Student (Skyrim)

The student seems to be a random encounter.

If certain criteria are met a possibly random encounter can occur between you and a student, who wishes to enter the Mages College in Winterhold.

He asks you to help him learning ward, to which you can respond either "Maybe some other time" or "Sure, I can teach you."

when choosing "Sure I can teach you", the student uses firebolt, after several successful blocks with any ward he will say "Thank you, I think I'm ready to join the College now".

Bugs
(PS3) Loading through doors (into your house for example) will result in the Student disappearing from the city when you go back outside, a quest marker will be present, but is not visible on the map, leaving no way to finish or remove the quest from the log.