Is it permissible for us—men and women—to wear head and neck coverings at the university, despite the administration's prohibition of it?

The matter is clear in this regard for men, as they are not required to cover their hair and neck. As for women, it is not permissible for a woman to uncover the hair of her head and neck, even if that leads to discontinuing her studies. And whoever fears Allah, He will make for him a way out of every difficulty and provide for him from where he does not expect, for the Prophet, peace and blessings be upon him, said: "Indeed, you will not abandon anything for the sake of Allah, the Mighty and Majestic, except that Allah will replace it with something better for you."