Discrete mathematics

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.

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

Discrete mathematics

See also

Reference and further reading