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Formulas within an <m> tag must be within $...$ or $$...$$. Without, printing (PDF creation) would fail.

\label{Authoring_HTML_vs_Tex}
LON-CAPA renders resources in several formats, including on the web in
HTML and in LaTeX for renderings designed to be printed.

When creating problems, it is possible to use LaTeX directly by using
the <m> tag\index{m tag}\index{tag, <m>} (see
\ref{Authoring_Output_Tags}). Anything between the <m> tag in a resource
will be interpreted as .tex.

However, this should be used as a last resort for when you wish to do
something that is impossible to do in HTML. LON-CAPA will convert to
and from LaTeX and HTML whenever necessary, and it is much easier (and
therefore more likely to work) to convert HTML to LaTeX then to go the
other direction, because HTML is so much simpler than LaTeX. 

Thus, given the choice of 

\texttt{H<sub>2</sub>O}

or 

\texttt{$<$m$>$\$ H\textbackslash{}subscript\{2\}O \$$<$/m$>$}

it is better to use the HMTL version.

A necessarily-incomplete list of capabilities: LON-CAPA can convert
HTML tables in LaTeX tables, images into LaTeX images, LaTeX symbols
into HTML, and LaTeX math into HTML (though it does not usually look
as good as LaTeX).

If you really wish to have the web rendering and the LaTeX rendering
do something different, perhaps because the automatically generated
LaTeX->HTML conversion did not do what you wanted, you can surround
your LaTeX with <tex> </tex>\index{tex tag}\index{tag, <tex>} tags,
and your HTML version with <web> </web>\index{web tag}\index{tag,
<web>} tags. The stuff placed between the <tex> tags will only show on
the LaTeX rendering of the resource, and the stuff placed between the
<web> tags will only show on the HTML web rendering of the resource.