Discrete Mathematics

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 Algorithm s and Programming Language s. 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 — Analysis of Atonal Music

SEE ALSO

Important Publications In Discrete Mathematics

Reference and further reading

Donald E. Knuth , '' The Art Of Computer Programming ''

Kenneth H. Rosen, ''Handbook of Discrete and Combinatorial Mathematics'' CRC Press. ISBN 0849301491.

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.

¹ Also on (digital) topology, graph theory, combinatorics, axiomatic systems.

Mathematics Archives, Discrete Mathematics links to syllabi, tutorials, programs, etc. http://archives.math.utk.edu/topics/discreteMath.html

Ronald Graham , Donald E. Knuth , Oren Patashnik , '' Concrete Mathematics ''

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Discrete Mathematics

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