I haven't read into it, but I'm fairly certain that if you pick Bachelor of Science to do a maths major, you'd have to do at least a few compulsory science electives. A lot of universities just put maths into science, so students who want to study maths must do it through a Bachelor of Science. If given the choice (presuming that you're certain you want to do maths and that you don't want to do any proper science), you'd probably be better off doing a Bachelor of Mathematics. I suggest looking into the maths faculties of a wide range of universities and get an idea of what they offer; some areas in maths aren't as specialised in some universities.

The core units for your maths major, however, are exactly the same.