Simply, what is "major subject" in Latin? By a major subject I mean the subject a university student mainly focuses on. I have used the translation materia principalis, but I wonder if there is a more suitable one. In particular, is (or was) a Latin expression for this already in use somewhere?
Whenever I need to translate relatively new words into Latin, I find that the Morgan and Silva Furman University Lexicon is particularly useful. Here is the entry for "major", which is what we call a student's primary concentration in the U.S.
.univ major in, specialize in / speciale studium (alicuius rei) amplecti | major, specialization specializatio* [Latinitas] (HELF.)
.univ major, specialize / speciali studio se excolere (v. operam dare) (LRL)
So, specializatio seems to be somewhat adequate in describing a "major". It obviously is related to the English "specialization", which makes sense for the purpose it serves.
In the Medieval studia generalia, there were four "majors" one could study (although one of them was preliminary to the other three), and they were called facultates.
What we think of today as a University actually began as a corporation (or guild) of teachers or of students in a certain city; those were called universitates: u. magistrum for a teachers' guild, and u. scholarium for a students' guild. Sometimes there was a single guild for both, called universitas magistrum et scholarium.
When one entered University, one studied the trivium and then the quadrivium within the facultas artium, or the faculty of the (Liberal) Arts. Once students had obtained their title of Magister Artium, they could leave University or continue into one of the other three facultates: Law, Medicine or Theology.
Obviously, there's the issue that, in North America, the term "faculty" is used to refer to the teaching body of an institution, the corpus docens. However, since they are different languages, there is no problem in using the closest historical term to the modern English concept — even if they really looked nothing like Anglophone majors do today.
In any case, during the High Middle Ages, the same term (facultas) was used both for the course taught and for the subset of the universitas magistrum which taught the same course, so the facultas legis or the facultas medicinae could refer to both the subject which the students enrolled in it studied or to the teachers who taught those subjects.