There is a list of courses, which can be filtered by Type, Department, Faculty, All / My.
How the filtering part can be improved and simplified here?
Get rid of the filters. Just provide a powerful search box.
The filters are there to help the user find the required course. It is not that the user wants to do something with the list of filtered courses. The box will search each of the fields, Faculty, Department, etc. You can empower it with auto-completion and textual filters. See, for example, the way Gmail search bar is working.