Discrete mathematics
Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continuous f ...
is the study of
mathematical
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
structures
A structure is an arrangement and organization of interrelated elements in a material object or system, or the object or system so organized. Material structures include man-made objects such as buildings and machines and natural objects such as ...
that are fundamentally
discrete
Discrete may refer to:
*Discrete particle or quantum in physics, for example in quantum theory
* Discrete device, an electronic component with just one circuit element, either passive or active, other than an integrated circuit
* Discrete group, ...
rather than
continuous
Continuity or continuous may refer to:
Mathematics
* Continuity (mathematics), the opposing concept to discreteness; common examples include
** Continuous probability distribution or random variable in probability and statistics
** Continuous ...
. In contrast to
real number
In mathematics, a real number is a number that can be used to measure a continuous one- dimensional quantity such as a duration or temperature. Here, ''continuous'' means that pairs of values can have arbitrarily small differences. Every re ...
s that have the property of varying "smoothly", the objects studied in discrete mathematics – such as
integer
An integer is the number zero (0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...). The negations or additive inverses of the positive natural numbers are referred to as negative in ...
s,
graphs
Graph may refer to:
Mathematics
*Graph (discrete mathematics), a structure made of vertices and edges
**Graph theory, the study of such graphs and their properties
* Graph (topology), a topological space resembling a graph in the sense of discre ...
, and statements in
logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure o ...
– do not vary smoothly in this way, but have distinct, separated values.
Discrete mathematics, therefore, excludes topics in "continuous mathematics" such as
calculus
Calculus is the mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations.
Originally called infinitesimal calculus or "the ...
and
analysis
Analysis (: analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (38 ...
.
Included below are many of the standard terms used routinely in university-level courses and in research papers. This is not, however, intended as a complete list of mathematical terms; just a selection of typical ''
terms of art
Jargon, or technical language, is the specialized terminology associated with a particular field or area of activity. Jargon is normally employed in a particular communicative context and may not be well understood outside that context. The conte ...
'' that may be encountered.
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Discrete mathematical disciplines
For further reading in discrete mathematics, beyond a basic level, see these pages. Many of these disciplines are closely related to
computer science
Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, ...
.
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Concepts in discrete mathematics
Sets
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Functions
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Arithmetic
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Elementary algebra
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Mathematical relations
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Mathematical phraseology
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Combinatorics
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Probability
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Propositional logic
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Mathematicians associated with discrete mathematics
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* Leonhard Euler - Swiss mathematician (1707-1783)
* Claude Shannon - American mathematician (1916-2001)
* Donald Knuth - American mathematician and computer scientist (b. 1938)
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See also
References
External links
Archives* Jonathan Arbib & John Dwyer, ''Discrete Mathematics for Cryptography'', 1st Edition .
* John Dwyer & Suzy Jagger, ''Discrete Mathematics for Business & Computing'', 1st Edition 2010 .
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Discrete mathematics
Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continuous f ...
Discrete mathematics
Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continuous f ...
*
Discrete mathematics
Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continuous f ...