[elblanco]

Well, there is definitely a strong distinction between "programmer" (a trade) and "computer scientist".

I'd argue that beyond arithmetic and maybe a basic understanding of functions (e.g. f(x)), most "programmers" need to know very little math. But they also tend to produce shoddy, inefficient code and look at problems as "moving bits around".

Computer Scientists on the other hand need to have spent some time understanding the theory of computation. Calculus is one way of computing things, so is lambda calculus, and turing machines, and formal grammars, various algebras like regular languages, etc. Slinging code is just another way of computing things to a Computer Scientist.

Given this, most typical programming trade jobs are approached by Computer Scientists as a computation problem (or at least an application of a computation theory) vs. just hauling electrons about. This gets you something both qualitatively different in their code output as well as quantitatively different.