[psandersen]

A computer still deals with a finite amount of bits (e.g. 32-bit floating point numbers) so its a discrete system that is large enough to approximate a continuous system.

It may not matter much in practice except for numerical precision issues, but it is useful to understand the foundations and occasionally throw away abstractions for performance/other requirements.

[AstralStorm]

Even then, only small subset of discrete maths often called numerical methods is needed. (Discretizaton, discrete linear and nonlinear algebra, stability.) Going at a problem from fully discrete math point of view is often suicidal (results in unworkable algorithms) as integrals or difference equations are much more useful in practice than say discrete combinatorics. (Mostly used in cryptography.)

Graphs are sometimes useful in a narrow set of CS problems, as are similar structures. However, these are often not taught at discrete maths courses.

[fjsolwmv]

That's silly. Floating point math is an approximation of continuous math. It's only discrete in a narrow technical sense.

[coldtea]

Computers don't just do floating point. And when they do it, at the lower levels, they don't do it as floating point.