All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
No Muslim woman should travel without being accompanied by a Mahram for the sound Hadeeth reported by Al-Bukhari and Muslim that the Prophet said: “No woman should travel for more than three days except if accompanied by a Mahram of hers.”
This ruling concerns traveling within a Muslim country, so the prohibition becomes more emphatic if she is traveling to a non-Muslim country.
The scholars who permitted the travel of women with trustworthy company limited that permission to obligatory travel, such as Hajj.
As for traveling to non-Muslim countries without real necessity, it is forbidden even with a Mahram, let alone without a Mahram. Anyway, you should not travel without being accompanied by a Mahram. The knowledge you want to acquire in that place should not be a knowledge you can get in your country. You should also be sure that you can study without being tempted by vices and without mixing with non-Mahram men. This is almost impossible in universities in Muslim countries, let alone in universities in non-Muslim countries.
For more benefit on studying in non-Muslim countries, please refer to Fatwa 82091.
For more benefit on Muslims living in non-Muslim countries, please refer to Fataawa 81142, 86405, 88291, 377986, 81642, 369667, 81464 and 89879.
Allah knows best.