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Information about Discrete Mathematics

Discrete mathematics, also called finite mathematics or Decision Maths, 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:

See also

Applications

References and further reading

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Major fields of mathematics
In mathematics, a continuous function is a function for which, intuitively, small changes in the input result in small changes in the output. Otherwise, a function is said to be discontinuous.
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countable set is a set with the same cardinality (i.e., number of elements) as some subset of the set of natural numbers. The term was originated by Georg Cantor; it stems from the fact that the natural numbers are often called counting numbers.
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The integers (from the Latin integer, which means with untouched integrity, whole, entire) are the set of numbers including the whole numbers (0, 1, 2, 3, …) and their negatives (0, −1, −2, −3, …).
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graph is the basic object of study in graph theory. Informally speaking, a graph is a set of objects called points, nodes, or vertices connected by links called lines or edges.
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This article is about the term formal language as it is used in mathematics, logic and computer science. For information about a mode of expression that is more disciplined or precise than everyday speech, see Register (linguistics).

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Computer science, or computing science, is the study of the theoretical foundations of information and computation and their implementation and application in computer systems.
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In mathematics, computing, linguistics, and related disciplines, an algorithm is a finite list of well-defined instructions for accomplishing some task that, given an initial state, will proceed through a well-defined series of successive states, eventually terminating in an
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A programming language is an artificial language that can be used to control the behavior of a machine, particularly a computer. Programming languages, like natural languagess, are defined by syntactic and semantic rules which describe their structure and meaning respectively.
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The term finite mathematics refers either to
  • discrete mathematics, or to
  • a course conventionally required of business students, in which the curriculum brings together several mathematical topics, including basic probability theory, an introduction to linear

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In mathematics, the word continuum has at least two distinct meanings, outlined in the sections below. For other uses see Continuum.

Ordered set or shah's set

The term the continuum sometimes denotes the real line.
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Topology (Greek topos, "place," and logos, "study") is a branch of mathematics that is an extension of geometry. Topology begins with a consideration of the nature of space, investigating both its fine structure and its global structure.
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Analysis has its beginnings in the rigorous formulation of calculus. It is the branch of mathematics most explicitly concerned with the notion of a limit, whether the limit of a sequence or the limit of a function.
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Logic (from Classical Greek λόγος logos; meaning word, thought, idea, argument, account, reason, or principle) is the study of the principles and criteria of valid inference and demonstration.
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Set theory is the mathematical theory of sets, which represent collections of abstract objects. It encompasses the everyday notions, introduced in primary school, often as Venn diagrams, of collections of objects, and the elements of, and membership in, such collections.
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Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study.
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Combinatorics is a branch of pure mathematics concerning the study of discrete (and usually finite) objects. It is related to many other areas of mathematics, such as algebra, probability theory, ergodic theory and geometry, as well as to applied subjects such as computer science
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Combinatorial design theory is the part of combinatorial mathematics that deals with the existence and construction of systems of finite sets whose intersections have specified numerical properties.
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Combinatorial enumeration is a subfield of enumeration that deals with the counting of objects whose symmetries do not exist or, if they exist, are combinatorial in nature.

See also

  • combinatorics
  • superpattern

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graph theory is the study of graphs; mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges
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In mathematics, computing, linguistics, and related disciplines, an algorithm is a finite list of well-defined instructions for accomplishing some task that, given an initial state, will proceed through a well-defined series of successive states, eventually terminating in an
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Information theory is a branch of applied mathematics and engineering involving the quantification of information to find fundamental limits on compressing and reliably communicating data.
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Digital geometry deals with discrete sets (usually discrete point sets) considered to be digitized models or images of objects of the 2D or 3D Euclidean space.

Simply put, digitizing is replacing an object by a discrete set of its points.
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Computability theory may refer to:
  • Recursion theory, a branch of mathematical logic, contemporarily called computability theory.
  • Computability theory (computer science), locating basic questions of what is computable within the context of theoretical computer science.

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Complexity in general usage is the opposite of simplicity. Complexity in specific usage is the opposite of independence, while complication is the opposite of simplicity.
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Probability theory is the branch of mathematics concerned with analysis of random phenomena.[1] The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities
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This article or section may be confusing or unclear for some readers.
Please [improve the article] or discuss this issue on the talk page. This article has been tagged since September 2007.
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Linear algebra is the branch of mathematics concerned with the study of vectors, vector spaces (also called linear spaces), linear maps (also called linear transformations), and systems of linear equations.
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function expresses dependence between two quantities, one of which is given (the independent variable, argument of the function, or its "input") and the other produced (the dependent variable, value of the function, or "output").
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partially ordered set (or poset) formalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set. A poset consists of a set together with a binary relation that describes, for certain pairs of elements in the set, the requirement that one
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In mathematics, a proof is a demonstration that, assuming certain axioms, some statement is necessarily true. A proof is a logical argument, not an empirical one. That is, one must demonstrate that a proposition is true in all cases before it is considered a theorem of mathematics.
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