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Wikipedia on Functions and mappings

In mathematics and related technical fields, the term map or mapping is often a synonym for ''function''; see function (mathematics). Thus, for example, a ''partial map'' is a ''partial function'', and a ''total map'' is a ''total function''. Related terms like ''domain'', ''codomain'', ''injective'', ''continuous'', etc. can be applied equally to maps and functions, with the same meaning. In many branches of mathematics, the term denotes a function with a property specific to that branch, such as a ''continuous function'' in topology, a ''linear map'' in linear algebra, etc. Sets of maps with special properties are the subjects of many important theories: see for instance Lie group, mapping class group, permutation group. In formal logic, the term is sometimes used for a ''functional predicate'', whereas a function is a model of such a predicate in set theory. In graph theory, a map is a drawing of a graph on a surface without intersecting edges. More »
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Function (mathematics)
The mathematical concept of a function expresses the intuitive idea of deterministic dependence between two quantities, one of which is viewed as primary and the other as secondary . A function then is a way to associate a unique output for each input of a specified type, for example, a real number or an element of a given set. This definition covers most elementary functions, maps between algebraic structures, such as groups, and between geometric objects, such as manifolds. More »
Functional analysis
Functional analysis is the branch of mathematics, and specifically of analysis, concerned with the study of spaces of functions and operators acting on them. It has its historical roots in the study of transformations, such as the Fourier transform, and in the study of differential and integral equations. This usage of the word ''functional'' goes back to the calculus of variations, implying a function whose argument is a function. Its use in general has been attributed to mathematician and... More »
Continuous function
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. An intuitive though imprecise idea of continuity is given by the common statement that a continuous function is a function whose graph can be drawn without lifting the chalk from the blackboard. The context of this introduction is one in which the inputs and outputs of functions are real n... More »
Fractal
In colloquial usage, a fractal is "a rough or fragmented geometric shape that can be subdivided in parts, each of which is a reduced-size copy of the whole". The term was coined by Benoît Mandelbrot in 1975 and was derived from the Latin ''fractus'' meaning "broken" or "fractured". A fractal as a geometric object generally has the following features: * It has a fine structure at arbitrarily small scales. * It is too irregular to be easily described in traditional Euclidean geometric... More »
Inverse function
In mathematics, an inverse function is, in simple terms, a function which "does the reverse" of a given function. More »
Continuous function (topology)
In topology and related areas of mathematics a continuous function is a morphism between topological spaces. Intuitively, this is a function ''f'' where a set of points near ''f'' always contain the image of a set of points near ''x''. For a general topological space, this means a neighbourhood of ''f'' always contains the image of a neighbourhood of ''x''. In a metric space this means that the points within a given distance of ''f'' always contain the images of all the points within some... More »
Bounded operator
In functional analysis , a bounded linear operator is a linear transformation ''L'' between normed vector spaces ''X'' and ''Y'' for which the ratio of the norm of ''L'' to that of ''v'' is bounded by the same number, over all non-zero vectors ''v'' in ''X''. In other words, there exists some ''M'' > 0 such that for all ''v'' in ''X'', :\|Lv\|_Y \le M \|v\|_X.\, The smallest such ''M'' is called the operator norm \|L\|_{op} of ''L''. More »
Brownian motion
:''This article is about the physical phenomenon; for the stochastic process, see Wiener process. For the sports team, see Brownian Motion (Ultimate).'' ''Brownian motion'' is either the random movement of particles suspended in a fluid or the mathematical model used to describe such random movements, often called a Wiener process. The mathematical model of Brownian motion has several real-world applications. An often quoted example is stock market fluctuations. More »
Cantor set
In mathematics, the Cantor set, introduced by German mathematician Georg Cantor in 1883, is a set of points lying on a single line segment that has a number of remarkable and deep properties. Through consideration of it, Cantor and others helped lay the foundations of modern general topology. Although Cantor himself defined the set in a general, abstract way, the most common modern construction is the Cantor ternary set, built by removing the middle thirds of a line segment. More »
Bessel function
In mathematics, Bessel functions, first defined by the mathematician Daniel Bernoulli and generalized by Friedrich Bessel, are canonical solutions ''y'' of Bessel's differential equation: x^2 \frac{d^2 y}{dx^2} + x \frac{dy}{dx} + y More »
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