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.

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.

- 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\n