Praise be to Allah.
When you are in your city or you come back to it from the university, then you must offer your prayers in full, because this is your original home.
If the distance between your city and the city where the university is is the distance at which it becomes permissible to shorten prayers, which is approximately 80 km, then you may shorten your prayers during your journey.
When you reach the city where the university is, if you intend to remain there for more than four days, then you must offer your prayers in full from the moment you arrive there.
If you intend to stay there for four days or less, or you are not sure how long you will stay, then in that case you come under the ruling on travellers, so you may shorten the four-rak‘ah prayers – Zuhr, ‘Asr and ‘Isha’ – to two rak‘ahs, unless you are praying behind one who is a resident, in which case you must offer the prayer in full with him, and you must attend prayer in congregation in the mosque.
Please see also the answers to questions no. 38079 and 21091 .
And Allah knows best.