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Discrete mathematics, also called finite mathematics, is the study of mathematical structures that are fundamentally discrete in the sense that its objects can assume only distinct, separate values, rather than a values on a continuum. Objects studied in discrete mathematics are largely countable sets such as integers, finite graphs, and formal languages.
Discrete mathematics has become popular in recent decades because of its applications to computer science. Concepts and notations from discrete mathematics are useful in studying and describing objects and problems in computer algorithms and programming languages.
In some mathematics curricula, finite mathematics courses cover discrete mathematical concepts for business, whereas discrete mathematics courses emphasize concepts for computer science majors, and combinatorics and other specialized courses emphasize the mathematical theory.
Discrete mathematics is contrasted with "continuous mathematics", in which the mathematical continuum and more sophisticated topologies play a role. Mathematical analysis is a major branch of continuous mathematics.
Discrete mathematics includes the following topics:
▪ Logic - a study of reasoning
▪ Set theory - a study of collections of elements
▪ Number theory
▪ Combinatorics, including
▪ Design theory
▪ Enumerative combinatorics
▪ Graph theory
▪ Algorithmics - a study of methods of calculation
▪ Information theory
▪ Digital geometry
▪ Computability and complexity theories - dealing with theoretical and practical limitations of algorithms
▪ Partially ordered sets
▪ Counting and relations
"Discrete" mathematics, sometimes known as "finite" mathematics, is the study of sets or systems that have a finite number of elements. For example, between 0 and 100, there are a finite quantity of integers, but an infinite...