\documentclass[11pt]{article}
\usepackage[mtbold]{mathtime}
\usepackage{clrscode}
\input{page}

\newcommand{\defn}[1]{\textbf{\textit{#1}}}
\newcommand{\subheading}[1]{\subsubsection*{#1}}

\begin{document}

\title{Typesetting Math, Part 3}
\author{}
\date{}

\maketitle

\subheading{Math accents}

Just one quick thing to note: the \verb`\hat` accent is pretty wimpy:
$\hat{a}$.  I recommend using \verb`\widehat`: $\widehat{a}$.

\newcommand{\path}[1]{\stackrel{#1}{\leadsto}}

The \verb`\stackrel` command can be nice for various relational
notations.  For example, CLRS uses the following command:
\begin{verbatim}
\newcommand{\path}[1]{\stackrel{#1}{\leadsto}}
\end{verbatim}
In this way, when we write about a path named~$p$ that goes from
vertex~$u$ to vertex~$v$, we type the math-mode expression
\verb`$u \path{p} v$`, which produces $u \path{p} v$.

\subheading{Spacing}

Spacing in math mode can be rather subjective.  Lamport gives examples
in which it is quite clear that you need to add or remove a little
space, e.g., $\int\!\!\int z \, dx \, dy$ rather than $\int\int z dx
dy$.

But here's a place where a subjective opinion is in order.  Consider
an expression that multiplies a function value by a scalar: $c f(x)$.
That looks OK\@.  Would it look better with some space?  You make the
call: $c \, f(x)$, or even $c \: f(x)$.  When we were writing the
analysis of disjoint-set union, I thought that $O(m \alpha(n))$ ran
the $m$ and~$\alpha$ together, so I added a medium space: $O(m \:
\alpha(n))$.

Another place in which it pays to add space is when multiplying
fractions in a display.  Consider the following:
\[ \frac{ab}{cd} \frac{ef}{gh} \ . \]
These fractions are too darned close to each other.  We can either
add some space or put in the dot:
\[ \frac{ab}{cd} \; \frac{ef}{gh} \hspace{2em}\mbox{or}\hspace{2em}
	 \frac{ab}{cd} \cdot \frac{ef}{gh} \ . \]

\newcommand{\prob}[1]{\Pr\left\{ #1 \right\}}
\newcommand{\set}[1]{\left\{ #1 \right\}}
\newcommand{\card}[1]{\left| #1\right|}

If you are unfortunate enough to have a long subscript or superscript
in a summation-like formula, you could get more space than you want.
Here's something from page~1118 of CLRS:
\[ \sum_{S\subseteq \set{1, 2, \ldots, n} : \card{S}=k}
		\hspace*{-1em}\prob{A_S} \ . \]
That looks pretty good.  Here it is without the negative space:
\[ \sum_{S\subseteq \set{1, 2, \ldots, n} : \card{S}=k} \prob{A_S} \ . \]
The subscript under the summation claims too much horizontal space.

\subheading{Multiletter variables}

The italic font used for math is different than the italic font used
for regular text.  For single-letter variables names, you would never
notice the difference; can you distinguish $n$ from $\mathit{n}$?  But
you'll notice it for multiletter names.  Compare $color$ vs.\
$\mathit{color}$.  You can see a difference in spacing between 'l'
and~'o'.  It becomes even more noticeable in words that have
ligatures: $wiffle$ vs.\ $\mathit{wiffle}$.

If you're going to use multiletter variable names, do not just typeset
them directly in math mode.  Put them in math mode, but use the
\verb`\mathit` command: \verb`$\mathit{wiffle}$`.

There still is a potential problem.  Some of the variable names in
CLRS have hyphens.  In math mode, a hyphen is considered to be a minus
sign.  So \verb`$\mathit{heap-size}$` typesets as
$\mathit{heap-size}$.  The clrscode package has a macro \verb`\id`
that, in addition to using the correct italic font, also interprets
hyphens as hyphens.  Thus, \verb`$\id{heap-size}$` typesets as
$\id{heap-size}$.

The clrscode package also provides macros for typesetting other names
in CLRS style:
\begin{itemize}

\item \verb`\proc` for procedure names in small caps: the source
\verb`$\proc{Matrix-Multiply}$` typesets as $\proc{Matrix-Multiply}$.

\item \verb`\const` for constant names in small caps: the source
\verb`$\const{red-and-black}$` typesets as $\const{red-and-black}$.

\item \verb`\func` for fixed function names in roman: 
\verb`$\func{in-degree}$` typesets as $\func{in-degree}$.

\end{itemize}

Each of these macros is set up so that it may be used either in or out
of math mode.

\end{document}