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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 curriculums 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 cover
- logic - a study of reasoning,
- set theory - a group of objects,
- number theory,
- combinatorics,
- graph theory,
- algorithmics - an instruction of computations,
- information theory,
- the theory of computability and complexity, a study on theoretical limitations on algorithms,
- elementary probability theory and Markov chains,
- linear algebra.
Some applications: Game theory -- Queuing theory -- Graph
theory -- combinatorial geometry and combinatorial topology -- Linear programming -- cryptography (including
cryptology and cryptanalysis) -- theory of
computation
Reference and further reading
- 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
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