A great many real, live engineers that I know would object to anyone calling themselves an engineer without a lot of study of the big three: statics, dynamics, and thermodynamics; not just general mathematics. It's one of the reasons I don't call myself an engineer. (But I do get to harsh on them a bit about not being professional programmers---their code isn't pretty.)
The other reason, of course, is that the "software engineer" term comes from a group of people who really wanted the respect that comes with "engineer" but realized that the big three don't get very far, software-wise. (And coincidentally didn't want to do all that icky math stuff. Not to mention much of the icky programming stuff.)
Ironically, EE had by far the most maths and maths-related courses of the other degrees, at my Uni. But we were still required to study those ones, along with the civil and chemical engineers.
The other reason, of course, is that the "software engineer" term comes from a group of people who really wanted the respect that comes with "engineer" but realized that the big three don't get very far, software-wise. (And coincidentally didn't want to do all that icky math stuff. Not to mention much of the icky programming stuff.)