[cowboysauce]

> Do you use functions?

Unless you're using Haskell or something similar, mathematical functions and what most programming languages call "functions" are very different and are better referred to as procedures. Mathematical functions don't have any concept of some basic constructs like variables (state in general), I/O, or even sequential computation. Pure functional languages have to use things like monads to model procedures.

[tnecniv]

Sure, but you know what has state? ODEs and their discrete-time analogue, recurrence relations. You first meet ODEs in calculus. Even if you say “who cares about continuous time, my computer is fundamentally discrete!” you won’t have a concept of limiting behaviors without calculus.