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Encyclopedia > Discrete mathematics

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. The word discrete comes from the Latin word discretus which means separate. ... In mathematics, a continuous function is a function for which, intuitively, small changes in the input result in small changes in the output. ... In mathematics the term countable set is used to describe the size of a set, e. ... The integers consist of the positive natural numbers (1, 2, 3, â€¦), their negatives (âˆ’1, âˆ’2, âˆ’3, ...) and the number zero. ... In mathematics, logic, and computer science, a formal language is a set of finite-length words (i. ...

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.   Computer science is the study of the theoretical foundations of information and computation and their implementation and application in computer systems. ... Flowcharts are often used to represent algorithms. ... Computer code (HTML with JavaScript) in a tool that uses syntax highlighting (colors) to help the developer see the purpose of each piece of code. ... The term finite mathematics refers either to what discrete mathematics, or to a course conventionally required of business students, in which the curriculum brings together a certain hodge-podge of topics, including some basic probability theory, some linear programming, some theory of matrices and determinants, and sometimes an abbreviated account...

For contrast, see continuum, topology, and mathematical analysis. In mathematics, the word continuum sometimes denotes the real line. ... Topology (Greek topos, place and logos, study) is a branch of mathematics concerned with spatial properties preserved under bicontinuous deformation (stretching without tearing or gluing); these are the topological invariants. ... Analysis is the generic name given to any branch of mathematics that depends upon the concepts of limits and convergence. ...

Discrete mathematics includes the following topics:

Logic, from Classical Greek Î»ÏŒÎ³Î¿Ï‚ (logos), originally meaning the word, or what is spoken, (but coming to mean thought or reason) is most often said to be the study of criteria for the evaluation of arguments, although the exact definition of logic is a matter of controversy among philosophers. ... Set theory is the mathematical theory of sets, which represent collections of abstract objects. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... Combinatorics is a branch of mathematics that studies collections (usually finite) of objects that satisfy specified criteria. ... A labeled graph with 6 vertices and 7 edges. ... Flowcharts are often used to represent algorithms. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... Computation can be defined as finding a solution to a problem from given inputs by means of an algorithm. ... For the Computer Science term, see Computational complexity theory. ... Probability theory is the mathematical study of probability. ... In mathematics, a Markov chain is a discrete-time stochastic process with the Markov property named after Andrey Markov. ... Linear algebra is the branch of mathematics concerned with the study of vectors, vector spaces (also called linear spaces), linear transformations, and systems of linear equations in finite dimensions. ...

### References and further reading Wikibooks has more about this subject:

Image File history File links Wikibooks-logo-en. ... Wikibooks logo Wikibooks, previously called Wikimedia Free Textbook Project and Wikimedia-Textbooks, is part of the Wikimedia Foundation. ... Donald Knuth at a reception for the Open Content Alliance. ... Cover of books The Art of Computer Programming is a comprehensive monograph written by Donald Knuth which covers many kinds of programming algorithms and their analysis. ... Ronald L. Graham (born October 31, 1935) is a mathematician credited by the American Mathematical Society with being one of the principle architects of the rapid development worldwide of discrete mathematics in recent years. He has done important work in scheduling theory, computational geometry, Ramsey theory, and quasi-randomness. ... Donald Knuth at a reception for the Open Content Alliance. ... Oren Patashnik (born 1954) is a computer scientist. ... Concrete Mathematics by Ronald L. Graham, Donald E. Knuth and Oren Patashnik is a textbook that provides its readers with mathematical background that can be especially useful in computer science. ...

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• Important publications in discrete mathematics

This is a list of basic discrete mathematics topics, by Wikipedia page. ... This is a list of important publications in mathematics, organized by field. ...

### Applications Results from FactBites:

 Discrete mathematics - Wikipedia, the free encyclopedia (278 words) 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. 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.
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