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\title{Typesetting Math}
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\date{}

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% There's no section here, but I want this line to look like the first
% line in a section, so I have to put \noindent explicitly.
\noindent There's a lot to go over relating to typesetting math.

\section*{Subscripts and superscripts}

You should already know about subscripts, like $x_i$, and
superscripts, like $2^n$.  You don't need to put curly braces around
the subscript or superscript if it's just one character.  If it's more
than one character, then you need to put braces: $2^mn$ is not the
same as $2^{mn}$.

You can have subscripts in subscripts ($x_{i_j})$, subscripts in
superscripts ($2^{n_i}$), superscripts in superscripts ($2^{2^n}$),
and superscripts in subscripts ($x_{2^i}$).

\section*{Fractions}

In running text, try to avoid the \verb`\frac` command.  Typeset $a/b$
rather than $\frac{a}{b}$.

For more complicated fractions, you might have to use parentheses to
make things clear.  For example, $(m+1)/n$; you wouldn't need the
parentheses if you used \verb`\frac`: $\frac{m+1}{n}$.

Interestingly, I just got into a little brouhaha with a reader of
CLRS, who complained about the expression $n/ab$ in equations (3.4)
and~(3.5).  He thought that it meant $(n/a) \cdot b$, when we intended
it to mean $n/(ab)$.  To avoid any misinterpretation, we should have
either put in the parentheses or, since the fraction appears in a math
display, used the \verb`\frac` form.

It's OK to use \verb`\frac` in math displays.  Unless I explicitly say
otherwise, include environments like eqnarray in the category of math
displays.  So, we could have written equation~(3.4) as
\[ \left\lceil \frac{\lceil n/a \rceil}{b} \right\rceil
	= \left\lceil \frac{n}{ab} \right\rceil \ . \]

Notice, however, that it looks funny to have the two autosized
delimiter pairs be of different sizes.  What happened is that the
ceiling symbol in the numerator of the left-hand side is just an ooch
bigger than the numerator of the right-hand side.  If we put a
\defn{strut}---a rule of zero width, which makes it invisible---in the
right-hand side's numerator, then we can even out the delimiters:
\[ \left\lceil \frac{\lceil n/a \rceil}{b} \right\rceil
	= \left\lceil \frac{n\mathstrut}{ab} \right\rceil \ . \]
Here, I have used a \verb`\mathstrut`, which is defined in plain
\TeX{} as a strut whose height is that of a regular left parenthesis.
That was what I wanted, since it needed to match the height of the
ceiling symbol, which is close enough to the height of the ceiling
symbol for gummint work.

You can have fractions within fractions:
\[ a_0 + \frac{1}{a_1 + \frac{1}{a_2 + \frac{1}{a_3 + \frac{1}{a_4}}}} \ . \]
If you want the fractions within fractions to be taller, put in full
struts and explicitly say that all but the outermost fraction are to
be displayed in ``display style'':
\[ a_0 + \frac{1}{a_1 + \displaystyle\frac{\strut 1}{a_2 +
	\displaystyle\frac{\strut 1}{a_3 +
	\displaystyle\frac{\strut 1}{a_4}}}} \ . \]
The \verb`\strut` command is also from plain \TeX{}\@.

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