming {\TeX}nically inclined. Ties are
+used to prevent \LaTeX\ from breaking lines at
+certain places. \LaTeX\ will always choose line breaks
+that result in the most aesthetically pleasing paragraph
+as judged by its stringent rules. But because \LaTeX\
+does not actually understand the material it is setting
+so beautifully, it can make some poor choices.
+
+A {\em tie\/} is the character \verb@~@. It behaves as a
+normal interword space in all respects {\em except\/}
+that the line-breaking algorithm will never break a
+line at that point. Thus
+
+\moveright0.1\textwidth\vbox{%
+\footnotesize\begin{verbatim}
+Dr. Seuss should be typed as Dr.~Seuss
+\end{verbatim}
+}
+\unskip\noindent for this makes sure that \LaTeX\ will never
+leave the `Dr' at the end of one line and put the `Seuss'
+at the beginning of the next.
+
+One should try to get in to the habit of typing ties first-time,
+not after waiting to see if \LaTeX\ will make a poor choice This will allow
+you to make all sorts of changes to your text without ever
+having to go back and insert a tie at a point that has migrated
+to the end of a line from the middle of a line as a result
+of those changes. Remember, of course, that the line-breaks
+
+Here are some more examples of places where you should remember to
+place ties.
+
+\moveright0.1\textwidth\vbox{%
+\footnotesize\tt\begin{tabbing}
+Lemmas 3 and\verb!~!4\quad \= \kill
+Chapter\verb!~!10 \> Donald\verb!~!E. Knuth\\
+Appendix\verb!~!C \> width\verb!~!2\\
+Figure\verb!~!1 \> function\verb!~!f\\
+Theorem\verb!~!2 \> 1,\verb!~!2, or\verb!~!3\\
+Lemmas 3 and\verb!~!4 \> equals\verb!~!5\\
+\end{tabbing}
+}
+
+\subsection{Specially reserved symbols}\label{sec:reserved}
+In the sequel we will see that the the ten characters
+
+\moveright0.1\textwidth\hbox{\verb!# $ % & ~ _ ^ \ { }!}
+
+\noindent are reserved for special use. Indeed, we have seen already
+that {\tt\bs} and \verb@~@ are non-printing characters
+that perform special services (and we'll have a lot more to
+say about the use of {\tt\bs}).
+
+But what if we need one of these special symbols to appear
+in our document? The answer for seven of the symbols
+is to precede them by a {\tt\bs} character, so forming
+another {\em control symbol\/} (remember that
+{\tt\bs} followed by a space was also a control symbol).
+
+\moveright0.1\textwidth\vbox{%
+\footnotesize\begin{verbatim}
+It is not 100\% straightforward to typeset the
+characters \$ \& \% \_ \{ \}, but given the
+enormous convenience of the use they are normally
+reserved for this is a small price to pay.
+\end{verbatim}
+}
+\noindent produces
+
+\result{%
+It is not 100\% straightforward to typeset the
+characters \$ \& \% \_ \{ \}, but given the
+enormous convenience of the use they are normally
+reserved for this is a small price to pay.
+}
+
+\subsection{So what are control symbols and words?}
+In typing a document, we can think of ourselves as
+being in one of two distinct modes. We are either
+typing {\em literal text\/} (which will just be set into neat
+paragraphs for us) or we are typing text that will
+be {\em interpreted\/} by \LaTeX\ as an instruction
+to insert a special symbol or to perform some action.
+Thus we are either typing material that will go
+straight into the document (with some beautification),
+or we are giving commands to \LaTeX.
+
+Some commands are implicit, in that we don't have to
+do anything much extra. For instance, we command
+\LaTeX\ to end the present sentence by typing a
+period (that doesn't follow a capital letter). These are
+no so much commands as part of having to describe
+the logical structure of a document.
+
+A {\em control word\/} is something of the form
+\verb@\commandname@, where the command name
+is a word made up only of the letters a to~z and A to~Z. A
+{\em control symbol\/} consists of a {\tt\bs}
+followed by single symbol that is not a letter.
+
+Here are some examples:
+\begin{itemize}
+\item we have met the control space symbol \verb*@\ @ before,
+\item the commands to set symbols like \% and \$ are control symbols
+\item \verb!\@! was a control symbol that told told \LaTeX\ that
+ the very next period did really end the sentence,
+\item \verb@\LaTeX@ is a control word that tell \LaTeX\ to insert
+ its own name at the current point,
+\item \verb@\clubsuit@ instructs that a $\clubsuit$ be inserted,
+\item \verb@\pounds@ inserts a \pounds\ symbol,
+\item \verb@\S@ inserts a \P\ symbol,
+\item \verb@\em@ makes the ensuing text {\em be emphasised},
+\end{itemize}
+
+These examples show that control sequences can be used to
+access symbols not available from the keyboard,
+do some typesetting tricks like setting the word
+\LaTeX\ the way it does, and change the appearance of
+whole chunks of text as with \verb@\em@. We'll be meeting
+many more of these type of control sequences.
+
+Another enormously powerful class of control sequences is
+those that accept {\em arguments}. They tell \LaTeX\
+to take the parts of text you supply and do something
+with them---like make a fraction by setting the first
+argument over the second and drawing a line of the
+appropriate length between them. These are part of
+what makes \LaTeX\ so powerful, and here are some
+examples.
+
+\begin{itemize}
+\item \verb@\chapter{The beginning}@ causes \LaTeX\ to
+ start a new chapter with name ``The Beginning'', number
+ it in sequence, typeset the chapter heading in a suitable
+ font, and make an entry in the table of contents,
+\item \verb@\overline{words}@ causes $\overline{\mbox{words}}$ to
+ be overlined,
+\item \verb@\frac{a+b}{c+d}@ sets the given two argument as
+ a fraction, doing most of the dirty work for us: $\frac{a+b}{c+d}$,
+\item \verb@\sqrt[5]{a+b}@ typesets the fifth-root of $a+b$,
+ like this: $\sqrt[5]{a+b}$. The {\tt 5} is in square brackets
+ instead of braces because it is an optional argument and
+ could be ommited all together (giving the default of square root),
+\end{itemize}
+
+Mandatory arguments are given enclosed by braces, and
+optional arguments enclosed by square brackets. Each
+command knows how many arguments to expect, so
+you don't have to provide any indication of that.
+
+We have actually jumped the gun a little. The above examples
+include examples of {\em mathematical\/} typesetting, and we
+haven't yet seen how to tell \LaTeX\ that it is typesetting
+maths as opposed to some other random string of symbols
+that it doesn't understand either. We'll come to mathematical
+typesetting in good time.
+
+We need to dwell on a {\TeX}nicality for a moment. How does
+\LaTeX\ know where the name of a control sequence ends?
+Will it accept both \verb@\pounds3@ and \verb@\pounds 3@
+in order to set \pounds3, and will \verb@\emWalrus@
+and \verb@\em Walrus@ both be acceptable in order to
+get {\em Walrus\/}? The answer is easy when you remember
+that a control word consists only of alphabetic characters,
+and a control symbol consists of exactly one nonalphabetic
+character.
+
+So to determine which control sequence you typed,
+\LaTeX\ does the following:
+\begin{enumerate}
+\item when a {\tt\bs} character is encountered, \LaTeX\ knows
+ that either a control symbol or a control word will follow.
+\item If the {\tt\bs} is followed by a nonalphabetic character,
+ then \LaTeX\ knows that it is a control {\em symbol\/}
+ that you have typed. It then recognises which one it was,
+ typesets it, and goes on to read the character which follows
+ the symbol you typed.
+\item If the {\tt\bs} is followed by an alphabetic character, then
+ \LaTeX\ knows that it is a control word that you have typed.
+ But it has to work out where the name of the control word ends
+ and where the ensuing text takes over again. Since only alphabetic
+ characters are allowed, \LaTeX\ reads everything up to
+ just before that first
+ nonalphabetic character as the control sequence name. Since
+ it is common to delimit the end of a control word by a space,
+ \LaTeX\ will {\em ignore\/} any space that follows a control
+ word, since you want that space treated as end-of-control-word
+ space rather than interword space.
+\end{enumerate}
+
+This has one important consequence: The character in the input
+file immediately after a control symbol will be ``seen'' by \LaTeX,
+but {\em any space following a control word will be
+discarded and never processed.} This does not affect one much if you adopt
+the convention of always typing a space after a control sequence name.
+
+There is a rare circumstance where this necessitates a little extra work
+and thought, which we illustrate by example:
+
+\moveright0.1\textwidth\vbox{%
+\footnotesize\begin{verbatim}
+If we type a control word like \LaTeX in the running text
+then we must be cautious, because the string of spaces that
+come after it will be discarded by the \LaTeX\ system.
+\end{verbatim}
+}
+\noindent which produces the output
+
+\result{%
+If we type a control word like \LaTeX in the running text
+then we must be cautious, because the string of spaces that
+come after it will be discarded by the \LaTeX\ system.
+}
+
+\subsection{Commands to change appearance}\label{sec:groups}
+We've seen a little of how to access various symbols using
+control sequences and we mentioned the \verb@\em@
+command to emphasise text, but we didn't see how to use
+them. We look here at commands that change the appearance
+of the text.
+
+Each of the control words here is a directive rather
+than a control sequence that accepts an argument.
+This is because potential arguments consisting
+of text that wants to be emboldened or emphasised
+are very large, and it would be a nuisance to have
+to enclose such an argument in argument-enclosing
+braces.
+
+To delimit the area of text over which one of these commands
+has effect (its {\em scope}) we make that text into what
+is called a {\em group}. Groups are used extensively in
+\LaTeX\ to keep effects local to an area, rather than
+affecting the whole document. Apart from enhancing
+usability, this also in a sense protects distinct parts
+of a document from each other.
+
+The \LaTeX\ commands for changing type style are given
+in table~\ref{tab:typestyles}, and those for changing type
+size are given in table~\ref{tab:sizes}. Commands for
+selecting fonts other than these are not discussed here.
+
+\begin{table}[ht]
+\centering
+\begin{tabular}{llllllll}
+\verb@\rm@ & Roman & & \verb@\it@ & \it italic & & \verb@\sc@ & \sc Capitals\\
+\verb@\em@ & \em Emphasised & & \verb@\sl@ & \sl slanted & & \verb@\tt@ & \tt typewriter\\
+\verb@\bf@ & \bf boldface & & \verb@\sf@ & \sf sans serif & &\\
+\end{tabular}
+\caption{Commands for selecting type styles}
+\label{tab:typestyles}
+\end{table}
+
+Each of the type style selection commands selects the specified style but does
+not change the size of font being used. The default type style is roman (you
+are reading a roman style font now). To change type size you issue one of
+the type size changing commands in table~\ref{tab:sizes}, which will select
+the indicated size in the currently active style. The release of \LaTeX\
+3.0 (the present version is 2.09) will see the New Font Selection Scheme
+in place as a standard feature. This makes font matters much easier to deal
+with.
+
+% part 2 of 4
+\begin{table}[ht]
+\centering
+\begin{tabular}{l|r|r|r|}
+\multicolumn{1}{l}{size} &
+\multicolumn{1}{c}{default (10pt)} &
+ \multicolumn{1}{c}{11pt option} &
+ \multicolumn{1}{c}{12pt option}\\
+\cline{2-4}
+\verb|\tiny| & 5pt & 6pt & 6pt\\
+\cline{2-4}
+\verb|\scriptsize| & 7pt & 8pt & 8pt\\
+\cline{2-4}
+\verb|\footnotesize| & 8pt & 9pt & 10pt \\
+\cline{2-4}
+\verb|\small| & 9pt & 10pt & 11pt \\
+\cline{2-4}
+\verb|\normalsize| & 10pt & 11pt & 12pt \\
+\cline{2-4}
+\verb|\large| & 12pt & 12pt & 14pt \\
+\cline{2-4}
+\verb|\Large| & 14pt & 14pt & 17pt \\
+\cline{2-4}
+\verb|\LARGE| & 17pt & 17pt & 20pt\\
+\cline{2-4}
+\verb|\huge| & 20pt & 20pt & 25pt\\
+\cline{2-4}
+\verb|\Huge| & 25pt & 25pt & 25pt\\
+\cline{2-4}
+\end{tabular}
+\caption{\LaTeX\ size-changing commands.}\label{tab:styles}
+\label{tab:sizes}
+\end{table}
+
+The point-size option referred to in table~\ref{tab:sizes} is that
+specified in the \verb@\documentstyle@ command issued at the
+beginning of the input file. Through it you select that base
+(or default) font for your document to be 10, 11, or~12 point Roman.
+If no options are specified, the default is 10-point Roman. The
+table shows, for instance, that if I issue a \verb@\large@ in
+this document for which I chose the {\tt 12pt} document style
+option the result will be a {\large 14-point Roman typeface}.
+
+We mentioned that to restrict the scope of a type-changing
+command we will set the text to be affected off in a group.
+Let's look at an example of this.
+
+\moveright0.1\textwidth\vbox{%
+\footnotesize\begin{verbatim}
+When we want to {\em emphasise\/} some text we
+use the {\tt em} command, and use grouping to
+restrict the scope. We can change font {\large sizes}
+in much the same way. We can also obtain {\it italicised},
+{\bf emboldened}, {\sc Capitals} and {\sf sans serif} styles.
+\end{verbatim}
+}
+
+\result{%
+When we want to {\em emphasise\/} some text we
+use the {\tt em} command, and use grouping to
+restrict the scope. We can change font {\large sizes}
+in much the same way. We can also obtain {\it italicised},
+{\bf emboldened}, {\sc Capitals} and {\sf sans serif} styles.
+}
+
+Notice how clever grouping allows us to do all that without
+once having to use \verb@\rm@ or \verb@\normalsize@.
+
+One more thing slipped into that example---and {italic correction\/}
+\verb@\/@. This is a very small amount of additional space that
+we asked to be inserted to allow for the change from sloping
+{\em emphasised} text to upright text, because the interword
+space has been made to look less substantial from the terminal
+sloping character. One has to keep an eye open for circumstances
+where this is necessary. See the effect of omitting an italic correction
+after the emphasised text earlier in this paragraph.
+
+One might expect, by now, that \LaTeX\ would insert an italic correction
+for us. But there are enough occasions when it is not wanted, and there
+is no good rule for \LaTeX\ to use to decide just when to do it for us.
+So the italic correction is always left up to the typist.
+
+\subsection{Accents}
+\LaTeX\ provides accents for just about all occasions. They are
+accessed through a variety of control symbols and single-letter
+control worlds which accept a single argument---the letter to be
+accented. These control sequences are detailed in table~\ref{tab:accents}.
+
+\begin{table}[ht]
+\centering
+\begin{tabular}{lll}
+\verb@\`{o}@ & \`{o} & (grave accent)\\
+\verb@\'{o}@ & \'{o} &(acute accent)\\
+\verb@\^{o}@ & \^{o} & (circumflex or ``hat'')\\
+\verb@\"{o}@ & \"{o} & (umlaut or dieresis)\\
+\verb@\~{o}@ & \~{o} & (tilde or ``squiggle'')\\
+\verb@\={o}@ & \={o} & (macron or ``bar'')\\
+\verb@\.{o}@ & \.{o} & (dot accent)\\
+\verb@\u{o}@ & \u{o} & (breve accent)\\
+\verb@\v{o}@ & \v{o} & (h\'{a}\v{c}ek or ``check'')\\
+\verb@\H{o}@ & \H{o} & (long Hungarian umlaut)\\
+\verb@\t{oo}@ & \t{oo} & (tie-after accent)\\
+\verb@\c{o}@ & \c{o} & (cedilla accent)\\
+\verb@\d{o}@ & \d{o} & (dot-under accent)\\
+\verb@\b{o}@ & \b{o} & (bar-under accent)
+\end{tabular}
+\caption{Control sequences for accents}
+\label{tab:accents}
+\end{table}
+
+Thus we can produce \'{o} by typing \verb@\'{o}@,
+\v{a} by typing \verb@\v{a}@, and P\'{a}l Erd\"{o}s
+by typing \verb@P\'{a}l Erd\"{o}s@. Take special
+care when accenting an $i$ or a $j$, for they should
+lose their dots when accented. Use the control
+words \verb@\i@ and \verb@\j@ to produce dotless
+versions of these letters. Thus the best way to type
+to type \u{e}x\u{\i}gent is \verb"\u{e}x\u{\i}gent".
+
+\subsection{Over-ruling some of \TeX's choices}
+We've seen that ties can be used to stop linebreaks
+occurring between words. But how can we stop
+\LaTeX\ from hyphenating a particular word?
+More generally, how can we stop it from splitting
+any given group of characters across two lines.
+The answer is to make that group of characters
+appears as one solid {\em box\/}, through
+use of an \verb@\mbox@ command.
+
+\moveright0.1\textwidth\vbox{%
+\footnotesize\begin{verbatim}
+For instance, if we wanted to be sure that the word
+{\em currentitem\/} is not split across lines
+then we should type it as \mbox{\em currentitem}.
+\end{verbatim}
+}
+
+If for some reason we wish to break a line\\
+in the middle of nowhere, preventing \LaTeX\
+from justifying that line to the prevailing right
+margin, the we use the \verb@\newline@
+command. One can also use the abbreviated
+form \verb@\\@.
+
+\moveright0.1\textwidth\vbox{%
+\footnotesize\begin{verbatim}
+We start with a short line.\newline
+And now we continue with the normal
+text, remembering that where we press
+Return in the input file probably won't
+correspond to a line break in the final
+document. More short lines\\
+are easy, too.
+\end{verbatim}
+}
+\noindent will produce the line breaks we want
+
+\result{%
+We start with a short line.\newline
+And now we continue with the normal
+text, remembering that where we press
+Return in the input file probably won't
+correspond to a line break in the final
+document. More short lines\\
+are easy, too.
+}
+
+A warning is in order: \verb@\newline@
+must only end part of a line that is ``already
+set''. It cannot be used to add additional
+space between paragraphs, nor to leave
+space for a picture you want to paste in.
+This is not to be awkward, but is just part
+of \LaTeX\ holding up its end of the deal
+by making you have to specially request
+additional vertical space. This prevents
+unwanted extra space from entering
+your document.
+
+Later we shall see how to impose our own choice
+of page size, paragraph indentation, etc. For now
+we will continue to accept those declared for
+us in the document style.
+
+\subsection{Commenting your document}
+It is handy to be able to make comments
+to yourself in the source file for a document.
+Things like ``I must rewrite this section'' and
+``This is version 3 of the document'' are likely.
+It would also be useful to be able to make
+the compiler ignore certain parts of the
+document at times. For this purpose
+we can use the \verb@%@ character, for
+all text on an input line that is
+after a \verb@%@ which is not part of
+an occurrence of the control symbol
+\verb@\%@ is discarded by the compiler.
+Here is an example:
+
+\moveright0.1\textwidth\vbox{%
+\footnotesize\begin{verbatim}
+There was a 100\% turnout today,
+an all-time record. %perhaps I should check this claim!
+%Indeed, there are lots of unsubstantiated claims here!
+This made for an extremely productive session.
+\end{verbatim}
+}
+\noindent will yields
+
+\result{%
+There was a 100\% turnout today,
+an all-time record. %perhaps I should check this claim!
+%Indeed, there are lots of unsubstantiated claims here!
+This made for an extremely productive session.
+}
+
+\subsection{Footnotes}
+Inserting footnotes is easy---\LaTeX\ will position and
+number them for you. You just indicate {\em exactly\/}
+where the footnote marker should go, and provide the
+text of the footnote. The footnote text will be
+placed at the bottom of the present page in a somewhat
+smaller font, and be separated from the main text by
+a short horizontal rule\footnote{See for yourself! It's
+easy when you don't have to do any work.} to conform with
+convention. The footnote in the last line was typed
+like this:
+
+\moveright0.1\textwidth\vbox{%
+\footnotesize\begin{verbatim}
+...rule\footnote{See for yourself! It's easy ...work.} to conform
+\end{verbatim}
+}
+No space was typed between the {\tt rule} and the
+\verb@\footnote@, because we want the footnote
+marker to appear right next to the last letter of the word.
+
+Multiple footnotes\footnote{Here is another footnote} are
+obtained just by using the \verb@\footnote@ command
+again and again.
+
+\subsection{Topmatter}
+We declare the title and author information using the
+\verb@\title@ and \verb@\author@ commands, each of
+which accept a single argument. Multiple authors
+are all listed in the argument of \verb@\title@,
+separated by \verb@\and@'s. The \verb@\date@
+command can be used to date a document. After
+we have declared each of these, we issue a
+\verb@\maketitle@ command to have them typeset for
+us. In the \verb@book@ and \verb@article@ document
+styles this will result in a separate page; in
+the \verb@article@ style the ``top matter'' will
+be placed at the top of the first page. The style
+files determine the placement and the choice of font.
+
+\moveright0.1\textwidth\vbox{%
+\footnotesize\begin{verbatim}
+\title{A Thought for the Day}
+\author{Fred Basset \and Horace Hosepipe}
+\date{November 1992}
+\maketitle
+\end{verbatim}
+}
+\noindent will produce something along the lines of
+
+\result{%
+\begin{center}
+{\Large A Thought for the Day}\\
+\smallskip Fred Basset\quad Horace Hosepipe\\
+\smallskip November 1992
+\end{center}
+}
+
+This topmatter must appear {\em after\/} the
+\verb"\begin{document}" and before any other printing material.
+
+\subsection{Sectioning commands}
+As part of our task of describing the logical structure of
+the document, we must indicate to \LaTeX\ where to start sectional
+units. To do this we make use of the sectioning commands shown
+in table~\ref{tab:sectioning}.
+
+\begin{table}[ht]
+\centering
+{\tt
+\begin{tabular}{lll}
+\bs part & \bs subsection & \bs paragraph\\
+\bs chapter & \bs subsubsection & \bs subparagraph\\
+\bs section & & \\
+\end{tabular}
+}
+\caption{\LaTeX\ sectioning commands}
+\label{tab:sectioning}
+\end{table}
+
+Each sectioning command accepts a single argument---the section
+heading that is to be used. \LaTeX\ will provide the section
+numbering (and numbering of subsections within sections, etc.)\
+so there is no need to include any number in the argument.
+\LaTeX\ will also take care of whatever spacing is required to
+set the new logical unit off from the others, perhaps through
+a little extra space and using a larger font. It will
+also start a new page in the case that a new chapter is
+begun.
+
+The \verb@\part@ command is used for major subdivisions of
+substantial documents. The \verb@\paragraph@ and
+\verb@\subparagraph@ commands are, unfortunately
+confusing. They are used to section off a modest number of
+paragraphs of text---they don't start new paragraphs (remember that
+that was done by leaving a blank line in our input file).
+The names were retained for historical reasons.
+
+It is always a good idea to {\em plan\/} the overall
+sectional structure of a document in advance, or at least
+give it a little thought. Not that it would be difficult to
+change your mind later (you could use the global replace
+feature of an editor, for instance), but so that you have
+a good idea of the structure that you have to describe to
+\LaTeX.
+
+The sectioning command that began the present sectional unit
+of this document was
+
+\moveright0.1\textwidth\vbox{%
+\begin{verbatim}
+\subsection{Sectioning commands}
+\end{verbatim}
+}
+\noindent and that was all that was required to get the numbered
+section name and the table of contents entry.
+
+There are occasions when you want a heading to have all the
+appearance of a particular sectioning command, but shouldn't
+be numbered as a section in its own right or produce a table
+of contents entry. This can be achieved through using the
+{\em *-form\/} of the command, as in \verb@\section*{...}@.
+We'll see that many \LaTeX\ commands have such a *-form
+which modify their behaviour slightly.
+
+Not only will \LaTeX\ number your sectional units for you,
+it will compile a table of contents too. Just include the
+command \verb@\tableofcontents@ after the
+\verb@\begin{document}@ command and after the topmatter that
+should precede it.
+
+
+\subsection{\LaTeX\ environments}
+Perhaps the most powerful and convenient concept in the \LaTeX\
+syntax is that of an {\em environment}. We will see most of
+the ``heavy'' typesetting problems we will encounter can be best
+tackled by one or other of the \LaTeX\ environments.
+
+Some environments are used to {\em display\/} a portion of text,
+i.e.\ to set it off from the surrounding text by indenting it.
+The {\tt quote} and {\tt verse} environments are examples of
+these. The {\tt center} environment allows us to centre
+portions of text, while the {\tt flushright} environment
+sets small portions of text flush against the right margin.
+
+But the true power of \LaTeX\ begins to show itself when
+we look at environments such as those that provide facilities
+for itemised or enumerated lists, complex tabular arrangements,
+and for taking care of figure and table positioning and captioning.
+What we learn here will also be applicable in typesetting some
+complicated mathematical arrangements in the next chapter.
+
+All the environments are begun by a {\tt \bs begin{\{{\em name}\}}}
+command and ended by an {\tt \bs end{\em \{name\}}}, where
+{\em name\/} is the environment name. These commands also
+serve as begin-group and end-group\footnote{See section \ref{sec:groups}}
+markers, so that all commands are local to the present environment---they
+cannot affect text outside the environment.
+
+We can also have environment embedded within environment within
+environment and so on, limited only by memory available on the
+computer. We must, however, be careful to check that each of
+these {\em nested\/} environments is indeed contained within
+the one just outside of it.
+
+\nsubsubsection{{\tt em} environment}
+We start with a very simple environment, one which provides
+an alternative to the \verb@\em@ command. Remember that
+\verb@\em@ does not accept an argument; it applies to
+everything within its scope as dictated by the group
+within which it is used. This can be tricky if we wish
+to emphasise a large amount of text, for we may forget
+a group-delimiting brace and so upset the entire grouping
+structure of our document. In cases where we fear this might
+happen, we can proceed as follows.
+
+\moveright0.1\textwidth\vbox{%
+\footnotesize\begin{verbatim}
+\begin{em}
+We must always be careful to match our group-delimiting
+braces correctly. If the braces in a document are unevenly
+matched then \LaTeX\ will become confused because we will
+have, in effect, indicated different scopes than we
+intended for commands.
+\end{em}
+\end{verbatim}
+}
+\noindent which will give
+
+\result{%
+\begin{em}
+We must always be careful to match our group-delimiting
+braces correctly. If the braces in a document are unevenly
+matched then \LaTeX\ will become confused because we will
+have, in effect, indicated different scopes than we
+intended for commands.
+\end{em}
+}
+
+Although \LaTeX\ doesn't care too much for how we format
+our source file, it is obviously a good idea to lay it
+out logically and readably anyway. This helps minimise
+errors as well as aids in finding them. For this reason
+I have adopted the convention of always placing the
+environment \verb@\begin@ and \verb@\end@ commands on
+lines by themselves.
+
+\nsubsubsection{{\tt quote} and {\tt quotation} environments}
+This environment can be used to display a part
+of a sentence or paragraph, or even several
+paragraphs, in such a manner that the material
+stands out from the rest of the text. This can
+be used to enhance readability, or to simply
+emphasise something. Its syntax is simple:
+
+\moveright0.05\textwidth\vbox{%
+\footnotesize\begin{verbatim}
+Horace smiled and retaliated:
+\begin{quote}
+\em You can mock the non-WYSIWYG nature of \TeX\
+all you like. You don't understand that that is
+precisely what makes \TeX\ enormously more powerful
+than that lame excuse for a typesetter you use.
+And I'll bet that from start to finish of preparing
+a document I'm quicker than you are, even if you
+do type at twice the speed and have the so-called
+advantage of WYSIWYG. In your case, what you see
+is {\em all\/} you get!
+\end{quote}
+and then continued with composing his masterpiece of the
+typesetting art.
+\end{verbatim}
+}
+\noindent produces the following typeset material:
+
+\moveleft0.05\textwidth\vbox{\result{%
+\noindent Horace smiled and retaliated:
+\begin{quote}
+\noindent\em You can mock the non-WYSIWYG nature of \TeX\
+all you like. You don't understand that that is
+precisely what makes \TeX\ enormously more powerful
+than that lame excuse for a typesetter you use.
+And I'll bet that from start to finish of preparing
+a document I'm quicker than you are, even if you
+do type at twice the speed and have the so-called
+advantage of WYSIWYG. In your case, what you see
+is {\em all\/} you get!
+\end{quote}
+and then continued with composing his masterpiece of the
+typesetting art.
+}
+}
+
+That is a much more readable manner of presenting Horace's
+piece of mind than embedding it within a regular paragraph.
+The {\tt quote} environment was responsible for the margins
+being indented on both sides during the quote. This example
+has also been used to show how the commands that begin and
+end an environment restrict the scope of commands issued within
+that environment: The \verb@\em@ at the beginning of the
+quote did not affect the text following the quote. We have
+also learned here that if we use \verb@\em@ within already
+emphasised text, the result is roman type---and we don't
+require an italic correction here because the final letter
+of `all' was not sloping to the right.
+
+The {\tt quotation} environment is used in just the same way
+as the {\tt quote} environment above, but it is intended
+for setting long quotations of several paragraphs. It would
+be suitable for quoting a few paragraphs from the text of
+some speech, for instance. \LaTeX\ treats the given
+text just like normal text that it has to set into paragraphs,
+except that it indents the margins a little.
+
+\nsubsubsection{{\tt verse} environment}
+This is provided to facilitate the setting of poetry.
+When within the {\tt verse} environment, we use
+\verb@\newline@ (or \verb@\\@) to end a line; and
+what would normally signify a new paragraph
+serves to indicate the start of a new stanza.
+Let's have a shot at some cheap poetry.
+
+\moveright0.1\textwidth\vbox{%
+\footnotesize\begin{verbatim}
+\begin{verse}
+Roses are red\\
+Violets are blue\\
+I think \TeX\ is great\\
+And so will you!
+
+Roses are still red\\
+Violets are still blue\\
+I'm schizophrenic\\
+And so am I.
+\end{verse}
+\end{verbatim}
+}
+\noindent will produce the following stunningly-creative ``poem'':
+
+\result{%
+\begin{verse}
+Roses are red\\
+Violets are blue\\
+I think \TeX\ is great\\
+And so will you!
+
+Roses are still red\\
+Violets are still blue\\
+I'm schizophrenic\\
+And so am I.
+\end{verse}
+}
+
+
+
+\nsubsubsection{{\tt center} environment}
+This environment allows the centring of consecutive lines
+of text, new lines being indicated by a \verb@\\@. If you
+don't separate lines with the \verb@\\@ command then you'll
+get a centred paragraph the width of the page,
+which won't look any different to normal. If only one
+line is to be centred, then no \verb@\\@ is necessary.
+
+\moveright0.1\textwidth\vbox{%
+\footnotesize\begin{verbatim}
+The {\tt center} environment takes care of the vertical
+spacing before and after it, so we don't need to leave any.
+\begin{center}
+If we leave no blank line after the\\
+{\tt center} environment\\
+then the ensuing text will not\\
+be regarded as part of a new\\
+paragraph, and so will not be indented.\\
+\end{center}
+
+In this case we left a blank line after the environment,
+so the new text was regarded as starting a new paragraph.
+\end{verbatim}
+}
+\noindent gives the following text
+
+\result{%
+The {\tt center} environment takes care of the vertical
+spacing before and after it, so we don't need to leave any.
+\begin{center}
+If we leave no blank line after the\\
+{\tt center} environment\\
+then the ensuing text will not\\
+be regarded as part of a new\\
+paragraph, and so will not be indented.\\
+\end{center}
+
+In this case we left a blank line after the environment,
+so the new text was regarded as starting a new paragraph.
+}
+
+\nsubsubsection{{\tt flushright} and {\tt flushleft} environments}
+The {\tt flushright} environment causes each line to be set
+with its last character against the right margin, without trying
+to stretch the line to to current text width. The {\tt flushleft}
+environment is similar.
+
+\moveright0.1\textwidth\vbox{%
+\footnotesize\begin{verbatim}
+We can stop \LaTeX\ from justifying each line to both the
+left and the right margins.
+\begin{flushright}
+The {\tt flushright} environment is\\
+used for text with an even right margin\\
+and a ragged left margin.
+\end{flushright}
+\begin{flushleft}
+and the {\tt flushleft} environment is\\
+used for text with an even left margin\\
+and a ragged right margin.
+\end{flushleft}
+\end{verbatim}
+}
+\noindent gives the desired display
+
+\result{%
+We can stop \LaTeX\ from justifying each line to both the
+left and the right margins.
+\begin{flushright}
+The {\tt flushright} environment is\\
+used for text with an even right margin\\
+and a ragged left margin.
+\end{flushright}
+\begin{flushleft}
+and the {\tt flushleft} environment is\\
+used for text with an even left margin\\
+and a ragged right margin.
+\end{flushleft}
+}
+
+One must be wary not to lapse into ``word-processing'' mode
+when using these environments. Remember that pressing return
+at the end of a line in the input file does not serve to end
+the current line there, but just to indicate the end of another word.
+We have to use the \verb@\\@ command to end a line.
+
+\nsubsubsection{{\tt verbatim} environment}
+We can simulate typed text using the {\tt verbatim} environment.
+The \verb@\tt@ (typewriter text) type style can be used for
+simulating typed words, but runs into trouble if one of the
+characters in the simulated typed text is a specially reserved
+\LaTeX\ character. For instance, \verb@{\tt type \newline}@
+would not have the desired effect because \LaTeX\ would
+interpret the \verb@\newline@ is an instruction to start
+a new line.
+
+The {\tt verbatim} environment allows the simulation of multiple
+typed lines. {\em Everything\/} within the environment is
+typeset in typewriter font exactly as it appears in our source
+file---obeying spaces and line breaks as in the source file and
+not recognising the existence of any special symbols.
+
+% this is going to be ugly, because we can't demonstrate an
+% \end{verbatim} using the verbatim environment
+\moveright0.1\textwidth\vbox{%
+\footnotesize\begin{flushleft}
+\tt\bs begin\{verbatim\}\\
+In the verbatim environment we can type anything\\
+we like.\\
+So we don't need to look out for uses of \%, \$, \& etc,\\
+nor will control sequences like \bs newline have any\\
+effect.\\
+\bs end\{verbatim\}
+\end{flushleft}
+}
+\noindent will produce the simulated input text
+
+\moveright0.1\textwidth\vbox{%
+\footnotesize\begin{verbatim}
+In the verbatim environment we can type anything
+we like.
+So we don't need to look out for uses of %, $, & etc,
+nor will control sequences like \newline have any
+effect.
+\end{verbatim}
+}
+
+The only thing that cannot be typed in the {\tt verbatim}
+environment is the sequence \verb@\end{verbatim}@. You
+might notice that I still managed to simulate that
+control sequence above. One can always get what you want
+in \TeX, perhaps with a little creativity.
+
+If we want only to simulate a few typed words, such as when
+I say to use \verb@\newline@ to start a new line, then the
+\verb@\verb@ command is used. This command has a slightly
+odd syntax, pressed upon it by the use for which it was
+intended. It cannot accept an argument, because we may
+want to simulate typed text that is enclosed by
+\verb@{braces}@. What one does is to choose any character
+that is {\em not\/} in the text to be simulated, and use
+a pair of these characters as ``argument delimiters''. I usually use the
+\verb"@" or \verb@"@ charachters, as I rarely have any other uses for them.
+Thus
+
+\result{%
+\noindent use \verb"\%" to obtain a \% sign
+}
+\noindent is typed as
+
+\moveright0.1\textwidth\vbox{
+\footnotesize\begin{verbatim}
+use \verb"\%" to obtain a \% sign
+\end{verbatim}
+}
+
+\nsubsubsection{{\tt itemize}, {\tt enumerate}, {\tt description} environments}
+\LaTeX\ provides three predefined list-making environment, and a
+``primitive'' list environment for designing new list environments
+of your own. We shall just describe the predefined ones here.
+
+There is delightfully little to learn in order to be able to create
+lists. The only new command is \verb@\item@ which indicates the
+beginning of a new list item (and the end of the last one if this is
+not the first item). This command accepts an optional argument
+(which means you'd enclose it in square brackets) that can be
+used to provide an item label. If no optional argument is given, then
+\LaTeX\ will provide the item label for you; in an
+{\tt itemize} list it will bullet the items, in an
+{\tt enumerate} list it will number the items, and in a list
+of {\tt description}s the default is to have no label (which would look
+a bit odd, so you're expected to use the optional argument there).
+
+Remember that \verb@\item@ is used to separate list items; it
+does not accept the list item as an argument.
+
+\moveright0.1\textwidth\vbox{%
+\footnotesize\begin{verbatim}
+\begin{itemize}
+\item an item is begun with \verb@\item@
+\item if we don't specify labels, then
+ \LaTeX\ will bullet the items for us
+\item I indent lines after the first in the
+ input file, but that is just to keep things
+ readable. As always, \LaTeX\ ignores additional
+ spaces.
+
+\item a blank line between items is ignored, for
+ \LaTeX\ is responsible for spacing items.
+\item \LaTeX\ is in paragraph-setting mode when
+ it reads the text of an item, and so will
+ perform all the usual functions
+\end{itemize}
+\end{verbatim}
+}
+\noindent produces the following itemised list:
+
+\result{
+\begin{itemize}
+\item an item is begun with {\tt\bs item}%\verb blew up here!
+\item if we don't specify labels, then
+ \LaTeX\ will bullet the items for us
+\item I indent lines after the first in the
+ input file, but that is just to keep things
+ readable. As always, \LaTeX\ ignores additional
+ spaces.
+
+\item a blank line between items is ignored, for
+ \LaTeX\ is responsible for spacing items.
+\item \LaTeX\ is in paragraph-setting mode when
+ it reads the text of an item, and so will
+ perform all the usual functions
+\end{itemize}
+}
+
+Lists can also be embedded within one another,
+for they are just environments and we said that
+environments have this property. Remember that
+we must nest them in the correct order. We
+demonstrate with the following list, which also
+shows how to use the {\tt enumerate} environment.
+
+\moveright0.1\textwidth\vbox{%
+\footnotesize\begin{verbatim}
+\noindent I still have to do the following things:
+\begin{enumerate}
+\item Sort out LAN accounts for people on the course
+ \begin{itemize}
+ \item Have new accounts created for those not already
+ registered on the LAN
+ \item Make sure all users have a personal directory
+ on the data drive
+ \item Give read and scan rights to users in the \TeX\
+ directories
+ \item Add users to the appropriate LAN print queues
+ \end{itemize}
+\item Have a \TeX\ batch file added to a directory that
+ is on a public search path
+\item Finish typing these course notes and proof-read them
+\item Photocopy and bind the finished notes
+\end{enumerate}
+\end{verbatim}
+}
+\noindent will give the following list
+
+\result{
+I still have to do the following things:
+\begin{enumerate}
+\item Sort out LAN accounts for people on the course
+ \begin{itemize}
+ \item Have new accounts created for those not already
+ registered on the LAN
+ \item Make sure all users have a personal directory
+ on the data drive
+ \item Give read and scan rights to users in the \TeX\
+ directories
+ \item Add users to the appropriate LAN print queues
+ \end{itemize}
+\item Have a \TeX\ batch file added to a directory that
+ is on a public search path
+\item Finish typing these course notes and proof-read them
+\item Photocopy and bind the finished notes
+\end{enumerate}
+}
+
+See how I lay the source file out in a readable fashion.
+This is to assist myself, not \LaTeX.
+
+The {\tt description} environment is, unsurprisingly,
+for making lists of descriptions.
+
+\moveright0.1\textwidth\vbox{%
+\footnotesize\begin{verbatim}
+\begin{description}
+\item[\tt itemize] an environment for setting itemised lists.
+\item[\tt enumerate] an environment for setting numbered lists.
+\item[\tt description] an environment for listing descriptions.
+\end{description}
+\end{verbatim}
+}
+\noindent will typeset the following descriptions:
+
+\result{%
+\begin{description}
+\item[\tt itemize] an environment for setting itemised lists.
+\item[\tt enumerate] an environment for setting numbered lists.
+\item[\tt description] an environment for listing descriptions.
+\end{description}
+}
+
+Note that the scope of the \verb@\tt@ commands used in the
+item labels was restricted to the labels.
+
+\nsubsubsection{{\tt tabbing} environment}
+This environment simulates tabbing on typewriters.
+There one chose the tab stops in advance (analysing
+the material to be typed for the longest item in
+each column) and typed entries consecutively,
+hitting the tab key to move to the next tab stop
+and return to move to the next line.
+
+In the {\tt tabbing} environment, we proceed similarly.
+We look for the worst-case line (that which will
+determine the desired tab stops) and use it to
+set the tabs by inserting \verb@\=@ control symbols
+at the points where we want tab stops. We then discard
+that line using \verb@\kill@, since the worst-case line
+might not be the first line in the material we have to
+type. We then type each line, using \verb@\>@ to move
+to the next tab stop and \verb@\\@ to end a line.
+
+\moveright0.1\textwidth\vbox{%
+\footnotesize\begin{verbatim}
+\begin{tabbing}
+Cheddar cheese \= Recommended \= \$2.00 \kill
+Green Ham \> Recommended \> \$2.00
+Eggs \> 1 a week \> \$1.50
+Cheddar cheese \> Hmmm \> \$0.80
+Yak cheese \> Avoid \> \$0.05
+\end{tabbing}
+\end{verbatim}
+}
+\noindent gives the following uniformly-tabbed table
+
+\result{%
+\begin{tabbing}
+Cheddar cheese \= Recommended \= \$2.00 \kill
+Green Ham \> Recommended \> \$2.00\\
+Eggs \> 1 a week \> \$1.50\\
+Cheddar cheese \> Hmmm \> \$0.80\\
+Yak cheese \> Avoid \> \$0.05
+\end{tabbing}
+}
+
+In the format line I chose the longest entry
+from each of the prospective columns. I lined
+some of the \verb@\>@ commands up in the source
+just to keep things readable.
+
+Remember that excess spaces are ignored. \LaTeX\
+sets the \verb@\kill@ed line normally and sees where the
+tab stops requested will be needed in the typeset text.
+Note also that commands given within the {\tt tabbing}
+environment are local to {\em the current item}.
+
+Actually, we use the above approach in the case that
+we require uniformly tabbed columns. The format line
+is not compulsory, and we can define tab stops dynamically.
+See if you can make sense of the following.
+
+\moveright0.1\textwidth\vbox{%
+\footnotesize\begin{verbatim}
+\begin{tabbing}
+Entry in position 1,1 \= Entry 1,2 \= Entry 1,3\\
+Entry in position 2,1 \> Entry 2,2 \> Entry 2,3\\
+Entry 3,1 \= Entry 3,2 \> Entry 3,3\\
+Entry 4,1 \> Entry 4,2 \> Entry 4,3
+\end{tabbing}
+\end{verbatim}
+}
+\noindent which produces
+
+\result{%
+\begin{tabbing}
+Entry in position 1,1 \= Entry 1,2 \= Entry 1,3\\
+Entry in position 2,1 \> Entry 2,2 \> Entry 2,3\\
+Entry 3,1 \= Entry 3,2 \> Entry 3,3\\
+Entry 4,1 \> Entry 4,2 \> Entry 4,3
+\end{tabbing}
+}
+
+The are additional commands that can be used within
+the tabbing environment to achieve special effects,
+but we won't be discussing them here.
+
+\nsubsubsection{{\tt tabular} environment}
+The {\tt tabular} environment is used to produce
+tables of items, particularly when the table
+is predominantly rectangular and when line drawing
+is required. \LaTeX\ will make most decisions for
+us; for instance it will align everything for us
+without having to be told which are the longest
+entries in each column.
+
+This environment is the first of many that use the
+\TeX\ ``tabbing character'' {\tt \&}. This character
+is used to separate consecutive entries in a row
+of a table, array, etc. The end of a row is indicated
+in the usual manner, by using \verb@\\@.
+In this way the individual cells of the table, or array,
+are clearly described to \LaTeX, and it can analyse
+them to make typesetting decisions. Commands issued
+within a cell so defined are, again, local to that
+cell.
+
+The {\tt tabular} environment is also our first example
+of an {\em environment with arguments}. The arguments
+are given, in braces as usual, just after the closing
+brace after the environments name. In the case of
+{\tt tabular} there is a single mandatory argument
+giving the justification of the entries in each column:
+{\tt l} for left justified, {\tt r} for right justified,
+and {\tt c} for centred. There must be an entry for each
+column of the table, and there is no default. Let's start
+with a simple table.
+
+\moveright0.1\textwidth\vbox{%
+\footnotesize\begin{verbatim}
+\begin{tabular}{llrrl}
+\bf Student name & \bf Number & \bf Test 1 & \bf Test 2 & \bf Comment\\
+F. Basset & 865432 & 78 & 85 & Pleasing\\
+H. Hosepipe & 829134 & 5 & 10 & Improving\\
+I.N. Middle & 853931 & 48 & 47 & Can make it
+\end{tabular}
+\end{verbatim}
+}
+\noindent will produce the following no-frills table
+
+\result{%
+\begin{tabular}{llrrl}
+\bf Student name & \bf Number & \bf Test 1 & \bf Test 2 & \bf Comment\\
+F. Basset & 865432 & 78 & 85 & Pleasing\\
+H. Hosepipe & 829134 & 5 & 10 & Improving\\
+I.N. Middle & 853931 & 48 & 47 & Can make it
+\end{tabular}
+}
+Note that a \verb@\\@ was not necessary at the end
+of the last row. Also note that, once again, the alignment
+of the \verb@&@ characters was for human readability.
+It is conventional to set columns of numbers with right
+justification. The \verb@\bf@ directives apply only the
+entries in which they are given.
+
+A {\tt |} typed in the {\tt tabular} environment's argument
+causes a vertical line to be drawn at the indicated position
+and extending for the height of the entire table. An
+\verb@\hline@ given in the environment draws a horizontal
+line extending the width of the table to be drawn at the
+vertical position at which the command is given.
+A \verb@\cline@$\{i$-$j\}$ draws a line spanning columns
+$i$ to $j$, at the vertical position at which the
+command is given. A repeated line-drawing command
+causes a double line to be drawn. We illustrate line
+drawing in tables by putting some lines into our first
+table. We will type this example in a somewhat expanded
+form, trying to make it clear why the lines appear where they
+do.
+
+\moveright0.1\textwidth\vbox{%
+\footnotesize\begin{verbatim}
+\begin{tabular}{|l|l|r|r|l|}
+\hline
+\bf Student name & \bf Number & \bf Test 1 & \bf Test 2 & \bf Comment\\
+\hline
+F. Basset & 865432 & 78 & 85 & Pleasing\\
+\hline
+H. Hosepipe & 829134 & 5 & 10 & Improving\\
+\hline
+I.N. Middle & 853931 & 48 & 47 & Can make it\\
+\hline
+\end{tabular}
+\end{verbatim}
+}
+\noindent which will give
+
+\result{%
+\begin{tabular}{|l|l|r|r|l|}
+\hline
+\bf Student name & \bf Number & \bf Test 1 & \bf Test 2 & \bf Comment\\
+\hline
+F. Basset & 865432 & 78 & 85 & Pleasing\\
+\hline
+H. Hosepipe & 829134 & 5 & 10 & Improving\\
+\hline
+I.N. Middle & 853931 & 48 & 47 & Can make it\\
+\hline
+\end{tabular}
+}
+% part 3 of 4
+That way of laying out the source file makes it clear where
+the lines will go. As we (by now) well know, the returns that
+we pressed after the \verb@\\@s in typing this table might
+as well have been spaces as far as \LaTeX\ is concerned. Thus
+it is common to have the \verb@\hline@ commands following the
+\verb@\\@s on the input lines. We will do this in future examples.
+
+The \verb@\multicolumn@ column can be used to overrule the overall
+format of the table for a few columns. The syntax of this command
+is
+
+\begin{syntax}{multicolumn}
+\man{n}\man{pos}\man{item}
+\end{syntax}
+
+\noindent where $n$ is the number of columns
+of the original format that {\em item\/}
+is to span, and {\em pos\/} specifies the justification
+of the new argument.
+
+\moveright0.1\textwidth\vbox{%
+\footnotesize\begin{verbatim}
+\begin{tabular}{||l|c|c|c||} \hline
+\multicolumn{4}{|c|}{\LaTeX\ size changing commands}\\ \hline
+Style option & 10pt (default) & \tt 11pt & \tt 12pt\\ \hline
+\tt\bs footnotesize & 8pt & 9pt & 10pt\\ \hline
+\tt\bs small & 9pt & 10pt & 11pt\\ \hline
+\tt\bs large & 12pt & 12pt & 14pt\\ \hline
+\end{tabular}
+\end{verbatim}
+}
+\noindent produces the following table:
+
+\begin{center}\footnotesize
+\begin{tabular}{||l|c|c|c||} \hline
+\multicolumn{4}{|c|}{\LaTeX\ size changing commands}\\ \hline
+Style option & 10pt (default) & \tt 11pt & \tt 12pt\\ \hline
+\tt\bs footnotesize & 8pt & 9pt & 10pt\\ \hline
+\tt\bs small & 9pt & 10pt & 11pt\\ \hline
+\tt\bs large & 12pt & 12pt & 14pt\\ \hline
+\end{tabular}
+\end{center}
+
+\nsubsubsection{{\tt figure} and {\tt table} environments}
+Figures (diagrams, pictures, etc.)\ and tables (perhaps created
+with the {\tt tabular} environment) cannot be split across
+pages. So \LaTeX\ provides a mechanism for ``floating''
+them to a nearby place where there is room for them. This
+may mean that your figure or table may appear a little later in the
+document than its declaration in the source file might suggest.
+You can suggest to \LaTeX\ that it try to place the figure or
+table at the present position if there is room
+or, failing that, at the top or bottom of
+the present or following page. You can also ask for it to be presented by
+itself on a ``page of floats''.
+
+You suggest these options to \LaTeX\ through an optional
+argument to the environment. One lists a combination
+of the letters {\tt h}, {\tt t}, {\tt b}, and {\tt p} where
+\begin{description}
+\item[h] means that the object should be placed {\em here} if there
+ is room, so that things will appear in the same order as
+ in the source file,
+\item[t] means that the object can be placed at the {\em top\/} of the of a text
+ page, but no earlier than the present page.
+\item[b] means that the object can be placed at the {\em bottom\/} of a text
+ page, but no earlier than the present page.
+\item[p] means that the object should be set on a {\em page of floats\/} that consists
+ only of tables and figures.
+\end{description}
+
+A combination of these indicates decreasing order of preference.
+The default is {\tt tbp}. In this document I have tended to use
+{\tt htbp}.
+
+\LaTeX\ will also number and caption a figure or table for you,
+and compile a list of tables and a list of figures.
+Just include \verb@\listoffigures@ and \verb@\listoftables@
+next to your \verb@\tableofcontents@ command at the beginning
+of the document. To caption a table of figure, include
+\verb@\caption{@{\em caption text}\verb@}@ just before the
+\verb@\end{table}@ or \verb@\end{figure}@ command. Here's
+a sample source file.
+
+\moveright0.1\textwidth\vbox{%
+\footnotesize\begin{verbatim}
+\begin{table}[htbp]
+ \begin{tabular}{lrll}
+ ...
+ \end{tabular}
+\caption{Mark analysis}
+\end{table}
+\end{verbatim}
+}
+
+To leave space for a figure that will inserted by some
+other means at a later date, we can use the \verb@\vspace@
+command:
+
+\moveright0.1\textwidth\vbox{%
+\footnotesize\begin{verbatim}
+\begin{figure}[htbp]
+\vspace{9.5cm}
+\caption{An artists impression}
+\end{figure}
+\end{verbatim}
+}
+
+Including graphics files prepared with drawing packages is
+possible, but beyond the scope of this introduction.
+
+\subsection{The {\tt letter} document style}
+All this and we still don't know how to prepare
+a simple letter! Actually, there is very little
+to it.
+
+Figure~\ref{fig:letter} shows a sample letter. We declare
+our own address and signature before entering the {\tt letter}
+environment because we can use repeated {\tt letter}
+environments to prepare multiple letters from the same source
+file. The address of the intended recipient of a particular
+letter is given as an argument to the {\tt letter} environment.
+
+\begin{figure}[p]
+\moveright0.1\textwidth\vbox{%
+\footnotesize\begin{verbatim}
+\documentstyle[12pt]{letter}
+\begin{document}
+\address{(Underneath) Lion Bridge\\
+Midway down Commercial Road\\
+Pietermaritzburg\\
+3200}
+
+\signature{F. Basset\\
+Public nuisance}
+
+\begin{Letter}{Director of Public Parks\\
+Pietermaritzburg Municipality\\
+Pietermaritzburg}
+
+\opening{Kind Sir/Madam}
+
+I wish to complain about the shocking practice of
+fencing off the base of trees. I notice with grave
+concern that this has occurred in the park bordering
+my stately residence.
+
+This has already caused me great inconvenience
+and public embarrassment, as you can imagine it would
+for a hound of my social standing. I demand that
+you take these obscene obstructions away without
+delay.
+
+\closing{Yours anxiously}
+\end{letter}
+\end{document}
+\end{verbatim}
+}
+\vfil\caption{A sample letter}
+\label{fig:letter}
+\end{figure}
+
+\subsection{Common pitfalls; Error messages}
+By now it should be clear that we have to work quite
+accurately when preparing a document. Typing errors
+in the running text can be absorbed, but messing up
+a control sequence name will halt the compiler with
+an error message. Before we look at some common errors and
+some ways to avoid them, let's have a look at a sample
+error message.
+
+You'll have noticed by now that when you run \LaTeX\
+on a source file, the transcript of the compiler
+session is written on a log file. When errors have
+accumulated to the point that \LaTeX\ is hopelessly
+confused, it is time to debug your source file. The
+log file contains a reference to the line, or lines, of
+your source file that generated the error together with
+a description of the error.
+
+\TeX\ and \LaTeX\ error messages appear frightening at first
+sight, to say the least. They are actually very informative,
+but they can take some getting used to. Mistyped control
+sequences cause little pain, but a missing
+\verb@\end{@{\em environment}\verb@}@ can cause a good deal
+of confusion because it has the effect of making \LaTeX\
+try to set material into that environment that was never
+intended/designed to fit in such a place. Also, ommiting a mandatory
+argument can cause great confusion.
+
+Suppose we type \verb@\bold@ instead of \verb@\bf@ in the following
+line:
+
+\moveright0.1\textwidth\vbox{
+\footnotesize\begin{verbatim}
+this is going to be {\bold very} messy.
+\end{verbatim}
+}
+\noindent This produces the following error message:
+
+\moveright0.1\textwidth\vbox{
+\footnotesize\begin{verbatim}
+! Undefined control sequence.
+1.683 this is going to be {\bold
+ very} messy.
+?
+\end{verbatim}
+}
+That not so bad! The line beginning with {\tt!} tells us that we
+have tried to used a control sequence that was not known to
+\LaTeX; the {\tt 1.683} tells us that the error occurred on line
+683 of the source file; and the error message is split over two lines
+with the break occurring at the point where \LaTeX\ detected a problem.
+
+But suppose we try the following
+
+\moveright0.1\textwidth\vbox{%
+\footnotesize\begin{verbatim}
+\begin{tabular}{llrrl}
+Student name & Number & Test 1 & Test 2 & Comment\\
+F. Basset & 865432 & 78 & 85 & Pleasing\\
+H. Hosepipe & 829134 & 5 & 10 & Improving\\
+I.N. Middle & 853931 & 48 & 47 & Can make it
+
+This shows that H.~Hosepipe's newfound concentration has...
+\end{verbatim}
+}
+i.e., we omit to provide the \verb@\end{tabular}@ that
+delimits the end of the environment. Not having been
+told that the environment is supposed to be concluded,
+\LaTeX\ will try to set the text of the next paragraph
+as a table item---and will scream blue murder when it
+finds that it doesn't conform to the syntax demanded.
+
+\moveright0.1\textwidth\vbox{%
+\footnotesize\begin{verbatim}
+LaTeX error. See LaTeX manual for explanation.
+ Type H <return> for immediate help.
+! \begin{tabular} ended by \end{document}.
+\@latexerr ...diate help.}\errmessage {#1}
+
+\@checkend ...urrenvir \else \@badend {#1}
+ \fi
+\enddocument ->\@checkend {document}
+ \clearpage \begingroup \if@filesw...
+\end #1->\csname end#1\endcsname
+ \@checkend {#1}\expandafter \endgrou...
+l.58 \end{document}
+
+?
+\end{verbatim}
+}
+
+Now {\em that's\/} informative! Actually it {\em is} if we
+agree to ignore all but the the error indication line
+(the one beginning with the {\tt!}) and the line telling us
+where \LaTeX\ noticed that all was not well (the one beginning
+{\tt 1.58} in this case). The rest of the error message you can
+regard as being for your local \TeX\ wizard to sort your problem
+out if you are unable to after consulting the manuals.
+Tough as it looks, we can decipher this message straight
+away: the error indicator line tell us that a {\tt tabular}
+environment was ended incorrectly (in this case by an
+\verb@\end{document}@).
+
+\TeX\ error messages aren't all that bad once you've made
+enough errors to get used to a few! Most can be avoided
+through {\em careful\/} preparation of the source file.
+Typing accurately and knowledge of the command syntax is a good start,
+but there are some other precautions that make good sense:
+\begin{enumerate}
+\item Even if \LaTeX\ is happy with free-form input, try to
+ lay your input file out as regularly and logically as
+ possible. See our examples of environments for
+ formats to adopt.
+\item It is important that all group delimiters be properly matched,
+ i.e., braces and {\tt\bs begin\{\}}\ldots{\tt\bs end\{\}} must
+ come in pairs. A good habit to fall in to is to always type
+ such things in pairs and then move the cursor back between
+ them and type the intervening material.
+\item Don't forget command arguments when they are mandatory.
+ Always ask yourself what a particular commands {\em needs
+ from you\/} in order to make the decisions that are required of it.
+\item Remember the 10 characters that are specially reserved for
+ commenting, table item separation, etc.
+\item When we look at mathematical typesetting in the next chapter,
+ we will see that the same principles apply there.
+\item Try to use a text editor that has a \TeX\ mode, or at least
+ one that will match brackets for you.
+\end{enumerate}
+
+\section{Summary}
+We have learned pretty much all we need to know in order to
+prepare non-mathematical documents. There has been quite
+a lot of material, all told, but we're fortunate that the
+average document requires only a fraction of what we've
+listed here. Furthermore, we'll find that what we've
+learned equips us with a good deal of the framework
+needed for mathematical typesetting.
+
+The important thing to extract from this chapter is some
+feel for what I termed the ``spirit of \TeX'' at the
+chapter beginning. I cannot emphasise enough the
+importance of getting your mind out of ``word processing''
+mode and into ``typesetting'' mode. Always keep uppermost
+in your mind the task at hand: you are to describe the
+logical content of the document to \LaTeX, so furnishing
+it with enough information to perform all the formatting
+for you.
+
+Many of the earlier sections of this chapter will become
+trivially easy to you after just a little experimentation
+with \LaTeX. The best way to learn the syntax of the more
+complicated environments is to use them---try typesetting
+the examples, for instance. It is important that you come
+to terms with the {\tt tabular} environment, for its
+syntax is typical of many of the mathematical constructs
+that we will use.
+
+If you have not already done so, then now is the time
+to try preparing some documents of your own. Try
+including all the material from this chapter, for
+that is the best way to remember it all. When
+the initial lack of familiarity wears off, you'll
+find that \LaTeX\ is really a whole lot friendlier
+and easier to use than you expected.
+
+We must also recognise that there is a lot more to some of the command
+than detailed here. Some accept optional argumnets that were not mentioned,
+others have more options than we considered. And even once we have a full
+description of each command, there is still much to be learned for there
+is much that can be achieved through creative use of some of the environments.
+
+
+
+
+
+\chapter{Mathematical typesetting with \LaTeX}
+
+
+The last chapter taught us a good deal of what we need to know in order to
+prepare quite complicated non-mathematical documents. There are still a
+number of useful topics that we have not covered (such as cross-referencing),
+but we'll defer discussion of those until a later chapter. In the present
+chapter, we'll learn how \LaTeX\ typesets mathematics. It should come
+as no surprise that \LaTeX\ does most of the work for us.
+
+\section{Introduction}
+In text-only documents we saw that our task was to describe the logical
+components of each sentence, paragraph, section, table, etc.
+When we tell \LaTeX\ to go into {\em mathematical mode}, we have to
+describe the logical parts of a formula, matrix, operator, special symbol, etc.
+\TeX\ has been taught to recognize a binary operation, a binary relation,
+a variable, an operator that expects limits, and so on. We just need to
+supply the parts that make up each of these, and \TeX\ will take care of
+the rest. It will leave appropriate space around operators, italicise variables,
+set an operator name in roman type, leave the correct space after colons,
+place sub- and superscripts in the correct positions (based on what it is
+you're working with), choose the correct typesizes, \ldots\ the list of things it has been taught is
+enormous. When you want to revert to setting normal text again, you tell
+\LaTeX\ too leave maths mode and go back into the mode it was in (paragraphing
+mode).
+
+\LaTeX\ cannot be expected to perform these mode shifts itself, for it
+is not always clear just when it is mathematics that has been typed.
+For example, should an isolated letter {\tt a} in the input file be
+regarded as a word (as in the definite article) or a mathematical
+variable (as in the variable $a$). There are no reliable rules for
+\LaTeX\ to make such decisions by, so the begin-math and end-math
+mode switching is left entirely to you.
+
+The symbol \verb@$@ is specially reserved\footnote{See section \ref{sec:reserved}}
+by \LaTeX\ as the ``math shift'' symbol. When \LaTeX\ starts setting
+a document it is in paragraphing mode, ready to set lines of the
+input file into paragraphs. It remains in this mode until
+it encounters a \verb@$@ symbol, which shifts \LaTeX\ into mathematical
+mode. It now knows to be on the look-out for the components of a mathematical
+expression, rather than for words and paragraphs. It reads everything
+up to the next \verb@$@ sign in this mathemtical mode, and then shifts back to
+paragraphing mode (i.e.\ the mode it was in before we took it in to
+maths mode).
+
+You must be careful to balance your begin-math and end-math
+symbols. It is often a good idea to type two \verb@$@ symbols
+and then move back between them and type the mathematical
+expression. If the math-shift symbols in a document are
+not matched, then \LaTeX\ will become confused because
+it will be trying to set non-mathematical material as
+mathematics.
+
+For those who find having the same symbol for both math-begin
+and math-end confusing or dangerous, there are two control symbols that perform
+the same operations: the control symbol \verb@\(@ is
+a begin-math instruction, and the control symbol \verb@\)@
+is an end-math instruction. Since it is easy to ``lose'' a \verb@$@
+sign when typing a long formula, a math environment is provided
+for such occasions: you can use \verb@\begin{math}@ and
+\verb@\end{math}@ as the math-shift instructions. Of course, you
+could just decide to use \verb@$@ and take your chances.
+
+Let's have a look at some mathematics.
+
+\moveright0.1\textwidth\vbox{%
+\footnotesize\begin{verbatim}
+\LaTeX\ is normally in paragraphing mode, where
+it expects to find the usual paragraph material. Including
+a mathematical expression, like $2x+3y - 4z= -1$, in the
+paragraph text is easy. \TeX\ has been taught to recognize
+the basic elements of an expression, and typeset them appropriately,
+choosing spacing, positioning, fonts, and so on.
+Typing the above expression without entering maths
+mode produces the incorrect result: 2x+3y - 4z= -1
+\end{verbatim}
+}
+\noindent will produce the following paragraph
+
+\result{
+\LaTeX\ is normally in paragraphing mode, where
+it expects to find the usual paragraph material. Including
+a mathematical expression, like $2x+3y - 4z= -1$, in the
+paragraph text is easy. \TeX\ has been taught to recognize
+the basic elements of an expression, and typeset them appropriately,
+choosing spacing, positioning, fonts, and so on.
+Typing the above expression without entering maths
+mode produces the incorrect result: 2x+3y - 4z= -1
+}
+
+Notice that \LaTeX\ sets space around the binary relation
+$=$ and space around the binary operators $+$ and $-$ on the
+left hand side of the equation, ignoring the
+spacing we typed in the input. It was also able to recognize
+that the $-1$ on the right hand side of the equation was
+a unary minus---negating the $1$ rather than being used to
+indicate subtraction---and so did not put space around it.
+It also italicised the
+variables $x$, $y$, and $z$. However, it did not italicise
+the number $1$.
+
+In typing a mathematical expression we must remember to keep the
+following in mind:
+\begin{enumerate}
+\item All letters that are not part of an argument to some control
+sequence will be italicised. Arguments to control sequences will
+be set according to the definition of the command used. So
+typing \verb@$f(x)>0 for x > 1$@ will produce
+$$f(x)>0 for x > 1$$
+instead of the expression
+$$f(x)>0 \mbox{\quad for\quad} x>1$$
+that we intended. Numerals and punctuation marks are set
+in normal roman type but \LaTeX\ will take care of the
+spacing around punctuation symbols, as in
+
+\moveright0.1\textwidth\vbox{%
+\footnotesize\begin{verbatim}
+$f(x,y) \geq 0$
+\end{verbatim}
+}
+\noindent which produces
+$$f(x,y) \geq 0\quad.$$
+
+\item Even a single letter can constitute a formula, as in
+``the constant $a$''. To type this you enter \verb@$a$@ in
+your source file. If you do not go in to maths mode to type
+the symbol, you'll get things like ``the constant a''.
+
+\item Some symbols have a different meaning when typed in maths
+mode. Not only do ordinary letters become variables, but symbols
+such as \verb@-@ and \verb@+@ are now interpreted as mathematical
+symbols. Thus in maths mode \verb@-@ is no longer considered
+a hyphen, but as a minus sign.
+
+\item \LaTeX\ ignores all spaces and carriage returns
+when in maths mode, without exception. So typing something
+like \verb@the constant$ a$@ will produce ``the constant$ a$''.
+You should have typed \verb@the constant $a$@. \LaTeX\
+is responsible for all spacing when in maths mode, and
+(as in paragraphing mode) you have to specially ask to have
+spacing changed. Even if \LaTeX\ does ignore all spaces
+when in maths mode you should (as always in \TeX) still employ
+spaces to keep your source file readable.
+\end{enumerate}
+
+The above means that, at least for most material, a typist need
+not understand the mathematics in order to typeset it correctly.
+And even if one does understand the mathematics, \LaTeX\ is there to
+make sure that you adhere to accepted typesetting conventions (whether
+you were aware of their existence or not).
+
+So one could type either
+
+\moveright0.1\textwidth\vbox{
+\footnotesize\begin{verbatim}
+$f(x, y) = 2 (x+ y)y/(5xy - 3 )$
+\end{verbatim}
+
+\noindent{\normalsize or}
+
+\begin{verbatim}
+$f(x,y) = 2(x+y)y / (5xy-3)$
+\end{verbatim}
+}
+\noindent and you'd still get the correct result
+$$f(x,y) = 2(x+y)y / (5xy-3)\quad.$$
+
+There are some places where this can go wrong. For instance,
+if we wish to speak of the $x$-$y$ plane then one has to know
+that it is an {\em endash\/} that is supposed to be placed between
+the $x$ and the $y$, not a minus sign (as \verb@$x-y$@ would produce).
+But typing \verb@$x--y$@ will produce $x--y$ since both dashes are
+interpreted as minus signs.
+To avoid speaking of the $x-y$ plane or the $x--y$ plane, we should type
+it as \verb@the $x$--$y$ plane@. We are fortunate that \LaTeX\
+can recognise and cope with by far the majority of our mathematical
+typesetting needs.
+
+Another thing to look out for is the use of braces in an expression.
+Typing
+
+\moveright0.1\textwidth\vbox{
+\footnotesize\begin{verbatim}
+${x : f(x)>0}$
+\end{verbatim}
+}
+\noindent will not produce any braces. This is because, as we well
+know, braces are reserved for delimiting groups in the input file.
+Looking back to section~\ref{sec:reserved}, we see how it should be done:
+
+\moveright0.1\textwidth\vbox{
+\footnotesize\begin{verbatim}
+$ \{ x: f(x)>0 \} $
+\end{verbatim}
+}
+
+Math shift commands also behave as scope delimiters, so that
+commands issued in an expression cannot affect anything else in
+a document.
+
+\section{Displaying a formula}\label{sec:display}
+\LaTeX\ considers an expression \verb@$ ... $@ to be word-like in the
+sense that it considers it to be eligible for splitting across lines
+of a paragraph (but without hyphenation, of course). \LaTeX\ assigns
+quite a high penalty to doing this, thus trying to avoid it (remember
+that \LaTeX\ tries to minimize the ``badness'' of a paragraph).
+When there is no other way, it will split the expression at a suitable place.
+But there are some expressions which are just too long to fit into the
+running text without looking awkward. These are best ``displayed'' on
+a line by themselves. Also, some expressions are sufficiently important
+that they should be made to stand out. These, too, should be displayed
+on a line of their own.
+
+The mechanism for displaying an expression is the {\em display math\/}
+mode, which is begun by typing \verb@$$@ and ended by typing the same
+sequence (which again means that we'd better be sure to type them in pairs).
+Corresponding to the alternatives \verb@\(@ and \verb@\)@ that we had
+for the math shift character \verb@$@, we may use \verb@\[@ and
+\verb@\]@ as the display-math shift sequences. One can also
+use the environment
+
+\moveright0.1\textwidth\vbox{%
+\footnotesize\begin{verbatim}
+\begin{displaymath} ... \end{displaymath}
+\end{verbatim}
+}
+\noindent which is equivalent to \verb@$$ ... $$@ and is suitable for
+use with long displayed expressions. If you wish \LaTeX\
+to number your equations for you you can use the environment
+
+\moveright0.1\textwidth\vbox{
+\footnotesize\begin{verbatim}
+\begin{equation} ... \end{equation}
+\end{verbatim}
+}
+\noindent which is the same as the \verb@displaymath@ environment, except that
+an equation number will be generated.
+
+It is poor style to have a displayed expression either begin a paragraph
+or be a paragraph by itself. This can be avoided if you agree to
+{\em never leave a blank line in your input file before a math display}.
+
+We will see later how to typeset an expression that is to span
+multiple lines. For now, let's look at an example of displaying
+an expression:
+
+\moveright0.1\textwidth\vbox{%
+\footnotesize\begin{verbatim}
+For each $a$ for which the Lebesgue-set $L_a(f) \neq \emptyset$ we define
+$$ % We could have used \begin{displaymath} here
+{\cal B}_a(f) = \{ L_{a+r}(f) : r > 0 \},
+$$ % and \end{displaymath} here
+and these are easily seen to be completely regular.
+\end{verbatim}}
+\noindent which produces
+
+\result{
+For each $a$ for which the Lebesgue-set $L_a(f) \neq \emptyset$ we define
+$$
+{\cal B}_a(f) = \{ L_{a+r}(f) : r > 0 \},
+$$
+and these are easily seen to be completely regular.
+}
+
+That illustrates how to display an expression, but also shows that
+we've got a lot more to learn about mathematical typesetting. Before
+we have a look at how to arrange symbols all over the show (e.g.\
+the subscripting above) we must learn how to access the multitude
+of symbols that are used in mathematical texts.
+
+\section{Using mathematical symbols}\label{sec:symbols}
+\LaTeX\ puts all the esoteric symbols of mathematics at
+our fingertips. They are all referenced by name, with the naming system
+being perfectly logical and systematic. None of the control words that
+access these symbols accepts an argument, but we'll soon see that
+some of them prepare \LaTeX\ for something that might follow. For instance,
+when you ask for the symbol `$\sum$' \LaTeX\ is warned that any sub- or
+superscripts that follow should be positioned appropriately as limits
+to a summation. In keeping
+with the \TeX\ spirit, none of this requires any additional work on your
+part.
+
+We'll also see that some of the symbols behave differently depending on
+where they are used. For instance, when I ask for $\sum_{i=1}^{n}a_i$ within
+the running text, the limits are places differently to when I ask
+for that expression to be displayed:
+$$\sum_{i=1}^{n}a_i\quad.$$
+Again, I typed nothing different here---just asked for display math mode.
+
+It is important to note that {\em almost all of the special maths symbols are
+unavailable in ordinary paragraphing mode}. If you need to use one there,
+then use an in-line math expression \verb@$...$@.
+
+\subsection{Symbols available from the keyboard}
+A small percentage of the available symbols can be obtained from just
+a single key press. They are $+$ $-$ $=$ $<$ $>$ $|$ $/$ $($ $)$
+$[$ $]$ and $*$. Note that these must be typed {\em within maths mode\/}
+to be interpreted as math symbols.
+
+Of course, all of $a$--$z$, $A$--$Z$, the numerals $0, 1, 2, \ldots, 9$ and
+the punctuation characters $,$ $;$ and $:$ are available directly from the keyboard.
+Alphabetic letters will be assumed to be variables that are to be
+italicised, unless told otherwise\footnote{See section \ref{sec:mathtext}}.
+The numerals receive no special attention, appearing precisely as in
+normal paragraphing mode. The punctuation symbols
+are still set in standard roman type when read in maths mode, but a little
+space is left after them so that expressions like $\{x_i : i=1,2,\ldots,10\}$
+look like they should. Note that this means that normal sentence punctuation
+should not migrate into an expression.
+
+\subsection{Greek letters}
+
+\newcommand{\ds}[1]{$\csname#1\endcsname$ & \tt\bs #1 }
+\newcommand{\dsf}[4]{\ds{#1}&\ds{#2}&\ds{#3}&\ds{#4}}
+\newcommand{\dst}[3]{\ds{#1}&\ds{#2}&\ds{#3}}
+
+Tables \ref{tab:lgreek} and \ref{tab:ugreek} show the control sequences that produce the
+letters of the Greek alphabet. We see that a lowercase Greek letter
+is simply is accessed by typing the control word of the same name
+as the symbol, using all lowercase letters. To obtain an uppercase
+Greek letter, simply capitalise the {\em first\/} letter of its name.
+
+Just as \verb@$mistake$@ produces $mistake$ because the letters
+are interpreted as variables, so too will \verb@$\tai \epsilon \chi$@
+produce the incorrectly spaced $\tau \epsilon \chi$ if you try to
+type greek words like this. \TeX\ can be taught to set Greek, but
+this is not the way. $\tau\!\epsilon\!\chi$, % and nor is this
+incidentally, is the Greek word for ``art'' and it is from the initials of the
+Greek letters constituting this word that the name \TeX\ was derived.
+\TeX\ is ``the art of typesetting''.
+
+\begin{table}[thbp]
+\centering\footnotesize
+\begin{tabular}{llllllll}
+\dsf{alpha}{beta}{gamma}{delta}\\
+\dsf{epsilon}{varepsilon}{zeta}{eta}\\
+\dsf{theta}{vartheta}{iota}{kappa}\\
+\dsf{lambda}{mu}{nu}{xi}\\
+\dsf{pi}{varpi}{rho}{varrho}\\
+\dsf{sigma}{varsigma}{tau}{upsilon}\\
+\dsf{phi}{varphi}{chi}{psi}\\
+\ds{omega}
+\end{tabular}
+\caption{\rm Lowercase Greek letters}
+\label{tab:lgreek}
+\end{table}
+
+\begin{table}[htbp]
+\centering\footnotesize
+\begin{tabular}{llllllll}
+\dsf{Gamma}{Delta}{Theta}{Lambda}\\
+\dsf{Xi}{Pi}{Sigma}{Upsilon}\\
+\dst{Phi}{Psi}{Omega}
+\end{tabular}
+\caption{\rm Uppercase Greek letters}
+\label{tab:ugreek}
+\end{table}
+
+\subsection{Calligraphic uppercase letters}
+The letters $\cal A, \ldots, \cal Z$ are available through use of the
+style changing command \verb@\cal@. This command behaves like
+the other style changing commands \verb@\em@, \verb@\it@, etc.\
+so its scope must be delimited as with them. Thus we can type
+
+\moveright0.1\textwidth\vbox{
+\footnotesize\begin{verbatim}
+... for the filter $\cal F$ we have $\varphi({\cal F}) = \cal G$.
+\end{verbatim}
+}
+\noindent to obtain
+
+\result{%
+for the filter $\cal F$ we have $\varphi({\cal F}) = \cal G$.
+}
+
+There is no need to tabulate all the calligraphic letters, since they
+are all obtained by just a type style changing command. We will just
+list them so that we can see, for reference purposes, what they all look like.
+Here they are:
+
+\newcommand{\calf}[5]{\cal{#1}\cal{#2}\cal{#3}\cal{#4}\cal{#5}}
+$$ % cos we're using AmSLaTeX, things have changed!
+\calf{A}{B}{C}{D}{E}\calf{F}{G}{H}{I}{J}\calf{K}{L}{M}{N}{O}
+\calf{P}{Q}{R}{S}{T}\calf{U}{V}{W}{X}{Y}\cal Z
+$$
+
+\subsection{Binary operators}
+\LaTeX\ has been taught to recognise binary operators and set the
+appropriate space either side of one---i.e., it sets the first
+argument followed by a little space, then the operator followed
+by the same little space and finally the second argument.
+Table~\ref{tab:binops} shows the binary operators that are available
+via \LaTeX\ control words (recall that the binary operators $+$,
+$-$, and $*$ can be typed from the keyboard). Here are some examples of their use:
+
+\begin{mathegs}
+\verb@$a+b$@ & $a+b$\\
+\verb@$(a+b) \ otimes c$@ & $(a+b)\otimes c$\\
+\verb@$(a \vee b) \wedge c$@ & $(a \vee b)\wedge c$\\
+\verb@$X - (A \cap B) = (X-A) \cup (X-B)$@ & $X - (A \cap B) = (X-A) \cup (X-B)$
+\end{mathegs}
+
+\begin{table}
+\centering\footnotesize
+\begin{tabular}{llllllll}
+\dsf{pm}{cap}{diamond}{oplus}\\
+\dsf{mp}{cup}{bigtriangleup}{ominus}\\
+\dsf{times}{uplus}{bigtriangledown}{otimes}\\
+\dsf{div}{sqcap}{triangleleft}{oslash}\\
+\dsf{ast}{sqcup}{triangleright}{odot}\\
+\dsf{star}{vee}{wedge}{bigcirc}\\
+\dsf{dagger}{setminus}{amalg}{circ}\\
+\dsf{ddagger}{cdot}{wr}{bullet}
+\end{tabular}
+\caption{\rm Binary Operation Symbols}
+\label{tab:binops}
+\end{table}
+
+\subsection{Binary relations}
+\LaTeX\ has been taught to recognize the use of binary relations, too.
+Table~\ref{tab:binrels} shows those available via \LaTeX\ control words.
+There are a few that you can obtain directly from the keyboard:
+$<$, $>$, $=$, and $|$.
+
+To negate a symbol you can precede the control word that gives the symbol
+by a \verb@\not@. Some symbols come with ready-made negations, which
+should be used above the \verb@\not@'ing method because the slope of the
+negating line is just slightly changed to look more pleasing.
+Thus \verb@\notin@ should be used above \verb@\not\in@, and
+\verb@\neq@ should be used above \verb@\not =@.
+
+If negating a symbol produces a slash whose horizontal positioning
+is not to your liking, then use the math spacing characters described
+in section~\ref{sec:mathspace} to adjust it.
+
+
+\begin{table}[htbp]
+\centering\footnotesize
+\begin{tabular}{llllllll}
+\dsf{leq}{geq}{equiv}{models}\\
+\dsf{prec}{succ}{sim}{perp}\\
+\dsf{preceq}{succeq}{simeq}{mid}\\
+\dsf{ll}{gg}{asymp}{parallel}\\
+\dsf{subset}{supset}{approx}{bowtie}\\
+\ds{subseteq} & \ds{supseteq}& \ds{cong} & $\bowtie$ & \tt\bs Join\\ % lazy?
+\dsf{sqsubset}{sqsupset}{neq}{smile}\\
+\dsf{sqsubseteq}{sqsupseteq}{doteq}{frown}\\
+\dst{in}{ni}{propto}\\
+\ds{vdash} & \ds{dashv}
+\end{tabular}
+\caption{\rm Binary relations}
+\label{tab:binrels}
+\end{table}
+
+\subsection{Miscellaneous symbols}
+Table~\ref{tab:miscsym} shows a number of general-purpose symbols.
+Remember that these are only available in maths mode. Note that
+\verb@\imath@ and \verb@\jmath@ should be used when you need to
+accent an $i$ or a~$j$ in maths mode\footnote{See section \ref{sec:mathacc}}%
+---you cannot use \verb@\i@ or \verb@\j@ that were available in
+paragraphing mode. To get a prime symbol, you can use \verb@\prime@
+or you can just type \verb@'@ when in maths mode, as in
+\verb@$f''(x)=x$@ which produces $f''(x)=x$.
+
+\begin{table}[htbp]
+\centering\footnotesize
+\begin{tabular}{llllllll}
+\dsf{aleph}{prime}{forall}{infty}\\
+\dsf{hbar}{emptyset}{exists}{Box}\\
+\dsf{imath}{nabla}{neg}{triangle}\\
+\dsf{jmath}{surd}{flat}{triangle}\\
+\dsf{ell}{top}{natural}{clubsuit}\\
+\dsf{wp}{bot}{sharp}{diamondsuit}\\
+\dsf{Re}{|}{backslash}{heartsuit}\\
+\dsf{Im}{angle}{partial}{spadesuit}\\
+\ds{mho}
+\end{tabular}
+\caption{\rm Miscellaneous symbols}
+\label{tab:miscsym}
+\end{table}
+
+\subsection{Arrow symbols}
+
+\LaTeX\ has a multitude of arrow symbols, which it will set the correct
+space around. Note that vertical arrows can all be used as
+delimiters---see section~\ref{sec:delims}. The available symbols
+are listed in table~\ref{tab:arrows}.
+
+\begin{table}[htbp]
+\centering\footnotesize
+\begin{tabular}{llllll}
+\dst{leftarrow}{longleftarrow}{uparrow}\\
+\dst{Leftarrow}{Longleftarrow}{Uparrow}\\
+\dst{rightarrow}{longrightarrow}{downarrow}\\
+\dst{Rightarrow}{Longrightarrow}{Downarrow}\\
+\dst{leftrightarrow}{longleftrightarrow}{updownarrow}\\
+\dst{Leftrightarrow}{Longleftrightarrow}{Updownarrow}\\
+\dst{mapsto}{longmapsto}{nearrow}\\
+\dst{hookleftarrow}{hookrightarrow}{searrow}\\
+\dst{leftharpoonup}{rightharpoonup}{swarrow}\\
+\dst{leftharpoondown}{rightharpoondown}{nwarrow}\\
+\ds{rightleftharpoons} & \ds{leadsto}
+\end{tabular}
+\caption{\rm Arrow symbols}
+\label{tab:arrows}
+\end{table}
+
+\subsection{Expression delimiters}\label{sec:delims}
+A pair of delimters often enclose an expression, as in
+$$
+\left[\begin{array}{cc}
+a_{11} & a_{12} \\
+a_{21} & a_{22}
+\end{array}\right]
+\mbox{\quad and\quad}
+f(x) = \left\{ \begin{array}{ll}
+x & \mbox{if } x < 1 \\
+x^2 & \mbox{if } x \geq 1
+\end{array}\right.
+\quad.$$
+\LaTeX\ will scale delimiters to the correct size (determined by what
+they enclose) for you, if you ask it to. There are times when you don't
+want a delimiter to be scaled, so it is left up to you to ask for
+scaling.
+
+To ask that a delimter be scaleable, you precede it by
+\verb@\left@ or \verb@\right@ according as it is the left or right
+member of the pair. Scaled delimiters must be balanced correctly.
+It sometimes occurs, as in the right-hand example above, that only
+one member of a delimiting pair is to be visible. For this purpose,
+use the commands \verb@\left.@ and \verb@\right.@ which will produce
+no visible delimiter but can be used to correctly balance the
+delimiters in an expression. For examples of the use of delimiters,
+see section~\ref{sec:arrays} where we learn about arrays.
+
+Table~\ref{tab:delims} shows the symbols that \LaTeX\ will
+recognise as delimiters, i.e.\ symbols that may follow
+a \verb@\left@ or a \verb@\right@. Note that you have to
+use \verb@\left\{@ and \verb@\right\}@ in order to get
+scaled braces.
+
+\begin{table}[htbp]
+\centering\footnotesize
+\begin{tabular}{llllll}
+$($ & \makebox[90pt][l]{(} & $)$ & \makebox[90pt][l]{)} & $\uparrow$ & \makebox[90pt][l]{\tt\bs uparrow}\\
+$[$ & ] & $]$ & ] & $\downarrow$ & \tt\bs downarrow\\
+$\{$ & \verb@\{@ & $\}$ & \verb@\}@ & $\updownarrow$ & \tt\bs updownarrow\\
+\dst{lfloor}{rfloor}{Uparrow}\\
+\dst{lceil}{rceil}{Downarrow}\\
+\dst{langle}{rangle}{Updownarrow}\\
+$/$ & / & \ds{backslash}\\
+$|$ & | & \ds{|}
+\end{tabular}
+\caption{\rm Delimiters}
+\label{tab:delims}
+\end{table}
+
+\subsection{Operators like $\displaystyle\int$ and $\displaystyle\sum$}
+These behave differently when used in display-math mode as
+compared with in-text math mode. When used in text, they
+will appear in their small form and any limits provided will
+be set so as to reduce the overall height of the operator,
+as in $\sum_{i=1}^{N}f_i$. When used in display-math mode, \LaTeX\
+will choose to use the larger form and will not try to
+reduce the height of the operator, as in
+$$
+\sum_{i=1}^{N} f_i \quad .
+$$
+
+Table~\ref{tab:bigops} describes what variable-size symbols are
+available, showing both the small (in text) and the large (displayed)
+form of each. In section~\ref{sec:subsup} we will learn how to
+place limits on these operators.
+
+\begin{table}[htbp]
+\centering\footnotesize
+\newcommand{\od}[1]{\makebox[27pt]{$\csname#1\endcsname\hfil\displaystyle\csname#1\endcsname$} & \tt\bs #1}
+\newcommand{\odt}[3]{\od{#1} & \od{#2} & \od{#3}}
+\begin{tabular}{ll@{\hspace{1.5cm}}ll@{\hspace{1.5cm}}ll}
+\odt{sum}{bigcap}{bigodot}\\
+\odt{prod}{bigcup}{bigotimes}\\
+\odt{coprod}{bigsqcup}{bigoplus}\\
+\odt{int}{bigvee}{biguplus}\\
+\od{oint} & \od{bigwedge}
+\end{tabular}
+\caption{\rm Variable-sized symbols}
+\label{tab:bigops}
+\end{table}
+
+\subsection{Accents}\label{sec:mathacc}
+The accenting commands that we learned for paragraphing mode do not
+apply in maths mode. Consult table~\ref{tab:mathacc} to see how
+to accent a symbol in maths mode (all the examples there accent
+the symbol $u$, but they work with any letter). Remember that $i$ and $j$
+should lose their dots when accented, so \verb@\imath@ and
+\verb@\jmath@ should be used.
+
+There also exist commands that give a ``wide hat'' or a
+``wide tilde'' to their argument, \verb@\widehat@ and
+\verb@\widetilde@.
+
+\begin{table}[htbp]
+\centering\footnotesize
+\newcommand{\da}[1]{$\csname#1\endcsname{u}$ & \tt\bs #1\{u\}}
+\newcommand{\daf}[4]{\da{#1} & \da{#2} & \da{#3} & \da{#4}}
+\begin{tabular}{llllllll}
+\daf{hat}{acute}{bar}{dot}\\
+\daf{check}{grave}{vec}{ddot}\\
+\da{breve} & \da{tilde}
+\end{tabular}
+\caption{\rm Math accents}
+\label{tab:mathacc}
+\end{table}
+
+\section{Some common mathematical structures}
+In this section we shall begin to learn how to manipulate
+all the symbols listed in section~\ref{sec:symbols}.
+Indeed, by the end of this section we'll be able to typeset
+some quite large expressions. In the section following
+this we will learn how use various alignment environments
+that allow us to prepare material like multi-line expressions
+and arrays.
+
+\subsection{Subscripts and superscripts}\label{sec:subsup}
+Specifying a sub- or superscript is as easy as you'd hope---%
+you just give an indication that you want a sub- or superscript
+to the last expression and provide the material to be
+placed there, and \LaTeX\ will position things correctly.
+So sub- and superscripting a single symbol, an operator, or a big
+array all involve the same input, and \LaTeX\ places the material
+according to what the expression is that is being sub- or superscripted:
+$$
+x^2\quad,\quad \prod_{i=1}^{N}X_i \quad,\quad
+\left[\begin{array}{ccc}
+a_{11} & a_{12} & a_{13}\\
+a_{21} & a_{22} & a_{23}\\
+a_{31} & a_{32} & a_{33}
+\end{array}\right]^2
+\quad.$$
+
+To tell \LaTeX\ that you want a single character set as a superscript
+to the last expression, you just type a \verb@^@ before it. The
+``last expression'' is the preceding group or, if there is no preceding
+group, the single character or symbol that the \verb@^@ follows:
+
+\begin{mathegs}
+\verb@$x^2$@ & $x^2$\\
+\verb@$a^b$@ & $a^b$\\
+\verb@$Y^X$@ & $Y^X$\\
+\verb@$\gamma^2$@ & $\gamma^2$\\
+\verb@$(A+B)^2$@ & $(A+B)^2$\\
+\verb@$\left[ \frac{x^2+1}{x^2 + y^2} \right]^n$@ & $\left[ \frac{x^2+1}{x^2 + y^2} \right]^n$
+\end{mathegs}
+
+Subscripts of a single character are equally easy---you just use
+the underscore character \verb@_@ where you used \verb@^@ for
+superscripting:
+
+\begin{mathegs}
+\verb@$x_2$@ & $x_2$\\
+\verb@$x_i$@ & $x_i$\\
+\verb@$\Gamma_1(x)$@ & $\Gamma_1(x)$
+\end{mathegs}
+
+%part 4 of 4
+Now let's see how to set a sub- or superscript that consists of more than
+just one character. This is no more difficult than before if we remember
+the following rule: {\em \verb@_@ and \verb@^@ set the group that
+follows them as a sub- and superscripts to the group that precedes
+the sub- and superscript symbols.} We see now now that our initial examples worked by considering a single
+character to be a group by itself. Here are some examples:
+
+\begin{mathegs}
+\verb@$a^2b^3$@ & $a^2b^3$\\
+\verb@$2^{21}$@ & $2^{21}$\\
+\verb@$2^21$@ & $2^21$\\
+\verb@$a^{x+1}$@ & $a^{x+1}$\\
+\verb@$a^{x^2+1}$@ & $a^{x^2+1}$\\
+\verb@$(x+1)^3$@ & $(x+1)^3$\\
+\verb@$\Gamma_{\alpha\beta\gamma}$@ & $\Gamma_{\alpha\beta\gamma}$\\
+\verb@${}_1A_2$@ & ${}_1A_2$\\
+\end{mathegs}
+
+In the very last example we see a case of setting a subscript to
+an empty group, which
+resulted in a kind of ``pre-subscript''. With some imagination this
+can be put to all sorts of uses.
+
+In all of the above examples the sub- and superscripts were set
+to single-character groups. Nowhere did we group an expression
+before sub- or superscripting it. Even in setting the expression
+$(x+1)^3$, the superscript ${}^3$ was really only set to the
+character $)$. If we had wanted to group the $(x+1)$ before
+setting the superscript, we would have typed \verb@${(x+1)}^3$@ which
+gives ${(x+1)}^3$, with the superscript slightly raised. One has
+to go to this trouble because, to most people, something like
+$(x^a)^b$ is just as acceptable and as readable as ${(x^a)}^b$.
+It also has the advantage of aligning the base lines in expressions
+such as
+$$
+(ab)^{-2} = [(ab)^{-1}]^2 = [b^{-1}a^{-1}]^2 = b^{-1}a^{-1}b^{-1}a^{-1}
+$$
+which looks more pleasing than if we use additional grouping to force
+$$
+{(ab)}^{-2} = {[{(ab)}^{-1}]}^2 = {[b^{-1}a^{-1}]}^2 = b^{-1}a^{-1}b^{-1}a^{-1}\quad,
+$$
+and the latter has rather more braces in it that require balancing.
+
+Here are some more examples, showing how \LaTeX\ will set things just as we
+want without any further work on our part:
+
+\begin{mathegs}
+\verb@$x^{y^z}$@ & $x^{y^z}$\\
+\verb@$2^{(2^2)}$@ & $2^{(2^2)}$\\
+\verb@$2^{2^{2^{\aleph_0}}}$@ & $2^{2^{2^{\aleph_0}}}$\\
+\verb@$\Gamma^{z_c^d}$@ & $\Gamma^{z_c^d}$
+\end{mathegs}
+
+We can also make use of empty groups in order to stagger sub- and
+superscripts to an expression, as in
+
+\moveright0.1\textwidth\vbox{
+\footnotesize\begin{verbatim}
+$\Gamma_{\alpha\beta}{}^{\gamma}{}_\delta$
+\end{verbatim}
+}
+\noindent which will yield
+
+\result{%
+$\Gamma_{\alpha\beta}{}^{\gamma}{}_\delta$
+}
+
+One can specify the sub- and superscripts to a group in any order,
+but it is best to be consistent. The most natural order seems to
+be to have subscripts first, but you may think otherwise.
+It is also a good idea to always include your sub- and superscripts
+in braces (i.e.\ make them a group), whether they consist of just
+a single character or not. This enhances readability and also helps
+avoid the unfortunate case where you believe that a particular control
+word gives a single symbol yet it really is defined in terms of several.
+
+\subsection{Primes}
+\LaTeX\ provides the control word \verb@\prime@ ($\prime$) for
+priming symbols. Note that it is not automatically at the superscript
+height, so that to get $f^\prime$ you would have to type
+
+\moveright0.1\textwidth\vbox{
+\footnotesize\begin{verbatim}
+$f^\prime$ .
+\end{verbatim}
+}
+\noindent To make lighter work of this, \LaTeX\ will interpret
+a right-quote character as a prime if used in maths mode.
+Thus we can type
+
+\moveright0.1\textwidth\vbox{
+\footnotesize\begin{verbatim}
+$f'(g(x)) g'(x) h''(x)$
+\end{verbatim}
+}
+\noindent in order to get
+
+\noindent
+
+\result{%
+$f'(g(x)) g'(x) h''(x)\quad.$
+}
+
+\subsection{Fractions}
+\LaTeX\ provides the \verb@\frac@ command that accepts two
+arguments: the numerator and the denominator (in that order).
+Before we look at examples of its use, let us just note that many simple
+in-text fractions are often better written in the form
+$\mbox{\it num} / \!\mbox{\it den}$, as with $3/8$ which can be typed
+as \verb@$3/8$@. This is also often the better form for
+a fraction that occurs {\em within\/} some expression.
+
+\begin{mathegs}
+\verb@$\frac{x+1}{x+2}$@ & $\displaystyle\frac{x+1}{x+2}$\\
+\verb@$\frac{1}{x^2+1}$@ & $\displaystyle\frac{1}{x^2+1}$\\
+\verb@$\frac{1+x^2}{x^2+y^2} + x^2 y$@ & $\displaystyle\frac{1+x^2}{x^2+y^2} + x^2 y$\\
+\verb@$\frac{1}{1 + \frac{x}{2}}$@ & $\displaystyle\frac{1}{1 + \frac{x}{2}}$\\
+\verb@$\frac{1}{1+x/2}$@ & $\displaystyle\frac{1}{1+x/2}$
+\end{mathegs}
+
+\subsection{Roots}
+The \verb@\sqrt@ command accepts two arguments. The first,
+and optional, argument specifies what order of root you desire
+if it is anything other than the square root. The second, and
+mandatory, argument specifies the expression that the root sign
+should enclose:
+
+{\renewcommand{\arraystretch}{1.6}
+\begin{mathegs}
+\verb@$\sqrt{a+b}$@ & $\displaystyle\sqrt{a+b}$\\
+\verb@$\sqrt[5]{a+b}$@ & $\displaystyle\sqrt[5]{a+b}$\\
+\verb@$\sqrt[n]{\frac{1+x}{1+x^2}}$@ & $\displaystyle\sqrt[n]{\frac{1+x}{1+x^2}}$\\
+\verb@$\frac{\sqrt{x+1}} {\sqrt[3]{x^3+1}}$@ & $\displaystyle\frac{\sqrt{x+1}} {\sqrt[3]{x^3+1}}$
+\end{mathegs}
+}
+
+\subsection{Ellipsis}
+Simply typing three periods in a row will not give the correct
+spacing of the periods if it is an ellipsis that is desired. So
+\LaTeX\ provides the commands \verb@\ldots@ and \verb@\cdots@.
+Centered ellipsis should be used between symbols like
+$+$, $-$, $*$, $\times$, and $=$. Here are some examples:
+
+\begin{mathegs}
+\verb@$a_1+ \cdots + a_n$@ & $a_1+ \cdots + a_n$\\
+\verb@$x_1 \times x_2 \times \cdots \times x_n$@ & $x_1 \times x_2 \times \cdots \times x_n$\\
+\verb@$v_1 = v_2 = \cdots = v_n = 0$@ & $v_1 = v_2 = \cdots = v_n = 0$\\
+\verb@$f(x_1,\ldots,x_n) = 0$@ & $f(x_1,\ldots,x_n) = 0$
+\end{mathegs}
+
+\subsection{Text within an expression}\label{sec:mathtext}
+One can use the \verb@\mbox@ command to insert normal text into
+an expression. This command forces \LaTeX\ temporarily out of
+maths mode, so that its argument will be treated as normal text.
+It's use is simple, but we must be wary on one count: remember that
+\LaTeX\ ignores all space characters when in maths mode; so to
+surround words in an expression that were placed by an
+\verb@\mbox@ command by space you must include the space
+in the \verb@\mbox@ argument.
+
+\begin{mathegs}
+\verb@$f_i(x) \leq 0 \mbox{ for } x \in I$@ & $f_i(x) \leq 0 \mbox{ for } x \in I$\\
+\verb@$\Gamma(n)=(n-1)! \mbox{ when $n$ is an integer}$@ & $\Gamma(n)=(n-1)! \mbox{ when $n$ is an integer}$
+\end{mathegs}
+
+In section~\ref{sec:mathspace} we'll learn of some special spacing commands
+that can be used in math mode. These are often very useful in positioning
+text within an expression, enhancing readability and logical layout.
+
+\subsection{Log-like functions}
+There are a number of function names and operation symbols that should
+be set in normal (roman) type in an expression, such as in
+$$
+f(\theta) = \sin\theta + \log(\theta+1) - \sinh(\theta^2+1)
+$$
+and
+$$
+\lim_{h \rightarrow 0} \frac{\sin h}{h} = 1\quad.
+$$
+
+We know that simply typing \verb@$log\theta$@ would produce the
+incorrect result
+$$
+log\theta
+$$
+and that using \verb@$\mbox{log}\theta$@ would leave us having to insert
+a little extra space between the log and the $\theta$
+$$
+\mbox{log}\theta\quad.
+$$
+So \LaTeX\ provides a collection of ``log-like functions'' defined
+as control sequences. Table~\ref{tab:loglike} shows those that are
+available. Here are some examples of their use:
+
+\begin{table}[tbp]
+{\centering\footnotesize\tt
+\begin{tabular}{llllllll}
+\bs arccos & \bs cos & \bs csc &\bs exp & \bs ker & \bs limsup & \bs min & \bs sinh\\
+\bs arcsin & \bs cosh & \bs deg & \bs gcd & \bs lg & \bs ln & \bs Pr & \bs sup\\
+\bs arctan & \bs cot & \bs det & \bs hom & \bs lim & \bs log & \bs sec & \bs tan\\
+\bs arg & \bs coth & \bs dim & \bs inf & \bs liminf & \bs max & \bs sin & \bs tanh
+\end{tabular}}
+\caption{\rm Log-like functions}
+\label{tab:loglike}
+\end{table}
+
+\begin{mathegs}
+\verb@$f(x)=\sin x + \log(x^2)$@ & $f(x)=\sin x + \log(x^2)$\\
+\verb@$\delta = \min \{ \delta_1, \delta_2 \}$@ & $\delta = \min \{ \delta_1, \delta_2 \}$\\
+\verb@$\chi(X) = \sup_{x\in X} \chi(x)$@ & $\chi(X) = \sup_{x\in X} \chi(x)$\\
+\verb@$\lim_{n \rightarrow \infty} S_n = \gamma$@ & $\lim_{n \rightarrow \infty} S_n = \gamma$
+\end{mathegs}
+
+Notice how \LaTeX\ does more than just set an operation like
+sup in roman type. It also knew where a subscript to that operator
+should go.
+
+\subsection{Over- and Underlining and bracing}
+The \verb@\underline@ command will place an unbroken line
+under its argument, and the \verb@\overline@ command will place
+an unbroken line over its argument. These two commands can also
+be used in normal paragraphing mode (but be careful: \LaTeX\ will
+not break the line within an under- or overlined phrase, so don't
+go operating on large phrases).
+
+You can place horizontal braces above or below an expression
+by making that expression the argument of \verb@\overbrace@
+or \verb@\underbrace@. You can place a label on an overbrace
+(resp.\ underbrace) by superscripting (resp.\ subscripting the
+group defined by the bracing command.
+
+\begin{mathegs}
+\verb@$\overline{a+bi} = a- bi$@ & $\overline{a+bi} = a- bi$\\
+\verb@$\overline{\overline{a+bi}} = a+bi$@ & $\overline{\overline{a+bi}} = a+bi$\\
+\end{mathegs}
+
+And some examples of horizontal bracing:
+
+\moveright0.1\textwidth\vbox{
+\footnotesize\begin{verbatim}
+$A^n=\overbrace{A \times A \times \ldots \times A}^{\mbox{$n$ terms}}$
+
+$\forall x \underbrace{\exists y (y \succ x)}_{\mbox{scope of $\forall$}}$
+\end{verbatim}
+}
+\noindent will produce
+$$A^n=\overbrace{A \times A \times \ldots \times A}^{\mbox{$n$ terms}}$$
+and
+$$\forall x \underbrace{\exists y (y \succ x)}_{\mbox{scope of $\forall$}}$$
+
+\subsection{Stacking symbols}
+\LaTeX\ allows you to set one symbol above another through the
+\verb@\stackrel@ command. This command accepts two arguments,
+and sets the first centrally above the second.
+
+\begin{mathegs}
+\verb@$X \stackrel{f^*}{\rightarrow}Y$@ & $X \stackrel{f^*}{\rightarrow}Y$\\
+\verb@$f(x) \stackrel{\triangle}{=} x^2 + 1$@ & $f(x) \stackrel{\triangle}{=} x^2 + 1$
+\end{mathegs}
+
+\subsection{Operators; Sums, Integrals, etc.}
+Each of the operation symbols in table~\ref{tab:bigops} can occur
+with limits. They are specified as sub- and superscripts to the
+operator, and \LaTeX\ will position them appropriately. In an in-text
+formula they will appear in more-or-less the usual scripting positions;
+but in a displayed formula they will be set below and above the
+symbol (which will also be a little larger). The following should
+give you an idea of how to use them:
+
+\begin{mathegs}
+\verb@$\sum_{i=1}^{N} a_i$@ & $\sum_{i=1}^{N} a_i$\\
+\verb@$\int_a^b f$@ & $\int_a^b f$\\
+\verb@$\oint_{\cal C}f(x)\,dx$@ & $\oint_{\cal C}f(x)\,dx$\\
+\verb@$\prod_{\alpha \in A} X_\alpha$@ & $\prod_{\alpha \in A} X_\alpha$\\
+\verb@$\lim_{N\rightarrow\infty}\sum_{i=1}^{N}f(x_i)\Delta x_i$@ & $\lim_{N\rightarrow\infty}\sum_{i=1}^{N}f(x_i)\Delta x_i$
+\end{mathegs}
+
+We'll have more to say about the use of \verb@\,@ in section~\ref{sec:mathspace}.
+Let's have a look at each of those expressions when displayed:
+
+$$
+\sum_{i=1}^{N} a_i\quad,\quad
+\int_a^b f\quad,\quad
+\oint_{\cal C}f(x)\,dx\quad,\quad
+\prod_{\alpha \in A} X_\alpha\quad,\quad
+\lim_{N\rightarrow\infty}\sum_{i=1}^{N}f(x_i)\Delta x_i
+$$
+
+\subsection{Arrays}\label{sec:arrays}
+
+The \verb@array@ environment is provided for typesetting arrays
+and array-like material. It accepts two arguments, one optional
+and one mandatory. The optional argument specifies the vertical
+alignment of the array---use \verb@t@, \verb@b@, or \verb@c@ to align
+the top, bottom, or centre of the array with the centreline of the
+line it occurs on (the default being \verb@c@). The second argument
+is as for the \verb@tabular@ environment: a series of \verb@l@,
+\verb@r@, and \verb@c@'s that specify the number of columns and the
+justification of these columns. The body of the \verb@array@ environment
+uses the same syntax as the \verb@tabular@ environment to specify
+the individual entries of the array.
+
+For instance the input
+
+\moveright0.1\textwidth\vbox{
+\footnotesize\begin{verbatim}
+... let $A = \begin{array}{rrr}
+12 & 3 & 4\\
+-2 & 1 & 0\\
+3 & 7 & 9
+\end{array}$ ...
+\end{verbatim}
+}
+\noindent will produce the output
+
+\result{%
+let $A = \left[\begin{array}{rrr}
+12 & 3 & 4\\
+-2 & 1 & 0\\
+3 & 7 & 9
+\end{array}\right]
+$}
+
+Note that we had to choose and supply the enclosing brackets
+ourselves (they are not placed for us so that we can use the
+\verb@array@ environment for array-like material; also,
+we get to choose what type of brackets we want this way).
+As in the \verb@tabular@ environment, the scope of a command
+given inside a matrix entry is restricted to that entry.
+
+We can use ellipsis within arrays as in the following example:
+
+\moveright0.1\textwidth\vbox{
+\footnotesize\begin{verbatim}
+\det A = \left| \begin{array}{cccc}
+a_{11} & a_{12} & \cdots & a_{1n}\\
+a_{21} & a_{22} & \cdots & a_{2n}\\
+\vdots & \vdots & \ddots & \vdots\\
+a_{m1} & a_{m2} & \cdots & a_{mn}
+\end{array} \right|
+\end{verbatim}
+}
+\noindent which produces
+
+\result{%
+$\det A = \left| \begin{array}{cccc}
+a_{11} & a_{12} & \cdots & a_{1n}\\
+a_{21} & a_{22} & \cdots & a_{2n}\\
+\vdots & \vdots & \ddots & \vdots\\
+a_{m1} & a_{m2} & \cdots & a_{mn}
+\end{array} \right|$
+}
+
+
+The \verb@array@ environment is often used to typeset material that
+is not, strictly speaking, an array:
+
+\moveright0.1\textwidth\vbox{
+\footnotesize\begin{verbatim}
+f(x) = \left\{ \begin{array}{ll}
+ x & \mbox{for $x<1$}\\
+x^2 & \mbox{for $x \geq 1$}
+\end{array} \right.
+\end{verbatim}
+}
+\noindent which will yield
+
+\result{%
+$f(x) = \left\{ \begin{array}{ll}
+ x & \mbox{for $x<1$}\\
+x^2 & \mbox{for $x \geq 1$}
+\end{array} \right.$
+}
+
+\subsection{Changes to spacing}\label{sec:mathspace}
+Sometimes \LaTeX\ needs a little help in spacing an expression,
+or perhaps you think that the default spacing needs adjusting.
+For these purposes we have the following spacing commands:\medskip
+
+\begin{tabular}{lllll}
+\verb@\,@ & thin space & & \verb@\:@ & medium space\\
+\verb@\!@ & negative thin space && \verb@\;@ & thick space\\
+\verb@\quad@ & a quad of space && \verb@\qquad@ & two quads of space
+\end{tabular}\medskip
+
+The spacing commands \verb@\,@, \verb@\quad@, and \verb@\qquad@ can
+be used in paragraphing mode, too. Here are some examples of these
+spacing commands used to make subtle modifications to some expressions.
+
+\begin{mathegs}
+\verb@$\sqrt{2} \, x$@ & $\sqrt{2} \, x$\\
+\verb@$\int_a^b f(x)\,dx$@ & $\int_a^b f(x)\,dx$\\
+\verb@$\Gamma_{\!2}$@ & $\Gamma_{\!2}$\\
+\verb@$\int_a^b \! \int_c^d f(x,y)\,dx\,dy$@ & $\int_a^b \! \int_c^d f(x,y)\,dx\,dy$\\
+\verb@$x / \! \sin x$@ & $x / \! \sin x$\\
+\verb@$\sqrt{\,\sin x}$@ & $\sqrt{\,\sin x}$
+\end{mathegs}
+
+\section{Alignment}
+Recall that the \verb@$equation$@
+environment can be used to display and automatically number a single-\
+line equation\footnote{See section \ref{sec:display}}.
+The \verb@eqnarray@ environment is used for displaying
+and automatically numbering either a single expression that spreads
+over several lines or multiple expressions, while taking care of
+alignment for us. The syntax is similar to that of the
+\verb@tabular@ and \verb@array@ environments, except that no argument
+is necessary to declare the number and justification of columns. The
+\verb@eqnarray*@ environment does this without numbering any equations.
+
+\moveright0.1\textwidth\vbox{
+\footnotesize\begin{verbatim}
+\begin{eqnarray}
+(a+b)(a+b) & = & a^2 + 2ab + b^2\\
+(a+b)(a-b) & = & a^2 - b^2
+\end{eqnarray}
+\end{verbatim}
+}
+\noindent will give
+
+\begin{eqnarray}
+(a+b)(a+b) & = & a^2 + 2ab + b^2\\
+(a+b)(a-b) & = & a^2 - b^2
+\end{eqnarray}
+
+See how we identify the columns so as to line the $=$ signs up.
+We can also leave entries empty, to obtain effect like the
+following:
+
+\vbox{
+\footnotesize\begin{verbatim}
+\begin{eqnarray*}
+\frac{d}{dx} \sin x & = & \lim_{h\rightarrow0}\frac{\sin(x+h)-\sin x}{h}\\
+& = & \lim_{h\rightarrow0}\frac{\sin x\cos h + \cos x\sinh - \sin x}{h}\\
+& = & \lim_{h\rightarrow0}\frac{\sin x(\cos h-1)}{h} + \cos x\frac{\sin h}{h}\\
+& = & \cos x
+\end{eqnarray*}
+\end{verbatim}
+}
+\noindent which produces
+
+\begin{eqnarray*}
+\frac{d}{dx} \sin x & = & \lim_{h\rightarrow0}\frac{\sin(x+h)-\sin x}{h}\\
+& = & \lim_{h\rightarrow0}\frac{\sin x\cos h + \cos x\sinh - \sin x}{h}\\
+& = & \lim_{h\rightarrow0}\left\{\frac{\sin x(\cos h-1)}{h} + \cos x\frac{\sin h}{h}\right\}\\
+& = & \cos x
+\end{eqnarray*}
+
+\section{Theorems, Propositions, Lemmas, $\ldots$}
+Suppose you document contains four kinds of theorem-like structures:
+``theorems'', ``propositions'', ``conjectures'', and ``wild guesses''.
+Then near the beginning of the document you should have something
+like the following:
+
+\moveright0.1\textwidth\vbox{
+\footnotesize\begin{verbatim}
+\newtheorem{thm}{Theorem}
+\newtheorem{prop}{Proposition}
+\newtheorm{conjec}{Conjecture}
+\newtheorem{wildshot}{Hypothesis} % make it sound good!
+\end{verbatim}
+}
+
+\newtheorem{thm}{Theorem}
+\newtheorem{prop}{Proposition}
+\newtheorem{conjec}{Conjecture}
+\newtheorem{wildshot}{Hypothesis}
+
+The first argument to \verb@\newtheorem@ defines a new
+theorem-like environment name of your own choosing. The second argument
+contains the text that you want inserted when your theorem is
+proclaimed:
+
+\moveright0.1\textwidth\vbox{
+\footnotesize\begin{verbatim}
+\begin{thm} $X$ is normal if, and only if, each pair of disjoint
+closed sets in $X$ is completely separated.
+\end{thm}
+
+\begin{wildshot} % remember, we chose the name 'wildshot'
+The property of Moore extends to all objects of the class $\Sigma$.
+\end{wildshot}
+\end{verbatim}
+}
+\noindent which will produce the following:
+
+\begin{thm} $X$ is normal if, and only if, each pair of disjoint
+closed sets in $X$ is completely separated.
+\end{thm}
+
+\begin{wildshot}
+The property of Moore extends to all objects of the class $\Sigma$.
+\end{wildshot}
+
+Notice that \LaTeX\ italicises the theorem statement, and that you
+still have to shift in to maths mode when you want to set symbols
+and expression. Typically, it is the style file that determines
+what a theorem will appear like---so don't go changing this if
+you are preparing for submission for publication (because the journal
+staff want to substitute their production style for your document style
+choice, and not be over-ridden by other commands).
+
+\section{Where to from here?}
+We have covered a good deal of \LaTeX's mathematical abilities,
+albeit rather superficial coverage here and there. There is
+much that has been impressive, but there is clearly a lot more
+to {\TeX}nical typesetting than we have covered here---it is
+not difficult to think of an expression that we don't yet know
+how to typeset. Also, there are places where \LaTeX\ is a
+little weak and it leaves us to do somewhat more work than
+the spirit of \TeX\ would suggest.
+
+Of course, we cannot criticise \LaTeX\ until we know its full
+capability. So the first place to go from here is the
+{\em\LaTeX\ User's Guide \& Reference Manual}. Particularly, the
+command reference guide in Appendix C of that book is an
+invaluable source of \LaTeX\ information that few can afford to
+do without. With good knowledge of the \LaTeX\ environments and their
+options (and we've left out many here) one can accomplish a good
+deal of most typesetting problems. A little imagination (say
+putting an environment to a slightly non-standard use) can often
+solve more difficult problems. Lastly, of course, much of
+raw \TeX\ still sits underneath \LaTeX\ and so it is true to say that
+you can do {\em anything\/} with \LaTeX---but you may need some
+divine inspiration from time to time (ask your local \TeX\ guru).
+
+In the next chapter we will look, very briefly, at a number of
+\LaTeX\ commands that we have not yet considered. Nothing
+exciting on the mathematical front, but there is some other
+important material (e.g.\ cross-referencing and page-sizing).
+For now, let's look at the ``way forward'' with respect to
+mathematical typesetting.
+
+\section{\AmSLaTeX}
+Back in the introduction we said that \AmSLaTeX\ was just a big
+macro package, the result of a marriage of \LaTeX\ and \AmSTeX\
+designed to endow the powerful general-purpose \LaTeX\ package with the
+mathematical prowess of \AmSTeX\ without compromising the \LaTeX\ syntax.
+Most of that is true, except that \AmSLaTeX\ is really just
+a document-style option (like \verb@12pt@) that can be used within
+a ``tweaked \LaTeX''. The most visible part of this tweak is the
+{\em new font selection scheme of Mittelbach and Sch\"{o}pf},
+discussed more fully in the next chapter. Almost every
+\LaTeX\ command and environment survived the transition to \AmSLaTeX, the
+exceptions being those that were considered redundant or under-used (space
+is at a premium with such a big package).
+The tweaked \LaTeX\ package is therefore able to deal with practically
+every existing \LaTeX\ document, giving just a few (often pleasant)
+surprises.
+
+With the \verb@amstex@ style option, one can just start a \LaTeX\
+document with
+
+\moveright0.1\textwidth\vbox{
+\footnotesize\begin{verbatim}
+\documentstyle[amstex]{article} % or report, book, etc
+\end{verbatim}
+}
+\noindent to gain access to the {\TeX}nical excellence of the
+AMS technical staff. It is not necessary to have read
+{\em The Joy of \TeX} (the \AmSTeX\ reference guide) to
+be able to use the \verb@amstex@ option, for \AmSLaTeX\
+comes with its own reference guide. Even so,
+{\em The Joy of TeX\/} is still highly recommended reading.
+The syntax of \AmSTeX\ has been changed to that of \LaTeX,
+but one can perform that transformation as you read ``{\em Joy\/}''
+and still learn much of the art of technical typesetting. Nowhere
+else will you find so comprehensive a coverage of the conventions
+and pitfalls of mathematical typesetting. In addition, {\em Joy\/}
+lists all the extra symbols that are available through the
+\verb@amstex@ option (if you thought \LaTeX\ had a fair selection
+of esoteric symbols, just wait 'til you see those!) and provides
+in-depth accounts where the \AmSLaTeX\ documentation is brief.
+
+Just as \AmSTeX\ comes with the AMS preprint style
+(\verb@amsppt@), \AmSLaTeX\ comes with a specialist style file for
+preparation of articles with \AmSLaTeX\ for submission to journals:
+\verb@amsart@. The \AmSLaTeX\ User's Guide is quite short and very
+terse in its explanations (assuming you to be competent in \LaTeX),
+but is supplemented by a large body of examples and a comprehensive
+sample article that is a showcase of the abilities of the \verb@amsart@
+style. You must read both these documents to really
+learn \AmSLaTeX. The AMS also distributes a guide to authors
+who wish to submit using \AmSLaTeX, and this is a must-read once
+you are familiar with some of \AmSLaTeX.
+
+\end{document}