Even a native speaker of U.S. English (and I suspect some other varieties,
though I can't speak for those) might have some difficulty with these
In English class for native speakers, I recall it being said that if the
subject of a sentence is a phrase such as "a/the number of books",
then the noun number is the actual subject, that is, the subject is
singular and the verb would be is rather than are.
But I think it would be very unusual for a native speaker to say,
"A number of books is available in the store."
One would more likely say, "A number of books are available in the store."
In other words, "a number of books" is treated idiomatically as if it were
the phrase "some books".
The first sentence speaks of a very specific number of books;
namely, it says that the number is three.
In that case, a native speaker would be likely to view the singular word
"number" as the subject of the sentence, and to say "is" in the
But to be honest, I suspect that many native speakers would still say "are".
So if I were writing these sentences in real life, as an educated native
speaker of U.S. English I would probably write:
1) The number of books in economics that we need to buy is three.
2) A number of books in economics that we can buy for the course are available in the college book store.