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.

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

• Donald E. Knuth, The Art of Computer Programming
• Kenneth H. Rosen, Discrete Mathematics and Its Applications 5th ed. McGraw Hill. ISBN 0072930330. Companion Web site: http://www.mhhe.com/math/advmath/rosen/
• Richard Johnsonbaugh, Discrete Mathematics 5th ed. Macmillan. ISBN 0130890081. Companion Web site: http://cwx.prenhall.com/bookbind/pubbooks/johnsonbaugh4/
• Norman L. Biggs, Discrete Mathematics 2nd ed. Oxford University Press. ISBN 0198507178. Companion Web site: http://www.oup.co.uk/isbn/0-19-850717-8 includes questions together with solutions.
• Neville Dean, Essence of Discrete Mathematics Prentice Hall. ISBN 0133459438. Not as in depth as above texts, but a gentle intro.
• Mathematics Archives, Discrete Mathematics links to syllabi, tutorials, programs, etc. http://archives.math.utk.edu/topics/discreteMath.html