What course would somebody study if they were exploring growth of human population, its effects, & consequences of population critical mass?
On completion what would have a doctorate / masters in...........
The faculty will almost certainly be social sciences, and the little boxes that spring to mind are those of demographics, economic history and possibly anthropology. There are also some newer universities that might pigeonhole this area of work with ecological studies.
What the degree will be called will vary from one university to another, but M.Sc, MSc(Econ), Ph.D., D.Sc and other similar degrees will certainly be among the possibilities.
Even something like fluid dynamics can be used in the study of populations.