Mathematics
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Areas of mathematics
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Analysis
Mathematical analysis
Mathematical analysis is a branch of mathematics that includes the theories of differentiation, integration, measure, limits, infinite series, and analytic functions.These theories are usually studied...
Mathematical analysis - Wikipedia
Finite difference
Bubble, Bubble … Boiling On The Double
The boiling of water is at the heart of many industrial processes, from the operation of electric power plants to chemical processing and desalination. But the details of what happens on a hot surface...
25 Stunning Photographs Of Sacred Geometry And Fractals In Nature
These wonderfully symmetrical plants show the fractal nature of math, physics and the universe. Could this be evidence of sacred geometry? "Look deep into nature, and then you will understand everythi...
Mandelbrot set
A zoom into the Seahorse Valley region of the Mandelbrot Set. Set to La Villageoise by Rameau, performed by Trevor Pinnock. (Music -- and therefore this ...
Calculus - Calculus I in 20 Minutes (The Original) by Thinkwell
http://bit.ly/qYnN40 Want to see the ENTIRE Calculus in 20 Minutes for FREE? Click on this link to see all 20 minutes in the full multimedia environment.
Fractal Zoom Mandelbrot Corner - YouTube
Nov 12, 2006 ... A fractal zoom on a mandelbrot set, finishing on a dendrite area. Made using XaoS (freeware program) Music: Aalborg Fantasy Soundtracks ...
Calculus - Math World
Finite difference
A finite difference is a mathematical expression of the form f(x + b) − f(x + a). If a finite difference is divided by b − a, one gets a difference ...
Finite difference - Wikipedia
Bubble, Bubble … Boiling On The Double
The boiling of water is at the heart of many industrial processes, from the operation of electric power plants to chemical processing and desalination. But the details of what happens on a hot surface...
Category theory
Category theory is used to formalize mathematical structure and its concepts as a collection of objects and arrows (also called morphisms). A category has two basic properties: the ability to compose ...
25 Stunning Photographs Of Sacred Geometry And Fractals In Nature
These wonderfully symmetrical plants show the fractal nature of math, physics and the universe. Could this be evidence of sacred geometry? "Look deep into nature, and then you will understand everythi...
Differential operator
In mathematics, a differential operator is an operator defined as a function of the differentiation operator. It is helpful, as a matter of notation first, to consider differentiation as an abstract o...
Uzawa iteration
In numerical mathematics, the Uzawa iteration is an algorithm for solving saddle point problems. It is named after Hirofumi Uzawa and was originally introduced in the context of concave programming.<...
Hyperbolic growth
When a quantity grows towards a singularity under a finite variation (a "finite-time singularity") it is said to undergo hyperbolic growth. More precisely, the reciprocal function has a hyperbola as ...
Hyperbolic growth - Wikipedia
Limit (mathematics)
In mathematics, a limit is the value that a function or sequence "approaches" as the input or index approaches some value. Limits are essential to calculus (and mathematical analysis in general) and a...
Limit (mathematics) - Wikipedia
Nevanlinna function
Characterizations of the exponential function
In mathematics, the exponential function can be characterized in many ways. The following characterizations (definitions) are most common. This article discusses why each characterization makes sense,...
Chisini mean
In mathematics, a function f of n variables leads to a Chisini mean M if for every vector <x1 ... xn>, there exists a unique M such that The arithmetic, harmonic, geometric, generalised, Heronia...
Chisini mean - Wikipedia
Multiplicity (mathematics)
In mathematics, the multiplicity of a member of a multiset is the number of times it appears in the multiset. For example, the number of times a given polynomial equation has a root at a given point....
Fourier integral operator
In mathematical analysis, Fourier integral operators have become an important tool in the theory of partial differential equations. The class of Fourier integral operators contains differential opera...
Superadditivity
In mathematics, a sequence { an }, n ≥ 1, is called superadditive if it satisfies the inequalityfor all m and n. The major reason for the use of superadditive sequences is the following lemma due to ...
Notation for differentiation
In differential calculus, there is no single uniform notation for differentiation. Instead, several different notations for the derivative of a function or variable have been proposed by different mat...
Wave front set
In mathematical analysis, more precisely in microlocal analysis, the wave front (set) WF(f) characterizes the singularities of a generalized function f, not only in space, but also with respect to its...
Perturbation theory
Perturbation theory comprises mathematical methods for finding an approximate solution to a problem, by starting from the exact solution of a related problem. A critical feature of the technique is a ...
Smooth function
In mathematical analysis, smoothness has to do with how many derivatives of a function exist and are continuous. The term smooth function is often used technically to mean a function that has derivati...
Smooth function - Wikipedia
Hyperreal number
The system of hyperreal numbers is a way of treating infinite and infinitesimal quantities. The hyperreals, or nonstandard reals, *R, are an extension of the real numbers R that contains numbers grea...
Hyperreal number - Wikipedia
Neighbourhood (mathematics)
In topology and related areas of mathematics, a neighbourhood (or neighborhood) is one of the basic concepts in a topological space. Intuitively speaking, a neighbourhood of a point is a set containin...
Neighbourhood (mathematics) - Wikipedia
Series (mathematics)
A series is, informally speaking, the sum of the terms of a sequence. Finite sequences and series have defined first and last terms, whereas infinite sequences and series continue indefinitely.In math...
Weighted mean
The weighted mean is similar to an arithmetic mean (the most common type of average), where instead of each of the data points contributing equally to the final average, some data points contribute mo...
Bounded set
In mathematical analysis and related areas of mathematics, a set is called bounded, if it is, in a certain sense, of finite size. Conversely, a set which is not bounded is called unbounded. The word ...
Stress majorization
Stress majorization is an optimization strategy used in multidimensional scaling (MDS) where, for a set of n m-dimensional data items, a configuration X of n points in r(<<m)-dimensional space i...