Discrete mathematics

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Discrete mathematics, sometimes called finite mathematics, is the study of mathematical structures that are fundamentally discrete, in the sense of not supporting or requiring the notion of continuity. Most, if not all, of the objects studied in finite mathematics are countable sets, such as the integers.

Discrete mathematics has become popular in recent decades because of its applications to computer science. Concepts and notations from discrete mathematics are useful to study or express objects or problems in computer algorithms and programming languages. In some mathematics curricula, finite mathematics courses cover discrete mathematical concepts for business, while discrete mathematics courses emphasize concepts for computer science majors.

See also the list of basic discrete mathematics topics.

For contrast, see continuum, topology, and mathematical analysis.

Discrete mathematics usually includes :

• logic - a study of reasoning
• set theory - a study of collections of elements
• number theory
• combinatorics - a study of counting
• graph theory
• algorithmics - a study of methods of calculation
• information theory
• the theory of computability and complexity - a study on theoretical limitations on algorithms
• elementary probability theory and Markov chains
• linear algebra - a study of related linear equations

Some applications: game theory — queuing theory — graph theory — combinatorial geometry and combinatorial topology — linear programming — cryptography (including cryptology and cryptanalysis) — theory of computation

See also

• Important publications in discrete mathematics

Reference and further reading

Our sister project, Wikibooks, (http://en.wikibooks.org) provides an electronic book on Discrete mathematics. (http://en.wikibooks.org/Discrete_mathematics.html)

• Donald E. Knuth, The Art of Computer Programming
• Kenneth H. Rosen, Discrete Mathematics and Its Applications
• Richard Johnsonbaugh, Discrete Mathematics 5th ed. Macmillan, New Jersey

de:Diskrete Mathematik es:Matemática discreta he:מתמטיקה דיסקרטית nl:Discrete wiskunde ja:離散数学 pl:Matematyka dyskretna sk:Diskrétna matematika zh:离散数学

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