source stringlengths 31 168 | text stringlengths 51 3k |
|---|---|
https://en.wikipedia.org/wiki/Student%27s%20t-distribution | In probability and statistics, Student's t-distribution (or simply the t-distribution) is
a continuous probability distribution that generalizes the standard normal distribution. Like the latter, it is symmetric around zero and bell-shaped.
However, has heavier tails and the amount of probability mass in the tails i... |
https://en.wikipedia.org/wiki/Orthogonal%20matrix | In linear algebra, an orthogonal matrix, or orthonormal matrix, is a real square matrix whose columns and rows are orthonormal vectors.
One way to express this is
where is the transpose of and is the identity matrix.
This leads to the equivalent characterization: a matrix is orthogonal if its transpose is equal ... |
https://en.wikipedia.org/wiki/Euler%27s%20criterion | In number theory, Euler's criterion is a formula for determining whether an integer is a quadratic residue modulo a prime. Precisely,
Let p be an odd prime and a be an integer coprime to p. Then
Euler's criterion can be concisely reformulated using the Legendre symbol:
The criterion dates from a 1748 paper by Leonha... |
https://en.wikipedia.org/wiki/Cayley%27s%20theorem | In group theory, Cayley's theorem, named in honour of Arthur Cayley, states that every group is isomorphic to a subgroup of a symmetric group.
More specifically, is isomorphic to a subgroup of the symmetric group whose elements are the permutations of the underlying set of .
Explicitly,
for each , the left-multipl... |
https://en.wikipedia.org/wiki/Direct%20sum%20of%20groups | In mathematics, a group G is called the direct sum of two normal subgroups with trivial intersection if it is generated by the subgroups. In abstract algebra, this method of construction of groups can be generalized to direct sums of vector spaces, modules, and other structures; see the article direct sum of modules fo... |
https://en.wikipedia.org/wiki/Algebraic%20structure | In mathematics, an algebraic structure consists of a nonempty set A (called the underlying set, carrier set or domain), a collection of operations on A (typically binary operations such as addition and multiplication), and a finite set of identities, known as axioms, that these operations must satisfy.
An algebraic st... |
https://en.wikipedia.org/wiki/Stand%20and%20Deliver | Stand and Deliver is a 1988 American drama film directed by Ramón Menéndez, written by Menéndez and Tom Musca, based on the true story of a high school mathematics teacher, Jaime Escalante. For portraying Escalante, Edward James Olmos was nominated for the Academy Award for Best Actor at the 61st Academy Awards. The fi... |
https://en.wikipedia.org/wiki/System%20of%20linear%20equations | In mathematics, a system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables.
For example,
is a system of three equations in the three variables . A solution to a linear system is an assignment of values to the variables such that all the equations are s... |
https://en.wikipedia.org/wiki/Chi-squared%20distribution | In probability theory and statistics, the chi-squared distribution (also chi-square or -distribution) with degrees of freedom is the distribution of a sum of the squares of independent standard normal random variables. The chi-squared distribution is a special case of the gamma distribution and is one of the most wid... |
https://en.wikipedia.org/wiki/General%20linear%20group | In mathematics, the general linear group of degree n is the set of invertible matrices, together with the operation of ordinary matrix multiplication. This forms a group, because the product of two invertible matrices is again invertible, and the inverse of an invertible matrix is invertible, with the identity matrix ... |
https://en.wikipedia.org/wiki/Zeta%20distribution | In probability theory and statistics, the zeta distribution is a discrete probability distribution. If X is a zeta-distributed random variable with parameter s, then the probability that X takes the integer value k is given by the probability mass function
where ζ(s) is the Riemann zeta function (which is undefined fo... |
https://en.wikipedia.org/wiki/Euclidean | Euclidean (or, less commonly, Euclidian) is an adjective derived from the name of Euclid, an ancient Greek mathematician. It is the name of:
Geometry
Euclidean space, the two-dimensional plane and three-dimensional space of Euclidean geometry as well as their higher dimensional generalizations
Euclidean geometry, the... |
https://en.wikipedia.org/wiki/Spectral%20theorem | In mathematics, particularly linear algebra and functional analysis, a spectral theorem is a result about when a linear operator or matrix can be diagonalized (that is, represented as a diagonal matrix in some basis). This is extremely useful because computations involving a diagonalizable matrix can often be reduced t... |
https://en.wikipedia.org/wiki/Matrix%20addition | In mathematics, matrix addition is the operation of adding two matrices by adding the corresponding entries together.
For a vector, , adding two matrices would have the geometric effect of applying each matrix transformation separately onto , then adding the transformed vectors.
However, there are other operations t... |
https://en.wikipedia.org/wiki/Hadamard%20product | In mathematics, the Hadamard product may refer to:
Hadamard product of two matrices, the matrix such that each entry is the product of the corresponding entries of the input matrices
Hadamard product of two power series, the power series whose coefficients are the product of the corresponding coefficients of the inpu... |
https://en.wikipedia.org/wiki/Matrix%20multiplication | In mathematics, particularly in linear algebra, matrix multiplication is a binary operation that produces a matrix from two matrices. For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix. The resulting matrix, known as the matrix product, has the ... |
https://en.wikipedia.org/wiki/Symmetric%20matrix | In linear algebra, a symmetric matrix is a square matrix that is equal to its transpose. Formally,
Because equal matrices have equal dimensions, only square matrices can be symmetric.
The entries of a symmetric matrix are symmetric with respect to the main diagonal. So if denotes the entry in the th row and th colum... |
https://en.wikipedia.org/wiki/Unitary%20matrix | In linear algebra, an invertible complex square matrix is unitary if its conjugate transpose is also its inverse, that is, if
where is the identity matrix.
In physics, especially in quantum mechanics, the conjugate transpose is referred to as the Hermitian adjoint of a matrix and is denoted by a dagger (†), so the... |
https://en.wikipedia.org/wiki/Short%20five%20lemma | In mathematics, especially homological algebra and other applications of abelian category theory, the short five lemma is a special case of the five lemma.
It states that for the following commutative diagram (in any abelian category, or in the category of groups), if the rows are short exact sequences, and if g and h ... |
https://en.wikipedia.org/wiki/Riemann%20curvature%20tensor | In the mathematical field of differential geometry, the Riemann curvature tensor or Riemann–Christoffel tensor (after Bernhard Riemann and Elwin Bruno Christoffel) is the most common way used to express the curvature of Riemannian manifolds. It assigns a tensor to each point of a Riemannian manifold (i.e., it is a ten... |
https://en.wikipedia.org/wiki/Skurup%20Municipality | Skurup Municipality (Skurups kommun) is a municipality in Skåne County in southern Sweden. Its seat is located in the town Skurup. It is considered part of Greater Malmö by Statistics Sweden.
The present municipality was formed in 1971 when the market town (köping) of Skurup was merged with Rydsgård and Vemmenhög.
Lo... |
https://en.wikipedia.org/wiki/Helix%2C%20Oregon | Helix is a city in Umatilla County, Oregon, United States. The population was 184 at the 2010 census. It is part of the Pendleton–Hermiston Micropolitan Statistical Area.
History
Helix, a geometry term and a part of the ear, was originally to be named Oxford, but authorities declined that option when the community's p... |
https://en.wikipedia.org/wiki/Tuple | In mathematics, a tuple is a finite sequence or ordered list of numbers or, more generally, mathematical objects, which are called the elements of the tuple. An -tuple is a tuple of elements, where is a non-negative integer. There is only one 0-tuple, called the empty tuple. A 1-tuple and a 2-tuple are commonly call... |
https://en.wikipedia.org/wiki/Parallelogram | In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. The congruence of opposite sides and opposite angles is a direct... |
https://en.wikipedia.org/wiki/Cholesky%20decomposition | In linear algebra, the Cholesky decomposition or Cholesky factorization (pronounced ) is a decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose, which is useful for efficient numerical solutions, e.g., Monte Carlo simulations. It was discovere... |
https://en.wikipedia.org/wiki/Fort%20Bliss | Fort Bliss is a United States Army post in New Mexico and Texas, with its headquarters in El Paso, Texas. Named in honor of LTC William Bliss (1815–1853), a mathematics professor who was the son-in-law of President Zachary Taylor, Ft. Bliss has an area of about ; it is the largest installation in FORSCOM (United States... |
https://en.wikipedia.org/wiki/Thorp%2C%20Washington | Thorp ( ) is an unincorporated community and census-designated place (CDP) in Kittitas County, Washington, United States. In 2015, the population was 317 according to statistics compiled by Data USA.
The town of Thorp is east of Seattle, northwest of Ellensburg, and southeast of Cle Elum. It is located at the narro... |
https://en.wikipedia.org/wiki/Five%20lemma | In mathematics, especially homological algebra and other applications of abelian category theory, the five lemma is an important and widely used lemma about commutative diagrams.
The five lemma is not only valid for abelian categories but also works in the category of groups, for example.
The five lemma can be thought... |
https://en.wikipedia.org/wiki/Splitting%20lemma | In mathematics, and more specifically in homological algebra, the splitting lemma states that in any abelian category, the following statements are equivalent for a short exact sequence
If any of these statements holds, the sequence is called a split exact sequence, and the sequence is said to split.
In the above ... |
https://en.wikipedia.org/wiki/Chain%20complex | In mathematics, a chain complex is an algebraic structure that consists of a sequence of abelian groups (or modules) and a sequence of homomorphisms between consecutive groups such that the image of each homomorphism is included in the kernel of the next. Associated to a chain complex is its homology, which describes h... |
https://en.wikipedia.org/wiki/Commutative%20diagram | In mathematics, and especially in category theory, a commutative diagram is a diagram such that all directed paths in the diagram with the same start and endpoints lead to the same result. It is said that commutative diagrams play the role in category theory that equations play in algebra.
Description
A commutative di... |
https://en.wikipedia.org/wiki/Nullity | Nullity may refer to:
Legal nullity, something without legal significance
Nullity (conflict), a legal declaration that no marriage had ever come into being
Mathematics
Nullity (linear algebra), the dimension of the kernel of a mathematical operator or null space of a matrix
Nullity (graph theory), the nullity of ... |
https://en.wikipedia.org/wiki/Landau%27s%20function | In mathematics, Landau's function g(n), named after Edmund Landau, is defined for every natural number n to be the largest order of an element of the symmetric group Sn. Equivalently, g(n) is the largest least common multiple (lcm) of any partition of n, or the maximum number of times a permutation of n elements can be... |
https://en.wikipedia.org/wiki/Gauss%E2%80%93Bonnet%20theorem | In the mathematical field of differential geometry, the Gauss–Bonnet theorem (or Gauss–Bonnet formula) is a fundamental formula which links the curvature of a surface to its underlying topology.
In the simplest application, the case of a triangle on a plane, the sum of its angles is 180 degrees. The Gauss–Bonnet theor... |
https://en.wikipedia.org/wiki/Homological%20algebra | Homological algebra is the branch of mathematics that studies homology in a general algebraic setting. It is a relatively young discipline, whose origins can be traced to investigations in combinatorial topology (a precursor to algebraic topology) and abstract algebra (theory of modules and syzygies) at the end of the ... |
https://en.wikipedia.org/wiki/Maximum%20likelihood%20estimation | In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable. The point in the parameter ... |
https://en.wikipedia.org/wiki/Ronald%20Fisher | Sir Ronald Aylmer Fisher (17 February 1890 – 29 July 1962) was a British polymath who was active as a mathematician, statistician, biologist, geneticist, and academic. For his work in statistics, he has been described as "a genius who almost single-handedly created the foundations for modern statistical science" and "... |
https://en.wikipedia.org/wiki/List%20of%20statisticians | This list of statisticians lists people who have made notable contributions to the theories or application of statistics, or to the related fields of probability or machine learning. Also included are actuaries and demographers.
A
Aalen, Odd Olai (1947–1987)
Abbey, Helen (1915–2001)
Abbott, Edith (1876–1957)
Abe... |
https://en.wikipedia.org/wiki/Sufficient%20statistic | In statistics, a statistic is sufficient with respect to a statistical model and its associated unknown parameter if "no other statistic that can be calculated from the same sample provides any additional information as to the value of the parameter". In particular, a statistic is sufficient for a family of probability... |
https://en.wikipedia.org/wiki/Magma%20%28algebra%29 | In abstract algebra, a magma, binar, or, rarely, groupoid is a basic kind of algebraic structure. Specifically, a magma consists of a set equipped with a single binary operation that must be closed by definition. No other properties are imposed.
History and terminology
The term groupoid was introduced in 1927 by Hein... |
https://en.wikipedia.org/wiki/Singular%20value%20decomposition | In linear algebra, the singular value decomposition (SVD) is a factorization of a real or complex matrix. It generalizes the eigendecomposition of a square normal matrix with an orthonormal eigenbasis to any matrix. It is related to the polar decomposition.
Specifically, the singular value decomposition of an comple... |
https://en.wikipedia.org/wiki/Homology%20%28mathematics%29 | In mathematics, homology is a general way of associating a sequence of algebraic objects, such as abelian groups or modules, with other mathematical objects such as topological spaces. Homology groups were originally defined in algebraic topology. Similar constructions are available in a wide variety of other context... |
https://en.wikipedia.org/wiki/Harmonic%20series%20%28mathematics%29 | In mathematics, the harmonic series is the infinite series formed by summing all positive unit fractions:
The first terms of the series sum to approximately , where is the natural logarithm and is the Euler–Mascheroni constant. Because the logarithm has arbitrarily large values, the harmonic series does not have a ... |
https://en.wikipedia.org/wiki/P%20and%20R%20measures | P and R measures are the statistics used to evaluate the efficiency and effectiveness of business processes, particularly automated business processes.
The P measures are the process measures – these statistics that record the number of times things occur. Examples include:
the number of times an error loop is used
... |
https://en.wikipedia.org/wiki/Kernel%20%28category%20theory%29 | In category theory and its applications to other branches of mathematics, kernels are a generalization of the kernels of group homomorphisms, the kernels of module homomorphisms and certain other kernels from algebra. Intuitively, the kernel of the morphism f : X → Y is the "most general" morphism k : K → X that yields... |
https://en.wikipedia.org/wiki/Enriched%20category | In category theory, a branch of mathematics, an enriched category generalizes the idea of a category by replacing hom-sets with objects from a general monoidal category. It is motivated by the observation that, in many practical applications, the hom-set often has additional structure that should be respected, e.g., th... |
https://en.wikipedia.org/wiki/Normal%20morphism | In category theory and its applications to mathematics, a normal monomorphism or conormal epimorphism is a particularly well-behaved type of morphism.
A normal category is a category in which every monomorphism is normal. A conormal category is one in which every epimorphism is conormal.
Definition
A monomorphism is n... |
https://en.wikipedia.org/wiki/J.%20Robert%20Janes | Joseph Robert Janes (born May 23, 1935) is a Canadian author born in Toronto.
A mining engineer by profession, he taught geology, geography and high school mathematics and later geology at Brock University until he dedicated himself to writing full-time in 1970.
Janes has published more than 20 adult novels, five mys... |
https://en.wikipedia.org/wiki/Infinite%20set | In set theory, an infinite set is a set that is not a finite set. Infinite sets may be countable or uncountable.
Properties
The set of natural numbers (whose existence is postulated by the axiom of infinity) is infinite. It is the only set that is directly required by the axioms to be infinite. The existence of any ot... |
https://en.wikipedia.org/wiki/Possibility | Possibility is the condition or fact of being possible. Latin origins of the word hint at ability.
Possibility may refer to:
Probability, the measure of the likelihood that an event will occur
Epistemic possibility, a topic in philosophy and modal logic
Possibility theory, a mathematical theory for dealing with ce... |
https://en.wikipedia.org/wiki/Parity%20%28mathematics%29 | In mathematics, parity is the property of an integer of whether it is even or odd. An integer is even if it is a multiple of two, and odd if it is not. For example, −4, 0, 82 are even because
By contrast, −3, 5, 7, 21 are odd numbers. The above definition of parity applies only to integer numbers, hence it cannot be a... |
https://en.wikipedia.org/wiki/Counterexample | A counterexample is any exception to a generalization. In logic a counterexample disproves the generalization, and does so rigorously in the fields of mathematics and philosophy. For example, the fact that "student John Smith is not lazy" is a counterexample to the generalization "students are lazy", and both a counte... |
https://en.wikipedia.org/wiki/Stereographic%20projection | In mathematics, a stereographic projection is a perspective projection of the sphere, through a specific point on the sphere (the pole or center of projection), onto a plane (the projection plane) perpendicular to the diameter through the point. It is a smooth, bijective function from the entire sphere except the cente... |
https://en.wikipedia.org/wiki/Examples%20of%20groups | Some elementary examples of groups in mathematics are given on Group (mathematics).
Further examples are listed here.
Permutations of a set of three elements
Consider three colored blocks (red, green, and blue), initially placed in the order RGB. Let a be the operation "swap the first block and the second block", an... |
https://en.wikipedia.org/wiki/Nilpotent%20group | In mathematics, specifically group theory, a nilpotent group G is a group that has an upper central series that terminates with G. Equivalently, its central series is of finite length or its lower central series terminates with {1}.
Intuitively, a nilpotent group is a group that is "almost abelian". This idea is motiv... |
https://en.wikipedia.org/wiki/Riemannian%20manifold | In differential geometry, a Riemannian manifold or Riemannian space , so called after the German mathematician Bernhard Riemann, is a real, smooth manifold M equipped with a positive-definite inner product gp on the tangent space TpM at each point p.
The family gp of inner products is called a Riemannian metric (or R... |
https://en.wikipedia.org/wiki/Special%20linear%20group | In mathematics, the special linear group of degree n over a field F is the set of matrices with determinant 1, with the group operations of ordinary matrix multiplication and matrix inversion. This is the normal subgroup of the general linear group given by the kernel of the determinant
where F× is the multiplicativ... |
https://en.wikipedia.org/wiki/Ultrafinitism | In the philosophy of mathematics, ultrafinitism (also known as ultraintuitionism, strict formalism, strict finitism, actualism, predicativism, and strong finitism) is a form of finitism and intuitionism. There are various philosophies of mathematics that are called ultrafinitism. A major identifying property common amo... |
https://en.wikipedia.org/wiki/Principal%20ideal | In mathematics, specifically ring theory, a principal ideal is an ideal in a ring that is generated by a single element of through multiplication by every element of The term also has another, similar meaning in order theory, where it refers to an (order) ideal in a poset generated by a single element which is t... |
https://en.wikipedia.org/wiki/Dedekind%20domain | In abstract algebra, a Dedekind domain or Dedekind ring, named after Richard Dedekind, is an integral domain in which every nonzero proper ideal factors into a product of prime ideals. It can be shown that such a factorization is then necessarily unique up to the order of the factors. There are at least three other c... |
https://en.wikipedia.org/wiki/Local%20field | In mathematics, a field K is called a (non-Archimedean) local field if it is complete with respect to a topology induced by a discrete valuation v and if its residue field k is finite. Equivalently, a local field is a locally compact topological field with respect to a non-discrete topology. Sometimes, real numbers R, ... |
https://en.wikipedia.org/wiki/Quadric | In mathematics, a quadric or quadric surface (quadric hypersurface in higher dimensions), is a generalization of conic sections (ellipses, parabolas, and hyperbolas). It is a hypersurface (of dimension D) in a -dimensional space, and it is defined as the zero set of an irreducible polynomial of degree two in D + 1 var... |
https://en.wikipedia.org/wiki/Centralizer%20and%20normalizer | In mathematics, especially group theory, the centralizer (also called commutant) of a subset S in a group G is the set of elements of G that commute with every element of S, or equivalently, such that conjugation by leaves each element of S fixed. The normalizer of S in G is the set of elements of G that satisfy th... |
https://en.wikipedia.org/wiki/Hyperboloid | In geometry, a hyperboloid of revolution, sometimes called a circular hyperboloid, is the surface generated by rotating a hyperbola around one of its principal axes. A hyperboloid is the surface obtained from a hyperboloid of revolution by deforming it by means of directional scalings, or more generally, of an affine t... |
https://en.wikipedia.org/wiki/Paraboloid | In geometry, a paraboloid is a quadric surface that has exactly one axis of symmetry and no center of symmetry. The term "paraboloid" is derived from parabola, which refers to a conic section that has a similar property of symmetry.
Every plane section of a paraboloid by a plane parallel to the axis of symmetry is a p... |
https://en.wikipedia.org/wiki/Danica%20McKellar | Danica Mae McKellar (born January 3, 1975) is an American actress, mathematics writer, and education advocate. She played Winnie Cooper in the television series The Wonder Years from 1988 to 1993, and from 2010 to 2022, has voiced Miss Martian in the animated superhero series Young Justice.
In 2015, McKellar was cast ... |
https://en.wikipedia.org/wiki/Nonlinear%20system | In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other scientists since most systems are inherently nonli... |
https://en.wikipedia.org/wiki/Wreath%20product | In group theory, the wreath product is a special combination of two groups based on the semidirect product. It is formed by the action of one group on many copies of another group, somewhat analogous to exponentiation. Wreath products are used in the classification of permutation groups and also provide a way of constr... |
https://en.wikipedia.org/wiki/Recurrence%20relation | In mathematics, a recurrence relation is an equation according to which the th term of a sequence of numbers is equal to some combination of the previous terms. Often, only previous terms of the sequence appear in the equation, for a parameter that is independent of ; this number is called the order of the relation.... |
https://en.wikipedia.org/wiki/Goldbach%27s%20weak%20conjecture | In number theory, Goldbach's weak conjecture, also known as the odd Goldbach conjecture, the ternary Goldbach problem, or the 3-primes problem, states that
Every odd number greater than 5 can be expressed as the sum of three primes. (A prime may be used more than once in the same sum.)
This conjecture is called "wea... |
https://en.wikipedia.org/wiki/Integration%20by%20parts | In calculus, and more generally in mathematical analysis, integration by parts or partial integration is a process that finds the integral of a product of functions in terms of the integral of the product of their derivative and antiderivative. It is frequently used to transform the antiderivative of a product of funct... |
https://en.wikipedia.org/wiki/Equal | Equal(s) may refer to:
Mathematics
Equality (mathematics).
Equals sign (=), a mathematical symbol used to indicate equality.
Arts and entertainment
Equals (film), a 2015 American science fiction film
Equals (game), a board game
The Equals, a British pop group formed in 1965
"Equal", a 2016 song by Chrisette Mic... |
https://en.wikipedia.org/wiki/Free%20variables%20and%20bound%20variables | In mathematics, and in other disciplines involving formal languages, including mathematical logic and computer science, a variable may be said to be either free or bound. The terms are opposites. A free variable is a notation (symbol) that specifies places in an expression where substitution may take place and is not a... |
https://en.wikipedia.org/wiki/Superposition | Superposition may refer to:
Science and mathematics
Law of superposition in geology and archaeology, which states that sedimentary layers are deposited in a time sequence, with the oldest on the bottom and the youngest on the top
Superposition calculus, used in logic for equational first-order reasoning
Superposit... |
https://en.wikipedia.org/wiki/Ernest%20Ansermet | Ernest Alexandre Ansermet (; 11 November 1883 – 20 February 1969) was a Swiss conductor.
Biography
Ansermet was born in Vevey, Switzerland. Originally he was a mathematics professor, teaching at the University of Lausanne. He began conducting at the Casino in Montreux in 1912, and from 1915 to 1923 was the conductor ... |
https://en.wikipedia.org/wiki/Manbij | Manbij (, , ) is a city in the northeast of Aleppo Governorate in northern Syria, 30 kilometers (19 mi) west of the Euphrates. In the 2004 census by the Central Bureau of Statistics (CBS), Manbij had a population of nearly 100,000. The population of Manbij is largely Arab, with Kurdish, Turkmen, Circassian, and Chechen... |
https://en.wikipedia.org/wiki/Linearity%20of%20differentiation | In calculus, the derivative of any linear combination of functions equals the same linear combination of the derivatives of the functions; this property is known as linearity of differentiation, the rule of linearity, or the superposition rule for differentiation. It is a fundamental property of the derivative that enc... |
https://en.wikipedia.org/wiki/Power%20rule | In calculus, the power rule is used to differentiate functions of the form , whenever is a real number. Since differentiation is a linear operation on the space of differentiable functions, polynomials can also be differentiated using this rule. The power rule underlies the Taylor series as it relates a power series w... |
https://en.wikipedia.org/wiki/Lucasian%20Professor%20of%20Mathematics | The Lucasian Chair of Mathematics () is a mathematics professorship in the University of Cambridge, England; its holder is known as the Lucasian Professor. The post was founded in 1663 by Henry Lucas, who was Cambridge University's Member of Parliament in 1639–1640, and it was officially established by King Charles II ... |
https://en.wikipedia.org/wiki/Constant%20of%20integration | In calculus, the constant of integration, often denoted by (or ), is a constant term added to an antiderivative of a function to indicate that the indefinite integral of (i.e., the set of all antiderivatives of ), on a connected domain, is only defined up to an additive constant. This constant expresses an ambiguity... |
https://en.wikipedia.org/wiki/Derive | Derive may refer to:
Derive (computer algebra system), a commercial system made by Texas Instruments
Dérive (magazine), an Austrian science magazine on urbanism
Dérive, a psychogeographical concept
Derived trait, or apomorphy
See also
Derivation (disambiguation)
Derivative (disambiguation) |
https://en.wikipedia.org/wiki/Inverse%20function%20rule | In calculus, the inverse function rule is a formula that expresses the derivative of the inverse of a bijective and differentiable function in terms of the derivative of . More precisely, if the inverse of is denoted as , where if and only if , then the inverse function rule is, in Lagrange's notation,
.
This form... |
https://en.wikipedia.org/wiki/Euler%20characteristic | In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré characteristic) is a topological invariant, a number that describes a topological space's shape or structure regardless of the way it is bent. It is commonly denoted by ... |
https://en.wikipedia.org/wiki/Value%20at%20risk | Value at risk (VaR) is a measure of the risk of loss of investment/Capital. It estimates how much a set of investments might lose (with a given probability), given normal market conditions, in a set time period such as a day. VaR is typically used by firms and regulators in the financial industry to gauge the amount of... |
https://en.wikipedia.org/wiki/T1%20space | {{DISPLAYTITLE:T1 space}}
In topology and related branches of mathematics, a T1 space is a topological space in which, for every pair of distinct points, each has a neighborhood not containing the other point. An R0 space is one in which this holds for every pair of topologically distinguishable points. The propert... |
https://en.wikipedia.org/wiki/Separated%20sets | In topology and related branches of mathematics, separated sets are pairs of subsets of a given topological space that are related to each other in a certain way: roughly speaking, neither overlapping nor touching. The notion of when two sets are separated or not is important both to the notion of connected spaces (an... |
https://en.wikipedia.org/wiki/Symmetric%20space%20%28disambiguation%29 | A symmetric space is, in differential geometry and representation theory, a smooth manifold whose group of symmetries contains an "inversion symmetry" about every point. Examples include:
Riemannian symmetric space
Hermitian symmetric space
Quaternion-Kähler symmetric space
Weakly symmetric space
In topology, symm... |
https://en.wikipedia.org/wiki/Hilbert%27s%20Nullstellensatz | In mathematics, Hilbert's Nullstellensatz (German for "theorem of zeros", or more literally, "zero-locus-theorem") is a theorem that establishes a fundamental relationship between geometry and algebra. This relationship is the basis of algebraic geometry. It relates algebraic sets to ideals in polynomial rings over alg... |
https://en.wikipedia.org/wiki/B%C3%A9zout%27s%20theorem | Bézout's theorem is a statement in algebraic geometry concerning the number of common zeros of polynomials in indeterminates. In its original form the theorem states that in general the number of common zeros equals the product of the degrees of the polynomials. It is named after Étienne Bézout.
In some elementary t... |
https://en.wikipedia.org/wiki/Karl%20Menger | Karl Menger (January 13, 1902 – October 5, 1985) was an Austrian–American mathematician, the son of the economist Carl Menger. In mathematics, Menger studied the theory of algebras and the dimension theory of low-regularity ("rough") curves and regions; in graph theory, he is credited with Menger's theorem. Outside of... |
https://en.wikipedia.org/wiki/Pafnuty%20Chebyshev | Pafnuty Lvovich Chebyshev () ( – ) was a Russian mathematician and considered to be the founding father of Russian mathematics.
Chebyshev is known for his fundamental contributions to the fields of probability, statistics, mechanics, and number theory. A number of important mathematical concepts are named after him, i... |
https://en.wikipedia.org/wiki/Emmy%20Noether | Amalie Emmy Noether (, ; ; 23 March 1882 – 14 April 1935) was a German mathematician who made many important contributions to abstract algebra. She discovered Noether's First and Second Theorems, which are fundamental in mathematical physics. She was described by Pavel Alexandrov, Albert Einstein, Jean Dieudonné, Herma... |
https://en.wikipedia.org/wiki/Face%20%28geometry%29 | In solid geometry, a face is a flat surface (a planar region) that forms part of the boundary of a solid object; a three-dimensional solid bounded exclusively by faces is a polyhedron.
In more technical treatments of the geometry of polyhedra and higher-dimensional polytopes, the term is also used to mean an element o... |
https://en.wikipedia.org/wiki/Row%20and%20column%20vectors | In linear algebra, a column vector with elements is an matrix consisting of a single column of entries, for example,
Similarly, a row vector is a matrix for some , consisting of a single row of entries,
(Throughout this article, boldface is used for both row and column vectors.)
The transpose (indicated by ) o... |
https://en.wikipedia.org/wiki/Wiener%20process | In mathematics, the Wiener process is a real-valued continuous-time stochastic process named in honor of American mathematician Norbert Wiener for his investigations on the mathematical properties of the one-dimensional Brownian motion. It is often also called Brownian motion due to its historical connection with the p... |
https://en.wikipedia.org/wiki/Church%E2%80%93Rosser%20theorem | In lambda calculus, the Church–Rosser theorem states that, when applying reduction rules to terms, the ordering in which the reductions are chosen does not make a difference to the eventual result.
More precisely, if there are two distinct reductions or sequences of reductions that can be applied to the same term, th... |
https://en.wikipedia.org/wiki/List%20of%20letters%20used%20in%20mathematics%2C%20science%2C%20and%20engineering | Latin and Greek letters are used in mathematics, science, engineering, and other areas where mathematical notation is used as symbols for constants, special functions, and also conventionally for variables representing certain quantities.
Some common conventions:
Intensive quantities in physics are usually denoted wi... |
https://en.wikipedia.org/wiki/Noetherian | In mathematics, the adjective Noetherian is used to describe objects that satisfy an ascending or descending chain condition on certain kinds of subobjects, meaning that certain ascending or descending sequences of subobjects must have finite length. Noetherian objects are named after Emmy Noether, who was the first to... |
https://en.wikipedia.org/wiki/Trigonometric%20tables | In mathematics, tables of trigonometric functions are useful in a number of areas. Before the existence of pocket calculators, trigonometric tables were essential for navigation, science and engineering. The calculation of mathematical tables was an important area of study, which led to the development of the first mec... |
https://en.wikipedia.org/wiki/Application | Application may refer to:
Mathematics and computing
Application software, computer software designed to help the user to perform specific tasks
Application layer, an abstraction layer that specifies protocols and interface methods used in a communications network
Function application, in mathematics and computer sc... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.