Discrete mathematics
From Psychology Wiki
Community portal · Tasks to do · News · Help
Clinical · Educational · Ind&Org · Other fields · Professional · Transpersonal · World
Assessment |
Biopsychology |
Comparative |
Cognitive |
Developmental |
Language
Personality |
Philosophy |
Research Methods |
Social |
Statistics
Statistics: Scientific method · Research methods · Experimental design · Undergraduate statistics courses · Statistical tests · Game theory · Decision theory
Discrete mathematics, also 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 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 - a study of counting;
- Graph theory;
- Digital geometry and digital topology;
- Algorithmics - a study of methods of calculation;
- Information theory;
- Computability and complexity theories - dealing with theoretical and practical limitations of algorithms;
- Elementary probability theory and Markov chains;
- Linear algebra - a study of related linear equations.
- Functions
- Partially Ordered Sets
- Probability
- Proofs
- Counting and Relations
- Collections
[edit] References and further reading
- 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/
- 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
[edit] See also
[edit] Applications
ar:رياضيات متقطعة an:Matematica discreta bs:Diskretna matematika bg:Дискретна математика ca:Matemàtica discreta cs:Diskrétní matematika da:Diskret matematik de:Diskrete Mathematik es:Matemática discreta eo:Diskreta matematiko fa:ریاضیات گسسته fr:Mathématiques discrètes ko:이산수학he:מתמטיקה בדידה lt:Diskrečioji matematika nl:Discrete wiskundept:Matemática discreta ru:Дискретная математика sk:Diskrétna matematika fi:Diskreetti matematiikka sv:Diskret matematik th:วิยุตคณิต vi:Toán học rời rạc zh:离散数学
| This page uses content from the English-language version of Wikipedia. The original article was at Discrete mathematics. The list of authors can be seen in the page history. As with Psychology Wiki, the text of Wikipedia is available under the GNU Free Documentation License. |
