1) As others have pointed out, the example you use is not really calculus as such but about mathematical proofs. This might have not been covered in your college degree. You can pick this up if you want to, at least to the level required to follow the binomial example. It's interesting, its application in most jobs out there is limited though.
2) Math generally can get really, really hard. Insanely hard. It gets harder and harder for long, long time after it has reached the level that most mortals can understand.
2b) Fortunately (for most of us), the ability to earn money with math doesn't seem to increase significantly beyond the basic calculus, algebra, ... level.
" The Atari + German book reference indicates:
* Interest in legacy computing / systems history "
No. I'm just that old. I read the book when the Atari ST was state of the art :-)