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https://en.wikipedia.org/wiki/Likelihood%20function | The likelihood function (often simply called the likelihood) is the joint probability (or probability density) of observed data viewed as a function of the parameters of a statistical model.
In maximum likelihood estimation, the arg max (over the parameter ) of the likelihood function serves as a point estimate fo... |
https://en.wikipedia.org/wiki/Borel%E2%80%93Cantelli%20lemma | In probability theory, the Borel–Cantelli lemma is a theorem about sequences of events. In general, it is a result in measure theory. It is named after Émile Borel and Francesco Paolo Cantelli, who gave statement to the lemma in the first decades of the 20th century. A related result, sometimes called the second Bore... |
https://en.wikipedia.org/wiki/Natural%20transformation | In category theory, a branch of mathematics, a natural transformation provides a way of transforming one functor into another while respecting the internal structure (i.e., the composition of morphisms) of the categories involved. Hence, a natural transformation can be considered to be a "morphism of functors". Informa... |
https://en.wikipedia.org/wiki/Likelihood-ratio%20test | In statistics, the likelihood-ratio test assesses the goodness of fit of two competing statistical models, specifically one found by maximization over the entire parameter space and another found after imposing some constraint, based on the ratio of their likelihoods. If the constraint (i.e., the null hypothesis) is su... |
https://en.wikipedia.org/wiki/Abelian%20category | In mathematics, an abelian category is a category in which morphisms and objects can be added and in which kernels and cokernels exist and have desirable properties. The motivating prototypical example of an abelian category is the category of abelian groups, Ab. The theory originated in an effort to unify several coho... |
https://en.wikipedia.org/wiki/Negative%20binomial%20distribution | In probability theory and statistics, the negative binomial distribution is a discrete probability distribution that models the number of failures in a sequence of independent and identically distributed Bernoulli trials before a specified (non-random) number of successes (denoted ) occurs. For example, we can define r... |
https://en.wikipedia.org/wiki/Lp%20space | {{DISPLAYTITLE:Lp space}}
In mathematics, the spaces are function spaces defined using a natural generalization of the -norm for finite-dimensional vector spaces. They are sometimes called Lebesgue spaces, named after Henri Lebesgue , although according to the Bourbaki group they were first introduced by Frigyes Rie... |
https://en.wikipedia.org/wiki/Injective%20function | In mathematics, an injective function (also known as injection, or one-to-one function) is a function that maps distinct elements of its domain to distinct elements; that is, implies . (Equivalently, implies in the equivalent contrapositive statement.) In other words, every element of the function's codomain is the... |
https://en.wikipedia.org/wiki/Inverse%20element | In mathematics, the concept of an inverse element generalises the concepts of opposite () and reciprocal () of numbers.
Given an operation denoted here , and an identity element denoted , if , one says that is a left inverse of , and that is a right inverse of . (An identity element is an element such that and fo... |
https://en.wikipedia.org/wiki/Universal%20algebra | Universal algebra (sometimes called general algebra) is the field of mathematics that studies algebraic structures themselves, not examples ("models") of algebraic structures.
For instance, rather than take particular groups as the object of study, in universal algebra one takes the class of groups as an object of stud... |
https://en.wikipedia.org/wiki/Congruence | Congruence may refer to:
Mathematics
Congruence (geometry), being the same size and shape
Congruence or congruence relation, in abstract algebra, an equivalence relation on an algebraic structure that is compatible with the structure
In modular arithmetic, having the same remainder when divided by a specified integ... |
https://en.wikipedia.org/wiki/Subalgebra | In mathematics, a subalgebra is a subset of an algebra, closed under all its operations, and carrying the induced operations.
"Algebra", when referring to a structure, often means a vector space or module equipped with an additional bilinear operation. Algebras in universal algebra are far more general: they are a com... |
https://en.wikipedia.org/wiki/Kernel%20%28algebra%29 | In algebra, the kernel of a homomorphism (function that preserves the structure) is generally the inverse image of 0 (except for groups whose operation is denoted multiplicatively, where the kernel is the inverse image of 1). An important special case is the kernel of a linear map. The kernel of a matrix, also called t... |
https://en.wikipedia.org/wiki/Isomorphism%20theorems | In mathematics, specifically abstract algebra, the isomorphism theorems (also known as Noether's isomorphism theorems) are theorems that describe the relationship between quotients, homomorphisms, and subobjects. Versions of the theorems exist for groups, rings, vector spaces, modules, Lie algebras, and various other ... |
https://en.wikipedia.org/wiki/Measure%20space | A measure space is a basic object of measure theory, a branch of mathematics that studies generalized notions of volumes. It contains an underlying set, the subsets of this set that are feasible for measuring (the -algebra) and the method that is used for measuring (the measure). One important example of a measure spa... |
https://en.wikipedia.org/wiki/Clifford%20algebra | In mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra. As -algebras, they generalize the real numbers, complex numbers, quaternions and several other hypercomplex number systems. The theory of Clifford algebras is intimately connected wit... |
https://en.wikipedia.org/wiki/Probability%20measure | In mathematics, a probability measure is a real-valued function defined on a set of events in a probability space that satisfies measure properties such as countable additivity. The difference between a probability measure and the more general notion of measure (which includes concepts like area or volume) is that a p... |
https://en.wikipedia.org/wiki/Dedekind%20cut | In mathematics, Dedekind cuts, named after German mathematician Richard Dedekind but previously considered by Joseph Bertrand, are а method of construction of the real numbers from the rational numbers. A Dedekind cut is a partition of the rational numbers into two sets A and B, such that all elements of A are less th... |
https://en.wikipedia.org/wiki/Inverse%20transform%20sampling | Inverse transform sampling (also known as inversion sampling, the inverse probability integral transform, the inverse transformation method, Smirnov transform, or the golden rule) is a basic method for pseudo-random number sampling, i.e., for generating sample numbers at random from any probability distribution given i... |
https://en.wikipedia.org/wiki/Topological%20vector%20space | In mathematics, a topological vector space (also called a linear topological space and commonly abbreviated TVS or t.v.s.) is one of the basic structures investigated in functional analysis.
A topological vector space is a vector space that is also a topological space with the property that the vector space operations ... |
https://en.wikipedia.org/wiki/Where%20Mathematics%20Comes%20From | Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being (hereinafter WMCF) is a book by George Lakoff, a cognitive linguist, and Rafael E. Núñez, a psychologist. Published in 2000, WMCF seeks to found a cognitive science of mathematics, a theory of embodied mathematics based on conceptual meta... |
https://en.wikipedia.org/wiki/Hurwitz%20polynomial | In mathematics, a Hurwitz polynomial, named after Adolf Hurwitz, is a polynomial whose roots (zeros) are located in the left half-plane of the complex plane or on the imaginary axis, that is, the real part of every root is zero or negative. Such a polynomial must have coefficients that are positive real numbers. The ... |
https://en.wikipedia.org/wiki/Fermat%20pseudoprime | In number theory, the Fermat pseudoprimes make up the most important class of pseudoprimes that come from Fermat's little theorem.
Definition
Fermat's little theorem states that if p is prime and a is coprime to p, then ap−1 − 1 is divisible by p. For an integer a > 1, if a composite integer x divides ax−1 − 1, then ... |
https://en.wikipedia.org/wiki/Exponential%20distribution | In probability theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the time between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate. It is a particular case of the g... |
https://en.wikipedia.org/wiki/Geometric%20distribution | In probability theory and statistics, the geometric distribution is either one of two discrete probability distributions:
The probability distribution of the number of Bernoulli trials needed to get one success, supported on the set ;
The probability distribution of the number of failures before the first success,... |
https://en.wikipedia.org/wiki/Gerhard%20Gentzen | Gerhard Karl Erich Gentzen (24 November 1909 – 4 August 1945) was a German mathematician and logician. He made major contributions to the foundations of mathematics, proof theory, especially on natural deduction and sequent calculus. He died of starvation in a Czech prison camp in Prague in 1945, having been interned a... |
https://en.wikipedia.org/wiki/Kazimierz%20Kuratowski | Kazimierz Kuratowski (; 2 February 1896 – 18 June 1980) was a Polish mathematician and logician. He was one of the leading representatives of the Warsaw School of Mathematics. He worked as a professor at the University of Warsaw and at the Mathematical Institute of the Polish Academy of Sciences (IM PAN). Between 1946 ... |
https://en.wikipedia.org/wiki/Simpson%27s%20paradox | Simpson's paradox is a phenomenon in probability and statistics in which a trend appears in several groups of data but disappears or reverses when the groups are combined. This result is often encountered in social-science and medical-science statistics, and is particularly problematic when frequency data are unduly gi... |
https://en.wikipedia.org/wiki/Rafael%20E.%20N%C3%BA%C3%B1ez | Rafael E. Núñez is a professor of cognitive science at the University of California, San Diego and a proponent of embodied cognition. He co-authored Where Mathematics Comes From with George Lakoff.
External links
Academic home page
Rafael E. Núñez, Eve Sweetser (2006). "With the Future Behind Them: Convergent Evide... |
https://en.wikipedia.org/wiki/Philosophy%20of%20mathematics | The philosophy of mathematics is the branch of philosophy that studies the assumptions, foundations, and implications of mathematics. It aims to understand the nature and methods of mathematics, and find out the place of mathematics in people's lives. The logical and structural nature of mathematics makes this branch o... |
https://en.wikipedia.org/wiki/Banach%20fixed-point%20theorem | In mathematics, the Banach fixed-point theorem (also known as the contraction mapping theorem or contractive mapping theorem or Banach-Caccioppoli theorem) is an important tool in the theory of metric spaces; it guarantees the existence and uniqueness of fixed points of certain self-maps of metric spaces, and provides ... |
https://en.wikipedia.org/wiki/Euler%27s%20identity | In mathematics, Euler's identity (also known as Euler's equation) is the equality
where
is Euler's number, the base of natural logarithms,
is the imaginary unit, which by definition satisfies , and
is pi, the ratio of the circumference of a circle to its diameter.
Euler's identity is named after the Swiss mathemati... |
https://en.wikipedia.org/wiki/Sacred%20geometry | Sacred geometry ascribes symbolic and sacred meanings to certain geometric shapes and certain geometric proportions. It is associated with the belief of a divine creator of the universal geometer. The geometry used in the design and construction of religious structures such as churches, temples, mosques, religious monu... |
https://en.wikipedia.org/wiki/Continued%20fraction | In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integer part and another reciprocal, and so on. In a finite continued fraction (or te... |
https://en.wikipedia.org/wiki/Catalan%27s%20constant | In mathematics, Catalan's constant , is defined by
where is the Dirichlet beta function. Its numerical value is approximately
It is not known whether is irrational, let alone transcendental. has been called "arguably the most basic constant whose irrationality and transcendence (though strongly
suspected) r... |
https://en.wikipedia.org/wiki/Euler%20numbers | In mathematics, the Euler numbers are a sequence En of integers defined by the Taylor series expansion
,
where is the hyperbolic cosine function. The Euler numbers are related to a special value of the Euler polynomials, namely:
The Euler numbers appear in the Taylor series expansions of the secant and hyperbolic ... |
https://en.wikipedia.org/wiki/Half-line | Half-line may refer to:
Half-line (geometry), half of a line
Alliterative verse#Metrical form, half of a line of poetry |
https://en.wikipedia.org/wiki/Logarithmic%20integral%20function | In mathematics, the logarithmic integral function or integral logarithm li(x) is a special function. It is relevant in problems of physics and has number theoretic significance. In particular, according to the prime number theorem, it is a very good approximation to the prime-counting function, which is defined as the ... |
https://en.wikipedia.org/wiki/Closed%20set | In geometry, topology, and related branches of mathematics, a closed set is a set whose complement is an open set. In a topological space, a closed set can be defined as a set which contains all its limit points. In a complete metric space, a closed set is a set which is closed under the limit operation.
This should n... |
https://en.wikipedia.org/wiki/Monster%20group | In the area of abstract algebra known as group theory, the monster group M (also known as the Fischer–Griess monster, or the friendly giant) is the largest sporadic simple group, having order
2463205976112133171923293141475971
= 808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000,000
≈ 8.... |
https://en.wikipedia.org/wiki/Atlas%20%28topology%29 | In mathematics, particularly topology, an atlas is a concept used to describe a manifold. An atlas consists of individual charts that, roughly speaking, describe individual regions of the manifold. If the manifold is the surface of the Earth, then an atlas has its more common meaning. In general, the notion of atlas un... |
https://en.wikipedia.org/wiki/Simple%20group | In mathematics, a simple group is a nontrivial group whose only normal subgroups are the trivial group and the group itself. A group that is not simple can be broken into two smaller groups, namely a nontrivial normal subgroup and the corresponding quotient group. This process can be repeated, and for finite groups on... |
https://en.wikipedia.org/wiki/Srinivasa%20Ramanujan | Srinivasa Ramanujan ( ; born Srinivasa Ramanujan Aiyangar, ; 22 December 188726 April 1920) was an Indian mathematician. Though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions, including solutions ... |
https://en.wikipedia.org/wiki/List%20of%20small%20groups | The following list in mathematics contains the finite groups of small order up to group isomorphism.
Counts
For n = 1, 2, … the number of nonisomorphic groups of order n is
1, 1, 1, 2, 1, 2, 1, 5, 2, 2, 1, 5, 1, 2, 1, 14, 1, 5, 1, 5, ...
For labeled groups, see .
Glossary
Each group is named by Small Groups libra... |
https://en.wikipedia.org/wiki/Vector%20quantization | Vector quantization (VQ) is a classical quantization technique from signal processing that allows the modeling of probability density functions by the distribution of prototype vectors. It was originally used for data compression. It works by dividing a large set of points (vectors) into groups having approximately th... |
https://en.wikipedia.org/wiki/Stochastic%20process | In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a sequence of random variables, where the index of the sequence has the interpretation of time. Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary... |
https://en.wikipedia.org/wiki/Chance | Chance may refer to:
Mathematics and Science
In mathematics, likelihood of something (by way of the Likelihood function or Probability density function).
Chance (statistics magazine)
Places
Chance, Kentucky, US
Chance, Maryland, US
Chance, Oklahoma, US
Chance, South Dakota, US
Chance, Virginia, US
Chancé, a... |
https://en.wikipedia.org/wiki/Union%20%28set%20theory%29 | In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection. It is one of the fundamental operations through which sets can be combined and related to each other.
A refers to a union of zero () sets and it is by definition equal to the empty set.
For explanation of t... |
https://en.wikipedia.org/wiki/Fibonacci%20coding | In mathematics and computing, Fibonacci coding is a universal code which encodes positive integers into binary code words. It is one example of representations of integers based on Fibonacci numbers. Each code word ends with "11" and contains no other instances of "11" before the end.
The Fibonacci code is closely rel... |
https://en.wikipedia.org/wiki/Great%20circle | In mathematics, a great circle or orthodrome is the circular intersection of a sphere and a plane passing through the sphere's center point.
Any arc of a great circle is a geodesic of the sphere, so that great circles in spherical geometry are the natural analog of straight lines in Euclidean space. For any pair of di... |
https://en.wikipedia.org/wiki/Maximal%20ideal | In mathematics, more specifically in ring theory, a maximal ideal is an ideal that is maximal (with respect to set inclusion) amongst all proper ideals. In other words, I is a maximal ideal of a ring R if there are no other ideals contained between I and R.
Maximal ideals are important because the quotients of rings b... |
https://en.wikipedia.org/wiki/Congruence%20relation | In abstract algebra, a congruence relation (or simply congruence) is an equivalence relation on an algebraic structure (such as a group, ring, or vector space) that is compatible with the structure in the sense that algebraic operations done with equivalent elements will yield equivalent elements. Every congruence rel... |
https://en.wikipedia.org/wiki/Golomb%20ruler | In mathematics, a Golomb ruler is a set of marks at integer positions along a ruler such that no two pairs of marks are the same distance apart. The number of marks on the ruler is its order, and the largest distance between two of its marks is its length. Translation and reflection of a Golomb ruler are considered tri... |
https://en.wikipedia.org/wiki/Point | A point is a small dot or the sharp tip of something. Point or points may refer to:
Mathematics
Point (geometry), an entity that has a location in space or on a plane, but has no extent; more generally, an element of some abstract topological space
Point, or Element (category theory), generalizes the set-theoretic ... |
https://en.wikipedia.org/wiki/Semidirect%20product | In mathematics, specifically in group theory, the concept of a semidirect product is a generalization of a direct product. There are two closely related concepts of semidirect product:
an inner semidirect product is a particular way in which a group can be made up of two subgroups, one of which is a normal subgroup. ... |
https://en.wikipedia.org/wiki/Random%20sequence | The concept of a random sequence is essential in probability theory and statistics. The concept generally relies on the notion of a sequence of random variables and many statistical discussions begin with the words "let X1,...,Xn be independent random variables...". Yet as D. H. Lehmer stated in 1951: "A random sequenc... |
https://en.wikipedia.org/wiki/Bounded%20set | In mathematical analysis and related areas of mathematics, a set is called bounded if it is, in a certain sense, of finite measure. Conversely, a set which is not bounded is called unbounded. The word "bounded" makes no sense in a general topological space without a corresponding metric.
Boundary is a distinct concept... |
https://en.wikipedia.org/wiki/Monotonic%20function | In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of order theory.
In calculus and analysis
In calculus, a function defined on a subset... |
https://en.wikipedia.org/wiki/IAL | IAL may refer to:
Intel Architecture Labs, a research arm of Intel Corporation during the 1990s
International Advanced Levels, an academic qualification offered by Edexcel
International Algebraic Language or ALGOL 58
International Artists' Lodge, trade union in Germany
International auxiliary language, a language for ... |
https://en.wikipedia.org/wiki/Algebraic%20notation%20%28chess%29 | Algebraic notation is the standard method for recording and describing the moves in a game of chess. It is based on a system of coordinates to uniquely identify each square on the board. It is used by most books, magazines, and newspapers.
An early form of algebraic notation was invented by the Syrian player Philip S... |
https://en.wikipedia.org/wiki/Mathematical%20analysis | Analysis is the branch of mathematics dealing with continuous functions, limits, and related theories, such as differentiation, integration, measure, infinite sequences, series, and analytic functions.
These theories are usually studied in the context of real and complex numbers and functions. Analysis evolved from ca... |
https://en.wikipedia.org/wiki/Ring%20%28mathematics%29 | In mathematics, rings are algebraic structures that generalize fields: multiplication need not be commutative and multiplicative inverses need not exist. In other words, a ring is a set equipped with two binary operations satisfying properties analogous to those of addition and multiplication of integers. Ring elements... |
https://en.wikipedia.org/wiki/Gottlob%20Frege | Friedrich Ludwig Gottlob Frege (; ; 8 November 1848 – 26 July 1925) was a German philosopher, logician, and mathematician. He was a mathematics professor at the University of Jena, and is understood by many to be the father of analytic philosophy, concentrating on the philosophy of language, logic, and mathematics. Th... |
https://en.wikipedia.org/wiki/Graph | Graph may refer to:
Mathematics
Graph (discrete mathematics), a structure made of vertices and edges
Graph theory, the study of such graphs and their properties
Graph (topology), a topological space resembling a graph in the sense of discrete mathematics
Graph of a function
Graph of a relation
Graph paper
Chart, a mea... |
https://en.wikipedia.org/wiki/Gaussian%20integer | In number theory, a Gaussian integer is a complex number whose real and imaginary parts are both integers. The Gaussian integers, with ordinary addition and multiplication of complex numbers, form an integral domain, usually written as or
Gaussian integers share many properties with integers: they form a Euclidean ... |
https://en.wikipedia.org/wiki/Normal%20space | In topology and related branches of mathematics, a normal space is a topological space X that satisfies Axiom T4: every two disjoint closed sets of X have disjoint open neighborhoods. A normal Hausdorff space is also called a T4 space. These conditions are examples of separation axioms and their further strengthenings ... |
https://en.wikipedia.org/wiki/Paracompact%20space | In mathematics, a paracompact space is a topological space in which every open cover has an open refinement that is locally finite. These spaces were introduced by . Every compact space is paracompact. Every paracompact Hausdorff space is normal, and a Hausdorff space is paracompact if and only if it admits partitions ... |
https://en.wikipedia.org/wiki/Locally%20compact%20space | In topology and related branches of mathematics, a topological space is called locally compact if, roughly speaking, each small portion of the space looks like a small portion of a compact space. More precisely, it is a topological space in which every point has a compact neighborhood.
In mathematical analysis locall... |
https://en.wikipedia.org/wiki/Nowhere%20dense%20set | In mathematics, a subset of a topological space is called nowhere dense or rare if its closure has empty interior. In a very loose sense, it is a set whose elements are not tightly clustered (as defined by the topology on the space) anywhere. For example, the integers are nowhere dense among the reals, whereas the in... |
https://en.wikipedia.org/wiki/Partition%20of%20unity | In mathematics, a partition of unity of a topological space is a set of continuous functions from to the unit interval [0,1] such that for every point :
there is a neighbourhood of where all but a finite number of the functions of are 0, and
the sum of all the function values at is 1, i.e.,
Partitions of unit... |
https://en.wikipedia.org/wiki/Statistician | A statistician is a person who works with theoretical or applied statistics. The profession exists in both the private and public sectors.
It is common to combine statistical knowledge with expertise in other subjects, and statisticians may work as employees or as statistical consultants.
Nature of the work
Accordin... |
https://en.wikipedia.org/wiki/Henri%20Poincar%C3%A9 | Jules Henri Poincaré (, ; ; 29 April 185417 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science. He is often described as a polymath, and in mathematics as "The Last Universalist", since he excelled in all fields of the discipline as it existed during his lifetime. Due to ... |
https://en.wikipedia.org/wiki/Wolfram%20Mathematica | Wolfram Mathematica is a software system with built-in libraries for several areas of technical computing that allow machine learning, statistics, symbolic computation, data manipulation, network analysis, time series analysis, NLP, optimization, plotting functions and various types of data, implementation of algorithm... |
https://en.wikipedia.org/wiki/Cox%27s%20theorem | Cox's theorem, named after the physicist Richard Threlkeld Cox, is a derivation of the laws of probability theory from a certain set of postulates. This derivation justifies the so-called "logical" interpretation of probability, as the laws of probability derived by Cox's theorem are applicable to any proposition. Logi... |
https://en.wikipedia.org/wiki/Interval%20%28mathematics%29 | In mathematics, a (real) interval is the set of all real numbers lying between two fixed endpoints with no "gaps". Each endpoint is either a real number or positive or negative infinity, indicating the interval extends without a bound. An interval can contain neither endpoint, either endpoint, or both endpoints.
For e... |
https://en.wikipedia.org/wiki/Conjugacy%20class | In mathematics, especially group theory, two elements and of a group are conjugate if there is an element in the group such that This is an equivalence relation whose equivalence classes are called conjugacy classes. In other words, each conjugacy class is closed under for all elements in the group.
Members of ... |
https://en.wikipedia.org/wiki/Urysohn%27s%20lemma | In topology, Urysohn's lemma is a lemma that states that a topological space is normal if and only if any two disjoint closed subsets can be separated by a continuous function.
Urysohn's lemma is commonly used to construct continuous functions with various properties on normal spaces. It is widely applicable since all... |
https://en.wikipedia.org/wiki/Unit%20interval | In mathematics, the unit interval is the closed interval , that is, the set of all real numbers that are greater than or equal to 0 and less than or equal to 1. It is often denoted (capital letter ). In addition to its role in real analysis, the unit interval is used to study homotopy theory in the field of topology.... |
https://en.wikipedia.org/wiki/Divisor | In mathematics, a divisor of an integer , also called a factor of , is an integer that may be multiplied by some integer to produce . In this case, one also says that is a multiple of An integer is divisible or evenly divisible by another integer if is a divisor of ; this implies dividing by leaves no remainder... |
https://en.wikipedia.org/wiki/Pascal%27s%20triangle | In mathematics, Pascal's triangle is a triangular array of the binomial coefficients arising in probability theory, combinatorics, and algebra. In much of the Western world, it is named after the French mathematician Blaise Pascal, although other mathematicians studied it centuries before him in Persia, India, China, ... |
https://en.wikipedia.org/wiki/Bayes%27%20theorem | In probability theory and statistics, Bayes' theorem (alternatively Bayes' law or Bayes' rule), named after Thomas Bayes, describes the probability of an event, based on prior knowledge of conditions that might be related to the event. For example, if the risk of developing health problems is known to increase with age... |
https://en.wikipedia.org/wiki/Bayesian%20inference | Bayesian inference ( or ) is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available. Bayesian inference is an important technique in statistics, and especially in mathematical statistics. Bayesian updating is parti... |
https://en.wikipedia.org/wiki/Sophist | A sophist () was a teacher in ancient Greece in the fifth and fourth centuries BC. Sophists specialized in one or more subject areas, such as philosophy, rhetoric, music, athletics and mathematics. They taught arete, "virtue" or "excellence", predominantly to young statesmen and nobility.
Etymology
The Greek word is ... |
https://en.wikipedia.org/wiki/Numeral | A numeral is a figure, symbol, or group of figures or symbols denoting a number. It may refer to:
Numeral system used in mathematics
Numeral (linguistics), a part of speech denoting numbers (e.g. one and first in English)
Numerical digit, the glyphs used to represent numerals
See also
Numerology, belief in a divi... |
https://en.wikipedia.org/wiki/Adrien-Marie%20Legendre | Adrien-Marie Legendre (; ; 18 September 1752 – 9 January 1833) was a French mathematician who made numerous contributions to mathematics. Well-known and important concepts such as the Legendre polynomials and Legendre transformation are named after him. He is also known for his contributions to the method of least squa... |
https://en.wikipedia.org/wiki/Alternating%20group | In mathematics, an alternating group is the group of even permutations of a finite set. The alternating group on a set of elements is called the alternating group of degree , or the alternating group on letters and denoted by or
Basic properties
For , the group An is the commutator subgroup of the symmetric group ... |
https://en.wikipedia.org/wiki/Parity%20of%20a%20permutation | In mathematics, when X is a finite set with at least two elements, the permutations of X (i.e. the bijective functions from X to X) fall into two classes of equal size: the even permutations and the odd permutations. If any total ordering of X is fixed, the parity (oddness or evenness) of a permutation of X can be def... |
https://en.wikipedia.org/wiki/Multivariate%20random%20variable | In probability, and statistics, a multivariate random variable or random vector is a list or vector of mathematical variables each of whose value is unknown, either because the value has not yet occurred or because there is imperfect knowledge of its value. The individual variables in a random vector are grouped toget... |
https://en.wikipedia.org/wiki/Domain%20of%20a%20function | In mathematics, the domain of a function is the set of inputs accepted by the function. It is sometimes denoted by or , where is the function. In layman's terms, the domain of a function can generally be thought of as "what x can be".
More precisely, given a function , the domain of is . In modern mathematical lang... |
https://en.wikipedia.org/wiki/Codomain | In mathematics, the codomain or set of destination of a function is the set into which all of the output of the function is constrained to fall. It is the set in the notation . The term range is sometimes ambiguously used to refer to either the codomain or image of a function.
A codomain is part of a function if ... |
https://en.wikipedia.org/wiki/SMP | SMP may refer to:
Organisations
Scale Model Products, 1950s, acquired by Aluminum Model Toys
School Mathematics Project, UK developer of mathematics textbooks
Sekolah Menengah Pertama, "junior high school" in Indonesia
Shanghai Municipal Police, until 1943
Sipah-e-Muhammad Pakistan, Pakistani group banned as terr... |
https://en.wikipedia.org/wiki/Multivariate%20normal%20distribution | In probability theory and statistics, the multivariate normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional (univariate) normal distribution to higher dimensions. One definition is that a random vector is said to be k-variate normally distribu... |
https://en.wikipedia.org/wiki/Differential%20calculus | In mathematics, differential calculus is a subfield of calculus that studies the rates at which quantities change. It is one of the two traditional divisions of calculus, the other being integral calculus—the study of the area beneath a curve.
The primary objects of study in differential calculus are the derivative of... |
https://en.wikipedia.org/wiki/Conformal%20map | In mathematics, a conformal map is a function that locally preserves angles, but not necessarily lengths.
More formally, let and be open subsets of . A function is called conformal (or angle-preserving) at a point if it preserves angles between directed curves through , as well as preserving orientation. Conformal... |
https://en.wikipedia.org/wiki/Astronomy | Astronomy is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution. Objects of interest include planets, moons, stars, nebulae, galaxies, meteoroids, asteroids, and comets. Relevant phenomena include supernova explosion... |
https://en.wikipedia.org/wiki/Convergence%20of%20random%20variables | In probability theory, there exist several different notions of convergence of random variables. The convergence of sequences of random variables to some limit random variable is an important concept in probability theory, and its applications to statistics and stochastic processes. The same concepts are known in more... |
https://en.wikipedia.org/wiki/Strong%20convergence | In mathematics, strong convergence may refer to:
The strong convergence of random variables of a probability distribution.
The norm-convergence of a sequence in a Hilbert space (as opposed to weak convergence).
The convergence of operators in the strong operator topology. |
https://en.wikipedia.org/wiki/Weak%20convergence | In mathematics, weak convergence may refer to:
Weak convergence of random variables of a probability distribution
Weak convergence of measures, of a sequence of probability measures
Weak convergence (Hilbert space) of a sequence in a Hilbert space
more generally, convergence in weak topology in a Banach space or a... |
https://en.wikipedia.org/wiki/Extreme%20value%20theory | Extreme value theory or extreme value analysis (EVA) is a branch of statistics dealing with the extreme deviations from the median of probability distributions. It seeks to assess, from a given ordered sample of a given random variable, the probability of events that are more extreme than any previously observed. Extr... |
https://en.wikipedia.org/wiki/Haar%20wavelet | In mathematics, the Haar wavelet is a sequence of rescaled "square-shaped" functions which together form a wavelet family or basis. Wavelet analysis is similar to Fourier analysis in that it allows a target function over an interval to be represented in terms of an orthonormal basis. The Haar sequence is now recognised... |
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