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https://en.wikipedia.org/wiki/Superfactorial | In mathematics, and more specifically number theory, the superfactorial of a positive integer is the product of the first factorials. They are a special case of the Jordan–Pólya numbers, which are products of arbitrary collections of factorials.
Definition
The th superfactorial may be defined as:
Following the usu... |
https://en.wikipedia.org/wiki/Glossary%20of%20differential%20geometry%20and%20topology | This is a glossary of terms specific to differential geometry and differential topology. The following three glossaries are closely related:
Glossary of general topology
Glossary of algebraic topology
Glossary of Riemannian and metric geometry.
See also:
List of differential geometry topics
Words in italics denote a ... |
https://en.wikipedia.org/wiki/Hadamard%20matrix | In mathematics, a Hadamard matrix, named after the French mathematician Jacques Hadamard, is a square matrix whose entries are either +1 or −1 and whose rows are mutually orthogonal. In geometric terms, this means that each pair of rows in a Hadamard matrix represents two perpendicular vectors, while in combinatorial t... |
https://en.wikipedia.org/wiki/Solid%20geometry | Solid geometry or stereometry is the geometry of three-dimensional Euclidean space (3D space).
A solid figure is the region of 3D space bounded by a two-dimensional surface; for example, a solid ball consists of a sphere and its interior.
Solid geometry deals with the measurements of volumes of various solids, includ... |
https://en.wikipedia.org/wiki/Triangle%20%28disambiguation%29 | A triangle is a geometric shape with three sides.
Triangle may also refer to:
Mathematics
Exact triangle, a collection of objects in category theory
Triangle inequality, Euclid's proposition that the sum of any two sides of a triangle is longer than the third side
American expression for set square, an object used ... |
https://en.wikipedia.org/wiki/Berry%E2%80%93Esseen%20theorem | In probability theory, the central limit theorem states that, under certain circumstances, the probability distribution of the scaled mean of a random sample converges to a normal distribution as the sample size increases to infinity. Under stronger assumptions, the Berry–Esseen theorem, or Berry–Esseen inequality, giv... |
https://en.wikipedia.org/wiki/List%20of%20factorial%20and%20binomial%20topics | This is a list of factorial and binomial topics in mathematics. See also binomial (disambiguation).
Abel's binomial theorem
Alternating factorial
Antichain
Beta function
Bhargava factorial
Binomial coefficient
Pascal's triangle
Binomial distribution
Binomial proportion confidence interval
Binomial-QMF (Daubechies wav... |
https://en.wikipedia.org/wiki/Telescoping%20series | In mathematics, a telescoping series is a series whose general term is of the form , i.e. the difference of two consecutive terms of a sequence .
As a consequence the partial sums only consists of two terms of after cancellation. The cancellation technique, with part of each term cancelling with part of the next ter... |
https://en.wikipedia.org/wiki/Circle%20group | In mathematics, the circle group, denoted by or , is the multiplicative group of all complex numbers with absolute value 1, that is, the unit circle in the complex plane or simply the unit complex numbers
The circle group forms a subgroup of , the multiplicative group of all nonzero complex numbers. Since is abelian... |
https://en.wikipedia.org/wiki/Dodecagon | In geometry, a dodecagon, or 12-gon, is any twelve-sided polygon.
Regular dodecagon
A regular dodecagon is a figure with sides of the same length and internal angles of the same size. It has twelve lines of reflective symmetry and rotational symmetry of order 12. A regular dodecagon is represented by the Schläfli sy... |
https://en.wikipedia.org/wiki/Nomenclature%20of%20Territorial%20Units%20for%20Statistics | Nomenclature of Territorial Units for Statistics or NUTS () is a geocode standard for referencing the administrative divisions of countries for statistical purposes. The standard, adopted in 2003, is developed and regulated by the European Union, and thus only covers the EU member states in detail. The Nomenclature of ... |
https://en.wikipedia.org/wiki/Cusp | A cusp is the most pointed end of a curve. It often refers to cusp (anatomy), a pointed structure on a tooth.
Cusp or CUSP may also refer to:
Mathematics
Cusp (singularity), a singular point of a curve
Cusp catastrophe, a branch of bifurcation theory in the study of dynamical systems
Cusp form, in modular form the... |
https://en.wikipedia.org/wiki/Formula%20for%20primes | In number theory, a formula for primes is a formula generating the prime numbers, exactly and without exception. No such formula which is efficiently computable is known. A number of constraints are known, showing what such a "formula" can and cannot be.
Formulas based on Wilson's theorem
A simple formula is
for pos... |
https://en.wikipedia.org/wiki/Pappus%27s%20centroid%20theorem | In mathematics, Pappus's centroid theorem (also known as the Guldinus theorem, Pappus–Guldinus theorem or Pappus's theorem) is either of two related theorems dealing with the surface areas and volumes of surfaces and solids of revolution.
The theorems are attributed to Pappus of Alexandria and Paul Guldin. Pappus's s... |
https://en.wikipedia.org/wiki/Gibbs%20sampling | In statistics, Gibbs sampling or a Gibbs sampler is a Markov chain Monte Carlo (MCMC) algorithm for obtaining a sequence of observations which are approximated from a specified multivariate probability distribution, when direct sampling is difficult. This sequence can be used to approximate the joint distribution (e.g... |
https://en.wikipedia.org/wiki/Complex%20manifold | In differential geometry and complex geometry, a complex manifold is a manifold with an atlas of charts to the open unit disc in , such that the transition maps are holomorphic.
The term complex manifold is variously used to mean a complex manifold in the sense above (which can be specified as an integrable complex ma... |
https://en.wikipedia.org/wiki/Skew-Hermitian%20matrix |
In linear algebra, a square matrix with complex entries is said to be skew-Hermitian or anti-Hermitian if its conjugate transpose is the negative of the original matrix. That is, the matrix is skew-Hermitian if it satisfies the relation
where denotes the conjugate transpose of the matrix . In component form, this ... |
https://en.wikipedia.org/wiki/Zariski%20tangent%20space | In algebraic geometry, the Zariski tangent space is a construction that defines a tangent space at a point P on an algebraic variety V (and more generally). It does not use differential calculus, being based directly on abstract algebra, and in the most concrete cases just the theory of a system of linear equations.
M... |
https://en.wikipedia.org/wiki/First%20fundamental%20form | In differential geometry, the first fundamental form is the inner product on the tangent space of a surface in three-dimensional Euclidean space which is induced canonically from the dot product of . It permits the calculation of curvature and metric properties of a surface such as length and area in a manner consiste... |
https://en.wikipedia.org/wiki/Group%20scheme | In mathematics, a group scheme is a type of object from algebraic geometry equipped with a composition law. Group schemes arise naturally as symmetries of schemes, and they generalize algebraic groups, in the sense that all algebraic groups have group scheme structure, but group schemes are not necessarily connected, ... |
https://en.wikipedia.org/wiki/Representativeness%20heuristic | The representativeness heuristic is used when making judgments about the probability of an event being representional in character and essence of known protyical event. It is one of a group of heuristics (simple rules governing judgment or decision-making) proposed by psychologists Amos Tversky and Daniel Kahneman in t... |
https://en.wikipedia.org/wiki/RSA%20numbers | In mathematics, the RSA numbers are a set of large semiprimes (numbers with exactly two prime factors) that were part of the RSA Factoring Challenge. The challenge was to find the prime factors of each number. It was created by RSA Laboratories in March 1991 to encourage research into computational number theory and th... |
https://en.wikipedia.org/wiki/Computational%20number%20theory | In mathematics and computer science, computational number theory, also known as algorithmic number theory, is the study of
computational methods for investigating and solving problems in number theory and arithmetic geometry, including algorithms for primality testing and integer factorization, finding solutions to di... |
https://en.wikipedia.org/wiki/Isosceles%20trapezoid | In Euclidean geometry, an isosceles trapezoid (isosceles trapezium in British English) is a convex quadrilateral with a line of symmetry bisecting one pair of opposite sides. It is a special case of a trapezoid. Alternatively, it can be defined as a trapezoid in which both legs and both base angles are of equal measure... |
https://en.wikipedia.org/wiki/Exotic%20probability | Exotic probability is a branch of probability theory that deals with probabilities which are outside the normal range of [0, 1].
According to the author of various papers on exotic probability, Saul Youssef, the valid possible alternatives for probability values are the real numbers, the complex numbers and the quate... |
https://en.wikipedia.org/wiki/A5 | A5 and variants may refer to:
Science and mathematics
A5 regulatory sequence in biochemistry
A5, the abbreviation for the androgen Androstenediol
Annexin A5, a human cellular protein
ATC code A05 Bile and liver therapy, a subgroup of the Anatomical Therapeutic Chemical Classification System
British NVC community ... |
https://en.wikipedia.org/wiki/1729%20%28number%29 | 1729 is the natural number following 1728 and preceding 1730. It is notably the first taxicab number.
In mathematics
1729 is the smallest taxicab number, and is variously known as Ramanujan's number or the Ramanujan–Hardy number, after an anecdote of the British mathematician G. H. Hardy when he visited Indian mathem... |
https://en.wikipedia.org/wiki/Gyrocar | A gyrocar is a two-wheeled automobile. The difference between a bicycle or motorcycle and a gyrocar is that in a bike, dynamic balance is provided by the rider, and in some cases by the geometry and mass distribution of the bike itself, and the gyroscopic effects from the wheels. Steering a motorcycle is done by prece... |
https://en.wikipedia.org/wiki/Taxicab%20number | In mathematics, the nth taxicab number, typically denoted Ta(n) or Taxicab(n), also called the nth Ramanujan–Hardy number, is defined as the smallest integer that can be expressed as a sum of two positive integer cubes in n distinct ways. The most famous taxicab number is 1729 = Ta(2) = 13 + 123 = 93 + 103.
The name i... |
https://en.wikipedia.org/wiki/Krohn%E2%80%93Rhodes%20theory | In mathematics and computer science, the Krohn–Rhodes theory (or algebraic automata theory) is an approach to the study of finite semigroups and automata that seeks to decompose them in terms of elementary components. These components correspond to finite aperiodic semigroups and finite simple groups that are combined ... |
https://en.wikipedia.org/wiki/Casimir%20element | In mathematics, a Casimir element (also known as a Casimir invariant or Casimir operator) is a distinguished element of the center of the universal enveloping algebra of a Lie algebra. A prototypical example is the squared angular momentum operator, which is a Casimir element of the three-dimensional rotation group.
M... |
https://en.wikipedia.org/wiki/5-cell | In geometry, the 5-cell is the convex 4-polytope with Schläfli symbol {3,3,3}. It is a 5-vertex four-dimensional object bounded by five tetrahedral cells. It is also known as a C5, pentachoron, pentatope, pentahedroid, or tetrahedral pyramid. It is the 4-simplex (Coxeter's polytope), the simplest possible convex 4-pol... |
https://en.wikipedia.org/wiki/Almost%20complex%20manifold | In mathematics, an almost complex manifold is a smooth manifold equipped with a smooth linear complex structure on each tangent space. Every complex manifold is an almost complex manifold, but there are almost complex manifolds that are not complex manifolds. Almost complex structures have important applications in sym... |
https://en.wikipedia.org/wiki/Canonical%20form | In mathematics and computer science, a canonical, normal, or standard form of a mathematical object is a standard way of presenting that object as a mathematical expression. Often, it is one which provides the simplest representation of an object and allows it to be identified in a unique way. The distinction between "... |
https://en.wikipedia.org/wiki/Gorenstein%20ring | In commutative algebra, a Gorenstein local ring is a commutative Noetherian local ring R with finite injective dimension as an R-module. There are many equivalent conditions, some of them listed below, often saying that a Gorenstein ring is self-dual in some sense.
Gorenstein rings were introduced by Grothendieck in h... |
https://en.wikipedia.org/wiki/Quantitative%20analysis | Quantitative analysis may refer to:
Quantitative research, application of mathematics and statistics in economics and marketing
Quantitative analysis (chemistry), the determination of the absolute or relative abundance of one or more substances present in a sample
Quantitative analysis (finance), the use of mathema... |
https://en.wikipedia.org/wiki/Map%20%28mathematics%29 | In mathematics, a map or mapping is a function in its general sense. These terms may have originated as from the process of making a geographical map: mapping the Earth surface to a sheet of paper.
The term map may be used to distinguish some special types of functions, such as homomorphisms. For example, a linear ma... |
https://en.wikipedia.org/wiki/Zero-dimensional%20space | In mathematics, a zero-dimensional topological space (or nildimensional space) is a topological space that has dimension zero with respect to one of several inequivalent notions of assigning a dimension to a given topological space. A graphical illustration of a nildimensional space is a point.
Definition
Specifically... |
https://en.wikipedia.org/wiki/Jakob%20Rosanes | Jakob Rosanes (also Jacob; 16 August 1842 – 6 January 1922) was a German mathematician who worked on algebraic geometry and invariant theory. He was also a chess master.
Rosanes was a grandson of Rabbi Akiva Eiger, one of the most revered Jewish religious scholars of the Talmud and halachic decisors of the 18th centur... |
https://en.wikipedia.org/wiki/Semi-locally%20simply%20connected | In mathematics, specifically algebraic topology, semi-locally simply connected is a certain local connectedness condition that arises in the theory of covering spaces. Roughly speaking, a topological space X is semi-locally simply connected if there is a lower bound on the sizes of the “holes” in X. This condition is n... |
https://en.wikipedia.org/wiki/Regular%20polytope | In mathematics, a regular polytope is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry. All its elements or -faces (for all , where is the dimension of the polytope) — cells, faces and so on — are also transitive on the symmetries of the polytope, and are re... |
https://en.wikipedia.org/wiki/Complex%20structure | A complex structure may refer to:
In mathematics
Almost complex manifold
Complex manifold
Linear complex structure
Generalized complex structure
Complex structure deformation
Complex vector bundle#Complex structure
In law
Complex structure theory in English law
See also
Real structure |
https://en.wikipedia.org/wiki/Locally%20convex%20topological%20vector%20space | In functional analysis and related areas of mathematics, locally convex topological vector spaces (LCTVS) or locally convex spaces are examples of topological vector spaces (TVS) that generalize normed spaces. They can be defined as topological vector spaces whose topology is generated by translations of balanced, abso... |
https://en.wikipedia.org/wiki/Quadratic%20integral | In mathematics, a quadratic integral is an integral of the form
It can be evaluated by completing the square in the denominator.
Positive-discriminant case
Assume that the discriminant q = b2 − 4ac is positive. In that case, define u and A by
and
The quadratic integral can now be written as
The partial fraction d... |
https://en.wikipedia.org/wiki/Projection%20%28linear%20algebra%29 | In linear algebra and functional analysis, a projection is a linear transformation from a vector space to itself (an endomorphism) such that . That is, whenever is applied twice to any vector, it gives the same result as if it were applied once (i.e. is idempotent). It leaves its image unchanged. This definition of ... |
https://en.wikipedia.org/wiki/Hessenberg%20matrix | In linear algebra, a Hessenberg matrix is a special kind of square matrix, one that is "almost" triangular. To be exact, an upper Hessenberg matrix has zero entries below the first subdiagonal, and a lower Hessenberg matrix has zero entries above the first superdiagonal. They are named after Karl Hessenberg.
A Hessenb... |
https://en.wikipedia.org/wiki/Tridiagonal%20matrix | In linear algebra, a tridiagonal matrix is a band matrix that has nonzero elements only on the main diagonal, the subdiagonal/lower diagonal (the first diagonal below this), and the supradiagonal/upper diagonal (the first diagonal above the main diagonal). For example, the following matrix is tridiagonal:
The determin... |
https://en.wikipedia.org/wiki/Pisot%E2%80%93Vijayaraghavan%20number | In mathematics, a Pisot–Vijayaraghavan number, also called simply a Pisot number or a PV number, is a real algebraic integer greater than 1, all of whose Galois conjugates are less than 1 in absolute value. These numbers were discovered by Axel Thue in 1912 and rediscovered by G. H. Hardy in 1919 within the context of ... |
https://en.wikipedia.org/wiki/Transcendental%20curve | In analytical geometry , a transcendental curve is a curve that is not an algebraic curve. Here for a curve, C, what matters is the point set (typically in the plane) underlying C, not a given parametrisation. For example, the unit circle is an algebraic curve (pedantically, the real points of such a curve); the usual ... |
https://en.wikipedia.org/wiki/List%20of%20mathematics%20history%20topics | This is a list of mathematics history topics, by Wikipedia page. See also list of mathematicians, timeline of mathematics, history of mathematics, list of publications in mathematics.
1729 (anecdote)
Adequality
Archimedes Palimpsest
Archimedes' use of infinitesimals
Arithmetization of analysis
Brachistochrone curve
Ch... |
https://en.wikipedia.org/wiki/Koszul%20complex | The Koszul complex is a concept in mathematics introduced by Jean-Louis Koszul.
Definition
Let A be a commutative ring and s: Ar → A an A-linear map. Its Koszul complex Ks is
where the maps send
where means the term is omitted and means the wedge product. One may replace Ar with any A-module.
Motivating exampl... |
https://en.wikipedia.org/wiki/Sampling%20distribution | In statistics, a sampling distribution or finite-sample distribution is the probability distribution of a given random-sample-based statistic. If an arbitrarily large number of samples, each involving multiple observations (data points), were separately used in order to compute one value of a statistic (such as, for ex... |
https://en.wikipedia.org/wiki/Schur%27s%20lemma | In mathematics, Schur's lemma is an elementary but extremely useful statement in representation theory of groups and algebras. In the group case it says that if M and N are two finite-dimensional irreducible representations
of a group G and φ is a linear map from M to N that commutes with the action of the group, the... |
https://en.wikipedia.org/wiki/Iwahori%E2%80%93Hecke%20algebra | In mathematics, the Iwahori–Hecke algebra, or Hecke algebra, named for Erich Hecke and Nagayoshi Iwahori, is a deformation of the group algebra of a Coxeter group.
Hecke algebras are quotients of the group rings of Artin braid groups. This connection found a spectacular application in Vaughan Jones' construction of n... |
https://en.wikipedia.org/wiki/Hecke%20operator | In mathematics, in particular in the theory of modular forms, a Hecke operator, studied by , is a certain kind of "averaging" operator that plays a significant role in the structure of vector spaces of modular forms and more general automorphic representations.
History
used Hecke operators on modular forms in a pap... |
https://en.wikipedia.org/wiki/Radon%20measure | In mathematics (specifically in measure theory), a Radon measure, named after Johann Radon, is a measure on the -algebra of Borel sets of a Hausdorff topological space that is finite on all compact sets, outer regular on all Borel sets, and inner regular on open sets. These conditions guarantee that the measure is "c... |
https://en.wikipedia.org/wiki/Heegner%20number | In number theory, a Heegner number (as termed by Conway and Guy) is a square-free positive integer d such that the imaginary quadratic field has class number 1. Equivalently, the ring of algebraic integers of has unique factorization.
The determination of such numbers is a special case of the class number problem, a... |
https://en.wikipedia.org/wiki/Homotopy%20lifting%20property | In mathematics, in particular in homotopy theory within algebraic topology, the homotopy lifting property (also known as an instance of the right lifting property or the covering homotopy axiom) is a technical condition on a continuous function from a topological space E to another one, B. It is designed to support the... |
https://en.wikipedia.org/wiki/Deterministic%20system | In mathematics, computer science and physics, a deterministic system is a system in which no randomness is involved in the development of future states of the system. A deterministic model will thus always produce the same output from a given starting condition or initial state.
In physics
Physical laws that are desc... |
https://en.wikipedia.org/wiki/Centerpoint | Centerpoint (alternatively spelled centrepoint) may refer to:
Centerpoint (geometry), a generalization of the median to two or more dimensions
Organizations
CenterPoint Energy, an electric and natural gas utility in the U.S.A.
CenterPoint Properties, Chicago industrial real estate developer
Centrepoint (charity),... |
https://en.wikipedia.org/wiki/Free%20monoid | In abstract algebra, the free monoid on a set is the monoid whose elements are all the finite sequences (or strings) of zero or more elements from that set, with string concatenation as the monoid operation and with the unique sequence of zero elements, often called the empty string and denoted by ε or λ, as the identi... |
https://en.wikipedia.org/wiki/Linear%20separability | In Euclidean geometry, linear separability is a property of two sets of points. This is most easily visualized in two dimensions (the Euclidean plane) by thinking of one set of points as being colored blue and the other set of points as being colored red. These two sets are linearly separable if there exists at least o... |
https://en.wikipedia.org/wiki/Constructible%20polygon | In mathematics, a constructible polygon is a regular polygon that can be constructed with compass and straightedge. For example, a regular pentagon is constructible with compass and straightedge while a regular heptagon is not. There are infinitely many constructible polygons, but only 31 with an odd number of sides ar... |
https://en.wikipedia.org/wiki/Chiliagon | In geometry, a chiliagon () or 1,000-gon is a polygon with 1,000 sides. Philosophers commonly refer to chiliagons to illustrate ideas about the nature and workings of thought, meaning, and mental representation.
Regular chiliagon
A regular chiliagon is represented by Schläfli symbol {1,000} and can be constructed as a... |
https://en.wikipedia.org/wiki/Myriagon | In geometry, a myriagon or 10000-gon is a polygon with 10000 sides. Several philosophers have used the regular myriagon to illustrate issues regarding thought.
Regular myriagon
A regular myriagon is represented by Schläfli symbol {10,000} and can be constructed as a truncated 5000-gon, t{5000}, or a twice-truncated 25... |
https://en.wikipedia.org/wiki/256%20%28number%29 | 256 (two hundred [and] fifty-six) is the natural number following 255 and preceding 257.
In mathematics
256 is a composite number, with the factorization 256 = 28, which makes it a power of two.
256 is 4 raised to the 4th power, so in tetration notation, 256 is 24.
256 is the value of the expression , where .
256 i... |
https://en.wikipedia.org/wiki/Simply%20connected%20space | In topology, a topological space is called simply connected (or 1-connected, or 1-simply connected) if it is path-connected and every path between two points can be continuously transformed (intuitively for embedded spaces, staying within the space) into any other such path while preserving the two endpoints in questio... |
https://en.wikipedia.org/wiki/Ideal%20number | In number theory an ideal number is an algebraic integer which represents an ideal in the ring of integers of a number field; the idea was developed by Ernst Kummer, and led to Richard Dedekind's definition of ideals for rings. An ideal in the ring of integers of an algebraic number field is principal if it consists of... |
https://en.wikipedia.org/wiki/Internal%20and%20external%20angles | In geometry, an angle of a polygon is formed by two adjacent sides. For a simple (non-self-intersecting) polygon, regardless of whether it is convex or non-convex, this angle is called an (or interior angle) if a point within the angle is in the interior of the polygon. A polygon has exactly one internal angle per ve... |
https://en.wikipedia.org/wiki/Bisect | Bisect, or similar, may refer to:
Mathematics
Bisection, in geometry, dividing something into two equal parts
Bisection method, a root-finding algorithm
Equidistant set
Other uses
Bisect (philately), the use of postage stamp halves
Bisector (music), a half octave in diatonic set theory
Bisection (software engin... |
https://en.wikipedia.org/wiki/Ernest%20Esclangon | Ernest Benjamin Esclangon (17 March 1876 – 28 January 1954) was a French astronomer and mathematician.
Born in Mison, Alpes-de-Haute-Provence, in 1895 he started to study mathematics at the École Normale Supérieure, graduating in 1898. Looking for some means of financial support while he completed his doctorate on qua... |
https://en.wikipedia.org/wiki/Dan%20Grimaldi | Dan Grimaldi (born March 7, 1946) is an American actor and mathematics professor who is known for his roles as twins Philly and Patsy Parisi on the HBO television series The Sopranos, various characters on Law & Order (1991-2001), Don't Go in the House (1979), The Junkman (1983), Men of Respect (1990), and The Yards (2... |
https://en.wikipedia.org/wiki/Submanifold | In mathematics, a submanifold of a manifold M is a subset S which itself has the structure of a manifold, and for which the inclusion map satisfies certain properties. There are different types of submanifolds depending on exactly which properties are required. Different authors often have different definitions.
Form... |
https://en.wikipedia.org/wiki/Hypersurface | In geometry, a hypersurface is a generalization of the concepts of hyperplane, plane curve, and surface. A hypersurface is a manifold or an algebraic variety of dimension , which is embedded in an ambient space of dimension , generally a Euclidean space, an affine space or a projective space.
Hypersurfaces share, with ... |
https://en.wikipedia.org/wiki/Codimension | In mathematics, codimension is a basic geometric idea that applies to subspaces in vector spaces, to submanifolds in manifolds, and suitable subsets of algebraic varieties.
For affine and projective algebraic varieties, the codimension equals the height of the defining ideal. For this reason, the height of an ideal is... |
https://en.wikipedia.org/wiki/Singular%20perturbation | In mathematics, a singular perturbation problem is a problem containing a small parameter that cannot be approximated by setting the parameter value to zero. More precisely, the solution cannot be uniformly approximated by an asymptotic expansion
as . Here is the small parameter of the problem and are a sequence of ... |
https://en.wikipedia.org/wiki/Brazilian%20Institute%20of%20Geography%20and%20Statistics | The Brazilian Institute of Geography and Statistics (; IBGE) is the agency responsible for official collection of statistical, geographic, cartographic, geodetic and environmental information in Brazil. IBGE performs a decennial national census; questionnaires account for information such as age, household income, lite... |
https://en.wikipedia.org/wiki/Ordered%20ring | In abstract algebra, an ordered ring is a (usually commutative) ring R with a total order ≤ such that for all a, b, and c in R:
if a ≤ b then a + c ≤ b + c.
if 0 ≤ a and 0 ≤ b then 0 ≤ ab.
Examples
Ordered rings are familiar from arithmetic. Examples include the integers, the rationals and the real numbers. (The... |
https://en.wikipedia.org/wiki/Cubic%20surface | In mathematics, a cubic surface is a surface in 3-dimensional space defined by one polynomial equation of degree 3. Cubic surfaces are fundamental examples in algebraic geometry. The theory is simplified by working in projective space rather than affine space, and so cubic surfaces are generally considered in projectiv... |
https://en.wikipedia.org/wiki/Karl%20L.%20Littrow | Karl Ludwig Edler von Littrow (18 July 1811 – 16 November 1877) was an Austrian astronomer.
Born in Kazan, Russian Empire, he was the son of astronomer Joseph Johann Littrow. He studied mathematics and astronomy at the universities of Vienna and Berlin, receiving his doctorate at the University of Krakow in 1832. In 1... |
https://en.wikipedia.org/wiki/Lists%20of%20mathematics%20topics | Lists of mathematics topics cover a variety of topics related to mathematics. Some of these lists link to hundreds of articles; some link only to a few. The template to the right includes links to alphabetical lists of all mathematical articles. This article brings together the same content organized in a manner better... |
https://en.wikipedia.org/wiki/Hilbert%27s%20eighth%20problem | Hilbert's eighth problem is one of David Hilbert's list of open mathematical problems posed in 1900. It concerns number theory, and in particular the Riemann hypothesis, although it is also concerned with the Goldbach Conjecture. The problem as stated asked for more work on the distribution of primes and generalization... |
https://en.wikipedia.org/wiki/Indian%20Agricultural%20Statistics%20Research%20Institute | The Indian Agricultural Statistics Research Institute is an institute under the Indian Council of Agricultural Research (ICAR) with the mandate for developing new techniques for the design of agricultural experiments as well as to analyze data in agriculture. The institute is affiliated with and is located in the campu... |
https://en.wikipedia.org/wiki/Abraham%20Fraenkel | Abraham Fraenkel (; February 17, 1891 – October 15, 1965) was a German-born Israeli mathematician. He was an early Zionist and the first Dean of Mathematics at the Hebrew University of Jerusalem. He is known for his contributions to axiomatic set theory, especially his additions to Ernst Zermelo's axioms, which resulte... |
https://en.wikipedia.org/wiki/Von%20Neumann%E2%80%93Bernays%E2%80%93G%C3%B6del%20set%20theory | In the foundations of mathematics, von Neumann–Bernays–Gödel set theory (NBG) is an axiomatic set theory that is a conservative extension of Zermelo–Fraenkel–choice set theory (ZFC). NBG introduces the notion of class, which is a collection of sets defined by a formula whose quantifiers range only over sets. NBG can de... |
https://en.wikipedia.org/wiki/Semigroupoid | In mathematics, a semigroupoid (also called semicategory, naked category or precategory) is a partial algebra that satisfies the axioms for a small category, except possibly for the requirement that there be an identity at each object. Semigroupoids generalise semigroups in the same way that small categories generalise... |
https://en.wikipedia.org/wiki/Chess%20symbols%20in%20Unicode | Chess symbols are part of Unicode. Instead of using images, one can represent chess pieces by characters that are defined in the Unicode character set. This makes it possible to:
Use figurine algebraic notation, which replaces the letter that stands for a piece by its symbol, e.g. ♘c6 instead of Nc6. This enables the... |
https://en.wikipedia.org/wiki/Independence%20%28disambiguation%29 | Independence generally refers to the self-government of a nation, country, or state by its residents and population.
Independence may also refer to:
Mathematics
Algebraic independence
Independence (graph theory), edge-wise non-connectedness
Independence (mathematical logic), logical independence
Independence (probabi... |
https://en.wikipedia.org/wiki/David%20van%20Dantzig | David van Dantzig (September 23, 1900 – July 22, 1959) was a Dutch mathematician, well known for the construction in topology of the dyadic solenoid. He was a member of the Significs Group.
Biography
Born to a Jewish family in Amsterdam in 1900, Van Dantzig started to study Chemistry at the University of Amsterdam in... |
https://en.wikipedia.org/wiki/Surface%20integral | In mathematics, particularly multivariable calculus, a surface integral is a generalization of multiple integrals to integration over surfaces. It can be thought of as the double integral analogue of the line integral. Given a surface, one may integrate a scalar field (that is, a function of position which returns a ... |
https://en.wikipedia.org/wiki/Definition%20%28disambiguation%29 | A definition is a statement of the meaning of a term.
Definition may also refer to:
Science, mathematics and computing
In computer programming languages, a declaration that reserves memory for a variable or gives the body of a subroutine
Defining equation (physical chemistry), physico-chemical quantities defined i... |
https://en.wikipedia.org/wiki/Togliatti%20%28disambiguation%29 | Togliatti, or Tolyatti, is a city in Russia.
Togliatti may also refer to:
Eugenio Giuseppe Togliatti (1890–1977), Italian mathematician
Togliatti surface, an algebraic surface discovered by him
Palmiro Togliatti (1893–1964), leader of the Italian Communist Party
The Togliatti amnesty, drafted by Palmiro Togliatti in 1... |
https://en.wikipedia.org/wiki/Category%20of%20medial%20magmas | In mathematics, the category of medial magmas, also known as the medial category, and denoted Med, is the category whose objects are medial magmas (that is, sets with a medial binary operation), and whose morphisms are magma homomorphisms (which are equivalent to homomorphisms in the sense of universal algebra).
The c... |
https://en.wikipedia.org/wiki/Shelah%20cardinal | In axiomatic set theory, Shelah cardinals are a kind of large cardinals. A cardinal is called Shelah iff for every , there exists a transitive class and an elementary embedding with critical point ; and .
A Shelah cardinal has a normal ultrafilter containing the set of weakly hyper-Woodin cardinals below it.
Refer... |
https://en.wikipedia.org/wiki/Remarkable%20cardinal | In mathematics, a remarkable cardinal is a certain kind of large cardinal number.
A cardinal κ is called remarkable if for all regular cardinals θ > κ, there exist π, M, λ, σ, N and ρ such that
π : M → Hθ is an elementary embedding
M is countable and transitive
π(λ) = κ
σ : M → N is an elementary embedding with c... |
https://en.wikipedia.org/wiki/Extremal%20graph%20theory | Extremal graph theory is a branch of combinatorics, itself an area of mathematics, that lies at the intersection of extremal combinatorics and graph theory. In essence, extremal graph theory studies how global properties of a graph influence local substructure.
Results in extremal graph theory deal with quantitative c... |
https://en.wikipedia.org/wiki/Mathcounts | Mathcounts, stylized as MATHCOUNTS, is a non-profit organization that provides grades 6-8 extracurricular mathematics programs in all U.S. states, plus the District of Columbia, Puerto Rico, Guam and U.S. Virgin Islands. Its mission is to provide engaging math programs for middle school students of all ability levels t... |
https://en.wikipedia.org/wiki/Pfaffian | In mathematics, the determinant of an m×m skew-symmetric matrix can always be written as the square of a polynomial in the matrix entries, a polynomial with integer coefficients that only depends on m. When m is odd, the polynomial is zero. When m=2n is even, it is a nonzero polynomial of degree n, and is unique up to ... |
https://en.wikipedia.org/wiki/Ideal%20%28order%20theory%29 | In mathematical order theory, an ideal is a special subset of a partially ordered set (poset). Although this term historically was derived from the notion of a ring ideal of abstract algebra, it has subsequently been generalized to a different notion. Ideals are of great importance for many constructions in order and l... |
https://en.wikipedia.org/wiki/MBD | MBD or MBd may refer to:
Man bites dog (journalism), a shortened version of an aphorism in journalism
Maxwell–Boltzmann distribution, a probability distribution in physics and chemistry
Megabaud (MBd), equal to one million baud, symbol rate in telecommunications
Member Board of Directors
Metabolic bone disease
Me... |
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