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.

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\n