From a SEO standpoint, it would make more sense to have them all hosted at stanford.edu/someclass, since the classes would then benefit from the "trust-factor" of the root domain. You'll notice that most of Google's web properties are hosted at google.com/something and not something.google.com or a separate domain, presumably for the same reason.
Consider: maps., docs., mail., plus., groups., translate., books., scholar. There are probably a bunch more -- I don't think Google is scared of subdomains.
