1

I am writing an introduction:

Humanities courses are very useful to students. Yet, in my opinion, schools should focus more on science and mathematics courses. The benefits of these courses vastly exceed the convenience of humanities courses. There are main three advantages for mathematics courses over humanities.

Should I add counterparts to the end of the paragraph?

2

It should be

There are three main advantages for mathematics courses over their humanities counterparts

As it stands, you are comparing courses in mathematics to humanities as a subject, and not just humanities courses. So yes, counterparts would be relevant here.

2

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.
–or–
Mathematics courses have three main advantages over humanities courses.

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