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https://en.wikipedia.org/wiki/On%20the%20Cruelty%20of%20Really%20Teaching%20Computer%20Science | "On the Cruelty of Really Teaching Computing Science" is a 1988 scholarly article by E. W. Dijkstra which argues that computer programming should be understood as a branch of mathematics, and that the formal provability of a program is a major criterion for correctness.
Despite the title, most of the article is on Dij... |
https://en.wikipedia.org/wiki/List%20of%20partition%20topics | Generally, a partition is a division of a whole into non-overlapping parts. Among the kinds of partitions considered in mathematics are
partition of a set or an ordered partition of a set,
partition of a graph,
partition of an integer,
partition of an interval,
partition of unity,
partition of a matrix; see bloc... |
https://en.wikipedia.org/wiki/Persistence%20of%20a%20number | In mathematics, the persistence of a number is the number of times one must apply a given operation to an integer before reaching a fixed point at which the operation no longer alters the number.
Usually, this involves additive or multiplicative persistence of a non-negative integer, which is how often one has to repl... |
https://en.wikipedia.org/wiki/Monte%20Carlo%20algorithm | In computing, a Monte Carlo algorithm is a randomized algorithm whose output may be incorrect with a certain (typically small) probability. Two examples of such algorithms are the Karger–Stein algorithm and the Monte Carlo algorithm for minimum feedback arc set.
The name refers to the Monte Carlo casino in the Princip... |
https://en.wikipedia.org/wiki/Littlewood%20conjecture | In mathematics, the Littlewood conjecture is an open problem () in Diophantine approximation, proposed by John Edensor Littlewood around 1930. It states that for any two real numbers α and β,
where is the distance to the nearest integer.
Formulation and explanation
This means the following: take a point (α, β) in t... |
https://en.wikipedia.org/wiki/Double%20Mersenne%20number | In mathematics, a double Mersenne number is a Mersenne number of the form
where p is prime.
Examples
The first four terms of the sequence of double Mersenne numbers are :
Double Mersenne primes
A double Mersenne number that is prime is called a double Mersenne prime. Since a Mersenne number Mp can be prime only i... |
https://en.wikipedia.org/wiki/International%20Congress%20of%20Mathematicians | The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU).
The Fields Medals, the IMU Abacus Medal (known before 2022 as the Nevanlinna Prize), the Gauss Prize, and the Chern Medal are ... |
https://en.wikipedia.org/wiki/Tsirelson%20space | In mathematics, especially in functional analysis, the Tsirelson space is the first example of a Banach space in which neither an ℓ p space nor a c0 space can be embedded. The Tsirelson space is reflexive.
It was introduced by B. S. Tsirelson in 1974. The same year, Figiel and Johnson published a related article () wh... |
https://en.wikipedia.org/wiki/Outer%20automorphism%20group | In mathematics, the outer automorphism group of a group, , is the quotient, , where is the automorphism group of and ) is the subgroup consisting of inner automorphisms. The outer automorphism group is usually denoted . If is trivial and has a trivial center, then is said to be complete.
An automorphism of a grou... |
https://en.wikipedia.org/wiki/Sergei%20Novikov%20%28mathematician%29 | Sergei Petrovich Novikov (also Serguei) (Russian: Серге́й Петро́вич Но́виков) (born 20 March 1938) is a Soviet and Russian mathematician, noted for work in both algebraic topology and soliton theory. In 1970, he won the Fields Medal.
Early life
Novikov was born on 20 March 1938 in Gorky, Soviet Union (now Nizhny Novgo... |
https://en.wikipedia.org/wiki/Approximation%20property | In mathematics, specifically functional analysis, a Banach space is said to have the approximation property (AP), if every compact operator is a limit of finite-rank operators. The converse is always true.
Every Hilbert space has this property. There are, however, Banach spaces which do not; Per Enflo published the fi... |
https://en.wikipedia.org/wiki/Ba%20space | In mathematics, the ba space of an algebra of sets is the Banach space consisting of all bounded and finitely additive signed measures on . The norm is defined as the variation, that is
If Σ is a sigma-algebra, then the space is defined as the subset of consisting of countably additive measures. The notation ba i... |
https://en.wikipedia.org/wiki/Giacomo%20Albanese | Giacomo Albanese (11 July 1890 – 8 June 1947) was an Italian mathematician known for his work in algebraic geometry. He took a permanent position in the University of São Paulo, Brazil, in 1936.
Biography
Albanese attended the school in Palermo, Sicily. He graduated from there in 1909. Then he entered the Scuola Norm... |
https://en.wikipedia.org/wiki/Polynomially%20reflexive%20space | In mathematics, a polynomially reflexive space is a Banach space X, on which the space of all polynomials in each degree is a reflexive space.
Given a multilinear functional Mn of degree n (that is, Mn is n-linear), we can define a polynomial p as
(that is, applying Mn on the diagonal) or any finite sum of these. If ... |
https://en.wikipedia.org/wiki/Stefan%20Mazurkiewicz | Stefan Mazurkiewicz (25 September 1888 – 19 June 1945) was a Polish mathematician who worked in mathematical analysis, topology, and probability. He was a student of Wacław Sierpiński and a member of the Polish Academy of Learning (PAU). His students included Karol Borsuk, Bronisław Knaster, Kazimierz Kuratowski, Stan... |
https://en.wikipedia.org/wiki/Hadwiger%27s%20theorem | In integral geometry (otherwise called geometric probability theory), Hadwiger's theorem characterises the valuations on convex bodies in It was proved by Hugo Hadwiger.
Introduction
Valuations
Let be the collection of all compact convex sets in A valuation is a function such that and for every that satisfy
... |
https://en.wikipedia.org/wiki/Dirichlet%20function | In mathematics, the Dirichlet function is the indicator function of the set of rational numbers , i.e. if is a rational number and if is not a rational number (i.e. is an irrational number).
It is named after the mathematician Peter Gustav Lejeune Dirichlet. It is an example of pathological function which provide... |
https://en.wikipedia.org/wiki/Abstract%20nonsense | In mathematics, abstract nonsense, general abstract nonsense, generalized abstract nonsense, and general nonsense are nonderogatory terms used by mathematicians to describe long, theoretical parts of a proof they skip over when readers are expected to be familiar with them. These terms are mainly used for abstract meth... |
https://en.wikipedia.org/wiki/Hugo%20Hadwiger | Hugo Hadwiger (23 December 1908 in Karlsruhe, Germany – 29 October 1981 in Bern, Switzerland) was a Swiss mathematician, known for his work in geometry, combinatorics, and cryptography.
Biography
Although born in Karlsruhe, Germany, Hadwiger grew up in Bern, Switzerland. He did his undergraduate studies at the Univers... |
https://en.wikipedia.org/wiki/Algebraic%20geometry%20and%20analytic%20geometry | In mathematics, algebraic geometry and analytic geometry are two closely related subjects. While algebraic geometry studies algebraic varieties, analytic geometry deals with complex manifolds and the more general analytic spaces defined locally by the vanishing of analytic functions of several complex variables. The de... |
https://en.wikipedia.org/wiki/Chow%27s%20theorem | In mathematics, Chow's theorem may refer to a number of theorems due to Wei-Liang Chow:
Chow's theorem: The theorem that asserts that any analytic subvariety in projective space is actually algebraic.
Chow–Rashevskii theorem: In sub-Riemannian geometry, the theorem that asserts that any two points are connected by a ... |
https://en.wikipedia.org/wiki/Arithmetic%20group | In mathematics, an arithmetic group is a group obtained as the integer points of an algebraic group, for example They arise naturally in the study of arithmetic properties of quadratic forms and other classical topics in number theory. They also give rise to very interesting examples of Riemannian manifolds and hence ... |
https://en.wikipedia.org/wiki/Smith%20number | In number theory, a Smith number is a composite number for which, in a given number base, the sum of its digits is equal to the sum of the digits in its prime factorization in the same base. In the case of numbers that are not square-free, the factorization is written without exponents, writing the repeated factor as ... |
https://en.wikipedia.org/wiki/Halton%20sequence | In statistics, Halton sequences are sequences used to generate points in space for numerical methods such as Monte Carlo simulations. Although these sequences are deterministic, they are of low discrepancy, that is, appear to be random for many purposes. They were first introduced in 1960 and are an example of a quas... |
https://en.wikipedia.org/wiki/Lerp | Lerp or LERP may refer to:
Lerp (biology), a structure produced by larvae of psyllid insects as a protective cover
Linear interpolation (Lerp), a method of curve fitting in mathematics
Emil Lerp (1886-1966), German inventor of first gasoline transportable chainsaw
Liberia Equal Rights Party
Lyari Expressway Reset... |
https://en.wikipedia.org/wiki/Coimage | In algebra, the coimage of a homomorphism
is the quotient
of the domain by the kernel.
The coimage is canonically isomorphic to the image by the first isomorphism theorem, when that theorem applies.
More generally, in category theory, the coimage of a morphism is the dual notion of the image of a morphism. If , th... |
https://en.wikipedia.org/wiki/Haboush%27s%20theorem | In mathematics Haboush's theorem, often still referred to as the Mumford conjecture, states that for any semisimple algebraic group G over a field K, and for any linear representation ρ of G on a K-vector space V, given v ≠ 0 in V that is fixed by the action of G, there is a G-invariant polynomial F on V, without const... |
https://en.wikipedia.org/wiki/Paley%E2%80%93Wiener%20theorem | In mathematics, a Paley–Wiener theorem is any theorem that relates decay properties of a function or distribution at infinity with analyticity of its Fourier transform. The theorem is named for Raymond Paley (1907–1933) and Norbert Wiener (1894–1964). The original theorems did not use the language of distributions, a... |
https://en.wikipedia.org/wiki/Aggregate | Aggregate or aggregates may refer to:
Computing and mathematics
Aggregate (data warehouse), a part of the dimensional model that is used to speed up query time by summarizing tables
Aggregate analysis, a technique used in amortized analysis in computer science, especially in analysis of algorithms
Aggregate class, ... |
https://en.wikipedia.org/wiki/Alabama%20School%20of%20Mathematics%20and%20Science | The Alabama School of Mathematics and Science (ASMS) is a public residential high school in the Midtown neighborhood of Mobile, Alabama. ASMS is a member of the National Consortium of Secondary STEM Schools (NCSSS). It graduated its first class in 1993.
The school was founded in 1989 as a unique public-private partne... |
https://en.wikipedia.org/wiki/Analytical%20hierarchy | In mathematical logic and descriptive set theory, the analytical hierarchy is an extension of the arithmetical hierarchy. The analytical hierarchy of formulas includes formulas in the language of second-order arithmetic, which can have quantifiers over both the set of natural numbers, , and over functions from to . Th... |
https://en.wikipedia.org/wiki/Wheel%20theory | A wheel is a type of algebra (in the sense of universal algebra) where division is always defined. In particular, division by zero is meaningful. The real numbers can be extended to a wheel, as can any commutative ring.
The term wheel is inspired by the topological picture of the real projective line together with a... |
https://en.wikipedia.org/wiki/Analytic%20set | In the mathematical field of descriptive set theory, a subset of a Polish space is an analytic set if it is a continuous image of a Polish space. These sets were first defined by and his student .
Definition
There are several equivalent definitions of analytic set. The following conditions on a subspace A of a Po... |
https://en.wikipedia.org/wiki/Bendixson%E2%80%93Dulac%20theorem | In mathematics, the Bendixson–Dulac theorem on dynamical systems states that if there exists a function (called the Dulac function) such that the expression
has the same sign () almost everywhere in a simply connected region of the plane, then the plane autonomous system
has no nonconstant periodic solutions ... |
https://en.wikipedia.org/wiki/Hausdorff%20paradox | The Hausdorff paradox is a paradox in mathematics named after Felix Hausdorff. It involves the sphere (a 3-dimensional sphere in ). It states that if a certain countable subset is removed from , then the remainder can be divided into three disjoint subsets and such that and are all congruent. In particular, it fol... |
https://en.wikipedia.org/wiki/Bohr%20compactification | In mathematics, the Bohr compactification of a topological group G is a compact Hausdorff topological group H that may be canonically associated to G. Its importance lies in the reduction of the theory of uniformly almost periodic functions on G to the theory of continuous functions on H. The concept is named after Ha... |
https://en.wikipedia.org/wiki/Giuseppe%20Vitali | Giuseppe Vitali (26 August 1875 – 29 February 1932) was an Italian mathematician who worked in several branches of mathematical analysis. He gives his name to several entities in mathematics, most notably the Vitali set with which he was the first to give an example of a non-measurable subset of real numbers.
Biograph... |
https://en.wikipedia.org/wiki/Thomas%20Kurtz | Thomas Kurtz may refer to:
Thomas E. Kurtz (born 1928), professor of mathematics and computer scientist
Thomas G. Kurtz (born 1941), professor of mathematics and statistics
Tom Kurtz, rhythm guitarist for the band Starstruck that recorded the hit song Black Betty#Ram Jam version |
https://en.wikipedia.org/wiki/Pietro%20Cataldi | Pietro Antonio Cataldi (15 April 1548, Bologna – 11 February 1626, Bologna) was an Italian mathematician. A citizen of Bologna, he taught mathematics and astronomy and also worked on military problems. His work included the development of continued fractions and a method for their representation. He was one of many mat... |
https://en.wikipedia.org/wiki/Hyperbolic%20orthogonality | In geometry, the relation of hyperbolic orthogonality between two lines separated by the asymptotes of a hyperbola is a concept used in special relativity to define simultaneous events. Two events will be simultaneous when they are on a line hyperbolically orthogonal to a particular time line. This dependence on a cert... |
https://en.wikipedia.org/wiki/Flux%20%28disambiguation%29 | Flux is a rate of flow through a surface or substance in physics, and has a related meaning in applied mathematics.
Flux may also refer to:
Science and technology
Biology and healthcare
Flux (biology), movement of a substance between compartments
Flux (metabolism), the rate of turnover of molecules through a metab... |
https://en.wikipedia.org/wiki/Ernst%20Leonard%20Lindel%C3%B6f | Ernst Leonard Lindelöf (; 7 March 1870 – 4 June 1946) was a Finnish mathematician, who made contributions in real analysis, complex analysis and topology. Lindelöf spaces are named after him. He was the son of mathematician Lorenz Leonard Lindelöf and brother of the philologist .
Biography
Lindelöf studied at the Univ... |
https://en.wikipedia.org/wiki/196%20%28number%29 | 196 (one hundred [and] ninety-six) is the natural number following 195 and preceding 197.
In mathematics
196 is a square number, the square of 14. As the square of a Catalan number, it counts the number of walks of length 8 in the positive quadrant of the integer grid that start and end at the origin, moving diagonall... |
https://en.wikipedia.org/wiki/151%20%28number%29 | 151 (one hundred [and] fifty-one) is a natural number. It follows 150 and precedes 152.
In mathematics
151 is the 36th prime number, the previous is 149, with which it comprises a twin prime. 151 is also a palindromic prime, a centered decagonal number, and a lucky number.
151 appears in the Padovan sequence, precede... |
https://en.wikipedia.org/wiki/Algebra%20of%20sets | In mathematics, the algebra of sets, not to be confused with the mathematical structure of an algebra of sets, defines the properties and laws of sets, the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion. It also provides systematic procedures for... |
https://en.wikipedia.org/wiki/Near | NEAR or Near may refer to:
People
Thomas J. Near, US evolutionary ichthyologist
Near, a developer who created the higan emulator
Science, mathematics, technology, biology, and medicine
National Emergency Alarm Repeater (NEAR), a former alarm device to warn civilians of a foreign nuclear attack on the United Stat... |
https://en.wikipedia.org/wiki/Probably | Probably may refer to:
Probability, the chance that something is likely to happen or be the case
"Probably" (South Park), an episode of the TV series South Park
"Probably" (song), a song by Fool's Garden
See also
Probability (disambiguation)
Problem (disambiguation)
Pro (disambiguation) |
https://en.wikipedia.org/wiki/Finitely%20generated%20group | In algebra, a finitely generated group is a group G that has some finite generating set S so that every element of G can be written as the combination (under the group operation) of finitely many elements of S and of inverses of such elements.
By definition, every finite group is finitely generated, since S can be t... |
https://en.wikipedia.org/wiki/Screw%20%28disambiguation%29 | A screw is an externally threaded fastener. "Screw" or "screws" may also refer to:
Engineering and mathematics
Devices with a helical thread:
Screw (simple machine)
Screw thread, screw thread principles and standards
Archimedes' screw, a simple machine for transporting water to a higher elevation
Leadscrew, a type o... |
https://en.wikipedia.org/wiki/Maurer%E2%80%93Cartan%20form | In mathematics, the Maurer–Cartan form for a Lie group is a distinguished differential one-form on that carries the basic infinitesimal information about the structure of . It was much used by Élie Cartan as a basic ingredient of his method of moving frames, and bears his name together with that of Ludwig Maurer.
As... |
https://en.wikipedia.org/wiki/Wolfgang%20Krull | Wolfgang Krull (26 August 1899 – 12 April 1971) was a German mathematician who made fundamental contributions to commutative algebra, introducing concepts that are now central to the subject.
Krull was born and went to school in Baden-Baden. He attended the Universities of Freiburg, Rostock and finally Göttingen from... |
https://en.wikipedia.org/wiki/Indecomposability | Indecomposability or indecomposable may refer to any of several subjects in mathematics:
Indecomposable module, in algebra
Indecomposable distribution, in probability
Indecomposable continuum, in topology
Indecomposability (intuitionistic logic), a principle in constructive analysis and in computable analysis
Ind... |
https://en.wikipedia.org/wiki/Functional%20calculus | In mathematics, a functional calculus is a theory allowing one to apply mathematical functions to mathematical operators. It is now a branch (more accurately, several related areas) of the field of functional analysis, connected with spectral theory. (Historically, the term was also used synonymously with calculus of v... |
https://en.wikipedia.org/wiki/Minimal%20counterexample | In mathematics, a minimal counterexample is the smallest example which falsifies a claim, and a proof by minimal counterexample is a method of proof which combines the use of a minimal counterexample with the ideas of proof by induction and proof by contradiction. More specifically, in trying to prove a proposition P, ... |
https://en.wikipedia.org/wiki/Valuation%20ring | In abstract algebra, a valuation ring is an integral domain D such that for every element x of its field of fractions F, at least one of x or x−1 belongs to D.
Given a field F, if D is a subring of F such that either x or x−1 belongs to
D for every nonzero x in F, then D is said to be a valuation ring for the field F ... |
https://en.wikipedia.org/wiki/Algebraic | Algebraic may refer to any subject related to algebra in mathematics and related branches like algebraic number theory and algebraic topology. The word algebra itself has several meanings.
Algebraic may also refer to:
Algebraic data type, a datatype in computer programming each of whose values is data from other data... |
https://en.wikipedia.org/wiki/R.%20H.%20Bing | R. H. Bing (October 20, 1914 – April 28, 1986) was an American mathematician who worked mainly in the areas of geometric topology and continuum theory. His father was named Rupert Henry, but Bing's mother thought that "Rupert Henry" was too British for Texas. She compromised by abbreviating it to R. H. Consequentl... |
https://en.wikipedia.org/wiki/Riesz%E2%80%93Thorin%20theorem | In mathematics, the Riesz–Thorin theorem, often referred to as the Riesz–Thorin interpolation theorem or the Riesz–Thorin convexity theorem, is a result about interpolation of operators. It is named after Marcel Riesz and his student G. Olof Thorin.
This theorem bounds the norms of linear maps acting between spaces.... |
https://en.wikipedia.org/wiki/Nobuo%20Yoneda | was a Japanese mathematician and computer scientist.
In 1952, he graduated the Department of Mathematics, the Faculty of Science, the University of Tokyo, and obtained his Bachelor of Science. That same year, he was appointed Assistant Professor in the Department of Mathematics of the University of Tokyo. He obtained ... |
https://en.wikipedia.org/wiki/Integrability%20conditions%20for%20differential%20systems | In mathematics, certain systems of partial differential equations are usefully formulated, from the point of view of their underlying geometric and algebraic structure, in terms of a system of differential forms. The idea is to take advantage of the way a differential form restricts to a submanifold, and the fact that ... |
https://en.wikipedia.org/wiki/European%20Mathematical%20Society | The European Mathematical Society (EMS) is a European organization dedicated to the development of mathematics in Europe. Its members are different mathematical societies in Europe, academic institutions and individual mathematicians. The current president is Jan Philip Solovej, professor at the Department of Mathemati... |
https://en.wikipedia.org/wiki/Chern%E2%80%93Weil%20homomorphism | In mathematics, the Chern–Weil homomorphism is a basic construction in Chern–Weil theory that computes topological invariants of vector bundles and principal bundles on a smooth manifold M in terms of connections and curvature representing classes in the de Rham cohomology rings of M. That is, the theory forms a bridge... |
https://en.wikipedia.org/wiki/Total%20least%20squares | In applied statistics, total least squares is a type of errors-in-variables regression, a least squares data modeling technique in which observational errors on both dependent and independent variables are taken into account. It is a generalization of Deming regression and also of orthogonal regression, and can be appl... |
https://en.wikipedia.org/wiki/Plane%20curve | In mathematics, a plane curve is a curve in a plane that may be either a Euclidean plane, an affine plane or a projective plane. The most frequently studied cases are smooth plane curves (including piecewise smooth plane curves), and algebraic plane curves.
Plane curves also include the Jordan curves (curves that enclo... |
https://en.wikipedia.org/wiki/Principal%20branch | In mathematics, a principal branch is a function which selects one branch ("slice") of a multi-valued function. Most often, this applies to functions defined on the complex plane.
Examples
Trigonometric inverses
Principal branches are used in the definition of many inverse trigonometric functions, such as the sele... |
https://en.wikipedia.org/wiki/Hyperfinite%20type%20II%20factor | In mathematics, there are up to isomorphism exactly two separably acting hyperfinite type II factors; one infinite and one finite. Murray and von Neumann proved that up to isomorphism there is a unique von Neumann algebra that is a factor of type II1 and also hyperfinite; it is called the hyperfinite type II1 factor.
T... |
https://en.wikipedia.org/wiki/Q1 | Q1 or Q-1 may refer to:
Quarter 1, as in the first quarter of a calendar year or fiscal year
first quartile in descriptive statistics
The first quarto, usually meaning the earliest published version, of one of William Shakespeare's works
Q1 Tower, a residential apartment building in Surfers Paradise, Australia
DIG... |
https://en.wikipedia.org/wiki/Q2 | Q2 or Q-2 may refer to:
The second quarter of a calendar year (April, May, June) or fiscal year
The second quarto of William Shakespeare's works
Q2 (statistics), the second quartile in descriptive statistics (i.e. the median)
Q2 Stadium, a sports stadium in Austin, Texas
Quake II, first person shooter game develo... |
https://en.wikipedia.org/wiki/Crelle%27s%20Journal | Crelle's Journal, or just Crelle, is the common name for a mathematics journal, the Journal für die reine und angewandte Mathematik (in English: Journal for Pure and Applied Mathematics).
History
The journal was founded by August Leopold Crelle (Berlin) in 1826 and edited by him until his death in 1855. It was one of... |
https://en.wikipedia.org/wiki/Infinite%20conjugacy%20class%20property | In mathematics, a group is said to have the infinite conjugacy class property, or to be an ICC group, if the conjugacy class of every group element but the identity is infinite.
The von Neumann group algebra of a group is a factor if and only if the group has the infinite conjugacy class property. It will then be, pro... |
https://en.wikipedia.org/wiki/Addition%20theorem | In mathematics, an addition theorem is a formula such as that for the exponential function:
ex + y = ex · ey,
that expresses, for a particular function f, f(x + y) in terms of f(x) and f(y). Slightly more generally, as is the case with the trigonometric functions and , several functions may be involved; this is more... |
https://en.wikipedia.org/wiki/List%20of%20manifolds | This is a list of particular manifolds, by Wikipedia page. See also list of geometric topology topics. For categorical listings see :Category:Manifolds and its subcategories.
Generic families of manifolds
Euclidean space, Rn
n-sphere, Sn
n-torus, Tn
Real projective space, RPn
Complex projective space, CPn
Quate... |
https://en.wikipedia.org/wiki/Automorphic%20function | In mathematics, an automorphic function is a function on a space that is invariant under the action of some group, in other words a function on the quotient space. Often the space is a complex manifold and the group is a discrete group.
Factor of automorphy
In mathematics, the notion of factor of automorphy arises fo... |
https://en.wikipedia.org/wiki/Algebraic%20function | In mathematics, an algebraic function is a function that can be defined
as the root of an irreducible polynomial equation. Quite often algebraic functions are algebraic expressions using a finite number of terms, involving only the algebraic operations addition, subtraction, multiplication, division, and raising to a ... |
https://en.wikipedia.org/wiki/Subfield | Subfield may refer to:
an area of research and study within an academic discipline
Field extension, used in field theory (mathematics)
a Division (heraldry)
a division in MARC standards |
https://en.wikipedia.org/wiki/Abelian%20surface | In mathematics, an abelian surface is a 2-dimensional abelian variety.
One-dimensional complex tori are just elliptic curves and are all algebraic, but Riemann discovered that most complex tori of dimension 2 are not algebraic via the Riemann bilinear relations. Essentially, these are conditions on the parameter space... |
https://en.wikipedia.org/wiki/Estimation%20of%20covariance%20matrices | In statistics, sometimes the covariance matrix of a multivariate random variable is not known but has to be estimated. Estimation of covariance matrices then deals with the question of how to approximate the actual covariance matrix on the basis of a sample from the multivariate distribution. Simple cases, where observ... |
https://en.wikipedia.org/wiki/Monadic | Monadic may refer to:
Monadic, a relation or function having an arity of one in logic, mathematics, and computer science
Monadic, an adjunction if and only if it is equivalent to the adjunction given by the Eilenberg–Moore algebras of its associated monad, in category theory
Monadic, in computer programming, a feat... |
https://en.wikipedia.org/wiki/Simon%20Donaldson | Sir Simon Kirwan Donaldson (born 20 August 1957) is an English mathematician known for his work on the topology of smooth (differentiable) four-dimensional manifolds, Donaldson–Thomas theory, and his contributions to Kähler geometry. He is currently a permanent member of the Simons Center for Geometry and Physics at S... |
https://en.wikipedia.org/wiki/Divided%20differences | In mathematics, divided differences is an algorithm, historically used for computing tables of logarithms and trigonometric functions. Charles Babbage's difference engine, an early mechanical calculator, was designed to use this algorithm in its operation.
Divided differences is a recursive division process. Given a s... |
https://en.wikipedia.org/wiki/Monomial%20basis | In mathematics the monomial basis of a polynomial ring is its basis (as a vector space or free module over the field or ring of coefficients) that consists of all monomials. The monomials form a basis because every polynomial may be uniquely written as a finite linear combination of monomials (this is an immediate cons... |
https://en.wikipedia.org/wiki/Hilbert%E2%80%93Schmidt%20operator | In mathematics, a Hilbert–Schmidt operator, named after David Hilbert and Erhard Schmidt, is a bounded operator that acts on a Hilbert space and has finite Hilbert–Schmidt norm
where is an orthonormal basis. The index set need not be countable. However, the sum on the right must contain at most countably many non-... |
https://en.wikipedia.org/wiki/Whitehead%20theorem | In homotopy theory (a branch of mathematics), the Whitehead theorem states that if a continuous mapping f between CW complexes X and Y induces isomorphisms on all homotopy groups, then f is a homotopy equivalence. This result was proved by J. H. C. Whitehead in two landmark papers from 1949, and provides a justificatio... |
https://en.wikipedia.org/wiki/Cupola%20%28disambiguation%29 | A cupola is a relatively small, most often dome-like, tall structure on top of a building.
Cupola may also refer to:
Science, mathematics, and technology
Cupola (cave formation), a recess in the ceiling of a lava tube
Cupola (geology), a type of igneous rock intrusion
Cupola (geometry), a geometric solid
Cupola (... |
https://en.wikipedia.org/wiki/Truncated%20power%20function | In mathematics, the truncated power function with exponent is defined as
In particular,
and interpret the exponent as conventional power.
Relations
Truncated power functions can be used for construction of B-splines.
is the Heaviside function.
where is the indicator function.
Truncated power functions are re... |
https://en.wikipedia.org/wiki/Semi-local%20ring | In mathematics, a semi-local ring is a ring for which R/J(R) is a semisimple ring, where J(R) is the Jacobson radical of R.
The above definition is satisfied if R has a finite number of maximal right ideals (and finite number of maximal left ideals). When R is a commutative ring, the converse implication is also tru... |
https://en.wikipedia.org/wiki/Triple%20product | In geometry and algebra, the triple product is a product of three 3-dimensional vectors, usually Euclidean vectors. The name "triple product" is used for two different products, the scalar-valued scalar triple product and, less often, the vector-valued vector triple product.
Scalar triple product
The scalar triple p... |
https://en.wikipedia.org/wiki/Concepts%20of%20Modern%20Mathematics | Concepts of Modern Mathematics is a book by mathematician and science popularizer Ian Stewart about then-recent developments in mathematics. It was originally published by Penguin Books in 1975, updated in 1981, and reprinted by Dover publications in 1995 and 2015.
Overview
The book arose out of an extramural class th... |
https://en.wikipedia.org/wiki/Enrico%20Betti | Enrico Betti Glaoui (21 October 1823 – 11 August 1892) was an Italian mathematician, now remembered mostly for his 1871 paper on topology that led to the later naming after him of the Betti numbers. He worked also on the theory of equations, giving early expositions of Galois theory. He also discovered Betti's theorem,... |
https://en.wikipedia.org/wiki/Nuisance%20parameter | In statistics, a nuisance parameter is any parameter which is unspecified but which must be accounted for in the hypothesis testing of the parameters which are of interest.
The classic example of a nuisance parameter comes from the normal distribution, a member of the location–scale family. For at least one normal di... |
https://en.wikipedia.org/wiki/Marginal%20likelihood | A marginal likelihood is a likelihood function that has been integrated over the parameter space. In Bayesian statistics, it represents the probability of generating the observed sample from a prior and is therefore often referred to as model evidence or simply evidence.
Concept
Given a set of independent identically ... |
https://en.wikipedia.org/wiki/Combinatorial%20group%20theory | In mathematics, combinatorial group theory is the theory of free groups, and the concept of a presentation of a group by generators and relations. It is much used in geometric topology, the fundamental group of a simplicial complex having in a natural and geometric way such a presentation.
A very closely related topic ... |
https://en.wikipedia.org/wiki/Cauchy%20space | In general topology and analysis, a Cauchy space is a generalization of metric spaces and uniform spaces for which the notion of Cauchy convergence still makes sense. Cauchy spaces were introduced by H. H. Keller in 1968, as an axiomatic tool derived from the idea of a Cauchy filter, in order to study completeness in ... |
https://en.wikipedia.org/wiki/Ideal%20quotient | In abstract algebra, if I and J are ideals of a commutative ring R, their ideal quotient (I : J) is the set
Then (I : J) is itself an ideal in R. The ideal quotient is viewed as a quotient because if and only if . The ideal quotient is useful for calculating primary decompositions. It also arises in the description o... |
https://en.wikipedia.org/wiki/Barry%20Greenstein | Barry Greenstein (born December 30, 1954, in Chicago, Illinois) is an American professional poker player and former mathematics postgraduate student. He has won a number of major events, including three at the World Series of Poker and two on the World Poker Tour. Greenstein donates his profit from tournament winnings ... |
https://en.wikipedia.org/wiki/Integer%20square%20root | In number theory, the integer square root (isqrt) of a non-negative integer is the non-negative integer which is the greatest integer less than or equal to the square root of ,
For example,
Introductory remark
Let and be non-negative integers.
Algorithms that compute (the decimal representation of) run forever ... |
https://en.wikipedia.org/wiki/Selberg%20trace%20formula | In mathematics, the Selberg trace formula, introduced by , is an expression for the character of the unitary representation of a Lie group on the space of square-integrable functions, where is a cofinite discrete group. The character is given by the trace of certain functions on .
The simplest case is when is coc... |
https://en.wikipedia.org/wiki/Ehresmann%27s%20lemma | In mathematics, or specifically, in differential topology, Ehresmann's lemma or Ehresmann's fibration theorem states that if a smooth mapping , where and are smooth manifolds, is
a surjective submersion, and
a proper map (in particular, this condition is always satisfied if M is compact),
then it is a locally triv... |
https://en.wikipedia.org/wiki/Singular%20point%20of%20an%20algebraic%20variety | In the mathematical field of algebraic geometry, a singular point of an algebraic variety is a point that is 'special' (so, singular), in the geometric sense that at this point the tangent space at the variety may not be regularly defined. In case of varieties defined over the reals, this notion generalizes the notio... |
https://en.wikipedia.org/wiki/L1 | L1, L01, L.1, L 1 or L-1 may refer to:
Mathematics, science and technology
Math
L1 distance in mathematics, used in taxicab geometry
L1, the space of Lebesgue integrable functions
ℓ1, the space of absolutely convergent sequences
Science
L1 family, a protein family of cell adhesion molecules
L1 (protein), a cel... |
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