What is the ruling on a woman traveling for study without a mahram? And if it is unlawful, is expiation due upon her, or must she abandon her studies given her knowledge of her parents' disapproval and the absence of an alternative?

It is not permissible to travel for university studies without a mahram, due to the resulting negative consequences. She should seek studies that do not require impermissible travel. If that is not possible, and her father insists on her studying, then he or one of her mahrams must accompany her during the journey until she reaches her place of residence. It is not a condition for him to remain with her for the entire duration of her studies. There is no expiation for traveling without a mahram; rather, it is forbidden and must be avoided. Allah Almighty says: (And whoever fears Allah – He will make for him a way out And will provide for him from where he does not expect. And whoever relies upon Allah – then He is sufficient for him. Indeed, Allah will accomplish His purpose. Allah has already set for everything a [decreed] extent.) [At-Talaq/2-3]. And on the authority of Abu Hurayrah, may Allah be pleased with him, from the Prophet, peace and blessings be upon him, who said: (It is not permissible for a woman who believes in Allah and the Last Day to travel for a day's journey except with a mahram.) Narrated by Al-Bukhari (1088) and Muslim (1338).