How to manage users and collections in MongoDB?
At the time of writing this (2.4 is the stable release) you would have to split up these collections into three databases instead.  The ability to do collection level permissions is not available, so you need to do it at the database level.  If you alter your model to have 3 databases (Books, Students, Professors), then you can add the relevant users to each database using db.addUser as you require.

However, if that is not possible for some reason, it is worth noting that collection level access control is slated to be a feature in 2.6 (the next major release) which is due soon (tm).  The usual caveats apply, nothing is truly in a release until you see the actual binary and confirm it, but this feature (as part of SERVER-1105) is already marked as committed and closed.  It is available for testing in the development releases right now.  The documentation (once complete) will be available at:

http://docs.mongodb.org/master/release-notes/2.6/#collection-level-access-control