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This is perhaps half a math question and half a typesetting one. In what circumstances do I use \mapsto and when \rightarrow? I feel like the standard seems to be: when you're specifying the operator you use \rightarrow, but if you're just saying that one domain maps to another you use \mapsto. Is that correct?

e.g. I would say Q\times\Gamma\mapsto Q but \delta:Q\times\Gamma\rightarrow Q.

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You use \mapsto to denote the actual function mapping. For example, consider the function $f:\mathbb N\to\mathbb N$ given by $f(n)=5n$. You could write that second part as $n\mapsto5n$.

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See also the Wikipedia article. – Caramdir Nov 10 '10 at 1:16
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The \mapsto notation is useful for talking about a function without inventing a name for it, e.g. "the map $\mathbb{R}\to \mathbb{R}$ given by $x\mapsto x^2$ is not injective". Note that \to is a nice shorthand for \rightarrow, which at the same time is more semantic. – Villemoes Nov 10 '10 at 10:36
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I'd prefer using \colon instead of :; in fact I'd even more prefer $f\from\mathbb N\to\mathbb N$, with \newcommand*\from{\colon}. – Hendrik Vogt Nov 10 '10 at 14:41
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@Hendrik: I like the idea of using \from. I think I've seen equal numbers of : and \colon in books (or the equivalent spacing) so I think it's just up to personal preference (or editor preference, really). I have no strong feelings on that one. – TH. Nov 11 '10 at 5:43
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