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From: Norbert Preining <norbert@preining.info>
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+\title{Maths in \LaTeX: Part~4, Numbered and Unnumbered Things}
+\author[R.~A.~Bailey]{R.~A.~Bailey\\
+Queen Mary and Westfield College, \\University of London}
+\newenvironment{oneoff}[1]{\equation%
+               \addtocounter{equation}{-1}%
+                \renewcommand{\theequation}{\mbox{#1}}}%
+              {\endequation}
+%%%
+\newcommand{\writer}[1]{{\sc #1}:}
+\newcommand{\book}[1]{{\it #1},}
+\newcommand{\publish}[2]{{\rm #1, #2,}}
+\newcommand{\byear}[1]{{\rm (#1).}}
+\newtheorem{preqn}{Exercise}
+\newenvironment{qn}{\begin{preqn}\normalfont\rm}{\end{preqn}}
+\newcommand{\latexword}[1]{{\normalfont\tt #1}}
+%%% and the above should be in typewriter-ordinary IRRESPECTIVE of the
+%%% surrounding fonts
+%%%
+%%%
+%%% editor: I have been as generic as I can, but of course you can't
+%%% put \verb inside a \newcommand. I have consistently used + as the
+%%% delimiter for \verb, except when I needed the + in Maths!
+%%%
+\newcommand{\lamport}{{\it \LaTeX: A Document Preparation System\/} by Leslie 
+Lamport}
+\newcommand{\shortlamp}{{\it The Manual}}
+%%%
+\let\torl\AllTeX
+%%% editor, can you do a better macro for the above?
+%%%
+\newcommand{\littlehead}[1]{\textit{#1}}
+\begin{Article}
+\section*{Recall}
+This is the fourth in a sequence of tutorials on typesetting Mathematics in 
+\LaTeX. The first three appeared in issues~4.4, 4.5 and~5.1 of \BV. The series
+includes some things which can be found in \cite{leslie}, but I am 
+working in more things which, while straightforward and necessary for 
+Mathematical work, are  not in \cite{leslie} or \cite{newleslie}. In this 
+tutorial I concentrate not on Mathematical formulae but on things like 
+equations and theorems which Mathematicians like to display in special ways and
+to number (or not).
+
+In case you missed the first three
+tutorials, I remind you that
+I expect you, the reader, to do some work. Every so 
+often comes a group of exercises, which you are supposed to do. Use \LaTeX\ to 
+typeset everything in the exercise except sentences in italics, which are 
+instructions. If you are not satisfied that you can do the exercise, then tell 
+me. Either write
+to me 
+at
+\begin{verse}
+School of Mathematical Sciences\\
+Queen Mary and Westfield College\\
+Mile End Road\\
+London E1 4NS
+\end{verse}
+with hard copy of your input and output, 
+or email me at \mbox{\tt r.a.bailey@qmw.ac.uk}
+with a copy of the 
+smallest possible piece of \LaTeX\ input file that contains your
+attempt at the answer.
+In either case
+I will include a solution in the following issue of \BV: you will remain 
+anonymous if you wish.
+
+
+\section*{Answers}
+I promised to answer all questions arising from this series of articles (as far
+as I can).
+
+\subsection*{Size of parentheses}
+Charles M.~Goldie asks why I put $(t^{g^{-1}})v$ in Exercise~26 instead of 
+using \verb+\bigl(+ and \verb+\bigr)+ to make the parentheses larger than 
+what they enclose.
+%\[\bigl(t^{g^{-1}}\bigr)\]
+%\[\Bigl(t^{g^{-1}}\Bigr)\]
+The answer is that you would need \verb+\Bigl(+ and \verb+\Bigr)+ to make them 
+large enough in this case: I should have used
+\verb+\left+ and \verb+\right+ (see 
+Part~2 of this series) but I was lazy.
+
+Both he and Charles Leedham-Green have asked why I permit, or 
+even encourage, deeply nested parentheses, as in
+\begin{equation}
+u(P((1 - \varepsilon)z)),  
+\label{goldie}
+\end{equation}
+without using commands like \verb+\bigl(+ to make some of the outer
+parentheses somewhat larger. In Chapter~17 of \cite{dek}, Knuth
+advises that authors should use \verb+\bigl+ and its relatives to
+specify the size of parentheses and other expandable fences, to
+improve the readability of their formulae. However, I have
+deliberately avoided telling people about these commands.
+
+I have two reasons for ignoring Knuth's advice. The first is that I
+regard \LaTeX\ primarily as a system for {\em authors}, not for
+typesetters. Authors should not be stopping to worry about the size of
+parentheses, particularly if the level of nesting may change in a
+later version of the document. Conventions on size of fence should be
+a matter for the style designer, not the author. If someone can write
+a style file that automatically detects the level of nesting and
+adjusts the size accordingly, well and good. I have no objection to
+using such a style file; I do object to interrupting my Mathematical
+thoughts to fret over niceties of sizing.
+
+My second reason is related to the first. Journal editors and
+executive editors tend to have policies about the size of fences, and
+they will impose these policies whatever we as authors do. So it is
+generally a {\em complete waste of time\/} for authors to use
+\verb+\Bigr+ and the like, or for referees to insist on them.
+
+This is not to say that I disapprove of \verb+\left+ and
+\verb+\right+.  These commands automatically adjust the size of the
+fence to fit what is inside it. Adding, say, an extra item inside a
+\verb+\left( ... \right)+ does not cause the author to rethink the
+size of the parentheses. In fact, in my \mbox{basic} style file I have
+macros such as \verb+\probab+, \verb+\setof+ and \verb+\card+ which
+use \verb+\left+ and \verb+\right+ precisely so that I can type as I
+think, {\em the set of \ldots\/} rather than {\em squiggly brackets,
+  now what size and how much space?} (Oh, all right:
+\begin{verbatim}
+   \newcommand{\card}[1]{\left|#1\right|}
+\end{verbatim}
+---you can guess the others.)
+In fact, \verb+\left+ and \verb+\right+ make no difference to the formula 
+in~(\ref{goldie}), so neither of my questioners will be satisfied by my answer.
+
+\subsection*{Interchangeability of parentheses, brackets and braces}
+Charles M.~Goldie also asks if I have an opinion about whether nested
+parentheses should be routinely replaced so that one uses the sequence
+$\{[( \ldots )]\}$, which is demanded by some journals. I do have an
+opinion, quite a strong one, probably because one of the journals in
+which I publish most frequently insists on the sequence $[\{( \ldots
+)\}]$ and shows surprise (or the executive editor does) each time that
+I explain that I am using $\{ \ldots \}$ to denote a {\em set}. My
+opinion has been admirably expressed by Ellen Swanson in her bible of
+Mathematical typesetting~\cite{swan}:
+\begin{quote}
+  Often, however, the author of research mathematics attaches a
+  special meaning to different types of enclosures, and this author
+  believes that they {\it should be left in whatever order and variety
+    the author has indicated in the manuscript.}
+\end{quote}
+(her italics).
+
+\addtocounter{section}{4}
+\section{Numbered and Unnumbered Displays}
+\subsection{Unnumbered Maths displays}
+Use \verb+\[+ and \verb+\]+ for an unnumbered single line of displayed
+Maths: see Part~1. If you have two or more lines of displayed Maths
+that must be vertically aligned then you need one of the
+\latexword{array} environments. I shall deal with them in the final
+tutorial in this series.
+
+\subsection{Unnumbered word displays}
+Sometimes what you want to display is not simply a formula but a
+verbal condition that may or may not involve short pieces of notation.
+For example:
+\begin{quote}
+each basis vector~$f$ in~$V_{T,B}$ is orthogonal to every basis vector 
+in~$V_{B,T}$ except $f\psi$.
+\end{quote}
+If this will fit on a single line then you can use
+\verb+\[\mbox{...}\]+, but this is not very satisfactory because you
+have to stop and think how long it is and it is subject to changes in
+the line width. I find that the \latexword{quote} environment works
+well for such displays.
+
+\subsection{Numbered Maths displays}
+Use the \latexword{equation} environment for a numbered single line of
+displayed Maths such as (\ref{goldie}) in the `Answers' section above.
+If you have two or more consecutive equations or formulae that do not
+need to be vertically aligned, simply use one \latexword{equation}
+environment per line. For vertical alignment, wait until the tutorial
+on arrays.
+
+If you put a \verb+\label+ within an \latexword{equation} you can painlessly 
+refer back (or forward) to that equation.
+\begin{verbatim}
+   For contrasts, we put
+   \begin{equation}
+   W_T = V_T \cap V_0^\perp
+   \label{contrasts}
+   \end{equation}
+   The space~$W_T$ was defined 
+   in Equation~(\ref{contrasts}).
+\end{verbatim}
+\begin{quote}
+  For contrasts, we put
+\begin{equation}
+W_T = V_T \cap V_0^\perp
+\label{contrasts}
+\end{equation}
+The space~$W_T$ was defined in Equation~(\ref{contrasts}).
+\end{quote}
+
+\subsection{Numbered word displays}
+Sometimes word displays also need to be numbered for reference.
+\LaTeX\ does not directly provide an environment for this, but I find
+that the following works quite well.
+\begin{verbatim}
+   There is a bijection ...
+   \begin{equation}
+   \begin{minipage}[t]{0.8\linewidth}
+   each basis vector~$f$ ...
+   \end{minipage}
+   \end{equation}
+   Using ...
+\end{verbatim}
+\begin{quote}
+   There is a bijection~$\psi$ between the bases which satisfies:
+   \begin{equation}
+   \begin{minipage}[t]{0.8\linewidth}
+   each basis vector~$f$ in~$V_{T,B}$ is orthogonal to every basis vector 
+   in~$V_{B,T}$ except $f\psi$.
+   \end{minipage}
+   \end{equation}
+   Using~$\psi$, we can show that \ldots
+\end{quote}
+These displays are numbered in the same sequence as the
+\latexword{equation}s, and can be labelled and referred to in just the
+same way.  Note that I have made no attempt to make the indentation
+the same as that in \latexword{quote}.
+
+You can suppress the \verb+[t]+ if you want the number to be
+vertically centred on the display. You can replace 0.8 by any
+reasonable fraction. There is a catch, however: if you have numbered
+word displays labelled (9) and~(10) you may find that the second one
+comes out shifted to the left, to allow space for the wider label.
+Whether or not this happens depends on the settings of other
+parameters, such as \verb+\linewidth+. With the default width for A4
+paper in 10pt in \LaTeXe, I found that I had to decrease 0.8 to 0.75
+in order to have satisfactory word displays numbered (9) and~(10).
+
+Of course, if you have two or more such displays you should make an
+environment for them. I do it as follows.
+\begin{verbatim}
+   \newenvironment{condition}%
+    {\equation%
+     \begin{minipage}[t]{0.8\linewidth}}%
+    {\end{minipage}\endequation}
+\end{verbatim}
+You may wonder why I have used \verb+\equation+ and
+\verb+\endequation+ in the definition instead of
+\verb+\begin{equation}+ and \verb+\end{equation}+. This is because of
+the clever things that \LaTeX\ does with spaces before and after
+displayed material. When you type the line
+\begin{verbatim}
+   \end{equation}
+\end{verbatim}
+\LaTeX\ ignores the spaces on the rest of the line; if you type the line
+\begin{verbatim}
+   \end{condition}
+\end{verbatim}
+and the final part of the \latexword{condition} environment is
+\verb+\end{equation}+ then this forgetfulness about spaces is not
+passed through to \verb+\end{condition}+. Use of the more primitive
+\verb+\equation+ and \verb+\endequation+ does pass on the
+forgetfulness.
+
+\subsection{Numbering equations within sections}
+By default, \latexword{equation}s are numbered~1, 2, \ldots\ right
+through the document in the \latexword{article} class. To make them
+numbered within sections you need
+\begin{verbatim}
+   \renewcommand{\theequation}%
+     {\thesection.\arabic{equation}}
+\end{verbatim}
+Then the first equation in Section~1 will be numbered~1.1, the
+next~1.2, and so on. However, if there are four equations in
+Section~1, then the first equation in Section~2 will be numbered~2.5
+because the \latexword{equation} counter has not been reset at the
+start of the new section. To correct this, you also need
+\begin{verbatim}
+   \@addtoreset{equation}{section}
+\end{verbatim}
+Because of the \verb+@+~sign in this command, you must either place it
+in a style file or make sure that it comes between the commands
+\verb+\makeatletter+ and \verb+\makeatother+ in the preamble to the
+document.
+
+\subsection{One-off numbering of equations}
+Occasionally you want to number an equation not in the main sequence
+but by a particular symbol, such as ($*$) or (1.1$'$). Use the
+following \latexword{oneoff} environment in place of
+\latexword{equation}, putting the desired symbol as the single
+parameter.
+\begin{verbatim}
+\newenvironment{oneoff}[1]{\equation%
+  \addtocounter{equation}{-1}%
+  \renewcommand{\theequation}{\mbox{#1}}}%
+  {\endequation}
+\end{verbatim}
+For example,
+\begin{verbatim}
+   \begin{oneoff}{$*$}
+   a(p_i,q) - a(p_j,q) = 0 \bmod s
+   \end{oneoff}
+\end{verbatim}
+\begin{quote}
+   \begin{oneoff}{$*$}
+   a(p_i,q) - a(p_j,q) = 0 \bmod s
+   \end{oneoff}
+\end{quote}
+(See \cite[page~92]{leslie} or \cite[pages~98--99]{newleslie} for how these 
+counter commands work.)
+Note that automatic cross-referencing does not work for such equations.
+
+If you want a one-off equation numbered~1.1$'$ related to
+Equation~(1.1) then give the latter a label (say, \latexword{rowsum})
+and then do
+\begin{verbatim}
+   \begin{oneoff}{\ref{rowsum}$'$} ...
+\end{verbatim}
+
+\subsection{Subsequences of equations}
+Suppose that between Equations~(5) and~(7) you want a sequence of
+equations numbered~(6a), (6b) etc. Put the following in the preamble
+to the document (or in the style file).
+\begin{verbatim}
+\newsavebox{\saveeqn}
+\newcounter{subeqnno}
+\renewcommand{\thesubeqnno}{\alph{subeqnno}}
+\newenvironment{subequations}%
+    {\refstepcounter{equation}%
+     \savebox{\saveeqn}{\theequation}%
+     \setcounter{subeqnno}{0}}%
+    {}
+\newenvironment{subeqn}%
+    {\refstepcounter{subeqnno}%
+     \oneoff{\usebox{\saveeqn}\thesubeqnno}}%
+    {\endoneoff}
+\end{verbatim}
+(See \cite[page~101]{leslie} or \cite[pages107--108]{newleslie} for
+details of \verb+\savebox+.)  Then use \latexword{subeqn} in place of
+\latexword{equation} for each of the equations~(6a), (6b) etc., and
+place the whole sub\-sequence in the \latexword{subequations}
+environment.
+
+Automatic cross-referencing doesn't work for these either. The reason
+is that in constructing \latexword{oneoff} and \latexword{subeqn} I
+have {\em used\/} the \latexword{equation} environment rather than
+{\em mimicking\/} it, with the result that any \verb+\label+ picks up
+the \latexword{equation} counter. To do this properly you would have
+to copy out the \latexword{equation} part of \latexword{latex.tex}
+(which is well documented) and hack it (for 2.09ers; of course,
+\LaTeXe\ persons would have to hack part of \latexword{ltmath.dtx} and
+\latexword{classes.dtx}, which some would argue are even better
+documented). I have never needed this construct often enough to bother
+to do it properly, but I am sure that it could be done.
+
+\section*{Exercises}
+\addtocounter{preqn}{47}
+\begin{qn}
+\it Make  a numbered displayed equation saying
+\[
+t\left(vP_g\right) = \left(t^{g^{-1}}\right)v
+\]
+and a sentence which refers to it.
+\end{qn}
+
+
+\begin{qn}
+\it Make an unnumbered word display saying
+\begin{quote}
+\rm There is a natural surjective homomorphism $\phi\colon G \to G/N$ with 
+$\ker(\phi) \simeq \mathop{\rm Im}(\phi)$.
+\end{quote}
+\end{qn}
+
+\begin{qn}
+\it
+Make  a displayed numbered verbal condition saying
+\begin{quote}
+\rm
+for all $A$, $B$, $C$ in $\cal P$: if $A\prec B$ and $B\prec C$ then $A\prec 
+C$; and if $A  \preceq B$ and $B\preceq A$ then $A=B$.
+\end{quote}
+Then add a sentence which refers to it.
+\end{qn}
+
+\section{Theorems and their friends}
+\subsection{Basics}
+To make a new environment called \latexword{thm} for theorems, do
+\begin{verbatim}
+   \newtheorem{thm}{Theorem}
+\end{verbatim}
+  \newtheorem{thm}{Theorem} This sets up the environment, which is
+  then used as follows.
+\begin{verbatim}
+   \begin{thm}
+   The kernel of a homomorphism 
+   is a congruence.
+   \label{basic} 
+   \end{thm}
+   In Theorem~\ref{basic} we ... 
+\end{verbatim}
+\begin{quote}
+  \begin{thm}
+  The kernel of a homomorphism is a congruence.
+  \label{basic} 
+  \end{thm}
+  In Theorem~\ref{basic} we \ldots
+\end{quote}
+The theorems are all given the heading `Theorem'. They are numbered 
+automatically, and may be cross-referred to in the usual way.
+
+For clarity in the rest of this section, I shall call the item like
+\latexword{thm} the {\em theorem environment}, the item like
+\latexword{Theorem} the {\em theorem name}, the text like `Theorem~1'
+the {\em theorem head}, and the text like `The kernel of \ldots' the
+{\em theorem body}.
+
+Note that there is nothing to prevent two different theorem
+environments having the same theorem name. Indeed, the theorem name
+can be empty.
+
+By default, the theorem head is in bold and the theorem body is in
+italics. The theorems are numbered in arabic numbers, in a single
+sequence throughout the document (in the \latexword{article} class).
+All of these defaults can be changed, as I show below.
+
+It may not be obvious to the novice user, but there is more to an
+environment created with \verb+\newtheorem+ than special layout and
+automatic numbering.  The spacing before and after each theorem
+environment is controlled, and penalties are set so that no page break
+will come after the first line of a theorem environment unless there
+is a natural break-point in the text.
+
+Unfortunately, there is a bug (oops, feature) in \LaTeX\ which means
+that if you put \verb+\label{...}+ immediately after
+\verb+\begin{thm}+ you spoil this page-breaking penalty. But the
+\verb+\label+ should be somewhere easy to find, so I always play safe
+and put it immediately before \verb+\end{thm}+.
+
+\subsection{Named theorems}
+If you have a theorem environment \latexword{thm} then you can use an optional 
+argument to \latexword{thm} to obtain a named theorem. For example,
+\begin{verbatim}
+   \begin{thm}[The Central Limit Theorem]
+   If $X_1$, ...
+\end{verbatim}
+\begin{quote}
+  \begin{thm}[The Central Limit Theorem]
+  If $X_1$, $X_2$, \ldots, $X_n$ are independent \ldots
+  \end{thm}
+\end{quote}
+or 
+\begin{verbatim}
+   \begin{thm}[Galois, 1832]
+\end{verbatim}
+\begin{quote}
+  \begin{thm}[Galois, 1832]
+  If $L:K$ is a finite normal \ldots
+  \end{thm}
+\end{quote}
+
+\subsection{Sequences of numbering}
+Two optional arguments to \verb+\newtheorem+ give you control of which
+theorem environments are numbered in which sequences. Although it is
+logical to number theorems, lemmas, corollaries etc.\ all in their own
+sequences, it is much easier to find your way around a long document
+if they are all in a single sequence. To get a theorem environment
+\latexword{lem} numbered in the same sequence as \latexword{thm}, do
+\begin{verbatim}
+   \newtheorem{lem}[thm]{Lemma}
+\end{verbatim}
+  \newtheorem{lem}[thm]{Lemma}
+After the theorems we have had so far, if we now do
+\begin{verbatim}
+   \begin{lem}
+   With the above notation ...
+   \end{lem}
+\end{verbatim}
+we get
+\begin{quote}
+  \begin{lem}
+  With the above notation \ldots
+   \end{lem}
+\end{quote}
+
+
+The other optional argument numbers the theorem environment inside something 
+else. If you want the second example in Section~3 to be numbered~3.2 
+irrespective of how many examples there were in previous sections, then do
+\begin{verbatim}
+   \newtheorem{eg}{Example}[section]
+\end{verbatim}
+You can use at most one optional argument with each \verb+\newtheorem+
+command.
+
+You can even number one theorem environment inside another: for
+example
+\begin{verbatim}
+   \newtheorem{cor}{Corollary}[thm]
+\end{verbatim}
+if you want the corollaries after Theorem~10 to be Corollary~10.1, 
+Corollary~10.2, etc. Be careful not to create a circle of environments numbered
+within each other.
+
+\subsection{Unnumbered environments}
+There are several items, such as definitions, remarks and notation,
+that clearly should be theorem-like environments except that they
+should not be numbered. It would be possible to set them all up and
+then separately adjust the counter on each one so that it is not
+numbered. However, it is easier to take advantage of the
+number-in-the-same-sequence option. Set up a single unnumbered counter
+with
+\begin{verbatim}
+   \newcounter{unnumber}
+   \renewcommand{\theunnumber}{}
+\end{verbatim}
+and then put the other unnumbered theorem environments in the same sequence 
+with
+\begin{verbatim}
+   \newtheorem{rem}[unnumber]{Remark}
+   \newtheorem{def}[unnumber]{Definition}
+\end{verbatim}
+
+
+\subsection{Other systems of numbering}
+Many Mathematicians want the possibility of having Theorem~A, Theorem~B etc.\ 
+as well as Theorem~1 etc. This is no problem. Use the commands given in 
+\cite[page~92]{leslie} or \cite[page~98]{newleslie} to alter the way a theorem 
+environment is numbered. Thus
+\begin{verbatim}
+   \newtheorem{thma}{Theorem}
+   \renewcommand{\thethma}{\Alph{thma}}
+   \begin{thma} The subgroups ...
+   ...
+   \begin{thma} The irreducible  ...
+   \label{char}
+   ...  
+   The result of Theorem~\ref{char} \ldots
+\end{verbatim}
+  \newtheorem{thma}{Theorem}
+  \renewcommand{\thethma}{\Alph{thma}}
+\begin{quote}
+  \begin{thma} The subgroups \ldots
+  \end{thma}
+  \begin{thma} The irreducible  \ldots
+  \label{char}
+  \end{thma}
+The result of Theorem~\ref{char} \ldots
+\end{quote}
+
+Other possibilities for numbering are
+\[
+\begin{tabular}{ll}
+\verb+\alph{thma}+ & Theorem~b\\
+\verb+\roman{thma}+ & Theorem~ii\\
+\verb+\Roman{thma}+ & Theorem~II
+\end{tabular}
+\]
+
+
+
+\subsection{Changing the fonts}
+Fonts are handled differently in \LaTeX\ 2.09, 
+in NFSS, and in the new standard \LaTeX, \LaTeXe. 
+All the suggestions that I give in this section work in both \LaTeX\ 2.09 and 
+\LaTeXe. They do not work at all if you run NFSS without \LaTeXe. If you are 
+using \LaTeXe, you {\em must\/} use the forms like \verb+\sc+ given here: the 
+commands like \verb+\textsc+ will not do the right thing, because they 
+{\em add\/} small capitals (say) to the default fonts instead of 
+{\em replacing\/} the default fonts.
+
+The \verb+\newtheorem+ command in \LaTeX\ is the most wonderful thing
+to happen to Mathematical writers in a long time, because so many of
+our constructs fit it. However, one of the worst things to happen to
+Mathematical writers is the hard-wiring of the fonts for the theorem
+heads and the theorem bodies. Ordinary \LaTeX\ simply does not give
+you the flexibility to change these easily. Yet the defaults are not
+always appropriate, and different journals demand different fonts for
+these purposes. I suspect that this hard-wiring is one reason that
+some Mathematicians have been reluctant to use \LaTeX. What can the
+ordinary user do about this problem?
+
+I shall give four answers, because different solutions are appropriate
+in different circumstances.
+
+(i)~\littlehead{Bare hands} Sometimes (for example, when sending an
+article to \BV) you cannot submit your favourite style files along
+with your main file. So you need a `bare hands' way of changing the
+fonts, without losing too much genericity. Here's how.
+
+To make a theorem environment \latexword{prop} whose theorem head is
+set in small capitals, do
+\begin{verbatim}
+   \newtheorem{prop}{\sc Proposition}
+\end{verbatim}
+For a small document, this will do. To be more generic, you could do
+\begin{verbatim}
+   \newcommand{\headfont}{\sc}
+   \newtheorem{prop}{\headfont Proposition}
+\end{verbatim}
+so that only one line has to be changed if you decide to change the
+font of all the theorem heads.
+
+To make a theorem environment \latexword{qn} whose theorem body font
+is set in roman, use a two-stage process. The exercises in this
+sequence of tutorials are defined by
+\begin{verbatim}
+   \newtheorem{preqn}{Exercise}
+   \newenvironment{qn}{\preqn\rm}%
+                      {\endpreqn}
+\end{verbatim}
+(The exercises in this particular tutorial are bad examples, because
+they all have italic instructions.)
+
+(ii)~\littlehead{Mittelbach's style file} Frank Mittelbach wrote the
+style file \latexword{theorem.sty}, which should be available from all
+good CTAN hosts. It is described in \cite[pages~251--255]{companion}.
+It enables you to change the fonts and the layout of theorem
+environments. However, it does not do exactly what I need.
+
+(iii)~\littlehead{My style file} When I first started to use \LaTeX\ 
+it was obvious to me that a flexible means of changing the fonts for
+theorem heads and theorem bodies had to be provided. I hacked
+\verb+@begintheorem+ from \latexword{latex.tex} to produce a style
+file which lets me give a single command to set the font for theorem
+heads, another to set the font for (most) theorem bodies, and another
+to say that all subsequently declared theorem environments will have
+their bodies set in `ordinary' type: not necessarily in roman, but in
+{\em whatever font the surrounding text is in}.  However, like many
+others, I deplore the proliferation of personal style files because
+they inhibit portability of documents, so I haven't made this style
+file generally available.
+
+(iv)~\littlehead{American Mathematical Society} The old version of
+\latexword{amstex.sty} (see \cite{amslatex}) gives the user the
+possibility of declaring theorem environments in three classes---plain
+theorems, definitions and remarks. However, it does not give the user
+any control over the fonts used in those environments. I do not know
+if the forthcoming package \latexword{amsthm.sty} will give any more
+freedom.
+
+\subsection{Proofs}
+We all need a proof environment, so everyone invents her own, some
+more successfully than others. I think that the proof environment
+should be made with \verb+\newtheorem+, so that all the benefits of
+spacing, of page-break penalties and of consistent head fonts can be
+retained. Of course, proofs should be unnumbered and (usually) set in
+the same font as the surrounding text.  So I simply use the foregoing
+methods to create an environment \latexword{pf} with name
+\latexword{Proof} which is unnumbered and has its body
+set either in the surrounding text font or in roman.
+%\begin{verbatim}
+%  \plaintheorems
+%  \newtheorem{pf}[unnumber]{Proof}
+%\end{verbatim}
+
+What should you do about the end-of-proof symbol? Some people want it put in 
+automatically. In principle this could be done with something like
+\begin{verbatim}
+   \newenvironment{proof}{\pf}%
+                         {\eop\endpf}
+\end{verbatim}
+where \verb+\eop+ is your favourite end-of-proof symbol, for example
+\begin{verbatim}
+\unskip\protect\nolinebreak\mbox{\quad$\Box$}
+\end{verbatim}
+This is not really satisfactory if you have any proofs that end in
+displayed Maths (or any other sort of display). Traditionally the
+end-of-proof sign goes in the display, not on a new line; but if you
+have a display inside an environment then \LaTeX\ finishes off the
+display and gets ready for a new line before it reads the instructions
+for the end of the environment. So my advice is to have an \verb+\eop+
+macro and put it in by hand at the end of every proof, either just
+inside the final display (if this is the last thing in the proof) or
+just before the \verb+\end{pf}+.
+
+
+\subsection{Questions and Exercises}
+
+A theorem environment is ideal for questions on exam papers and
+coursework sheets, and exercises in text books. It is usually better
+than \latexword{enumerate} because it retains the normal text\-width,
+paragraph indentation and paragraph separation.  If you want the
+questions to be headed simply `1', `2', etc. then do
+\begin{verbatim}
+   \newtheorem{question}{}
+\end{verbatim}
+
+If the questions have parts and subparts, it is sensible to use 
+\latexword{enumerate} for them. In that case you probably need to change the 
+default numbering of the \latexword{enumerate} environments so that, say, parts
+are labelled~`(a)' etc.\ and subparts~`(ii)' etc. The next section shows how 
+to do this.
+
+\section*{Exercises}
+\begin{qn}
+\it
+Create a short document with two sections. 
+In the first section put one theorem, 
+a lemma subtitled `Burnside', another theorem, and a remark. The remark should 
+be neither numbered nor in italic. In the second section put another lemma, 
+another theorem, a corollary numbered in the same sequence as the theorems, and
+finally a theorem in a roman-numbered sequence.
+Include cross-references to all the numbered items.
+\label{thmdoc}
+\end{qn}
+
+\begin{qn}
+\it
+Redo the previous question, in such a way that lemmas and equations are 
+numbered within sections.
+\end{qn}
+
+\section{Other numbered things}
+\subsection{Numbered lists}
+If you use \latexword{enumerate} within a theorem environment then you will 
+probably have to change the way that the different levels of enumerated list 
+are numbered. This is controlled by commands containing the strings 
+\latexword{enumi}, \latexword{enumii}, \latexword{enumiii} and
+\latexword{enumiv}. Thus the $N$th level of nesting is controlled by 
+\latexword{enumN}.
+
+The counter for \latexword{enumN} is called simply \latexword{enumN}. To alter 
+whether the counter is displayed as an arabic numeral, a letter etc., you 
+change \verb+\theenumN+ (see \cite[pages~91--92]{leslie} or 
+\cite[pages~97--99]{newleslie}.) To alter the printed labels which are
+put on the items in the
+list, change \verb+\labelenumN+ to be a suitable text containing 
+\verb+\theenumN+.
+
+I find that two levels of nesting are quite sufficient within exam questions 
+and homework problems. My style files for exams and homeworks contain the lines
+\begin{verbatim}
+  \renewcommand{\theenumi}{\alph{enumi}}
+  \renewcommand{\labelenumi}{(\theenumi)}
+  \renewcommand{\theenumii}{\roman{enumii}}
+  \renewcommand{\labelenumii}{(\theenumii)}
+\end{verbatim}
+In a book, you might need to put something similar in the start  of an 
+\latexword{exercises} environment.
+
+If you are lazy then you might try to alter just \verb+\labelenumN+. The 
+list items will have the correct printed  labels but your printed
+cross-references will not match.
+The cross-reference generated by a \verb+\ref+ call to a \verb+\label+ in the 
+$N$th level of nested \latexword{enumerate}s has the form
+\begin{verbatim}
+   \p@enumN\theenumN
+\end{verbatim}
+where \verb+\p@enumN+ usually picks up the \verb+\theenumM+ 
+from higher levels ($M < N$), and 
+possibly some punctuation. If you don't like the settings of \verb+\p@enumN+ 
+that \LaTeX\ gives you by default, you will have to change them in a style file.
+
+\subsection{Footnotes}
+Mathematicians usually don't use footnotes, because the footnote marks would be 
+interpreted as superscripts or operators. However, we do sometimes like to put 
+information at the bottom of the first page of a document, under a horizontal 
+line: perhaps an address for correspondence, or a list of AMS subject 
+categories. You can do this with a \verb+\footnote+ early in the document, so 
+long as you have first done
+\begin{verbatim}
+   \renewcommand{\thefootnote}{}
+\end{verbatim}
+It is best to put this command in a small group around the use of 
+\verb+\footnote+.
+
+\section*{Exercises}
+\begin{qn}
+\textit{Modify the document in Exercise~\ref{thmdoc} so that one of the theorems 
+has parts and subparts. The parts should be labelled} 
+\begin{quote}
+[A], [B], \ldots
+\end{quote}
+\textit{and the subparts}
+\begin{quote}
+1/, 2/, \ldots .
+\end{quote}
+\label{enumex}
+\end{qn}
+
+\begin{qn}
+\textit{Modify the document in Exercise~\ref{enumex} so that the foot of the 
+first page carries the text}
+\begin{quote}
+Key words: construction of designs; neighbour balance; optimality; 
+randomization; software.
+\end{quote}
+
+\end{qn}
+
+\begin{thebibliography}{9}
+\bibitem{amslatex}
+\writer{American Mathematical Society}
+\book{\AMS-\LaTeX\ Version~1.0 User's Guide}
+\publish{American Mathematical Society}{Providence, Rhode Island}
+\byear{1990}
+
+\bibitem{companion}
+\writer{Goossens,~M., Mittelbach,~F. \& Samarin,~A.}
+\book{The \LaTeX\ Companion}
+\publish{Addison-Wesley}{Reading, Mass.}
+\byear{1994}
+
+\bibitem{dek}
+\writer{Knuth,~D.~E.}
+\book{The \TeX book}
+\publish{Addison-Wesley}{Reading, Mass.}
+\byear{1984}
+
+\bibitem{leslie}
+\writer{Lamport,~L.}
+\book{\LaTeX: A Document Preparation System}
+first edition,
+\publish{Addison-Wesley}{Reading, Mass.}
+\byear{1986}
+
+\bibitem{newleslie}
+\writer{Lamport,~L.}
+\book{\LaTeX: A Document Preparation System}
+second edition, 
+\publish{Addison-Wesley}{Reading, Mass.}
+\byear{1994}
+
+\bibitem{swan}
+\writer{Swanson, E.}
+\book{Mathematics into Type}
+revised edition,
+\publish{American Mathematical Society}{Providence, Rhode Island}
+\byear{1979}
+\end{thebibliography}
+\end{Article}
+\endinput
+
+leslie
+newleslie
+\bibitem{hart}
+%\writer{Oxford University Press}
+\book{Hart's Rules for Compositors and Readers}
+\publish{Oxford University Press}{Oxford}
+\byear{1967}
+\bibitem{chamb}
+\book{The Chambers Dictionary}
+\publish{Chambers Harrap}{Edinburgh}
+\byear{1993}
+\bibitem{chicago}
+\book{The Chicago Manual of Style}
+\publish{The University of Chicago Press}{Chicago}
+\byear{1982}
+
+Like many others, I deplore the proliferation of personal style files
+because they inhibit portability of documents. Yet when I first
+started to use \LaTeX\ it was obvious to me that a flexible means of
+changing the fonts for theorem heads and theorem bodies had to be
+provided. I hacked \verb+@begintheorem+ from \latexword{latex.tex} to
+produce the code in Figure~\ref{rabcode}. My only excuse for
+reproducing it here is that none of the widely available styles gives
+the necessary flexibility.
+\begin{figure*}
+\begin{verbatim}
+%commands to change the type face in theorems
+%default is heading in small caps, content in roman
+\newif\ifplaintheorems
+\def\plaintheorems{\plaintheoremstrue}
+\def\fancytheorems{\plaintheoremsfalse}
+
+\let\thmheadfont\sc
+\let\thmcontfont\rm
+\def\theoremheadfontis#1{\def\thmheadfont{#1}}
+\def\theoremcontfontis#1{\def\thmcontfont{#1}}
+
+\def\@xnthm#1#2[#3]{\expandafter\@ifdefinable\csname #1\endcsname
+{\@definecounter{#1}\@addtoreset{#1}{#3}%
+\expandafter\xdef\csname the#1\endcsname{\expandafter\noexpand
+  \csname the#3\endcsname \@thmcountersep \@thmcounter{#1}}%
+     \ifplaintheorems \global\@namedef{#1}{\@thm{#1}{#2}}%
+     \else \global\@namedef{#1}{\thmcontfont\@thm{#1}{#2}}\fi%
+\global\@namedef{end#1}{\@endtheorem}}}
+
+\def\@ynthm#1#2{\expandafter\@ifdefinable\csname #1\endcsname
+{\@definecounter{#1}%
+\expandafter\xdef\csname the#1\endcsname{\@thmcounter{#1}}%
+     \ifplaintheorems \global\@namedef{#1}{\@thm{#1}{#2}}%
+     \else \global\@namedef{#1}{\thmcontfont\@thm{#1}{#2}}\fi%
+\global\@namedef{end#1}{\@endtheorem}}}
+
+\def\@othm#1[#2]#3{\expandafter\@ifdefinable\csname #1\endcsname
+  {\global\@namedef{the#1}{\@nameuse{the#2}}%
+\ifplaintheorems \global\@namedef{#1}{\@thm{#2}{#3}}%
+\else \global\@namedef{#1}{\thmcontfont\@thm{#2}{#3}}\fi%
+\global\@namedef{end#1}{\@endtheorem}}}
+
+\def\@begintheorem#1#2%
+     {\trivlist\item[\hskip\labelsep
+     \thmheadfont #1\ #2\unskip]}
+\def\@opargbegintheorem#1#2#3
+     {\trivlist\item[\hskip\labelsep
+     \thmheadfont #1\ #2\unskip\ (#3)]}
+\end{verbatim}
+\caption{Revised code to give flexible changes to fonts in theorems}
+\label{rabcode}
+\end{figure*}
+If you put this code into your style file then you can make all your theorem 
+heads come out in italic by doing
+\begin{verbatim}
+  \theoremheadfontis{\it}
+\end{verbatim}
+To put all the theorem bodies in slanted type do
+\begin{verbatim}
+  \theoremcontfontis{\sl}
+\end{verbatim}
+Each of these commands should be used at most once in the document. However, 
+you can also use the command
+\begin{verbatim}
+  \plaintheorems
+\end{verbatim}
+After this command has been issued, any theorem environments declared 
+subsequently will have their bodies set in `ordinary' type: not necessarily in 
+roman, but in {\em whatever font the surrounding text is in}. This seems to me 
+most suitable for remarks, definitions and so on. The command 
+\verb+\fancytheorems+ nullifies \verb+\plaintheorems+.
+
+\end{Article}
-- 
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