How many professors are there?
select count ( * ) from professor
which department has the most professors?
select * from professor as t1 join department as t2 on t1.dept_code = t2.dept_code group by t1.dept_code order by count ( * ) desc limit 1
What about the smallest?
select * from professor as t1 join department as t2 on t1.dept_code = t2.dept_code group by t1.dept_code order by count ( * ) limit 1