a) "He came home (on) Tuesday."
According to reputable sources, "on" is optional.
b) "The class will be offered (in) Fall 2011."
Supposed "Fall 2011" refers to a school term, could "in" be equally optional?
Personally, I am for using "in" in the 2nd sentence.
I would say "He came home on Tuesday" and "The class will be offered in Autumn 2011.
Many people would say them differently.
c) "He came home Tuesday."
d) "The class will be offered Fall 2011."
Then c) and d) are unacceptable in BrE, but possibly acceptable in AmE?