What is the ruling on studying the subject of "Mass Thought," which discusses democracy, and taking exams in it, knowing that it is a core subject at the university, and does the female student incur sin due to studying this subject?

There is no sin in studying democracy theoretically and understanding it. There is no legal impediment to it, for it is like other systems of governance that a student of knowledge and an educated person should be familiar with, so that he may know what conforms to the Sharia and approve it, and what contradicts it and forbid it. If a Muslim learns this with a sincere intention, he will be rewarded, Allah willing, just as Hudhayfah asked about evil for fear that it would overtake him.