Addition is written using the plus sign "+" between the terms; that is, in infix notation. The result is expressed with an equals sign. For example,1 + 1 = 2 (verbally, "one plus one equals two")2 + 2 ...
In mathematics, a product is the result of multiplying, or an expression that identifies factors to be multiplied. Thus, for instance, 6 is the product of 2 and 3 (the result of multiplication), and x ...
In the special case when the profinite group G is isomorphic to the additive group of the ring of p-adic integers Zp, the Iwasawa algebra Λ(G) is isomorphic to the ring of the formal power series Zp] ...
The Laplace operator is a second order differential operator in the n-dimensional Euclidean space, defined as the divergence (?·) of the gradient (??). Thus if ? is a twice-differentiable real-va ...
The definitions given below are valid for both Riemannian manifolds and pseudo-Riemannian manifolds, such as those of general relativity, with careful distinction being made between upper and lower in ...
The creation of Calculus was one of the greatest achievements of the 1600s, but the inventor of calculus is widely disputed: Was it Isaac Newton or Gottfried Wilhelm Leibniz? When Isaac Newton and Got ...
Differentiation is the action of computing a derivative. The derivative of a function f(x) of a variable x is a measure of the rate at which the value of the function changes with respect to the chang ...
The gamma function can be seen as a solution to the following interpolation problem:"Find a smooth curve that connects the points (x, y) given by y = (x ? 1)! at the positive integer values for x."A ...
The beta function is symmetric, meaning that\Beta(x,y) = \Beta(y,x).\!When x and y are positive integers, it follows from the definition of the gamma function \Gamma\ that:\Beta(x,y)=\dfrac{(x-1)!\,(y ...
Complex analysis is one of the classical branches in mathematics with roots in the 19th century and just prior. Important mathematicians associated with complex analysis include Euler, Gauss, Riemann, ...
The study of linear algebra first emerged from the study of determinants, which were used to solve systems of linear equations. Determinants were used by Leibniz in 1693, and subsequently, Gabriel Cra ...
In typical uncompressed bitmaps, image pixels are generally stored with a color depth of 1, 4, 8, 16, 24, 32, 48, or 64 bits per pixel. Pixels of 8 bits and fewer can represent either grayscale or ind ...
Groups just have one binary operation. To fully explain the behaviour of the different types of numbers, structures with two operators need to be studied. The most important of these are rings, and fi ...
For historical reasons, the word "algebra" has several related meanings in mathematics, as a single word or with qualifiers. Such a situation, where a single word has many meanings in the same area of ...
For an example of a function, let X be the set consisting of four shapes: a red triangle, a yellow rectangle, a green hexagon, and a red square; and let Y be the set consisting of five colors: red, bl ...
