Colleges do not ring a bell at the end of class. There would be too many classes starting and ending at different times and would ultimately be extremely disruptive.
There's no such thing as an American university that's short on qualified teaching staff in the Math department, as Dr. Clark said. There are so few tenure-track teaching jobs left, that there would be major competition for Professor Pierce's position, no matter how haunted the faculty housing was, and no matter how many parapsychology courses the head of the Math department taught.