Is computing strictly broader than mathematics?

We know with Coq and by software of formal calculations that computer science makes it possible to account for mathematics.

But is the reverse true : in fact there is no mathematical concept that accounts for global variables.

Indeed if g were a global variable, then we would have g which is not necessarily equal to g (indeed between the calls of g, the value of g could have been changed), which is impossible in maths , because of the principle of identity.

Question : How are global variables modeled mathematically?