Engineering is a practice. Like medicine, but we’re building machines that run in a virtual space. We architect and build houses in our minds. We send those projects to production to make the business money.
That’s engineering.
That’s engineering.
Software Engineering = Applied Math.
Both are about modelling, so you have a good idea if a solution works before you build it.
If you're gluing stuff together and hoping it's not going to fall apart too often you're not doing either.
That's precisely what the majority of "software engineers" are doing nowadays. That's what web development is. Those that are creating tools other developers use and build things using algorithms/data structures in novel ways (essentially applied math as you said), they are the real software engineers in my eyes.
Applied Physics = Applied Math.
So... different tradeoff? Sounds like engineering to me :).