The Tower is clearly not a tower. The original structure, built by Matrim al'Nasair using the One Power, was destroyed by the quakes that terrorized the Realm. His students rebuilt the structure in his absence, albeit, less impressively.
      It is now a large, two-story building. The top floor is housing, and the lower floor houses classrooms, the kitchens, and the main hall. Below ground is the training rooms and dungeons.