I talked to Mirabelle so she would show me around. As is standard with my luck, a dragon attacked and now Mirabelle will not finish the quest. This means:

No Sarthaal amulet (you need Tolfdir's permission to enter)

Impossible to become Archmage

Won't get to fight the dragonpriest (to get his mask)

And that's off the top of my head. If there is a way to fix this (barring reloading my last manual save because the autosave system svcks), please let me know. Otherwise, please work this in your next patch.

I think you can just go to the hall of elements and begin the lesson (with Tolfdir)