Question $2.$ The university's academic management database is designed to streamline the administration of courses, departments, professors, students, and facilities. This comprehensive system supports efficient scheduling, class management, and enrollment processes. By capturing the intricate relationships between these entities, the database ensures smooth coordination of academic activities, from assigning professors to classes, to managing student enrollments and classroom allocations.

Here are the RM diagram for the database: Please write SQL statements to answer the following queries according to the above RM diagram:

$(1)$ List the total number of courses offered by each department.

$(2)$ Find the names of all professors who teach in the "Computer Science" department.

$(3)$ List the names of students who are enrolled in more than three classes.

$(4)$ Find the building names where the "Introduction to Psychology" course is held.

$(5)$ Display the names of students along with the total number of credits they are enrolled in$,$ sorted by total credits in descending order.