NationMaster - 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. ...

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

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[1]. 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. ...

See also

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

Categories: Computer science | Discrete mathematics Atonality describes music that does not conform to the system of tonal hierarchies, which characterizes the sound of classical European music between the seventeenth and nineteenth centuries. ... Cryptanalysis (from the Greek kryptÃ³s, hidden, and analÃ½ein, to loosen or to untie) is the study of methods for obtaining the meaning of encrypted information, without access to the secret information which is normally required to do so. ... The German Lorenz cipher machine Cryptography or cryptology is a field of mathematics and computer science concerned with information security and related issues, particularly encryption and authentication. ... Cryptography (from Greek kryptós, hidden, and gráphein, to write) is, traditionally, the study of means of converting information from its normal, comprehensible form into an incomprehensible format, rendering it unreadable without secret knowledge — the art of encryption. ... In the theory of computation, a finite state machine (FSM) or finite state automaton (FSA) is an abstract machine that has only a finite, constant amount of memory. ... In mathematics, logic, and computer science, a formal language is a set of finite-length words (i. ... Game theory is a branch of applied mathematics that studies strategic situations where players choose different actions in an attempt to maximize their returns. ... A labeled graph with 6 vertices and 7 edges. ... Discrete geometry or combinatorial geometry may be loosely defined as study of geometrical objects and properties that are discrete or combinatorial, either by their nature or by their representation; the study that does not essentially rely on the notion of continuity. ... In mathematics, combinatorial topology was an older name for algebraic topology, dating from the time when topological invariants of spaces (for example the Betti numbers) were regarded as derived from combinatorial decompositions such as simplicial complexes. ... In mathematics, linear programming (LP) problems are optimization problems in which the objective function and the constraints are all linear. ... Musical analysis can be defined as a process attempting to answer the question how does this music work?. The method employed to answer this question, and indeed exactly what is meant by the question, differs from analyst to analyst. ... Operations research, operational research, or simply OR, is the use of mathematical models, statistics, and algorithms to aid in decision-making. ... Queueing theory (spelled queuing theory in the United States) is the mathematical study of waiting lines (or queues). ... The theory of computation is the branch of computer science that deals with whether and how efficiently problems can be solved on a computer. ...

References and further reading

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Applications

See also