102,846
edits
Changes
From Nordan Symposia
Jump to navigationJump to searchCreated page with 'File:lighterstill.jpgright|frame ==Etymology== [http://nordan.daynal.org/wiki/index.php?title=English#ca._1100-1500_.09THE_MIDDLE_ENGLISH_PERIOD Middle...'
[[File:lighterstill.jpg]][[File:Discrete.jpg|right|frame]]
==Etymology==
[http://nordan.daynal.org/wiki/index.php?title=English#ca._1100-1500_.09THE_MIDDLE_ENGLISH_PERIOD Middle English], from [[Latin]] discretus
*Date: [http://www.wikipedia.org/wiki/14th_Century 14th century]
==Definitions==
*1 : [[constituting]] a separate [[entity]] : [[individually]] distinct <several discrete [[sections]]>
*2 a : consisting of distinct or unconnected elements : noncontinuous
:b : taking on or having a [[finite]] or countably [[infinite]] [[number]] of [[values]] <discrete [[probabilities]]> <a discrete [[random]] [[variable]]>
==Description==
'''Discrete''' [[mathematics]] is the [[study]] of mathematical [[structures]] that are [[fundamentally]] discrete rather than [[continuous]]. In [[contrast]] to [http://en.wikipedia.org/wiki/Real_number real numbers] that have the property of varying "smoothly", the objects studied in discrete mathematics – such as [http://en.wikipedia.org/wiki/Integer integers], [http://en.wikipedia.org/wiki/Graph_(mathematics) graphs], and [[statements]] in [[logic]] – do not vary smoothly in this way, but have distinct, separated [[values]]. Discrete mathematics therefore excludes [[topics]] in "continuous mathematics" such as [http://en.wikipedia.org/wiki/Calculus calculus] and [[analysis]]. Discrete objects can often be enumerated by integers. More [[formally]], discrete mathematics has been characterized as the branch of [[mathematics]] dealing with [http://en.wikipedia.org/wiki/Countable_set countable sets] (sets that have the same cardinality as subsets of the integers, including [http://www.wikipedia.org/wiki/Rational_Numbers rational numbers] but not [http://www.wikipedia.org/wiki/Real_Numbers real numbers]). However, there is no exact, [[universally]] [[agreed]], definition of the term "discrete mathematics." Indeed, discrete mathematics is described less by what is included than by what is excluded: continuously varying [[quantities]] and related notions.
The set of objects [[studied]] in discrete mathematics can be [[finite]] or [[infinite]]. The term finite mathematics is sometimes applied to parts of the field of discrete mathematics that deals with finite sets, particularly those areas relevant to [[business]].
[[Research]] in discrete mathematics increased in the [http://www.wikipedia.org/wiki/20th_Century latter half of the twentieth century] partly due to the [[development]] of [http://en.wikipedia.org/wiki/Digital_computers digital computers] which operate in discrete steps and store [[data]] in discrete bits. [[Concepts]] and notations from discrete mathematics are useful in studying and describing objects and [[problems]] in branches of [[computer science]], such as computer [[algorithms]], programming [[languages]], [http://en.wikipedia.org/wiki/Cryptography cryptography], [http://en.wikipedia.org/wiki/Automated_theorem_proving automated theorem proving], and software development. Conversely, computer implementations are significant in applying [[ideas]] from discrete mathematics to real-world problems, such as in operations research.
Although the main objects of [[study]] in discrete mathematics are discrete objects, [[analytic]] [[methods]] from continuous mathematics are often employed as well.[http://en.wikipedia.org/wiki/Discrete_mathematics]
[[Category: Mathematics]]
==Etymology==
[http://nordan.daynal.org/wiki/index.php?title=English#ca._1100-1500_.09THE_MIDDLE_ENGLISH_PERIOD Middle English], from [[Latin]] discretus
*Date: [http://www.wikipedia.org/wiki/14th_Century 14th century]
==Definitions==
*1 : [[constituting]] a separate [[entity]] : [[individually]] distinct <several discrete [[sections]]>
*2 a : consisting of distinct or unconnected elements : noncontinuous
:b : taking on or having a [[finite]] or countably [[infinite]] [[number]] of [[values]] <discrete [[probabilities]]> <a discrete [[random]] [[variable]]>
==Description==
'''Discrete''' [[mathematics]] is the [[study]] of mathematical [[structures]] that are [[fundamentally]] discrete rather than [[continuous]]. In [[contrast]] to [http://en.wikipedia.org/wiki/Real_number real numbers] that have the property of varying "smoothly", the objects studied in discrete mathematics – such as [http://en.wikipedia.org/wiki/Integer integers], [http://en.wikipedia.org/wiki/Graph_(mathematics) graphs], and [[statements]] in [[logic]] – do not vary smoothly in this way, but have distinct, separated [[values]]. Discrete mathematics therefore excludes [[topics]] in "continuous mathematics" such as [http://en.wikipedia.org/wiki/Calculus calculus] and [[analysis]]. Discrete objects can often be enumerated by integers. More [[formally]], discrete mathematics has been characterized as the branch of [[mathematics]] dealing with [http://en.wikipedia.org/wiki/Countable_set countable sets] (sets that have the same cardinality as subsets of the integers, including [http://www.wikipedia.org/wiki/Rational_Numbers rational numbers] but not [http://www.wikipedia.org/wiki/Real_Numbers real numbers]). However, there is no exact, [[universally]] [[agreed]], definition of the term "discrete mathematics." Indeed, discrete mathematics is described less by what is included than by what is excluded: continuously varying [[quantities]] and related notions.
The set of objects [[studied]] in discrete mathematics can be [[finite]] or [[infinite]]. The term finite mathematics is sometimes applied to parts of the field of discrete mathematics that deals with finite sets, particularly those areas relevant to [[business]].
[[Research]] in discrete mathematics increased in the [http://www.wikipedia.org/wiki/20th_Century latter half of the twentieth century] partly due to the [[development]] of [http://en.wikipedia.org/wiki/Digital_computers digital computers] which operate in discrete steps and store [[data]] in discrete bits. [[Concepts]] and notations from discrete mathematics are useful in studying and describing objects and [[problems]] in branches of [[computer science]], such as computer [[algorithms]], programming [[languages]], [http://en.wikipedia.org/wiki/Cryptography cryptography], [http://en.wikipedia.org/wiki/Automated_theorem_proving automated theorem proving], and software development. Conversely, computer implementations are significant in applying [[ideas]] from discrete mathematics to real-world problems, such as in operations research.
Although the main objects of [[study]] in discrete mathematics are discrete objects, [[analytic]] [[methods]] from continuous mathematics are often employed as well.[http://en.wikipedia.org/wiki/Discrete_mathematics]
[[Category: Mathematics]]
