The mace is a traditional symbol of authority, used in institutions of European descent. And yes, its name actually derives from the weapon.
This here is the Ateneo mace, put on display in most formal events. It's an impressive piece of work, about a foot and a half in diameter at the head, all engraved metal. Quite heavy, too. I never see it paraded, and that's a bit of a shame. Might be because of the heft and the weight. But darned if I won't volunteer to carry it if ever given a chance.