Biker of the apocalypse has correctly pointed out a comparability problem that occurs if counterparts is left out. (Note, my personal preference is for versus rather than over in the context of Biker's example and your own. With over, I'd use a different construction, illustrated later.)
However, another comparability problem then occurs: use of counterparts suggests that for each mathematics course there is a corresponding humanities course. But generally there is no such correspondence. For that reason, I suggest not using the word counterparts, and instead just repeat the word courses. Eg,
There are three main advantages for mathematics courses versus humanities courses.
Mathematics courses have three main advantages over humanities courses.