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https://en.wikipedia.org/wiki/Basis%20function | In mathematics, a basis function is an element of a particular basis for a function space. Every function in the function space can be represented as a linear combination of basis functions, just as every vector in a vector space can be represented as a linear combination of basis vectors.
In numerical analysis and a... |
https://en.wikipedia.org/wiki/Liouville%20number | In number theory, a Liouville number is a real number with the property that, for every positive integer , there exists a pair of integers with such that
Liouville numbers are "almost rational", and can thus be approximated "quite closely" by sequences of rational numbers. Precisely, these are transcendental number... |
https://en.wikipedia.org/wiki/Natural%20deduction | In logic and proof theory, natural deduction is a kind of proof calculus in which logical reasoning is expressed by inference rules closely related to the "natural" way of reasoning. This contrasts with Hilbert-style systems, which instead use axioms as much as possible to express the logical laws of deductive reasonin... |
https://en.wikipedia.org/wiki/Coefficient | In mathematics, a coefficient is a multiplicative factor involved in some term of a polynomial, a series, or an expression. It may be a number (dimensionless), in which case it is known as a numerical factor. It may also be a constant with units of measurement, in which it is known as a constant multiplier. In general,... |
https://en.wikipedia.org/wiki/Buckingham%20%CF%80%20theorem | In engineering, applied mathematics, and physics, the Buckingham theorem is a key theorem in dimensional analysis. It is a formalization of Rayleigh's method of dimensional analysis. Loosely, the theorem states that if there is a physically meaningful equation involving a certain number n of physical variables, then ... |
https://en.wikipedia.org/wiki/Fundamental%20theorem%20of%20algebra | The fundamental theorem of algebra, also known as d'Alembert's theorem, or the d'Alembert–Gauss theorem, states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. This includes polynomials with real coefficients, since every real number is a complex number with i... |
https://en.wikipedia.org/wiki/Integer%20sequence | In mathematics, an integer sequence is a sequence (i.e., an ordered list) of integers.
An integer sequence may be specified explicitly by giving a formula for its nth term, or implicitly by giving a relationship between its terms. For example, the sequence 0, 1, 1, 2, 3, 5, 8, 13, ... (the Fibonacci sequence) is forme... |
https://en.wikipedia.org/wiki/P-adic%20number | In number theory, given a prime number , the -adic numbers form an extension of the rational numbers which is distinct from the real numbers, though with some similar properties; -adic numbers can be written in a form similar to (possibly infinite) decimals, but with digits based on a prime number rather than ten, and... |
https://en.wikipedia.org/wiki/Cantor%27s%20diagonal%20argument | In set theory, Cantor's diagonal argument, also called the diagonalisation argument, the diagonal slash argument, the anti-diagonal argument, the diagonal method, and Cantor's diagonalization proof, was published in 1891 by Georg Cantor as a mathematical proof that there are infinite sets which cannot be put into one-t... |
https://en.wikipedia.org/wiki/Hyperreal%20number | In mathematics, the system of hyperreal numbers is a way of treating infinite and infinitesimal (infinitely small but non-zero) quantities. The hyperreals, or nonstandard reals, *R, are an extension of the real numbers R that contains numbers greater than anything of the form
(for any finite number of terms).
Such ... |
https://en.wikipedia.org/wiki/Surreal%20number | In mathematics, the surreal number system is a totally ordered proper class containing not only the real numbers but also infinite and infinitesimal numbers, respectively larger or smaller in absolute value than any positive real number. Research on the Go endgame by John Horton Conway led to the original definition an... |
https://en.wikipedia.org/wiki/Sedenion | In abstract algebra, the sedenions form a 16-dimensional noncommutative and nonassociative algebra over the real numbers, usually represented by the capital letter S, boldface or blackboard bold . They are obtained by applying the Cayley–Dickson construction to the octonions, and as such the octonions are isomorphic t... |
https://en.wikipedia.org/wiki/Octonion | In mathematics, the octonions are a normed division algebra over the real numbers, a kind of hypercomplex number system. The octonions are usually represented by the capital letter O, using boldface or blackboard bold . Octonions have eight dimensions; twice the number of dimensions of the quaternions, of which they a... |
https://en.wikipedia.org/wiki/Hypercomplex%20number | In mathematics, hypercomplex number is a traditional term for an element of a finite-dimensional unital algebra over the field of real numbers.
The study of hypercomplex numbers in the late 19th century forms the basis of modern group representation theory.
History
In the nineteenth century number systems called quat... |
https://en.wikipedia.org/wiki/Quaternion | In mathematics, the quaternion number system extends the complex numbers. Quaternions were first described by the Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. Hamilton defined a quaternion as the quotient of two directed lines in a three-dimensional space, or, ... |
https://en.wikipedia.org/wiki/Zero%20divisor | In abstract algebra, an element of a ring is called a left zero divisor if there exists a nonzero in such that , or equivalently if the map from to that sends to is not injective. Similarly, an element of a ring is called a right zero divisor if there exists a nonzero in such that . This is a partial case ... |
https://en.wikipedia.org/wiki/Zorn%27s%20lemma | Zorn's lemma, also known as the Kuratowski–Zorn lemma, is a proposition of set theory. It states that a partially ordered set containing upper bounds for every chain (that is, every totally ordered subset) necessarily contains at least one maximal element.
The lemma was proved (assuming the axiom of choice) by Kazimie... |
https://en.wikipedia.org/wiki/Singular%20function | In mathematics, a real-valued function f on the interval [a, b] is said to be singular if it has the following properties:
f is continuous on [a, b]. (**)
there exists a set N of measure 0 such that for all x outside of N the derivative f (x) exists and is zero, that is, the derivative of f vanishes almost everywhere.... |
https://en.wikipedia.org/wiki/Geostatistics | Geostatistics is a branch of statistics focusing on spatial or spatiotemporal datasets. Developed originally to predict probability distributions of ore grades for mining operations, it is currently applied in diverse disciplines including petroleum geology, hydrogeology, hydrology, meteorology, oceanography, geochemis... |
https://en.wikipedia.org/wiki/Burali-Forti%20paradox | In set theory, a field of mathematics, the Burali-Forti paradox demonstrates that constructing "the set of all ordinal numbers" leads to a contradiction and therefore shows an antinomy in a system that allows its construction. It is named after Cesare Burali-Forti, who, in 1897, published a paper proving a theorem whic... |
https://en.wikipedia.org/wiki/Soliton | In mathematics and physics, a soliton is a nonlinear, self-reinforcing, localized wave packet that is strongly stable, in that it preserves its shape while propagating freely, at constant velocity, and recovers it even after collisions with other such localized wave packets. Its remarkable stability can be traced to a... |
https://en.wikipedia.org/wiki/Vacuous%20truth | In mathematics and logic, a vacuous truth is a conditional or universal statement (a universal statement that can be converted to a conditional statement) that is true because the antecedent cannot be satisfied.
It is sometimes said that a statement is vacuously true because it does not really say anything. For exampl... |
https://en.wikipedia.org/wiki/Extended%20real%20number%20line | In mathematics, the extended real number system is obtained from the real number system by adding two infinity elements: and where the infinities are treated as actual numbers. It is useful in describing the algebra on infinities and the various limiting behaviors in calculus and mathematical analysis, especially in... |
https://en.wikipedia.org/wiki/Taylor%27s%20theorem | In calculus, Taylor's theorem gives an approximation of a -times differentiable function around a given point by a polynomial of degree , called the -th-order Taylor polynomial. For a smooth function, the Taylor polynomial is the truncation at the order of the Taylor series of the function. The first-order Taylor poly... |
https://en.wikipedia.org/wiki/Martin%20Dunwoody | Martin John Dunwoody (born 3 November 1938) is an emeritus professor of Mathematics at the University of Southampton, England.
He earned his PhD in 1964 from the Australian National University. He held positions at the University of Sussex before becoming a professor at the University of Southampton in 1992. He has be... |
https://en.wikipedia.org/wiki/Distribution%20%28mathematics%29 | Distributions, also known as Schwartz distributions or generalized functions, are objects that generalize the classical notion of functions in mathematical analysis. Distributions make it possible to differentiate functions whose derivatives do not exist in the classical sense. In particular, any locally integrable fun... |
https://en.wikipedia.org/wiki/Cylinder%20%28disambiguation%29 | A cylinder is a basic curvilinear geometric shape.
Cylinder may also refer to:
Cylinder (algebra), the Cartesian product of a set with its superset
Cylinder (disk drive), a division of data in a disk drive
Cylinder (engine), the space in which a piston travels in an engine
Cylinder (firearms), the rotating part o... |
https://en.wikipedia.org/wiki/Embedded | Embedded or embedding (alternatively imbedded or imbedding) may refer to:
Science
Embedding, in mathematics, one instance of some mathematical object contained within another instance
Graph embedding
Embedded generation, a distributed generation of energy, also known as decentralized generation
Self-embedding, in... |
https://en.wikipedia.org/wiki/Embedding | In mathematics, an embedding (or imbedding) is one instance of some mathematical structure contained within another instance, such as a group that is a subgroup.
When some object is said to be embedded in another object , the embedding is given by some injective and structure-preserving map . The precise meaning of "... |
https://en.wikipedia.org/wiki/Julius%20Pl%C3%BCcker | Julius Plücker (16 June 1801 – 22 May 1868) was a German mathematician and physicist. He made fundamental contributions to the field of analytical geometry and was a pioneer in the investigations of cathode rays that led eventually to the discovery of the electron. He also vastly extended the study of Lamé curves.
Bio... |
https://en.wikipedia.org/wiki/Perfect%20square | A perfect square is an element of algebraic structure that is equal to the square of another element.
Square number, a perfect square integer
Entertainment
Perfect Square, a live recording by the band R.E.M.
Perfect Square (publisher), a children's imprint label by Viz Media.
See also
Perfect square dissection,... |
https://en.wikipedia.org/wiki/Magic%20square | In recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diagonals are the same. The 'order' of the magic square is the number of integers along one side (n), and the constant sum is called the 'magic c... |
https://en.wikipedia.org/wiki/Fourier%20transform | In physics, engineering and mathematics, the Fourier transform (FT) is an integral transform that converts a function into a form that describes the frequencies present in the original function. The output of the transform is a complex-valued function of frequency. The term Fourier transform refers to both this comple... |
https://en.wikipedia.org/wiki/Cyclic%20group | In group theory, a branch of abstract algebra in pure mathematics, a cyclic group or monogenous group is a group, denoted Cn, that is generated by a single element. That is, it is a set of invertible elements with a single associative binary operation, and it contains an element g such that every other element of the g... |
https://en.wikipedia.org/wiki/Axiom%20of%20extensionality | In axiomatic set theory and the branches of logic, mathematics, and computer science that use it, the axiom of extensionality, or axiom of extension, is one of the axioms of Zermelo–Fraenkel set theory. It says that sets having the same elements are the same set.
Formal statement
In the formal language of the Zermelo... |
https://en.wikipedia.org/wiki/Axiom%20of%20pairing | In axiomatic set theory and the branches of logic, mathematics, and computer science that use it, the axiom of pairing is one of the axioms of Zermelo–Fraenkel set theory. It was introduced by as a special case of his axiom of elementary sets.
Formal statement
In the formal language of the Zermelo–Fraenkel axioms, t... |
https://en.wikipedia.org/wiki/Axiom%20schema%20of%20specification | In many popular versions of axiomatic set theory, the axiom schema of specification, also known as the axiom schema of separation, subset axiom scheme or axiom schema of restricted comprehension is an axiom schema. Essentially, it says that any definable subclass of a set is a set.
Some mathematicians call it the axi... |
https://en.wikipedia.org/wiki/Axiom%20schema%20of%20replacement | In set theory, the axiom schema of replacement is a schema of axioms in Zermelo–Fraenkel set theory (ZF) that asserts that the image of any set under any definable mapping is also a set. It is necessary for the construction of certain infinite sets in ZF.
The axiom schema is motivated by the idea that whether a class ... |
https://en.wikipedia.org/wiki/Tait%27s%20conjecture | In mathematics, Tait's conjecture states that "Every 3-connected planar cubic graph has a Hamiltonian cycle (along the edges) through all its vertices". It was proposed by and disproved by , who constructed a counterexample with 25 faces, 69 edges and 46 vertices. Several smaller counterexamples, with 21 faces, 57 edg... |
https://en.wikipedia.org/wiki/Stephen%20Wolfram | Stephen Wolfram ( ; born 29 August 1959) is a British-American computer scientist, physicist, and businessman. He is known for his work in computer science, mathematics, and theoretical physics. In 2012, he was named a fellow of the American Mathematical Society.
As a businessman, he is the founder and CEO of the sof... |
https://en.wikipedia.org/wiki/Axiom%20of%20empty%20set | In axiomatic set theory, the axiom of empty set is a statement that asserts the existence of a set with no elements. It is an axiom of Kripke–Platek set theory and the variant of general set theory that Burgess (2005) calls "ST," and a demonstrable truth in Zermelo set theory and Zermelo–Fraenkel set theory, with or wi... |
https://en.wikipedia.org/wiki/Axiom%20of%20power%20set | In mathematics, the axiom of power set is one of the Zermelo–Fraenkel axioms of axiomatic set theory.
In the formal language of the Zermelo–Fraenkel axioms, the axiom reads:
where y is the power set of x, .
In English, this says:
Given any set x, there is a set such that, given any set z, this set z is a member of... |
https://en.wikipedia.org/wiki/Axiom%20of%20union | In axiomatic set theory, the axiom of union is one of the axioms of Zermelo–Fraenkel set theory. This axiom was introduced by Ernst Zermelo.
The axiom states that for each set x there is a set y whose elements are precisely the elements of the elements of x.
Formal statement
In the formal language of the Zermelo–Fra... |
https://en.wikipedia.org/wiki/Partial%20differential%20equation | In mathematics, a partial differential equation (PDE) is an equation which computes a function between various partial derivatives of a multivariable function.
The function is often thought of as an "unknown" to be solved for, similar to how is thought of as an unknown number to be solved for in an algebraic equation... |
https://en.wikipedia.org/wiki/Partial%20derivative | In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary). Partial derivatives are used in vector calculus and differential geometry.
Th... |
https://en.wikipedia.org/wiki/Alice%27s%20Adventures%20in%20Wonderland | Alice's Adventures in Wonderland (commonly Alice in Wonderland) is an 1865 English children's novel by Lewis Carroll, a mathematics don at Oxford University. It details the story of a young girl named Alice who falls through a rabbit hole into a fantasy world of anthropomorphic creatures. It is seen as an example of th... |
https://en.wikipedia.org/wiki/Stone%E2%80%93%C4%8Cech%20compactification | In the mathematical discipline of general topology, Stone–Čech compactification (or Čech–Stone compactification) is a technique for constructing a universal map from a topological space X to a compact Hausdorff space βX. The Stone–Čech compactification βX of a topological space X is the largest, most general compact H... |
https://en.wikipedia.org/wiki/East%20of%20England | The East of England is one of the nine official regions of England in the United Kingdom. This region was created in 1994 and was adopted for statistics purposes from 1999. It includes the ceremonial counties of Bedfordshire, Cambridgeshire, Essex, Hertfordshire, Norfolk and Suffolk. Essex has the highest population in... |
https://en.wikipedia.org/wiki/Pareto%20distribution | The Pareto distribution, named after the Italian civil engineer, economist, and sociologist Vilfredo Pareto, is a power-law probability distribution that is used in description of social, quality control, scientific, geophysical, actuarial, and many other types of observable phenomena; the principle originally applied ... |
https://en.wikipedia.org/wiki/Regular%20space | In topology and related fields of mathematics, a topological space X is called a regular space if every closed subset C of X and a point p not contained in C admit non-overlapping open neighborhoods. Thus p and C can be separated by neighborhoods. This condition is known as Axiom T3. The term "T3 space" usually means "... |
https://en.wikipedia.org/wiki/Scalar | Scalar may refer to:
Scalar (mathematics), an element of a field, which is used to define a vector space, usually the field of real numbers
Scalar (physics), a physical quantity that can be described by a single element of a number field such as a real number
Lorentz scalar, a quantity in the theory of relativity whic... |
https://en.wikipedia.org/wiki/Convolution%20theorem | In mathematics, the convolution theorem states that under suitable conditions the Fourier transform of a convolution of two functions (or signals) is the pointwise product of their Fourier transforms. More generally, convolution in one domain (e.g., time domain) equals point-wise multiplication in the other domain (e.g... |
https://en.wikipedia.org/wiki/Tangloids | Tangloids is a mathematical game for two players created by Piet Hein to model the calculus of spinors.
A description of the game appeared in the book "Martin Gardner's New Mathematical Diversions from Scientific American" by Martin Gardner from 1996 in a section on the mathematics of braiding.
Two flat blocks of woo... |
https://en.wikipedia.org/wiki/Euler%27s%20totient%20function | In number theory, Euler's totient function counts the positive integers up to a given integer that are relatively prime to . It is written using the Greek letter phi as or , and may also be called Euler's phi function. In other words, it is the number of integers in the range for which the greatest common divisor ... |
https://en.wikipedia.org/wiki/Fermat%27s%20little%20theorem | In number theory, Fermat's little theorem states that if is a prime number, then for any integer , the number is an integer multiple of . In the notation of modular arithmetic, this is expressed as
For example, if and , then , and is an integer multiple of .
If is not divisible by ; that is, if is coprime to ... |
https://en.wikipedia.org/wiki/Minkowski%27s%20theorem | In mathematics, Minkowski's theorem is the statement that every convex set in which is symmetric with respect to the origin and which has volume greater than contains a non-zero integer point (meaning a point in that is not the origin). The theorem was proved by Hermann Minkowski in 1889 and became the foundation of... |
https://en.wikipedia.org/wiki/Group%20object | In category theory, a branch of mathematics, group objects are certain generalizations of groups that are built on more complicated structures than sets. A typical example of a group object is a topological group, a group whose underlying set is a topological space such that the group operations are continuous.
Defini... |
https://en.wikipedia.org/wiki/Physical%20Quality%20of%20Life%20Index | The Physical Quality of Life Index (PQLI) is an attempt to measure the quality of life or well-being of a country. The value is the average of three statistics: basic literacy rate at the age of 15 years , infant mortality, and life expectancy at age one, all equally weighted on a 1 to 100 scale.
It was developed for ... |
https://en.wikipedia.org/wiki/Division%20%28mathematics%29 | Division is one of the four basic operations of arithmetic. The other operations are addition, subtraction, and multiplication. What is being divided is called the dividend, which is divided by the divisor, and the result is called the quotient.
At an elementary level the division of two natural numbers is, among oth... |
https://en.wikipedia.org/wiki/Symmetry | Symmetry () in everyday life refers to a sense of harmonious and beautiful proportion and balance. In mathematics, the term has a more precise definition and is usually used to refer to an object that is invariant under some transformations, such as translation, reflection, rotation, or scaling. Although these two mean... |
https://en.wikipedia.org/wiki/Category%20%28mathematics%29 | In mathematics, a category (sometimes called an abstract category to distinguish it from a concrete category) is a collection of "objects" that are linked by "arrows". A category has two basic properties: the ability to compose the arrows associatively and the existence of an identity arrow for each object. A simple e... |
https://en.wikipedia.org/wiki/Euclidean%20distance | In mathematics, the Euclidean distance between two points in Euclidean space is the length of a line segment between the two points.
It can be calculated from the Cartesian coordinates of the points using the Pythagorean theorem, therefore occasionally being called the Pythagorean distance. These names come from the an... |
https://en.wikipedia.org/wiki/Triangle%20inequality | In mathematics, the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side. This statement permits the inclusion of degenerate triangles, but some authors, especially those writing about elementary geometry, will exclud... |
https://en.wikipedia.org/wiki/Adjoint%20functors | In mathematics, specifically category theory, adjunction is a relationship that two functors may exhibit, intuitively corresponding to a weak form of equivalence between two related categories. Two functors that stand in this relationship are known as adjoint functors, one being the left adjoint and the other the right... |
https://en.wikipedia.org/wiki/Sylow%20theorems | In mathematics, specifically in the field of finite group theory, the Sylow theorems are a collection of theorems named after the Norwegian mathematician Peter Ludwig Sylow that give detailed information about the number of subgroups of fixed order that a given finite group contains. The Sylow theorems form a fundament... |
https://en.wikipedia.org/wiki/Sophus%20Lie | Marius Sophus Lie ( ; ; 17 December 1842 – 18 February 1899) was a Norwegian mathematician. He largely created the theory of continuous symmetry and applied it to the study of geometry and differential equations. He also made substantial contributions to the development of algebra.
Life and career
Marius Sophus Lie w... |
https://en.wikipedia.org/wiki/Reciprocal | Reciprocal may refer to:
In mathematics
Multiplicative inverse, in mathematics, the number 1/x, which multiplied by x gives the product 1, also known as a reciprocal
Reciprocal polynomial, a polynomial obtained from another polynomial by reversing its coefficients
Reciprocal rule, a technique in calculus for cal... |
https://en.wikipedia.org/wiki/Pigeonhole%20principle | In mathematics, the pigeonhole principle states that if items are put into containers, with , then at least one container must contain more than one item. For example, of three gloves (none of which is ambidextrous/reversible), at least two must be right-handed or at least two must be left-handed, because there are t... |
https://en.wikipedia.org/wiki/Aleph%20%28disambiguation%29 | Aleph is the first letter of many Semitic abjads (alphabets).
Aleph may also refer to:
Science, technology and mathematics
ALEPH experiment (Apparatus for LEP Physics at CERN), detector of the Large Electron-Positron Collider
Aleph kernel, a computer operating system kernel
Aleph number, in mathematics set theory
Al... |
https://en.wikipedia.org/wiki/Singularity%20%28mathematics%29 | In mathematics, a singularity is a point at which a given mathematical object is not defined, or a point where the mathematical object ceases to be well-behaved in some particular way, such as by lacking differentiability or analyticity.
For example, the reciprocal function has a singularity at , where the value of t... |
https://en.wikipedia.org/wiki/Partition%20function | Partition function may refer to:
Rotational partition function
Vibrational partition function
Partition function (number theory)
Partition function (mathematics), which generalizes its use in statistical mechanics and quantum field theory:
Partition function (statistical mechanics)
Partition function (quantum field t... |
https://en.wikipedia.org/wiki/Floor%20and%20ceiling%20functions | In mathematics and computer science, the floor function is the function that takes as input a real number , and gives as output the greatest integer less than or equal to , denoted or . Similarly, the ceiling function maps to the least integer greater than or equal to , denoted or .
For example, for floor: , , an... |
https://en.wikipedia.org/wiki/List%20of%20mathematical%20functions | In mathematics, some functions or groups of functions are important enough to deserve their own names. This is a listing of articles which explain some of these functions in more detail. There is a large theory of special functions which developed out of statistics and mathematical physics. A modern, abstract point of ... |
https://en.wikipedia.org/wiki/Complement%20%28set%20theory%29 | In set theory, the complement of a set , often denoted by (or ), is the set of elements not in .
When all sets in the universe, i.e. all sets under consideration, are considered to be members of a given set , the absolute complement of is the set of elements in that are not in .
The relative complement of with re... |
https://en.wikipedia.org/wiki/Boolean%20ring | In mathematics, a Boolean ring is a ring for which for all in , that is, a ring that consists of only idempotent elements. An example is the ring of integers modulo 2.
Every Boolean ring gives rise to a Boolean algebra, with ring multiplication corresponding to conjunction or meet , and ring addition to exclusive d... |
https://en.wikipedia.org/wiki/TI-89%20series | The TI-89 and the TI-89 Titanium are graphing calculators developed by Texas Instruments (TI). They are differentiated from most other TI graphing calculators by their computer algebra system, which allows symbolic manipulation of algebraic expressions—equations can be solved in terms of variables, whereas the TI-83/8... |
https://en.wikipedia.org/wiki/Computer%20algebra%20system | A computer algebra system (CAS) or symbolic algebra system (SAS) is any mathematical software with the ability to manipulate mathematical expressions in a way similar to the traditional manual computations of mathematicians and scientists. The development of the computer algebra systems in the second half of the 20th c... |
https://en.wikipedia.org/wiki/Vertex | Vertex, vertices or vertexes may refer to:
Science and technology
Mathematics and computer science
Vertex (geometry), a point where two or more curves, lines, or edges meet
Vertex (computer graphics), a data structure that describes the position of a point
Vertex (curve), a point of a plane curve where the first deri... |
https://en.wikipedia.org/wiki/Arc | Arc may refer to:
Mathematics
Arc (geometry), a segment of a differentiable curve
Circular arc, a segment of a circle
Arc (topology), a segment of a path
Arc length, the distance between two points along a section of a curve
Arc (projective geometry), a particular type of set of points of a projective plane
arc ... |
https://en.wikipedia.org/wiki/Recursively%20enumerable%20language | In mathematics, logic and computer science, a formal language is called recursively enumerable (also recognizable, partially decidable, semidecidable, Turing-acceptable or Turing-recognizable) if it is a recursively enumerable subset in the set of all possible words over the alphabet of the language, i.e., if there exi... |
https://en.wikipedia.org/wiki/Transition | Transition or transitional may refer to:
Mathematics, science, and technology
Biology
Transition (genetics), a point mutation that changes a purine nucleotide to another purine (A ↔ G) or a pyrimidine nucleotide to another pyrimidine (C ↔ T)
Transitional fossil, any fossilized remains of a lifeform that exhibits th... |
https://en.wikipedia.org/wiki/Baire%20category%20theorem | The Baire category theorem (BCT) is an important result in general topology and functional analysis. The theorem has two forms, each of which gives sufficient conditions for a topological space to be a Baire space (a topological space such that the intersection of countably many dense open sets is still dense). It is ... |
https://en.wikipedia.org/wiki/Sector | Sector may refer to:
Places
Sector, West Virginia, U.S.
Geometry
Circular sector, the portion of a disc enclosed by two radii and a circular arc
Hyperbolic sector, a region enclosed by two radii and a hyperbolic arc
Spherical sector, a portion of a sphere enclosed by a cone of radii from the center of the sphere
... |
https://en.wikipedia.org/wiki/Discriminant | In mathematics, the discriminant of a polynomial is a quantity that depends on the coefficients and allows deducing some properties of the roots without computing them. More precisely, it is a polynomial function of the coefficients of the original polynomial. The discriminant is widely used in polynomial factoring, nu... |
https://en.wikipedia.org/wiki/Interior%20%28topology%29 | In mathematics, specifically in topology,
the interior of a subset of a topological space is the union of all subsets of that are open in .
A point that is in the interior of is an interior point of .
The interior of is the complement of the closure of the complement of .
In this sense interior and closure are du... |
https://en.wikipedia.org/wiki/Alexandroff%20extension | In the mathematical field of topology, the Alexandroff extension is a way to extend a noncompact topological space by adjoining a single point in such a way that the resulting space is compact. It is named after the Russian mathematician Pavel Alexandroff.
More precisely, let X be a topological space. Then the Alexan... |
https://en.wikipedia.org/wiki/Linear%20combination | In mathematics, a linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of x and y would be any expression of the form ax + by, where a and b are constants). The concept of linear combinations is central to linear alg... |
https://en.wikipedia.org/wiki/Harmonic%20function | In mathematics, mathematical physics and the theory of stochastic processes, a harmonic function is a twice continuously differentiable function where is an open subset of that satisfies Laplace's equation, that is,
everywhere on . This is usually written as
or
Etymology of the term "harmonic"
The descriptor "har... |
https://en.wikipedia.org/wiki/Discrete%20space | In topology, a discrete space is a particularly simple example of a topological space or similar structure, one in which the points form a , meaning they are isolated from each other in a certain sense. The discrete topology is the finest topology that can be given on a set. Every subset is open in the discrete topolog... |
https://en.wikipedia.org/wiki/Krull%20dimension | In commutative algebra, the Krull dimension of a commutative ring R, named after Wolfgang Krull, is the supremum of the lengths of all chains of prime ideals. The Krull dimension need not be finite even for a Noetherian ring. More generally the Krull dimension can be defined for modules over possibly non-commutative ri... |
https://en.wikipedia.org/wiki/Metropolis%E2%80%93Hastings%20algorithm | In statistics and statistical physics, the Metropolis–Hastings algorithm is a Markov chain Monte Carlo (MCMC) method for obtaining a sequence of random samples from a probability distribution from which direct sampling is difficult. This sequence can be used to approximate the distribution (e.g. to generate a histogram... |
https://en.wikipedia.org/wiki/Noetherian%20ring | In mathematics, a Noetherian ring is a ring that satisfies the ascending chain condition on left and right ideals; if the chain condition is satisfied only for left ideals or for right ideals, then the ring is said left-Noetherian or right-Noetherian respectively. That is, every increasing sequence of left (or right) ... |
https://en.wikipedia.org/wiki/Artinian | Artinian may refer to:
Mathematics
Objects named for Austrian mathematician Emil Artin (1898–1962)
Artinian ideal, an ideal I in R for which the Krull dimension of the quotient ring R/I is 0
Artinian ring, a ring which satisfies the descending chain condition on (one-sided) ideals
Artinian module, a module which satis... |
https://en.wikipedia.org/wiki/Dyadic%20rational | In mathematics, a dyadic rational or binary rational is a number that can be expressed as a fraction whose denominator is a power of two. For example, 1/2, 3/2, and 3/8 are dyadic rationals, but 1/3 is not. These numbers are important in computer science because they are the only ones with finite binary representations... |
https://en.wikipedia.org/wiki/Linear%20span | In mathematics, the linear span (also called the linear hull or just span) of a set of vectors (from a vector space), denoted , is defined as the set of all linear combinations of the vectors in .
For example, two linearly independent vectors span a plane.
The linear span can be characterized either as the intersecti... |
https://en.wikipedia.org/wiki/Linear%20subspace | In mathematics, and more specifically in linear algebra, a linear subspace or vector subspace is a vector space that is a subset of some larger vector space. A linear subspace is usually simply called a subspace when the context serves to distinguish it from other types of subspaces.
Definition
If V is a vector space ... |
https://en.wikipedia.org/wiki/Julia%20set | In the context of complex dynamics, a branch of mathematics, the Julia set and the Fatou set are two complementary sets (Julia "laces" and Fatou "dusts") defined from a function. Informally, the Fatou set of the function consists of values with the property that all nearby values behave similarly under repeated iterati... |
https://en.wikipedia.org/wiki/Hyperbolic%20functions | In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points form a circle with a unit radius, the points form the right half of the unit hyperbola. Also, similarly to how the derivatives of and are and respe... |
https://en.wikipedia.org/wiki/Fuzzy%20set | In mathematics, fuzzy sets (a.k.a. uncertain sets) are sets whose elements have degrees of membership. Fuzzy sets were introduced independently by Lotfi A. Zadeh in 1965 as an extension of the classical notion of set.
At the same time, defined a more general kind of structure called an L-relation, which he studied in ... |
https://en.wikipedia.org/wiki/Geography%20of%20Mauritius | Mauritius is an island of Africa's southeast coast located in the Indian Ocean, east of Madagascar. It is geologically located within the Somali plate.
Statistics
Area (includes Agaléga, Cargados Carajos (Saint Brandon), and Rodrigues):
total:
2,011 km2
land:
2,030 km2
water:
10 km2
note: includes Agalega Islands, C... |
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