Why Discrete Math Is Important
Discrete math is important because the universe is discrete.  Continuous math is an approximation that sometimes, but not always, is rather convenient.Once I wrapped my mind around this, I started to understand something.  Manifolds are just graphs with many vertices.  Fourier analysis studies the eigen-decomposition of the laplacian on a graph, and is used to solve heat, wave and dispersion equations.  Stokes theorem (which in a discrete setting amounts to matrix associativity) is a self-evident fact.  Most of applied math is thus reduced to a few lines of octave code.Only when you lose discreteness or compactness things start to get nasty.  But this is just a flaw in our current definition of real numbers.