Unless I'm mistaken, this sentence translates to "Does your Sun Yatsen University have this course in linguistics?" From DeFrancis' Beginning Chinese Reader p. 271 – Lesson 23, Exercise 3, Item 3.
I think your confusion point may be on the 你們 part. The 你們 here is similar to 'you' in English expressions such as 'You fool' or 'You people'.
The 你們 here is not possessive but an acknowledgement/emphasis of the association between the listener and the true target entity.
Similar usage: 你們 德國人 真 聰明 （You Germans sure are brilliant)
However, please note this is different from cases such as 你們 公司 真 好 (Your company is damn awesome)
The difference is 'company' is generic, but 'Germans' and 'Sun Yatsen University' are specific. However, do pay attention to what the generic entity is referring to, if the generic entity is referring to a group of people to which the listener belongs, it is also not possessive. Such case can be 你們 這些人 真 壞 （You people are pretty awful)
語言學這科 cannot be translated as 'this course in linguistics' but 'the linguistics course'. 科 here is the 'course'/'subject', 這 here is to specify the 科 is referring to 語言學
The whole sentence means:
Does (your uni,) the Sun Yatsen University offer linguistics courses?
Since 'you Sun Yatsen University' is not a proper expression in English, it is omitted.