Discrete mathematics

Discrete mathematics, also called finite mathematics or decision mathematics, is the study of mathematical structures that are fundamentally discrete in the sense of not supporting or requiring the notion of continuity. Objects studied in finite mathematics are largely countable sets such as integers, finite graphs, and formal languages.

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 describe 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 includes the following topics:

Logic - a study of reasoning
Set theory - a study of collections of elements
Number theory
Combinatorics, including
Algorithmics - a study of methods of calculation
Information theory
Digital geometry
Computability and complexity theories - dealing with theoretical and practical limitations of algorithms
Partially ordered sets
Proofs
Counting and relations

References and further reading

Wikibooks has more on the topic of Discrete mathematics

Donald E. Knuth, The Art of Computer Programming
Kenneth H. Rosen, Handbook of Discrete and Combinatorial Mathematics CRC Press. ISBN 0-8493-0149-1.
Kenneth H. Rosen, Discrete Mathematics and Its Applications 5th ed. McGraw Hill. ISBN 0-07-293033-0. Companion Web site: http://www.mhhe.com/math/advmath/rosen/
Richard Johnsonbaugh, Discrete Mathematics 6th ed. Macmillan. ISBN 0-13-045803-1. Companion Web site: http://wps.prenhall.com/esm_johnsonbau_discrtmath_6/
Ralph P. Grimaldi, Discrete and Combinatorial Mathematics: An Applied Introduction 5th ed. Addison Wesley. ISBN 0-20-172634-3
Norman L. Biggs, Discrete Mathematics 2nd ed. Oxford University Press. ISBN 0-19-850717-8. 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 0-13-345943-8. Not as in depth as above texts, but a gentle intro.
Klette, R., and A. Rosenfeld (2004). Digital Geometry. Morgan Kaufmann. ISBN 1-55860-861-3. 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
Discrete Mathematics AJ Sadler