Two levels of mathematics

I've written about the connection between programming and mathematics before. My latest discovery is that there are two "levels" (for lack of a better word) Mathematics - one inhabited by engineers and one by mathematicians. This divide seems to carry over into books as well - thus, taking Calculus as an example, Gilbert Strang's book is an Engineer's guide and Spivak's book is for mathematicians.I am working through the latter, and while it is very clearly written, it is a whole different level from any book on Calculus I've worked with before.