*More formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable sets Indeed, discrete mathematics is described less by what is included than by what is excluded: continuously varying quantities and related notions.*

*More formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable sets Indeed, discrete mathematics is described less by what is included than by what is excluded: continuously varying quantities and related notions.*The set of objects studied in discrete mathematics can be finite or infinite.

The curriculum has thereafter developed in conjunction with efforts by ACM and MAA into a course that is basically intended to develop mathematical maturity in first-year students; therefore it is nowadays a prerequisite for mathematics majors in some universities as well.

Much research in graph theory was motivated by attempts to prove that all maps, like this one, can be colored using only four colors so that no areas of the same color share an edge.

Formal verification of statements in logic has been necessary for software development of safety-critical systems, and advances in automated theorem proving have been driven by this need.

Computational geometry has been an important part of the computer graphics incorporated into modern video games and computer-aided design tools.

At the same time, military requirements motivated advances in operations research.

The Cold War meant that cryptography remained important, with fundamental advances such as public-key cryptography being developed in the following decades.

In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic Discrete mathematics therefore excludes topics in "continuous mathematics" such as calculus or Euclidean geometry.

Discrete objects can often be enumerated by integers.

Operations research remained important as a tool in business and project management, with the critical path method being developed in the 1950s.

The telecommunication industry has also motivated advances in discrete mathematics, particularly in graph theory and information theory.

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