In mathematics, a contraction mapping, or contraction, on a metric space ( M, d ) is a function f from M to itself, with the property that there is some nonnegative real number < math > k < 1 </ math > such that for all x and y in M,

In category theory, a branch of mathematics, a functor is a special type of mapping between categories.

In mathematics, a linear map, linear mapping, linear transformation, or linear operator ( in some contexts also called linear function ) is a function between two modules ( including vector spaces ) that preserves the operations of module ( or vector ) addition and scalar multiplication.

In mathematics, the Banach fixed-point theorem ( also known as the contraction mapping theorem or contraction mapping principle ) is an important tool in the theory of metric spaces ; it guarantees the existence and uniqueness of fixed points of certain self-maps of metric spaces, and provides a constructive method to find those fixed points.

The Julia set of a function ƒ is commonly denoted J ( ƒ ), and the Fatou set is denoted F ( ƒ ).< ref > Note that for other areas of mathematics the notation can also represent the Jacobian matrix of a real valued mapping between smooth manifolds .</ ref > These sets are named after the French mathematicians Gaston Julia and Pierre Fatou whose work began the study of complex dynamics during the early 20th century.

* Contraction mapping, in mathematics, a type of function on a metric space

* Injective function in mathematics, a function mapping distinct arguments to distinct values

But generative art can also be made using systems of chemistry, biology, mechanics and robotics, smart materials, manual randomization, mathematics, data mapping, symmetry, tiling, and more.

* Bilinear transform, a complex conformal mapping in mathematics

In mathematics, the cokernel of a linear mapping of vector spaces f: X → Y is the quotient space Y / im ( f ) of the codomain of f by the image of f. The dimension of the cokernel is called the corank of f.

In mathematics, a reflection ( also spelled reflexion ) is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as set of fixed points ; this set is called the axis ( in dimension 2 ) or plane ( in dimension 3 ) of reflection.

Since then this mapping has become an avenue to higher mathematics.

Quantization, in mathematics and digital signal processing, is the process of mapping a large set of input values to a smaller set – such as rounding values to some unit of precision.

Analytic methods typically use the structure of mathematics to arrive at a simple, elegant solution, but the required derivation for all but the simplest domain geometries can be quite complex ( involving non-standard coordinates, conformal mapping, etc .).

* Operator ( mathematics ), a mapping from one vector space or module to another

In mathematics, a bilinear form on a vector space V is a bilinear mapping V × V → F, where F is the field of scalars.

In mathematics, the ( field ) norm is a mapping defined in field theory, to map elements of a larger field into a smaller one.

In most of mathematics and in some related technical fields, the term mapping, usually shortened to map, is either a synonym for function, or denotes a particular kind of function which is important in that branch, or denotes something conceptually similar to a function.

In mathematics, the Lefschetz fixed-point theorem is a formula that counts the fixed points of a continuous mapping from a compact topological space X to itself by means of traces of the induced mappings on the homology groups of X.

In mathematics, an invariant subspace of a linear mapping

In mathematics, a Tschirnhaus transformation, also known as Tschirnhausen transformation, is a type of mapping on polynomials developed by Ehrenfried Walther von Tschirnhaus in 1683.

In mathematics, in the sub-field of geometric topology, the mapping class group

In mathematics, shear mapping or transvection is a particular kind of linear mapping.

Next September, after receiving a degree from Yale's Master of Arts in Teaching Program, I will be teaching somewhere -- that much is guaranteed by the present shortage of mathematics teachers.

From the town surveyor, Hans learned drawing and mathematics and, from a university student, some academic subjects.

The term " arithmetic mean " is preferred in mathematics and statistics because it helps distinguish it from other means such as the geometric and harmonic mean.

Ethics cannot be based on the authoritative certainty given by mathematics and logic, or prescribed directly from the empirical findings of science.

In mathematics and computer science, an algorithm ( originating from al-Khwārizmī, the famous Persian mathematician Muḥammad ibn Mūsā al-Khwārizmī ) is a step-by-step procedure for calculations.

He stressed training in awareness of abstracting, using techniques that he had derived from his study of mathematics and science.

In mathematics, an automorphism is an isomorphism from a mathematical object to itself.

Ampère engaged in a diverse array of scientific inquiries during the years leading up to his election to the academy — writing papers and engaging in topics from mathematics and philosophy to chemistry and astronomy.

He also applied mathematics in generalizing physical laws from these experimental results.

Two aspects of this attitude deserve to be mentioned: 1 ) he did not only study science from books, as other academics did in his day, but actually observed and experimented with nature ( the rumours starting by those who did not understand this are probably at the source of Albert's supposed connections with alchemy and witchcraft ), 2 ) he took from Aristotle the view that scientific method had to be appropriate to the objects of the scientific discipline at hand ( in discussions with Roger Bacon, who, like many 20th century academics, thought that all science should be based on mathematics ).

He was educated at the Collège des Quatre-Nations ( also known as Collège Mazarin ) from 1754 to 1761, studying chemistry, botany, astronomy, and mathematics.

Grothendieck ’ s way of thinking has influenced generations of mathematicians long after his departure from mathematics.

This program culminated in the proofs of the Weil conjectures, the last of which was settled by Grothendieck's student Pierre Deligne in the early 1970s after Grothendieck had largely withdrawn from mathematics.

Francesco Lana de Terzi, a 17th century Jesuit professor of physics and mathematics from Brescia, Lombardy, has been referred to as the Father of Aeronautics.

Akio, however, found his true calling in mathematics and physics, and in 1944 he graduated from Osaka Imperial University with a degree in physics.

Arithmetic or arithmetics ( from the Greek word ἀριθμός, arithmos " number ") is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations.

Stroustrup has a master's degree in mathematics and computer science ( 1975 ) from the University of Aarhus, Denmark, and a Ph. D. in computer science ( 1979 ) from the University of Cambridge, England, where he was a student at Churchill College.

In mathematics, the Borsuk – Ulam theorem, named after Stanisław Ulam and Karol Borsuk, states that every continuous function from an n-sphere into Euclidean n-space maps some pair of antipodal points to the same point.

Similarly, the influences of philosophers such as Sir Francis Bacon ( 1561 – 1626 ) and René Descartes ( 1596 – 1650 ), who demanded more rigor in mathematics and in removing bias from scientific observations, led to a scientific revolution.

A term dating from the 1940s, " general abstract nonsense ", refers to its high level of abstraction, compared to more classical branches of mathematics.

In mathematics, specifically general topology and metric topology, a compact space is a mathematical space in which any infinite collection of points sampled from the space must — as a set — be arbitrarily close to some point of the space.

Though Gauss had up to that point been financially supported by his stipend from the Duke, he doubted the security of this arrangement, and also did not believe pure mathematics to be important enough to deserve support.