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https://en.wikipedia.org/wiki/Sigma%20function | In mathematics, by sigma function one can mean one of the following:
The sum-of-divisors function σa(n), an arithmetic function
Weierstrass sigma function, related to elliptic functions
Rado's sigma function, see busy beaver
See also sigmoid function. |
https://en.wikipedia.org/wiki/Mathematics%20and%20God | Connections between mathematics and God include the use of mathematics in arguments about the existence of God and about whether belief in God is beneficial.
Mathematical arguments for God's existence
In the 1070s, Anselm of Canterbury, an Italian medieval philosopher and theologian, created an ontological argument wh... |
https://en.wikipedia.org/wiki/Classical%20orthogonal%20polynomials | In mathematics, the classical orthogonal polynomials are the most widely used orthogonal polynomials: the Hermite polynomials, Laguerre polynomials, Jacobi polynomials (including as a special case the Gegenbauer polynomials, Chebyshev polynomials, and Legendre polynomials).
They have many important applications in suc... |
https://en.wikipedia.org/wiki/Girsanov%20theorem | In probability theory, the Girsanov theorem tells how stochastic processes change under changes in measure. The theorem is especially important in the theory of financial mathematics as it tells how to convert from the physical measure, which describes the probability that an underlying instrument (such as a share pric... |
https://en.wikipedia.org/wiki/Axial | Axial may refer to:
one of the anatomical directions describing relationships in an animal body
In geometry:
a geometric term of location
an axis of rotation
In chemistry, referring to an axial bond
a type of modal frame, in music
axial-flow, a type of fan
the Axial age in China, India, etc.
Axial Seamount an... |
https://en.wikipedia.org/wiki/PCC | PCC may refer to:
Science and technology
Pearson correlation coefficient (r), in statistics
Periodic counter-current chromatography, a type of affinity chromatography
Portable C Compiler, an early compiler for the C programming language
Precipitated calcium carbonate, a chemical compound
Proof-carrying code, a so... |
https://en.wikipedia.org/wiki/Raoul%20Bott | Raoul Bott (September 24, 1923 – December 20, 2005) was a Hungarian-American mathematician known for numerous foundational contributions to geometry in its broad sense. He is best known for his Bott periodicity theorem, the Morse–Bott functions which he used in this context, and the Borel–Bott–Weil theorem.
Early life... |
https://en.wikipedia.org/wiki/Frascati%20Manual | The Frascati Manual is a document setting forth the methodology for collecting statistics about research and development. The Manual was prepared and published by the Organisation for Economic Co-operation and Development.
Contents
The Frascati Manual classifies budgets according to what is done, what is studied, and... |
https://en.wikipedia.org/wiki/List%20of%20calculus%20topics | This is a list of calculus topics.
Limits
Limit (mathematics)
Limit of a function
One-sided limit
Limit of a sequence
Indeterminate form
Orders of approximation
(ε, δ)-definition of limit
Continuous function
Differential calculus
Derivative
Notation
Newton's notation for differentiation
Leibniz's notation... |
https://en.wikipedia.org/wiki/Dehn%20invariant | In geometry, the Dehn invariant is a value used to determine whether one polyhedron can be cut into pieces and reassembled ("dissected") into another, and whether a polyhedron or its dissections can tile space. It is named after Max Dehn, who used it to solve Hilbert's third problem by proving that not all polyhedra wi... |
https://en.wikipedia.org/wiki/Plateau%27s%20problem | In mathematics, Plateau's problem is to show the existence of a minimal surface with a given boundary, a problem raised by Joseph-Louis Lagrange in 1760. However, it is named after Joseph Plateau who experimented with soap films. The problem is considered part of the calculus of variations. The existence and regulari... |
https://en.wikipedia.org/wiki/Long%20line%20%28topology%29 | In topology, the long line (or Alexandroff line) is a topological space somewhat similar to the real line, but in a certain way "longer". It behaves locally just like the real line, but has different large-scale properties (e.g., it is neither Lindelöf nor separable). Therefore, it serves as an important counterexampl... |
https://en.wikipedia.org/wiki/Reinhard%20H%C3%B6ppner | Reinhard Höppner (2 December 1948 – 9 June 2014) was a German politician (SPD) and writer.
Höppner held a Dr. rer. nat. in mathematics.
In 1990, in the first (and last) free election in the assembly's history, he was elected a member of the East German People's Chamber (Volkskammer), becoming the assembly's vice pres... |
https://en.wikipedia.org/wiki/Radon%E2%80%93Nikodym%20theorem | In mathematics, the Radon–Nikodym theorem is a result in measure theory that expresses the relationship between two measures defined on the same measurable space. A measure is a set function that assigns a consistent magnitude to the measurable subsets of a measurable space. Examples of a measure include area and volum... |
https://en.wikipedia.org/wiki/Exponential%20family | In probability and statistics, an exponential family is a parametric set of probability distributions of a certain form, specified below. This special form is chosen for mathematical convenience, including the enabling of the user to calculate expectations, covariances using differentiation based on some useful algebra... |
https://en.wikipedia.org/wiki/MOS | MOS or Mos may refer to:
Technology
MOSFET (metal–oxide–semiconductor field-effect transistor), also known as the MOS transistor
Mathematical Optimization Society
Model output statistics, a weather-forecasting technique
MOS (filmmaking), term for a scene that is "motor only sync" or "motor only shot", or jokingly... |
https://en.wikipedia.org/wiki/Johann%20Radon | Johann Karl August Radon (; 16 December 1887 – 25 May 1956) was an Austrian mathematician. His doctoral dissertation was on the calculus of variations (in 1910, at the University of Vienna).
Life
Radon was born in Tetschen, Bohemia, Austria-Hungary, now Děčín, Czech Republic. He received his doctoral degree at the Un... |
https://en.wikipedia.org/wiki/Semiprime | In mathematics, a semiprime is a natural number that is the product of exactly two prime numbers. The two primes in the product may equal each other, so the semiprimes include the squares of prime numbers.
Because there are infinitely many prime numbers, there are also infinitely many semiprimes. Semiprimes are also ca... |
https://en.wikipedia.org/wiki/Almost%20prime | In number theory, a natural number is called k-almost prime if it has k prime factors. More formally, a number n is k-almost prime if and only if Ω(n) = k, where Ω(n) is the total number of primes in the prime factorization of n (can be also seen as the sum of all the primes' exponents):
A natural number is thus prime... |
https://en.wikipedia.org/wiki/Pointwise%20convergence | In mathematics, pointwise convergence is one of various senses in which a sequence of functions can converge to a particular function. It is weaker than uniform convergence, to which it is often compared.
Definition
Suppose that is a set and is a topological space, such as the real or complex numbers or a metric sp... |
https://en.wikipedia.org/wiki/Partition%20of%20a%20set | In mathematics, a partition of a set is a grouping of its elements into non-empty subsets, in such a way that every element is included in exactly one subset.
Every equivalence relation on a set defines a partition of this set, and every partition defines an equivalence relation. A set equipped with an equivalence rel... |
https://en.wikipedia.org/wiki/Pentagonal%20number%20theorem | In mathematics, Euler's pentagonal number theorem relates the product and series representations of the Euler function. It states that
In other words,
The exponents 1, 2, 5, 7, 12, ... on the right hand side are given by the formula for k = 1, −1, 2, −2, 3, ... and are called (generalized) pentagonal numbers . (The... |
https://en.wikipedia.org/wiki/Ludwig%20Immanuel%20Magnus | Ludwig Immanuel Magnus (March 15, 1790 – September 25, 1861) was a German Jewish mathematician who, in 1831, published a paper about the inversion transformation, which leads to inversive geometry.
His reputation as a mathematician was established by 1834 and an honorary doctorate conferred on him by the University of... |
https://en.wikipedia.org/wiki/Economic%20statistics | Economic statistics is a topic in applied statistics and applied economics that concerns the collection, processing, compilation, dissemination, and analysis of economic data. It is closely related to business statistics and econometrics. It is also common to call the data themselves "economic statistics", but for this... |
https://en.wikipedia.org/wiki/List%20of%20complex%20analysis%20topics | Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematics that investigates functions of complex numbers. It is useful in many branches of mathematics, including number theory and applied mathematics; as well as in physics, including hydrodynamics, thermodynami... |
https://en.wikipedia.org/wiki/Function%20space | In mathematics, a function space is a set of functions between two fixed sets. Often, the domain and/or codomain will have additional structure which is inherited by the function space. For example, the set of functions from any set into a vector space has a natural vector space structure given by pointwise addition a... |
https://en.wikipedia.org/wiki/Quantum%20group | In mathematics and theoretical physics, the term quantum group denotes one of a few different kinds of noncommutative algebras with additional structure. These include Drinfeld–Jimbo type quantum groups (which are quasitriangular Hopf algebras), compact matrix quantum groups (which are structures on unital separable C*... |
https://en.wikipedia.org/wiki/Ferdinand%20Georg%20Frobenius | Ferdinand Georg Frobenius (26 October 1849 – 3 August 1917) was a German mathematician, best known for his contributions to the theory of elliptic functions, differential equations, number theory, and to group theory. He is known for the famous determinantal identities, known as Frobenius–Stickelberger formulae, govern... |
https://en.wikipedia.org/wiki/Matrix%20similarity | In linear algebra, two n-by-n matrices and are called similar if there exists an invertible n-by-n matrix such that
Similar matrices represent the same linear map under two (possibly) different bases, with being the change of basis matrix.
A transformation is called a similarity transformation or conjugation of ... |
https://en.wikipedia.org/wiki/Second-order%20logic | In logic and mathematics, second-order logic is an extension of first-order logic, which itself is an extension of propositional logic. Second-order logic is in turn extended by higher-order logic and type theory.
First-order logic quantifies only variables that range over individuals (elements of the domain of discou... |
https://en.wikipedia.org/wiki/Cantor%27s%20theorem | In mathematical set theory, Cantor's theorem is a fundamental result which states that, for any set , the set of all subsets of the power set of has a strictly greater cardinality than itself.
For finite sets, Cantor's theorem can be seen to be true by simple enumeration of the number of subsets. Counting the empt... |
https://en.wikipedia.org/wiki/30%20%28number%29 | 30 (thirty) is the natural number following 29 and preceding 31.
In mathematics
30 is an even, composite, pronic number. With 2, 3, and 5 as its prime factors, it is a regular number and the first sphenic number, the smallest of the form , where is a prime greater than 3. It has an aliquot sum of 42, which is the se... |
https://en.wikipedia.org/wiki/Square%20root%20of%202 | The square root of 2 (approximately 1.4142) is a positive real number that, when multiplied by itself, equals the number 2. It may be written in mathematics as or . It is an algebraic number, and therefore not a transcendental number. Technically, it should be called the principal square root of 2, to distinguish it f... |
https://en.wikipedia.org/wiki/Diagonal%20argument | A diagonal argument, in mathematics, is a technique employed in the proofs of the following theorems:
Cantor's diagonal argument (the earliest)
Cantor's theorem
Russell's paradox
Diagonal lemma
Gödel's first incompleteness theorem
Tarski's undefinability theorem
Halting problem
Kleene's recursion theorem
See also
Di... |
https://en.wikipedia.org/wiki/Central%20extension | Central extension may refer to:
Central Extension (Long Island Rail Road), a rail line
Central extension (mathematics), a type of group extension |
https://en.wikipedia.org/wiki/Center%20%28algebra%29 | The term center or centre is used in various contexts in abstract algebra to denote the set of all those elements that commute with all other elements.
The center of a group G consists of all those elements x in G such that xg = gx for all g in G. This is a normal subgroup of G.
The similarly named notion for a semig... |
https://en.wikipedia.org/wiki/Lehmann%E2%80%93Scheff%C3%A9%20theorem | In statistics, the Lehmann–Scheffé theorem is a prominent statement, tying together the ideas of completeness, sufficiency, uniqueness, and best unbiased estimation. The theorem states that any estimator which is unbiased for a given unknown quantity and that depends on the data only through a complete, sufficient stat... |
https://en.wikipedia.org/wiki/Inclusion%E2%80%93exclusion%20principle | In combinatorics, a branch of mathematics, the inclusion–exclusion principle is a counting technique which generalizes the familiar method of obtaining the number of elements in the union of two finite sets; symbolically expressed as
where A and B are two finite sets and |S | indicates the cardinality of a set S (whic... |
https://en.wikipedia.org/wiki/Image%20%28category%20theory%29 | In category theory, a branch of mathematics, the image of a morphism is a generalization of the image of a function.
General definition
Given a category and a morphism in , the image
of is a monomorphism satisfying the following universal property:
There exists a morphism such that .
For any object with a mor... |
https://en.wikipedia.org/wiki/Cousin%20prime | In number theory, cousin primes are prime numbers that differ by four. Compare this with twin primes, pairs of prime numbers that differ by two, and sexy primes, pairs of prime numbers that differ by six.
The cousin primes (sequences and in OEIS) below 1000 are:
(3, 7), (7, 11), (13, 17), (19, 23), (37, 41), (43, ... |
https://en.wikipedia.org/wiki/Sexy%20prime | In number theory, sexy primes are prime numbers that differ from each other by 6. For example, the numbers 5 and 11 are both sexy primes, because both are prime and .
The term "sexy prime" is a pun stemming from the Latin word for six: .
If or (where is the lower prime) is also prime, then the sexy prime is part ... |
https://en.wikipedia.org/wiki/Schnirelmann%20density | In additive number theory, the Schnirelmann density of a sequence of numbers is a way to measure how "dense" the sequence is. It is named after Russian mathematician Lev Schnirelmann, who was the first to study it.
Definition
The Schnirelmann density of a set of natural numbers A is defined as
where A(n) denotes the ... |
https://en.wikipedia.org/wiki/60%20%28number%29 | 60 (sixty) () is the natural number following 59 and preceding 61. Being three times 20, it is called threescore in older literature (kopa in Slavic, Schock in Germanic).
In mathematics
60 is a highly composite number. Because it is the sum of its unitary divisors (excluding itself), it is a unitary perfect number, a... |
https://en.wikipedia.org/wiki/70%20%28number%29 | 70 (seventy) is the natural number following 69 and preceding 71.
In mathematics
70 is:
a sphenic number because its factors are 3 distinct primes.
a Pell number.
the seventh pentagonal number.
the fourth tridecagonal number.
the fifth pentatope number.
the number of ways to choose 4 objects out of 8 if order d... |
https://en.wikipedia.org/wiki/Constructible%20universe | In mathematics, in set theory, the constructible universe (or Gödel's constructible universe), denoted by , is a particular class of sets that can be described entirely in terms of simpler sets. is the union of the constructible hierarchy . It was introduced by Kurt Gödel in his 1938 paper "The Consistency of the Axio... |
https://en.wikipedia.org/wiki/80%20%28number%29 | 80 (eighty) is the natural number following 79 and preceding 81.
In mathematics
80 is:
the sum of Euler's totient function φ(x) over the first sixteen integers.
a semiperfect number, since adding up some subsets of its divisors (e.g., 1, 4, 5, 10, 20 and 40) gives 80.
a ménage number.
palindromic in bases 3 (222... |
https://en.wikipedia.org/wiki/Simple%20theorems%20in%20the%20algebra%20of%20sets | The simple theorems in the algebra of sets are some of the elementary properties of the algebra of union (infix operator: ∪), intersection (infix operator: ∩), and set complement (postfix ') of sets.
These properties assume the existence of at least two sets: a given universal set, denoted U, and the empty set, denote... |
https://en.wikipedia.org/wiki/Set-theoretic%20limit | In mathematics, the limit of a sequence of sets (subsets of a common set ) is a set whose elements are determined by the sequence in either of two equivalent ways: (1) by upper and lower bounds on the sequence that converge monotonically to the same set (analogous to convergence of real-valued sequences) and (2) by co... |
https://en.wikipedia.org/wiki/Korteweg%E2%80%93De%20Vries%20equation | In mathematics, the Korteweg–De Vries (KdV) equation is a partial differential equation (PDE) which serves as a mathematical model of waves on shallow water surfaces. It is particularly notable as the prototypical example of an integrable PDE and exhibits many of the expected behaviors for an integrable PDE, such as a ... |
https://en.wikipedia.org/wiki/Mean%20deviation | Mean deviation may refer to:
Statistics
Mean signed deviation, a measure of central tendency
Mean absolute deviation, a measure of statistical dispersion
Mean squared deviation, another measure of statistical dispersion
Other
Mean Deviation (book), a 2010 non-fiction book by former Metal Maniacs magazine editor J... |
https://en.wikipedia.org/wiki/Multiplicative%20order | In number theory, given a positive integer n and an integer a coprime to n, the multiplicative order of a modulo n is the smallest positive integer k such that .
In other words, the multiplicative order of a modulo n is the order of a in the multiplicative group of the units in the ring of the integers modulo n.
The ... |
https://en.wikipedia.org/wiki/Pierre-Simon%20Laplace | Pierre-Simon, Marquis de Laplace (; ; 23 March 1749 – 5 March 1827) was a French scholar and polymath whose work was important to the development of engineering, mathematics, statistics, physics, astronomy, and philosophy. He summarized and extended the work of his predecessors in his five-volume Mécanique céleste (Cel... |
https://en.wikipedia.org/wiki/Boole%27s%20inequality | In probability theory, Boole's inequality, also known as the union bound, says that for any finite or countable set of events, the probability that at least one of the events happens is no greater than the sum of the probabilities of the individual events. This inequality provides an upper bound on the probability of o... |
https://en.wikipedia.org/wiki/Leech%20lattice | In mathematics, the Leech lattice is an even unimodular lattice Λ24 in 24-dimensional Euclidean space, which is one of the best models for the kissing number problem. It was discovered by . It may also have been discovered (but not published) by Ernst Witt in 1940.
Characterization
The Leech lattice Λ24 is the unique... |
https://en.wikipedia.org/wiki/Binary%20Golay%20code | In mathematics and electronics engineering, a binary Golay code is a type of linear error-correcting code used in digital communications. The binary Golay code, along with the ternary Golay code, has a particularly deep and interesting connection to the theory of finite sporadic groups in mathematics. These codes are n... |
https://en.wikipedia.org/wiki/Finite%20volume%20method | The finite volume method (FVM) is a method for representing and evaluating partial differential equations in the form of algebraic equations.
In the finite volume method, volume integrals in a partial differential equation that contain a divergence term are converted to surface integrals, using the divergence theorem. ... |
https://en.wikipedia.org/wiki/Intuitionistic%20type%20theory | Intuitionistic type theory (also known as constructive type theory, or Martin-Löf type theory) is a type theory and an alternative foundation of mathematics.
Intuitionistic type theory was created by Per Martin-Löf, a Swedish mathematician and philosopher, who first published it in 1972. There are multiple versions of... |
https://en.wikipedia.org/wiki/Hell%2C%20Michigan | Hell is an unincorporated community in Livingston County in the U.S. state of Michigan. As an unincorporated community, Hell has no defined boundaries or population statistics of its own. Located within Putnam Township, the community is centered along Patterson Lake Road about northwest of Ann Arbor and southwest of ... |
https://en.wikipedia.org/wiki/VEGAS%20algorithm | The VEGAS algorithm, due to G. Peter Lepage, is a method for reducing error in Monte Carlo simulations by using a known or approximate probability distribution function to concentrate the search in those areas of the integrand that make the greatest contribution to the final integral.
The VEGAS algorithm is based on i... |
https://en.wikipedia.org/wiki/List%20of%20differential%20geometry%20topics | This is a list of differential geometry topics. See also glossary of differential and metric geometry and list of Lie group topics.
Differential geometry of curves and surfaces
Differential geometry of curves
List of curves topics
Frenet–Serret formulas
Curves in differential geometry
Line element
Curvature
Radius o... |
https://en.wikipedia.org/wiki/Ein | Ein or EIN may refer to:
Science and technology
Ein function, in mathematics
Endometrial intraepithelial neoplasia, a lesion of the uterine lining
Equivalent input noise, of a microphone
European Informatics Network, a 1970s computer network
Fictional characters
Ein, a character in the anime series Cowboy Bebop... |
https://en.wikipedia.org/wiki/Conway%20group | In the area of modern algebra known as group theory, the Conway groups are the three sporadic simple groups Co1, Co2 and Co3 along with the related finite group Co0 introduced by .
The largest of the Conway groups, Co0, is the group of automorphisms of the Leech lattice Λ with respect to addition and inner product. I... |
https://en.wikipedia.org/wiki/The%20Dot%20and%20the%20Line | The Dot and the Line: A Romance in Lower Mathematics is a 1965 animated short film directed by Chuck Jones and co-directed by Maurice Noble, based on the 1963 book of the same name written and illustrated by Norton Juster, who also provided the film's script. The film was narrated by Robert Morley and produced by Metro... |
https://en.wikipedia.org/wiki/Poisson%20algebra | In mathematics, a Poisson algebra is an associative algebra together with a Lie bracket that also satisfies Leibniz's law; that is, the bracket is also a derivation. Poisson algebras appear naturally in Hamiltonian mechanics, and are also central in the study of quantum groups. Manifolds with a Poisson algebra structu... |
https://en.wikipedia.org/wiki/Group%20extension | In mathematics, a group extension is a general means of describing a group in terms of a particular normal subgroup and quotient group. If and are two groups, then is an extension of by if there is a short exact sequence
If is an extension of by , then is a group, is a normal subgroup of and the quotient gr... |
https://en.wikipedia.org/wiki/Betti%20number | In algebraic topology, the Betti numbers are used to distinguish topological spaces based on the connectivity of n-dimensional simplicial complexes. For the most reasonable finite-dimensional spaces (such as compact manifolds, finite simplicial complexes or CW complexes), the sequence of Betti numbers is 0 from some po... |
https://en.wikipedia.org/wiki/Algebraic%20quantum%20field%20theory | Algebraic quantum field theory (AQFT) is an application to local quantum physics of C*-algebra theory. Also referred to as the Haag–Kastler axiomatic framework for quantum field theory, because it was introduced by . The axioms are stated in terms of an algebra given for every open set in Minkowski space, and mappings ... |
https://en.wikipedia.org/wiki/Axiom%20of%20countability | In mathematics, an axiom of countability is a property of certain mathematical objects that asserts the existence of a countable set with certain properties. Without such an axiom, such a set might not provably exist.
Important examples
Important countability axioms for topological spaces include:
sequential space: a ... |
https://en.wikipedia.org/wiki/%CE%A3-compact%20space | In mathematics, a topological space is said to be σ-compact if it is the union of countably many compact subspaces.
A space is said to be σ-locally compact if it is both σ-compact and (weakly) locally compact. That terminology can be somewhat confusing as it does not fit the usual pattern of σ-(property) meaning a co... |
https://en.wikipedia.org/wiki/List%20of%20number%20theory%20topics | This is a list of number theory topics. See also:
List of recreational number theory topics
Topics in cryptography
Divisibility
Composite number
Highly composite number
Even and odd numbers
Parity
Divisor, aliquot part
Greatest common divisor
Least common multiple
Euclidean algorithm
Coprime
Euclid's lemma
Bézout's ... |
https://en.wikipedia.org/wiki/Dimension%20theorem%20for%20vector%20spaces | In mathematics, the dimension theorem for vector spaces states that all bases of a vector space have equally many elements. This number of elements may be finite or infinite (in the latter case, it is a cardinal number), and defines the dimension of the vector space.
Formally, the dimension theorem for vector spaces s... |
https://en.wikipedia.org/wiki/Valuation%20%28algebra%29 | In algebra (in particular in algebraic geometry or algebraic number theory), a valuation is a function on a field that provides a measure of the size or multiplicity of elements of the field. It generalizes to commutative algebra the notion of size inherent in consideration of the degree of a pole or multiplicity of a ... |
https://en.wikipedia.org/wiki/List%20of%20algebraic%20topology%20topics | This is a list of algebraic topology topics.
Homology (mathematics)
Simplex
Simplicial complex
Polytope
Triangulation
Barycentric subdivision
Simplicial approximation theorem
Abstract simplicial complex
Simplicial set
Simplicial category
Chain (algebraic topology)
Betti number
Euler characteristic
Genus
Riemann–Hurwi... |
https://en.wikipedia.org/wiki/List%20of%20polynomial%20topics | This is a list of polynomial topics, by Wikipedia page. See also trigonometric polynomial, list of algebraic geometry topics.
Terminology
Degree: The maximum exponents among the monomials.
Factor: An expression being multiplied.
Linear factor: A factor of degree one.
Coefficient: An expression multiplying one of the... |
https://en.wikipedia.org/wiki/Arg%20max | In mathematics, the arguments of the maxima (abbreviated arg max or argmax) are the points, or elements, of the domain of some function at which the function values are maximized. In contrast to global maxima, which refers to the largest outputs of a function, arg max refers to the inputs, or arguments, at which the fu... |
https://en.wikipedia.org/wiki/Virasoro%20algebra | In mathematics, the Virasoro algebra (named after the physicist Miguel Ángel Virasoro) is a complex Lie algebra and the unique central extension of the Witt algebra. It is widely used in two-dimensional conformal field theory and in string theory.
Definition
The Virasoro algebra is spanned by generators for and the... |
https://en.wikipedia.org/wiki/Spinor%20bundle | In differential geometry, given a spin structure on an -dimensional orientable Riemannian manifold one defines the spinor bundle to be the complex vector bundle associated to the corresponding principal bundle of spin frames over and the spin representation of its structure group on the space of spinors .
A secti... |
https://en.wikipedia.org/wiki/Double%20cover | In mathematics, a double cover or double covering may refer to:
Double cover (topology), a two-to-one mapping from one topological space to another. Frequently occurring special cases include
The orientable double cover of a non-orientable manifold
The bipartite double cover of an undirected graph G, formed by the grap... |
https://en.wikipedia.org/wiki/List%20of%20geometric%20topology%20topics | This is a list of geometric topology topics.
Low-dimensional topology
Knot theory
Knot (mathematics)
Link (knot theory)
Wild knots
Examples of knots
Unknot
Trefoil knot
Figure-eight knot (mathematics)
Borromean rings
Types of knots
Torus knot
Prime knot
Alternating knot
Hyperbolic link
Knot invariants
Crossing numbe... |
https://en.wikipedia.org/wiki/Morse%20theory | In mathematics, specifically in differential topology, Morse theory enables one to analyze the topology of a manifold by studying differentiable functions on that manifold. According to the basic insights of Marston Morse, a typical differentiable function on a manifold will reflect the topology quite directly. Morse t... |
https://en.wikipedia.org/wiki/List%20of%20order%20theory%20topics | Order theory is a branch of mathematics that studies various kinds of objects (often binary relations) that capture the intuitive notion of ordering, providing a framework for saying when one thing is "less than" or "precedes" another.
An alphabetical list of many notions of order theory can be found in the order theo... |
https://en.wikipedia.org/wiki/Vandermonde%20matrix | In linear algebra, a Vandermonde matrix, named after Alexandre-Théophile Vandermonde, is a matrix with the terms of a geometric progression in each row: an matrix
with entries , the jth power of the number , for all zero-based indices and . Most authors define the Vandermonde matrix as the transpose of the above mat... |
https://en.wikipedia.org/wiki/Mandelbrot | Mandelbrot may refer to:
Benoit Mandelbrot (1924–2010), a mathematician associated with fractal geometry
Mandelbrot set, a fractal popularized by Benoit Mandelbrot
Mandelbrot Competition, a mathematics competition
Mandelbrot (cookie), dessert associated with Eastern European Jews
Szolem Mandelbrojt, a Polish-Frenc... |
https://en.wikipedia.org/wiki/Torsion-free | In mathematics, torsion-free may refer to:
Abstract algebra
Torsion-free group, a group whose only element of finite order is the identity
Torsion-free module, module over an integral domain where zero is the only torsion element
Torsion-free abelian group, an abelian group which is a torsion-free group
Torsion-... |
https://en.wikipedia.org/wiki/Projective%20representation | In the field of representation theory in mathematics, a projective representation of a group G on a vector space V over a field F is a group homomorphism from G to the projective linear group
where GL(V) is the general linear group of invertible linear transformations of V over F, and F∗ is the normal subgroup consist... |
https://en.wikipedia.org/wiki/Antichain | In mathematics, in the area of order theory, an antichain is a subset of a partially ordered set such that any two distinct elements in the subset are incomparable.
The size of the largest antichain in a partially ordered set is known as its width. By Dilworth's theorem, this also equals the minimum number of chains (... |
https://en.wikipedia.org/wiki/Lindemann%E2%80%93Weierstrass%20theorem | In transcendental number theory, the Lindemann–Weierstrass theorem is a result that is very useful in establishing the transcendence of numbers. It states the following:
In other words, the extension field has transcendence degree over .
An equivalent formulation , is the following: This equivalence transforms a... |
https://en.wikipedia.org/wiki/Linearly%20ordered%20group | In mathematics, specifically abstract algebra, a linearly ordered or totally ordered group is a group G equipped with a total order "≤" that is translation-invariant. This may have different meanings. We say that (G, ≤) is a:
left-ordered group if ≤ is left-invariant, that is a ≤ b implies ca ≤ cb for all a, b, c in ... |
https://en.wikipedia.org/wiki/Guido%20Fubini | Guido Fubini (19 January 1879 – 6 June 1943) was an Italian mathematician, known for Fubini's theorem and the Fubini–Study metric.
Life
Born in Venice, he was steered towards mathematics at an early age by his teachers and his father, who was himself a teacher of mathematics. In 1896 he entered the Scuola Normale Sup... |
https://en.wikipedia.org/wiki/Iterated%20integral | In multivariable calculus, an iterated integral is the result of applying integrals to a function of more than one variable (for example or ) in such a way that each of the integrals considers some of the variables as given constants. For example, the function , if is considered a given parameter, can be integrated w... |
https://en.wikipedia.org/wiki/1907%20in%20science | The year 1907 in science and technology involved some significant events, listed below.
Mathematics
Paul Koebe conjectures the result of the Koebe quarter theorem.
Physics
The Ehrenfest model of diffusion is proposed by Tatiana and Paul Ehrenfest to explain the second law of thermodynamics.
Albert Einstein introdu... |
https://en.wikipedia.org/wiki/Fotini%20Markopoulou-Kalamara | Fotini G. Markopoulou-Kalamara (; born April 3, 1971) is a Greek theoretical physicist interested in quantum gravity, foundational mathematics, quantum mechanics and a design engineer working on embodied cognition technologies. Markopoulou is co-founder and CEO of Empathic Technologies. She was a founding faculty memb... |
https://en.wikipedia.org/wiki/Group%20ring | In algebra, a group ring is a free module and at the same time a ring, constructed in a natural way from any given ring and any given group. As a free module, its ring of scalars is the given ring, and its basis is the set of elements of the given group. As a ring, its addition law is that of the free module and its mu... |
https://en.wikipedia.org/wiki/Diagonal | In geometry, a diagonal is a line segment joining two vertices of a polygon or polyhedron, when those vertices are not on the same edge. Informally, any sloping line is called diagonal. The word diagonal derives from the ancient Greek διαγώνιος diagonios, "from angle to angle" (from διά- dia-, "through", "across" an... |
https://en.wikipedia.org/wiki/Integral%20geometry | In mathematics, integral geometry is the theory of measures on a geometrical space invariant under the symmetry group of that space. In more recent times, the meaning has been broadened to include a view of invariant (or equivariant) transformations from the space of functions on one geometrical space to the space of ... |
https://en.wikipedia.org/wiki/Spherical%20circle | In spherical geometry, a spherical circle (often shortened to circle) is the locus of points on a sphere at constant spherical distance (the spherical radius) from a given point on the sphere (the pole or spherical center). It is a curve of constant geodesic curvature relative to the sphere, analogous to a line or circ... |
https://en.wikipedia.org/wiki/Farey%20sequence | In mathematics, the Farey sequence of order n is the sequence of completely reduced fractions, either between 0 and 1, or without this restriction, which when in lowest terms have denominators less than or equal to n, arranged in order of increasing size.
With the restricted definition, each Farey sequence starts with... |
https://en.wikipedia.org/wiki/Outline%20of%20combinatorics | Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures.
Essence of combinatorics
Matroid
Greedoid
Ramsey theory
Van der Waerden's theorem
Hales–Jewett theorem
Umbral calculus, binomial type polynomial sequences
Combinatorial species
Branches of combinatorics ... |
https://en.wikipedia.org/wiki/Logicism | In the philosophy of mathematics, logicism is a programme comprising one or more of the theses that — for some coherent meaning of 'logic' — mathematics is an extension of logic, some or all of mathematics is reducible to logic, or some or all of mathematics may be modelled in logic. Bertrand Russell and Alfred North W... |
https://en.wikipedia.org/wiki/Laplace%20transform%20applied%20to%20differential%20equations | In mathematics, the Laplace transform is a powerful integral transform used to switch a function from the time domain to the s-domain. The Laplace transform can be used in some cases to solve linear differential equations with given initial conditions.
First consider the following property of the Laplace transform:
O... |
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