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https://en.wikipedia.org/wiki/Abc%20conjecture | The abc conjecture (also known as the Oesterlé–Masser conjecture) is a conjecture in number theory that arose out of a discussion of Joseph Oesterlé and David Masser in 1985. It is stated in terms of three positive integers and (hence the name) that are relatively prime and satisfy . The conjecture essentially state... |
https://en.wikipedia.org/wiki/GRP | GRP may refer to:
Biochemistry
Gastrin-releasing peptide
Grp78, Grp94, Grp170, glucose-regulated proteins
Grape reaction product
Mathematics
Grp, the Category of groups
Technology and materials
Glass-reinforced-polymer, also known as Fiberglass, or Fibreglass.
Gentoo Reference Platform
Transport
Grove Park ... |
https://en.wikipedia.org/wiki/Splitting%20field | In abstract algebra, a splitting field of a polynomial with coefficients in a field is the smallest field extension of that field over which the polynomial splits, i.e., decomposes into linear factors.
Definition
A splitting field of a polynomial p(X) over a field K is a field extension L of K over which p factors int... |
https://en.wikipedia.org/wiki/Abelian%20extension | In abstract algebra, an abelian extension is a Galois extension whose Galois group is abelian. When the Galois group is also cyclic, the extension is also called a cyclic extension. Going in the other direction, a Galois extension is called solvable if its Galois group is solvable, i.e., if the group can be decomposed ... |
https://en.wikipedia.org/wiki/Common%20logarithm | In mathematics, the common logarithm is the logarithm with base 10. It is also known as the decadic logarithm and as the decimal logarithm, named after its base, or Briggsian logarithm, after Henry Briggs, an English mathematician who pioneered its use, as well as standard logarithm. Historically, it was known as logar... |
https://en.wikipedia.org/wiki/Dirichlet%20character | In analytic number theory and related branches of mathematics, a complex-valued arithmetic function is a Dirichlet character of modulus (where is a positive integer) if for all integers and :
that is, is completely multiplicative.
(gcd is the greatest common divisor)
; that is, is periodic with period .
Th... |
https://en.wikipedia.org/wiki/Algebraic%20number%20theory | Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations. Number-theoretic questions are expressed in terms of properties of algebraic objects such as algebraic number fields and their rings of integers, finite f... |
https://en.wikipedia.org/wiki/Laplace%20operator | In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a scalar function on Euclidean space. It is usually denoted by the symbols , (where is the nabla operator), or . In a Cartesian coordinate system, the Laplacian is given by the sum of second partial... |
https://en.wikipedia.org/wiki/Div | Div or DIV may refer to:
Science and technology
Division (mathematics), the mathematical operation that is the inverse of multiplication
Span and div, HTML tags that implement generic elements
div, a C mathematical function
Divergence, a mathematical operation in vector calculus
Digital Intrinsic Value, a digital... |
https://en.wikipedia.org/wiki/Goro%20Shimura | was a Japanese mathematician and Michael Henry Strater Professor Emeritus of Mathematics at Princeton University who worked in number theory, automorphic forms, and arithmetic geometry. He was known for developing the theory of complex multiplication of abelian varieties and Shimura varieties, as well as posing the Tan... |
https://en.wikipedia.org/wiki/Backslash | The backslash is a typographical mark used mainly in computing and mathematics. It is the mirror image of the common slash . It is a relatively recent mark, first documented in the 1930s. It is sometimes called a hack, whack, escape (from C/UNIX), reverse slash, slosh, downwhack, backslant, backwhack, bash, reverse s... |
https://en.wikipedia.org/wiki/Functional%20predicate | In formal logic and related branches of mathematics, a functional predicate, or function symbol, is a logical symbol that may be applied to an object term to produce another object term.
Functional predicates are also sometimes called mappings, but that term has additional meanings in mathematics.
In a model, a functio... |
https://en.wikipedia.org/wiki/Relational%20algebra | In database theory, relational algebra is a theory that uses algebraic structures for modeling data, and defining queries on it with a well founded semantics. The theory was introduced by Edgar F. Codd.
The main application of relational algebra is to provide a theoretical foundation for relational databases, particul... |
https://en.wikipedia.org/wiki/Tuple%20relational%20calculus | Tuple calculus is a calculus that was created and introduced by Edgar F. Codd as part of the relational model, in order to provide a declarative database-query language for data manipulation in this data model. It formed the inspiration for the database-query languages QUEL and SQL, of which the latter, although far le... |
https://en.wikipedia.org/wiki/Cayley%E2%80%93Dickson%20construction | In mathematics, the Cayley–Dickson construction, named after Arthur Cayley and Leonard Eugene Dickson, produces a sequence of algebras over the field of real numbers, each with twice the dimension of the previous one. The algebras produced by this process are known as Cayley–Dickson algebras, for example complex number... |
https://en.wikipedia.org/wiki/Relational%20calculus | The relational calculus consists of two calculi, the tuple relational calculus and the domain relational calculus, that is part of the relational model for databases and provide a declarative way to specify database queries. The raison d'être of relational calculus is the formalization of query optimization, which is f... |
https://en.wikipedia.org/wiki/Whole%20number | Whole number is a colloquial term in mathematics. The meaning is ambiguous. It may refer to either:
Natural number, an element of the set or of the set
Integer, an element of the set |
https://en.wikipedia.org/wiki/Underwood%20Dudley | Underwood Dudley (born January 6, 1937) is an American mathematician and writer. His popular works include several books describing crank mathematics by pseudomathematicians who incorrectly believe they have squared the circle or done other impossible things.
Career
Dudley was born in New York City. He received bache... |
https://en.wikipedia.org/wiki/Riemann%20sum | In mathematics, a Riemann sum is a certain kind of approximation of an integral by a finite sum. It is named after nineteenth century German mathematician Bernhard Riemann. One very common application is in numerical integration, i.e., approximating the area of functions or lines on a graph, where it is also known as t... |
https://en.wikipedia.org/wiki/Well-posed%20problem | In mathematics, a well-posed problem is one for which the following properties hold:
The problem has a solution
The solution is unique
The solution's behavior changes continuously with the initial conditions
This definition of a well-posed problem comes from the work of Jacques Hadamard on mathematical modeling of ... |
https://en.wikipedia.org/wiki/Computational%20geometry | Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry. Some purely geometrical problems arise out of the study of computational geometric algorithms, and such problems are also considered to be part of computational geometry. While modern comp... |
https://en.wikipedia.org/wiki/Error%20function | In mathematics, the error function (also called the Gauss error function), often denoted by , is a complex function of a complex variable defined as:
Some authors define without the factor of .
This nonelementary integral is a sigmoid function that occurs often in probability, statistics, and partial differential equ... |
https://en.wikipedia.org/wiki/Equational%20prover | EQP, an abbreviation for equational prover, is an automated theorem proving program for equational logic, developed by the Mathematics and Computer Science Division of the Argonne National Laboratory. It was one of the provers used for solving a longstanding problem posed by Herbert Robbins, namely, whether all Robbin... |
https://en.wikipedia.org/wiki/Crime%20statistics | Crime statistics refer to systematic, quantitative results about crime, as opposed to crime news or anecdotes. Notably, crime statistics can be the result of two rather different processes:
scientific research, such as criminological studies, victimisation surveys;
official figures, such as published by the police, p... |
https://en.wikipedia.org/wiki/Voronoi%20diagram | In mathematics, a Voronoi diagram is a partition of a plane into regions close to each of a given set of objects. It can be classified also as a tessellation. In the simplest case, these objects are just finitely many points in the plane (called seeds, sites, or generators). For each seed there is a corresponding regio... |
https://en.wikipedia.org/wiki/Asker | {{Historical populations
|footnote = Source: Statistics Norway.
|shading = off
|1951|13625
|1961|17755
|1971|31702
|1981|35977
|19... |
https://en.wikipedia.org/wiki/Hari%20Seldon | Hari Seldon is a fictional character in Isaac Asimov's Foundation series. In his capacity as mathematics professor at Streeling University on the planet Trantor, Seldon develops psychohistory, an algorithmic science that allows him to predict the future in probabilistic terms. On the basis of his psychohistory he is ab... |
https://en.wikipedia.org/wiki/General%20topology | In mathematics, general topology (or point set topology) is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology. It is the foundation of most other branches of topology, including differential topology, geometric topology, and algebraic topology.
The fundament... |
https://en.wikipedia.org/wiki/Ernst%20Zermelo | Ernst Friedrich Ferdinand Zermelo (, ; 27 July 187121 May 1953) was a German logician and mathematician, whose work has major implications for the foundations of mathematics. He is known for his role in developing Zermelo–Fraenkel axiomatic set theory and his proof of the well-ordering theorem. Furthermore, his 1929 wo... |
https://en.wikipedia.org/wiki/Gotthilf%20Hagen | Gotthilf Heinrich Ludwig Hagen (3 March 1797 – 3 February 1884) was a German civil engineer who made important contributions to fluid dynamics, hydraulic engineering and probability theory.
Life and work
Hagen was born in Königsberg, East Prussia (Kaliningrad, Russia) to Friedrich Ludwig Hagen and Helene Charlotte Alb... |
https://en.wikipedia.org/wiki/Dirichlet%20convolution | In mathematics, the Dirichlet convolution is a binary operation defined for arithmetic functions; it is important in number theory. It was developed by Peter Gustav Lejeune Dirichlet.
Definition
If are two arithmetic functions from the positive integers to the complex numbers, the Dirichlet convolution is a new arit... |
https://en.wikipedia.org/wiki/SPSS | SPSS Statistics is a statistical software suite developed by IBM for data management, advanced analytics, multivariate analysis, business intelligence, and criminal investigation. Long produced by SPSS Inc., it was acquired by IBM in 2009. Versions of the software released since 2015 have the brand name IBM SPSS Statis... |
https://en.wikipedia.org/wiki/Snub%20cube | In geometry, the snub cube, or snub cuboctahedron, is an Archimedean solid with 38 faces: 6 squares and 32 equilateral triangles. It has 60 edges and 24 vertices.
It is a chiral polyhedron; that is, it has two distinct forms, which are mirror images (or "enantiomorphs") of each other. The union of both forms is a comp... |
https://en.wikipedia.org/wiki/Stellation | In geometry, stellation is the process of extending a polygon in two dimensions, polyhedron in three dimensions, or, in general, a polytope in n dimensions to form a new figure. Starting with an original figure, the process extends specific elements such as its edges or face planes, usually in a symmetrical way, until ... |
https://en.wikipedia.org/wiki/Cubic%20equation | In algebra, a cubic equation in one variable is an equation of the form
in which is nonzero.
The solutions of this equation are called roots of the cubic function defined by the left-hand side of the equation. If all of the coefficients , , , and of the cubic equation are real numbers, then it has at least one real... |
https://en.wikipedia.org/wiki/Bruno%20de%20Finetti | Bruno de Finetti (13 June 1906 – 20 July 1985) was an Italian probabilist statistician and actuary, noted for the "operational subjective" conception of probability. The classic exposition of his distinctive theory is the 1937 , which discussed probability founded on the coherence of betting odds and the consequences o... |
https://en.wikipedia.org/wiki/De%20Finetti%27s%20theorem | In probability theory, de Finetti's theorem states that exchangeable observations are conditionally independent relative to some latent variable. An epistemic probability distribution could then be assigned to this variable. It is named in honor of Bruno de Finetti.
For the special case of an exchangeable sequence of... |
https://en.wikipedia.org/wiki/Hypergeometric%20distribution | In probability theory and statistics, the hypergeometric distribution is a discrete probability distribution that describes the probability of successes (random draws for which the object drawn has a specified feature) in draws, without replacement, from a finite population of size that contains exactly objects wit... |
https://en.wikipedia.org/wiki/Kalman%20filter | For statistics and control theory, Kalman filtering, also known as linear quadratic estimation (LQE), is an algorithm that uses a series of measurements observed over time, including statistical noise and other inaccuracies, and produces estimates of unknown variables that tend to be more accurate than those based on a... |
https://en.wikipedia.org/wiki/List%20of%20islands%20of%20Sweden | This is a list of islands of Sweden. According to 2013 statistics report there are in total 267,570 islands in Sweden, fewer than 1000 of which are inhabited. Their total area is 1.2 million hectares, which corresponds to 3 percent of the total land area of Sweden.
Rough population statistics are from 2015.
Ordered b... |
https://en.wikipedia.org/wiki/Empty%20product | In mathematics, an empty product, or nullary product or vacuous product, is the result of multiplying no factors. It is by convention equal to the multiplicative identity (assuming there is an identity for the multiplication operation in question), just as the empty sum—the result of adding no numbers—is by convention ... |
https://en.wikipedia.org/wiki/Discrete%20logarithm | In mathematics, for given real numbers a and b, the logarithm logb a is a number x such that . Analogously, in any group G, powers bk can be defined for all integers k, and the discrete logarithm logb a is an integer k such that . In number theory, the more commonly used term is index: we can write x = indr a (mod m) (... |
https://en.wikipedia.org/wiki/Fermi%20gas | A Fermi gas is an idealized model, an ensemble of many non-interacting fermions. Fermions are particles that obey Fermi–Dirac statistics, like electrons, protons, and neutrons, and, in general, particles with half-integer spin. These statistics determine the energy distribution of fermions in a Fermi gas in thermal equ... |
https://en.wikipedia.org/wiki/Kronecker%20delta | In mathematics, the Kronecker delta (named after Leopold Kronecker) is a function of two variables, usually just non-negative integers. The function is 1 if the variables are equal, and 0 otherwise:
or with use of Iverson brackets:
For example, because , whereas because .
The Kronecker delta appears naturally in m... |
https://en.wikipedia.org/wiki/List%20of%20unsolved%20problems%20in%20mathematics | Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set th... |
https://en.wikipedia.org/wiki/Metamathematics | Metamathematics is the study of mathematics itself using mathematical methods. This study produces metatheories, which are mathematical theories about other mathematical theories. Emphasis on metamathematics (and perhaps the creation of the term itself) owes itself to David Hilbert's attempt to secure the foundations o... |
https://en.wikipedia.org/wiki/Primality%20test | A primality test is an algorithm for determining whether an input number is prime. Among other fields of mathematics, it is used for cryptography. Unlike integer factorization, primality tests do not generally give prime factors, only stating whether the input number is prime or not. Factorization is thought to be a co... |
https://en.wikipedia.org/wiki/Rhombus | In plane Euclidean geometry, a rhombus (: rhombi or rhombuses) is a quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equal in length. The rhombus is often called a "diamond", after the diamonds suit in playing cards whi... |
https://en.wikipedia.org/wiki/K%C3%B6nig%27s%20theorem%20%28set%20theory%29 | In set theory, König's theorem states that if the axiom of choice holds, I is a set, and are cardinal numbers for every i in I, and for every i in I, then
The sum here is the cardinality of the disjoint union of the sets mi, and the product is the cardinality of the Cartesian product. However, without the use of ... |
https://en.wikipedia.org/wiki/Bias%20%28statistics%29 | Statistical bias, in the mathematical field of statistics, is a systematic tendency in which the methods used to gather data and generate statistics present an inaccurate, skewed or biased depiction of reality. Statistical bias exists in numerous stages of the data collection and analysis process, including: the source... |
https://en.wikipedia.org/wiki/Girolamo%20Fracastoro | Girolamo Fracastoro (; c. 1476/86 August 1553) was an Italian physician, poet, and scholar in mathematics, geography and astronomy. Fracastoro subscribed to the philosophy of atomism, and rejected appeals to hidden causes in scientific investigation. His studies of the mode of syphilis transmission are an early example... |
https://en.wikipedia.org/wiki/David%20H.%20Bailey%20%28mathematician%29 | David Harold Bailey (born 14 August 1948) is a mathematician and computer scientist. He received his B.S. in mathematics from Brigham Young University in 1972 and his Ph.D. in mathematics from Stanford University in 1976. He worked for 14 years as a computer scientist at NASA Ames Research Center, and then from 1998 to... |
https://en.wikipedia.org/wiki/Quotient%20ring | In ring theory, a branch of abstract algebra, a quotient ring, also known as factor ring, difference ring or residue class ring, is a construction quite similar to the quotient group in group theory and to the quotient space in linear algebra. It is a specific example of a quotient, as viewed from the general setting o... |
https://en.wikipedia.org/wiki/Jaime%20Escalante | Jaime Alfonso Escalante Gutiérrez (December 31, 1930 – March 30, 2010) was a Bolivian-American educator known for teaching students calculus from 1974 to 1991 at Garfield High School in East Los Angeles. Escalante was the subject of the 1988 film Stand and Deliver, in which he is portrayed by Edward James Olmos.
In 1... |
https://en.wikipedia.org/wiki/Function%20%28mathematics%29 | In mathematics, a function from a set to a set assigns to each element of exactly one element of . The set is called the domain of the function and the set is called the codomain of the function.
Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the pos... |
https://en.wikipedia.org/wiki/Informal%20mathematics | Informal mathematics, also called naïve mathematics, has historically been the predominant form of mathematics at most times and in most cultures, and is the subject of modern ethno-cultural studies of mathematics. The philosopher Imre Lakatos in his Proofs and Refutations aimed to sharpen the formulation of informal m... |
https://en.wikipedia.org/wiki/Division%20by%20zero | In mathematics, division by zero is division where the divisor (denominator) is zero. Such a division can be formally expressed as , where is the dividend (numerator). In ordinary arithmetic, the expression has no meaning, as there is no number that, when multiplied by , gives (assuming ); thus, division by zero is u... |
https://en.wikipedia.org/wiki/Felicific%20calculus | The felicific calculus is an algorithm formulated by utilitarian philosopher Jeremy Bentham (1747–1832) for calculating the degree or amount of pleasure that a specific action is likely to induce. Bentham, an ethical hedonist, believed the moral rightness or wrongness of an action to be a function of the amount of plea... |
https://en.wikipedia.org/wiki/Unifying%20theories%20in%20mathematics | There have been several attempts in history to reach a unified theory of mathematics. Some of the most respected mathematicians in the academia have expressed views that the whole subject should be fitted into one theory.
The unification of mathematical topics has been called mathematical consolidation: "By a consolid... |
https://en.wikipedia.org/wiki/Regression%20toward%20the%20mean | In statistics, regression toward the mean (also called reversion to the mean, and reversion to mediocrity) is the phenomenon where if one sample of a random variable is extreme, the next sampling of the same random variable is likely to be closer to its mean. Furthermore, when many random variables are sampled and the ... |
https://en.wikipedia.org/wiki/Alternativity | In abstract algebra, alternativity is a property of a binary operation. A magma G is said to be if for all and if for all A magma that is both left and right alternative is said to be ().
Any associative magma (that is, a semigroup) is alternative. More generally, a magma in which every pair of elements genera... |
https://en.wikipedia.org/wiki/Complex%20geometry | In mathematics, complex geometry is the study of geometric structures and constructions arising out of, or described by, the complex numbers. In particular, complex geometry is concerned with the study of spaces such as complex manifolds and complex algebraic varieties, functions of several complex variables, and holom... |
https://en.wikipedia.org/wiki/Algebraic%20element | In mathematics, if is a field extension of , then an element of is called an algebraic element over , or just algebraic over , if there exists some non-zero polynomial with coefficients in such that . Elements of which are not algebraic over are called transcendental over .
These notions generalize the algebrai... |
https://en.wikipedia.org/wiki/Statistics%20Canada | Statistics Canada (StatCan; ), formed in 1971, is the agency of the Government of Canada commissioned with producing statistics to help better understand Canada, its population, resources, economy, society, and culture. It is headquartered in Ottawa.
The agency is led by the chief statistician of Canada, currently Ani... |
https://en.wikipedia.org/wiki/Morlet%20wavelet | In mathematics, the Morlet wavelet (or Gabor wavelet) is a wavelet composed of a complex exponential (carrier) multiplied by a Gaussian window (envelope). This wavelet is closely related to human perception, both hearing and vision.
History
In 1946, physicist Dennis Gabor, applying ideas from quantum physics, intro... |
https://en.wikipedia.org/wiki/Hall%27s%20marriage%20theorem | In mathematics, Hall's marriage theorem, proved by , is a theorem with two equivalent formulations. In each case, the theorem gives a necessary and sufficient condition for an object to exist:
The combinatorial formulation answers whether a finite collection of sets has a transversal—that is, whether an element can be... |
https://en.wikipedia.org/wiki/Quadratic%20function | In mathematics, a quadratic polynomial is a polynomial of degree two in one or more variables. A quadratic function is the polynomial function defined by a quadratic polynomial. Before the 20th century, the distinction was unclear between a polynomial and its associated polynomial function; so "quadratic polynomial" an... |
https://en.wikipedia.org/wiki/Self-adjoint%20operator | In mathematics, a self-adjoint operator on an infinite-dimensional complex vector space V with inner product (equivalently, a Hermitian operator in the finite-dimensional case) is a linear map A (from V to itself) that is its own adjoint. If V is finite-dimensional with a given orthonormal basis, this is equivalent to... |
https://en.wikipedia.org/wiki/Orientability | In mathematics, orientability is a property of some topological spaces such as real vector spaces, Euclidean spaces, surfaces, and more generally manifolds that allows a consistent definition of "clockwise" and "anticlockwise". A space is orientable if such a consistent definition exists. In this case, there are two po... |
https://en.wikipedia.org/wiki/Percolation%20theory | In statistical physics and mathematics, percolation theory describes the behavior of a network when nodes or links are added. This is a geometric type of phase transition, since at a critical fraction of addition the network of small, disconnected clusters merge into significantly larger connected, so-called spanning c... |
https://en.wikipedia.org/wiki/Centroid | In mathematics and physics, the centroid, also known as geometric center or center of figure, of a plane figure or solid figure is the point defined by the arithmetic mean position of all the points in the surface of the figure. In a polytope, it can be found using the arithmetic mean position of the vertices. The same... |
https://en.wikipedia.org/wiki/Univalent | Univalent may refer to:
Univalent function – an injective holomorphic function on an open subset of the complex plane
Univalent foundations – a type-based approach to foundation of mathematics
Univalent relation – a binary relation R that satisfies
Valence (chemistry)#univalent – 1-valent. |
https://en.wikipedia.org/wiki/Axiomatic%20system | In mathematics and logic, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems. A theory is a consistent, relatively-self-contained body of knowledge which usually contains an axiomatic system and all its derived theorems. An axiomatic system tha... |
https://en.wikipedia.org/wiki/Irreducible%20polynomial | In mathematics, an irreducible polynomial is, roughly speaking, a polynomial that cannot be factored into the product of two non-constant polynomials. The property of irreducibility depends on the nature of the coefficients that are accepted for the possible factors, that is, the field to which the coefficients of the ... |
https://en.wikipedia.org/wiki/Calabi%E2%80%93Yau%20manifold | In algebraic geometry, a Calabi–Yau manifold, also known as a Calabi–Yau space, is a particular type of manifold which has properties, such as Ricci flatness, yielding applications in theoretical physics. Particularly in superstring theory, the extra dimensions of spacetime are sometimes conjectured to take the form of... |
https://en.wikipedia.org/wiki/Bose%E2%80%93Einstein%20statistics | In quantum statistics, Bose–Einstein statistics (B–E statistics) describes one of two possible ways in which a collection of non-interacting identical particles may occupy a set of available discrete energy states at thermodynamic equilibrium. The aggregation of particles in the same state, which is a characteristic of... |
https://en.wikipedia.org/wiki/Disjoint%20union | In mathematics, a disjoint union (or discriminated union) of a family of sets is a set often denoted by with an injection of each into such that the images of these injections form a partition of (that is, each element of belongs to exactly one of these images). A disjoint union of a family of pairwise disjoint ... |
https://en.wikipedia.org/wiki/Matrix%20representation%20of%20conic%20sections | In mathematics, the matrix representation of conic sections permits the tools of linear algebra to be used in the study of conic sections. It provides easy ways to calculate a conic section's axis, vertices, tangents and the pole and polar relationship between points and lines of the plane determined by the conic. The ... |
https://en.wikipedia.org/wiki/Birthday%20attack | A birthday attack is a bruteforce collision attack that exploits the mathematics behind the birthday problem in probability theory. This attack can be used to abuse communication between two or more parties. The attack depends on the higher likelihood of collisions found between random attack attempts and a fixed degre... |
https://en.wikipedia.org/wiki/Hermitian%20matrix | In mathematics, a Hermitian matrix (or self-adjoint matrix) is a complex square matrix that is equal to its own conjugate transpose—that is, the element in the -th row and -th column is equal to the complex conjugate of the element in the -th row and -th column, for all indices and :
or in matrix form:
Hermitian mat... |
https://en.wikipedia.org/wiki/Transfinite%20number | In mathematics, transfinite numbers or infinite numbers are numbers that are "infinite" in the sense that they are larger than all finite numbers. These include the transfinite cardinals, which are cardinal numbers used to quantify the size of infinite sets, and the transfinite ordinals, which are ordinal numbers used ... |
https://en.wikipedia.org/wiki/Normal%20operator | In mathematics, especially functional analysis, a normal operator on a complex Hilbert space H is a continuous linear operator N : H → H that commutes with its hermitian adjoint N*, that is: NN* = N*N.
Normal operators are important because the spectral theorem holds for them. The class of normal operators is well und... |
https://en.wikipedia.org/wiki/42%20%28number%29 | 42 (forty-two) is the natural number that follows 41 and precedes 43.
Mathematics
Forty-two (42) is a pronic number and an abundant number; its prime factorization () makes it the second sphenic number and also the second of the form ().
Additional properties of the number 42 include:
It is the number of isomorphis... |
https://en.wikipedia.org/wiki/Harmonic%20series | Harmonic series may refer to either of two related concepts:
Harmonic series (mathematics)
Harmonic series (music) |
https://en.wikipedia.org/wiki/List%20of%20statistics%20articles |
0–9
1.96
2SLS (two-stage least squares) redirects to instrumental variable
3SLS – see three-stage least squares
68–95–99.7 rule
100-year flood
A
A priori probability
Abductive reasoning
Absolute deviation
Absolute risk reduction
Absorbing Markov chain
ABX test
Accelerated failure time model
Acceptable quality limit... |
https://en.wikipedia.org/wiki/Covariance%20matrix | In probability theory and statistics, a covariance matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance–covariance matrix) is a square matrix giving the covariance between each pair of elements of a given random vector.
Intuitively, the covariance matrix generalizes the notion ... |
https://en.wikipedia.org/wiki/Counting%20measure | In mathematics, specifically measure theory, the counting measure is an intuitive way to put a measure on any set – the "size" of a subset is taken to be the number of elements in the subset if the subset has finitely many elements, and infinity if the subset is infinite.
The counting measure can be defined on any me... |
https://en.wikipedia.org/wiki/Algebra%20over%20a%20field | In mathematics, an algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product. Thus, an algebra is an algebraic structure consisting of a set together with operations of multiplication and addition and scalar multiplication by elements of a field and satisfying the axioms i... |
https://en.wikipedia.org/wiki/Kolmogorov%27s%20zero%E2%80%93one%20law | In probability theory, Kolmogorov's zero–one law, named in honor of Andrey Nikolaevich Kolmogorov, specifies that a certain type of event, namely a tail event of independent σ-algebras, will either almost surely happen or almost surely not happen; that is, the probability of such an event occurring is zero or one.
Tai... |
https://en.wikipedia.org/wiki/Tangent%20vector | In mathematics, a tangent vector is a vector that is tangent to a curve or surface at a given point. Tangent vectors are described in the differential geometry of curves in the context of curves in Rn. More generally, tangent vectors are elements of a tangent space of a differentiable manifold. Tangent vectors can also... |
https://en.wikipedia.org/wiki/Trace%20class | In mathematics, specifically functional analysis, a trace-class operator is a linear operator for which a trace may be defined, such that the trace is a finite number independent of the choice of basis used to compute the trace. This trace of trace-class operators generalizes the trace of matrices studied in linear alg... |
https://en.wikipedia.org/wiki/DHT | DHT may refer to:
Science and technology
Discrete Hartley transform, in mathematics
Distributed hash table, lookup service in computing
Chemistry
Dihydrotestosterone, hormone derived from testosterone
Dihydrotachysterol, synthetic vitamin D analog
Other
DHT (band), Belgian dance duo
Dr Hadwen Trust, UK charity p... |
https://en.wikipedia.org/wiki/Seven%20Bridges%20of%20K%C3%B6nigsberg | The Seven Bridges of Königsberg is a historically notable problem in mathematics. Its negative resolution by Leonhard Euler in 1736 laid the foundations of graph theory and prefigured the idea of topology.
The city of Königsberg in Prussia (now Kaliningrad, Russia) was set on both sides of the Pregel River, and includ... |
https://en.wikipedia.org/wiki/Triviality%20%28mathematics%29 | In mathematics, the adjective trivial is often used to refer to a claim or a case which can be readily obtained from context, or an object which possesses a simple structure (e.g., groups, topological spaces). The noun triviality usually refers to a simple technical aspect of some proof or definition. The origin of the... |
https://en.wikipedia.org/wiki/Trivial%20group | In mathematics, a trivial group or zero group is a group consisting of a single element. All such groups are isomorphic, so one often speaks of the trivial group. The single element of the trivial group is the identity element and so it is usually denoted as such: or depending on the context. If the group operation i... |
https://en.wikipedia.org/wiki/Hermann%20Minkowski | Hermann Minkowski (; ; 22 June 1864 – 12 January 1909) was a German mathematician and professor at Königsberg, Zürich and Göttingen. He created and developed the geometry of numbers and used geometrical methods to solve problems in number theory, mathematical physics, and the theory of relativity.
Minkowski is perhaps... |
https://en.wikipedia.org/wiki/Multiplier | Multiplier may refer to:
Mathematics
Multiplier (arithmetic), the number of multiples being computed in multiplication
Constant multiplier, a constant factor with units of measurement
Lagrange multiplier, a scalar variable used in mathematics to solve an optimisation problem for a given constraint
Multiplier (Fou... |
https://en.wikipedia.org/wiki/Integration%20by%20substitution | In calculus, integration by substitution, also known as u-substitution, reverse chain rule or change of variables, is a method for evaluating integrals and antiderivatives. It is the counterpart to the chain rule for differentiation, and can loosely be thought of as using the chain rule "backwards."
Substitution for a... |
https://en.wikipedia.org/wiki/List%20of%20named%20matrices | This article lists some important classes of matrices used in mathematics, science and engineering. A matrix (plural matrices, or less commonly matrixes) is a rectangular array of numbers called entries. Matrices have a long history of both study and application, leading to diverse ways of classifying matrices. A first... |
https://en.wikipedia.org/wiki/Bipolar | Bipolar may refer to:
Astronomy
Bipolar nebula, a distinctive nebular formation
Bipolar outflow, two continuous flows of gas from the poles of a star
Mathematics
Bipolar coordinates, a two-dimensional orthogonal coordinate system
Bipolar set, a derivative of a polar set
Bipolar theorem, a theorem in convex analy... |
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