Is it permissible to pray in a room devoid of religious symbols but containing some sacred Christian books, a room that the university has designated as a prayer room for Muslim students?

There is no objection to praying in the aforementioned room, which is your mosque, because it is your only available space, and the presence of books of other religions in it does not prevent this. If Muslims are able to designate a place for themselves to make it a mosque without sharing it with others, they must do so. Otherwise, let them worship Allah in the available place, in accordance with the verse: "So fear Allah as much as you are able." And since the room is free of statues, idols, and crosses, there is no concern about praying in it. If Christians come and pray in it, that does not prevent the establishment of Friday prayer and other prayers.