Discrete mathematics is the branch of mathematics dealing with objects that can assume only distinct, separated values. The term "discrete mathematics" is therefore
used in contrast with "continuous mathematics," which is the branch of
mathematics dealing with objects that can vary smoothly (and which includes, for
example, calculus). Whereas discrete objects can often
be characterized by integers, continuous objects require
real numbers.
The study of how discrete objects combine with one another and the probabilities of various outcomes is known as combinatorics.
Other fields of mathematics that are considered to be part of discrete mathematics
include graph theory and the theory
of computation. Topics in number theory such
as congruences and recurrence
relations are also considered part of discrete mathematics.
The study of topics in discrete mathematics usually includes the study of algorithms, their implementations, and efficiencies. Discrete mathematics is the mathematical
language of computer science, and as such, its importance has increased dramatically
in recent decades.
The related branch of mathematics known as concrete mathematics, while having some overlap with discrete mathematics, includes a
quite different set of topics (Graham et al. 1994, p. vi).
