Hear me out on this one:
For a lot of math departments, that is exactly why they teach this. Education is rooted in application. We have entire careers that depend on certain aspects of mathematics, so most companies gatekeep that career by a degree. The degree requires the class. The student taking the class may not even be old enough to drink alcohol yet, and they can't possibly be expected to know of all the applications. Knowing and not telling them is doing them a disservice.
I think for many people (myself included) understanding mathematics is rooted in application because it helps bridge the divide between intuition and rote memorization. Without the application, IMO instructors are doing a disservice to their students and pedagogy of mathematics itself. They’re intentionally ignoring a significant fraction of the class, unless they’re teaching some esoteric grad level pure math.
> For a lot of math departments, that is exactly why they teach this.
Depends on the course. That's why some departments have separate calculus courses for math majors - because otherwise the whole class will be full of non-math majors (engineers, etc) and focusing on their needs does a disservice to the students in their own department.
> The degree requires the class. The student taking the class may not even be old enough to drink alcohol yet, and they can't possibly be expected to know of all the applications.
If I'm a CS major, and the degree is requiring a class outside of the CS department, you shouldn't expect the professor of the class to know why the CS department is requiring it. It's on the CS department and its faculty to explain it.