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https://en.wikipedia.org/wiki/Index%20of%20a%20subgroup | In mathematics, specifically group theory, the index of a subgroup H in a group G is the
number of left cosets of H in G, or equivalently, the number of right cosets of H in G.
The index is denoted or or .
Because G is the disjoint union of the left cosets and because each left coset has the same size as H, the inde... |
https://en.wikipedia.org/wiki/John%20H.%20Coates | John Henry Coates (26 January 1945 – 9 May 2022) was an Australian mathematician who was the Sadleirian Professor of Pure Mathematics at the University of Cambridge in the United Kingdom from 1986 to 2012.
Early life and education
Coates was born the son of J. H. Coates and B. L. Lee on 26 January 1945 and grew up in... |
https://en.wikipedia.org/wiki/Parabolic | Parabolic usually refers to something in a shape of a parabola, but may also refer to a parable.
Parabolic may refer to:
In mathematics:
In elementary mathematics, especially elementary geometry:
Parabolic coordinates
Parabolic cylindrical coordinates
parabolic Möbius transformation
Parabolic geometry (disambiguation)... |
https://en.wikipedia.org/wiki/Bertrand%27s%20postulate | In number theory, Bertrand's postulate is a theorem stating that for any integer , there always exists at least one prime number with
A less restrictive formulation is: for every , there is always at least one prime such that
Another formulation, where is the -th prime, is: for
This statement was first conject... |
https://en.wikipedia.org/wiki/Hypergraph | In mathematics, a hypergraph is a generalization of a graph in which an edge can join any number of vertices. In contrast, in an ordinary graph, an edge connects exactly two vertices.
Formally, a directed hypergraph is a pair , where is a set of elements called nodes, vertices, points, or elements and is a set of pa... |
https://en.wikipedia.org/wiki/Mathematics%20of%20paper%20folding | The discipline of origami or paper folding has received a considerable amount of mathematical study. Fields of interest include a given paper model's flat-foldability (whether the model can be flattened without damaging it), and the use of paper folds to solve up-to cubic mathematical equations.
Computational origami ... |
https://en.wikipedia.org/wiki/Degeneracy%20%28mathematics%29 | In mathematics, a degenerate case is a limiting case of a class of objects which appears to be qualitatively different from (and usually simpler than) the rest of the class, and the term degeneracy is the condition of being a degenerate case.
The definitions of many classes of composite or structured objects often imp... |
https://en.wikipedia.org/wiki/Borwein%27s%20algorithm | In mathematics, Borwein's algorithm is an algorithm devised by Jonathan and Peter Borwein to calculate the value of . They devised several other algorithms. They published the book Pi and the AGM – A Study in Analytic Number Theory and Computational Complexity.
Ramanujan–Sato series
These two are examples of a Ramanu... |
https://en.wikipedia.org/wiki/Clopen%20set | In topology, a clopen set (a portmanteau of closed-open set) in a topological space is a set which is both open and closed. That this is possible may seem counter-intuitive, as the common meanings of and are antonyms, but their mathematical definitions are not mutually exclusive. A set is closed if its complement i... |
https://en.wikipedia.org/wiki/Yearbook | A yearbook, also known as an annual, is a type of a book published annually. One use is to record, highlight, and commemorate the past year of a school. The term also refers to a book of statistics or facts published annually. A yearbook often has an overarching theme that is present throughout the entire book.
Many h... |
https://en.wikipedia.org/wiki/List%20of%20Classical%20Greek%20phrases |
Αα
Ageōmétrētos mēdeìs eisítō.
"Let no one untrained in geometry enter."
Motto over the entrance to Plato's Academy (quoted in Elias' commentary on Aristotle's Categories: Eliae in Porphyrii Isagogen et Aristotelis categorias commentaria, CAG XVIII.1, Berlin 1900, p. 118.13–19).
.
Aeì Libúē phérei ti kainón.
"Libya... |
https://en.wikipedia.org/wiki/Fr%C3%A9chet%20space | In functional analysis and related areas of mathematics, Fréchet spaces, named after Maurice Fréchet, are special topological vector spaces.
They are generalizations of Banach spaces (normed vector spaces that are complete with respect to the metric induced by the norm).
All Banach and Hilbert spaces are Fréchet spac... |
https://en.wikipedia.org/wiki/Aggregate%20pattern | An Aggregate pattern can refer to concepts in either statistics or computer programming. Both uses deal with considering a large case as composed of smaller, simpler, pieces.
Statistics
An aggregate pattern is an important statistical concept in many fields that rely on statistics to predict the behavior of large gro... |
https://en.wikipedia.org/wiki/Automorphic%20number | In mathematics, an automorphic number (sometimes referred to as a circular number) is a natural number in a given number base whose square "ends" in the same digits as the number itself.
Definition and properties
Given a number base , a natural number with digits is an automorphic number if is a fixed point of the... |
https://en.wikipedia.org/wiki/Automorphic | Automorphic may refer to
Automorphic number, in mathematics
Automorphic form, in mathematics
Automorphic representation, in mathematics
Automorphic L-function, in mathematics
Automorphism, in mathematics
Rock microstructure#Crystal shapes |
https://en.wikipedia.org/wiki/Ackermann%20steering%20geometry | The Ackermann steering geometry is a geometric arrangement of linkages in the steering of a car or other vehicle designed to solve the problem of wheels on the inside and outside of a turn needing to trace out circles of different radii.
It was invented by the German carriage builder Georg Lankensperger in Munich in 1... |
https://en.wikipedia.org/wiki/Games%20started | In baseball statistics, games started (denoted by GS) indicates the number of games that a pitcher has started for his team. A pitcher is credited with starting the game if he throws the first pitch to the first opposing batter. If a player is listed in the starting lineup as the team's pitcher, but is replaced before ... |
https://en.wikipedia.org/wiki/Lists%20of%20integrals | Integration is the basic operation in integral calculus. While differentiation has straightforward rules by which the derivative of a complicated function can be found by differentiating its simpler component functions, integration does not, so tables of known integrals are often useful. This page lists some of the mo... |
https://en.wikipedia.org/wiki/James%20Joseph%20Sylvester | James Joseph Sylvester (3 September 1814 – 15 March 1897) was an English mathematician. He made fundamental contributions to matrix theory, invariant theory, number theory, partition theory, and combinatorics. He played a leadership role in American mathematics in the later half of the 19th century as a professor at ... |
https://en.wikipedia.org/wiki/Nth%20root | In mathematics, taking the nth root is an operation involving two numbers, the radicand and the index or degree. Taking the nth root is written as , where is the radicand and n is the index (also sometimes called the degree). This is pronounced as "the nth root of x". The definition then of an nth root of a number x i... |
https://en.wikipedia.org/wiki/Random%20walk | In mathematics, a random walk, sometimes known as a drunkard's walk, is a random process that describes a path that consists of a succession of random steps on some mathematical space.
An elementary example of a random walk is the random walk on the integer number line which starts at 0, and at each step moves +1 or ... |
https://en.wikipedia.org/wiki/Spearman%27s%20rank%20correlation%20coefficient | In statistics, Spearman's rank correlation coefficient or Spearman's ρ, named after Charles Spearman and often denoted by the Greek letter (rho) or as , is a nonparametric measure of rank correlation (statistical dependence between the rankings of two variables). It assesses how well the relationship between two varia... |
https://en.wikipedia.org/wiki/Unitary%20transformation | In mathematics, a unitary transformation is a transformation that preserves the inner product: the inner product of two vectors before the transformation is equal to their inner product after the transformation.
Formal definition
More precisely, a unitary transformation is an isomorphism between two inner product spac... |
https://en.wikipedia.org/wiki/Elliptic%20geometry | Elliptic geometry is an example of a geometry in which Euclid's parallel postulate does not hold. Instead, as in spherical geometry, there are no parallel lines since any two lines must intersect. However, unlike in spherical geometry, two lines are usually assumed to intersect at a single point (rather than two). Beca... |
https://en.wikipedia.org/wiki/Truncated%20binary%20encoding | Truncated binary encoding is an entropy encoding typically used for uniform probability distributions with a finite alphabet. It is parameterized by an alphabet with total size of number n. It is a slightly more general form of binary encoding when n is not a power of two.
If n is a power of two, then the coded value ... |
https://en.wikipedia.org/wiki/Subsequence | In mathematics, a subsequence of a given sequence is a sequence that can be derived from the given sequence by deleting some or no elements without changing the order of the remaining elements. For example, the sequence is a subsequence of obtained after removal of elements and The relation of one sequence being t... |
https://en.wikipedia.org/wiki/Haken%20manifold | In mathematics, a Haken manifold is a compact, P²-irreducible 3-manifold that is sufficiently large, meaning that it contains a properly embedded two-sided incompressible surface. Sometimes one considers only orientable Haken manifolds, in which case a Haken manifold is a compact, orientable, irreducible 3-manifold tha... |
https://en.wikipedia.org/wiki/Logarithmic | Logarithmic can refer to:
Logarithm, a transcendental function in mathematics
Logarithmic scale, the use of the logarithmic function to describe measurements
Logarithmic spiral,
Logarithmic growth
Logarithmic distribution, a discrete probability distribution
Natural logarithm |
https://en.wikipedia.org/wiki/Median%20test | In statistics, Mood's median test is a special case of Pearson's chi-squared test. It is a nonparametric test that tests the null hypothesis that the medians of the populations from which two or more samples are drawn are identical. The data in each sample are assigned to two groups, one consisting of data whose values... |
https://en.wikipedia.org/wiki/Markov%20chain%20Monte%20Carlo | In statistics, Markov chain Monte Carlo (MCMC) methods comprise a class of algorithms for sampling from a probability distribution. By constructing a Markov chain that has the desired distribution as its equilibrium distribution, one can obtain a sample of the desired distribution by recording states from the chain. Th... |
https://en.wikipedia.org/wiki/Rational%20%28disambiguation%29 | Rational may refer to:
Rational number, a number that can be expressed as a ratio of two integers
Rational point of an algebraic variety, a point defined over the rational numbers
Rational function, a function that may be defined as the quotient of two polynomials
Rational fraction, an expression built from the in... |
https://en.wikipedia.org/wiki/Probability-generating%20function | In probability theory, the probability generating function of a discrete random variable is a power series representation (the generating function) of the probability mass function of the random variable. Probability generating functions are often employed for their succinct description of the sequence of probabilitie... |
https://en.wikipedia.org/wiki/Flatness | Flatness may refer to:
Flatness (art)
Flatness (cosmology)
Flatness (liquids)
Flatness (manufacturing), a geometrical tolerance required in certain manufacturing situations
Flatness (mathematics)
Flatness (systems theory), a property of nonlinear dynamic systems
Spectral flatness
Flat intonation
Flat module in... |
https://en.wikipedia.org/wiki/Quotient%20space%20%28topology%29 | In topology and related areas of mathematics, the quotient space of a topological space under a given equivalence relation is a new topological space constructed by endowing the quotient set of the original topological space with the quotient topology, that is, with the finest topology that makes continuous the canonic... |
https://en.wikipedia.org/wiki/Abel%27s%20theorem | In mathematics, Abel's theorem for power series relates a limit of a power series to the sum of its coefficients. It is named after Norwegian mathematician Niels Henrik Abel.
Theorem
Let the Taylor series
be a power series with real coefficients with radius of convergence Suppose that the series
converges.
T... |
https://en.wikipedia.org/wiki/Electron%20density | Electron density or electronic density is the measure of the probability of an electron being present at an infinitesimal element of space surrounding any given point. It is a scalar quantity depending upon three spatial variables and is typically denoted as either or . The density is determined, through definition, b... |
https://en.wikipedia.org/wiki/Converge | Converge may refer to:
Converge (band), American hardcore punk band
Converge (Baptist denomination), American national evangelical Baptist body
Limit (mathematics)
Converge ICT, internet service provider in the Philippines
CONVERGE CFD software, created by Convergent Science
See also
Comverge, a company that p... |
https://en.wikipedia.org/wiki/Differintegral | In fractional calculus, an area of mathematical analysis, the differintegral is a combined differentiation/integration operator. Applied to a function ƒ, the q-differintegral of f, here denoted by
is the fractional derivative (if q > 0) or fractional integral (if q < 0). If q = 0, then the q-th differintegral of a f... |
https://en.wikipedia.org/wiki/Product%20%28category%20theory%29 | In category theory, the product of two (or more) objects in a category is a notion designed to capture the essence behind constructions in other areas of mathematics such as the Cartesian product of sets, the direct product of groups or rings, and the product of topological spaces. Essentially, the product of a family ... |
https://en.wikipedia.org/wiki/Markov%27s%20inequality | In probability theory, Markov's inequality gives an upper bound for the probability that a non-negative function of a random variable is greater than or equal to some positive constant. It is named after the Russian mathematician Andrey Markov, although it appeared earlier in the work of Pafnuty Chebyshev (Markov's te... |
https://en.wikipedia.org/wiki/Direct%20proof | In mathematics and logic, a direct proof is a way of showing the
truth or falsehood of a given statement by a straightforward combination of
established facts, usually axioms, existing lemmas and theorems, without making any further assumptions. In order to directly prove a conditional statement of the form "If p, then... |
https://en.wikipedia.org/wiki/Power%20of%20a%20test | In statistics, the power of a binary hypothesis test is the probability that the test correctly rejects the null hypothesis () when a specific alternative hypothesis () is true. It is commonly denoted by , and represents the chances of a true positive detection conditional on the actual existence of an effect to detect... |
https://en.wikipedia.org/wiki/Permutation%20matrix | In mathematics, particularly in matrix theory, a permutation matrix is a square binary matrix that has exactly one entry of 1 in each row and each column and 0s elsewhere. Each such matrix, say , represents a permutation of elements and, when used to multiply another matrix, say , results in permuting the rows (when... |
https://en.wikipedia.org/wiki/Reliability%20%28statistics%29 | In statistics and psychometrics, reliability is the overall consistency of a measure. A measure is said to have a high reliability if it produces similar results under consistent conditions:"It is the characteristic of a set of test scores that relates to the amount of random error from the measurement process that mig... |
https://en.wikipedia.org/wiki/Validity%20%28statistics%29 | Validity is the main extent to which a concept, conclusion, or measurement is well-founded and likely corresponds accurately to the real world. The word "valid" is derived from the Latin validus, meaning strong. The validity of a measurement tool (for example, a test in education) is the degree to which the tool measur... |
https://en.wikipedia.org/wiki/John%20Wallis | John Wallis (; ; ) was an English clergyman and mathematician, who is given partial credit for the development of infinitesimal calculus.
Between 1643 and 1689 he served as chief cryptographer for Parliament and, later, the royal court. He is credited with introducing the symbol ∞ to represent the concept of infinity.... |
https://en.wikipedia.org/wiki/Population%20process | In applied probability, a population process is a Markov chain in which the state of the chain is analogous to the number of individuals in a population (0, 1, 2, etc.), and changes to the state are analogous to the addition or removal of individuals from the population. Typical population processes include birth–death... |
https://en.wikipedia.org/wiki/Quadratic | In mathematics, the term quadratic describes something that pertains to squares, to the operation of squaring, to terms of the second degree, or equations or formulas that involve such terms. Quadratus is Latin for square.
Mathematics
Algebra (elementary and abstract)
Quadratic function (or quadratic polynomial), ... |
https://en.wikipedia.org/wiki/Constructive%20analysis | In mathematics, constructive analysis is mathematical analysis done according to some principles of constructive mathematics.
Introduction
The name of the subject contrasts with classical analysis, which in this context means analysis done according to the more common principles of classical mathematics. However, ther... |
https://en.wikipedia.org/wiki/Peter%20Gustav%20Lejeune%20Dirichlet | Johann Peter Gustav Lejeune Dirichlet (; 13 February 1805 – 5 May 1859) was a German mathematician who made contributions to number theory (including creating the field of analytic number theory), and to the theory of Fourier series and other topics in mathematical analysis; he is credited with being one of the first m... |
https://en.wikipedia.org/wiki/Indicator%20function | In mathematics, an indicator function or a characteristic function of a subset of a set is a function that maps elements of the subset to one, and all other elements to zero. That is, if is a subset of some set , then if and otherwise, where is a common notation for the indicator function. Other common notations a... |
https://en.wikipedia.org/wiki/For%20each | For each may refer to:
In mathematics, Universal quantification. Also read as: "for all"
In computer science, foreach loop
See also
Each (disambiguation) |
https://en.wikipedia.org/wiki/Hyperbolic%20geometry | In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate of Euclidean geometry is replaced with:
For any given line R and point P not on R, in the plane containing both line R and point P there are at least two distinct... |
https://en.wikipedia.org/wiki/Zariski%20topology | In algebraic geometry and commutative algebra, the Zariski topology is a topology which is primarily defined by its closed sets. It is very different from topologies which are commonly used in real or complex analysis; in particular, it is not Hausdorff. This topology was introduced primarily by Oscar Zariski and later... |
https://en.wikipedia.org/wiki/List%20of%20mathematical%20shapes | Following is a list of some mathematically well-defined shapes.
Algebraic curves
Cubic plane curve
Quartic plane curve
Rational curves
Degree 2
Conic sections
Unit circle
Unit hyperbola
Degree 3
Folium of Descartes
Cissoid of Diocles
Conchoid of de Sluze
Right strophoid
Semicubical parabola
Serpentine curve
Triden... |
https://en.wikipedia.org/wiki/Difference%20quotient | In single-variable calculus, the difference quotient is usually the name for the expression
which when taken to the limit as h approaches 0 gives the derivative of the function f. The name of the expression stems from the fact that it is the quotient of the difference of values of the function by the difference of the... |
https://en.wikipedia.org/wiki/Secant%20line | In geometry, a secant is a line that intersects a curve at a minimum of two distinct points.
The word secant comes from the Latin word secare, meaning to cut. In the case of a circle, a secant intersects the circle at exactly two points. A chord is the line segment determined by the two points, that is, the interval on... |
https://en.wikipedia.org/wiki/Projective%20space | In mathematics, the concept of a projective space originated from the visual effect of perspective, where parallel lines seem to meet at infinity. A projective space may thus be viewed as the extension of a Euclidean space, or, more generally, an affine space with points at infinity, in such a way that there is one poi... |
https://en.wikipedia.org/wiki/Negative | Negative may refer to:
Science and mathematics
Negative number
Negative mass
Negative energy
Negative charge, one of the two types of electric charge
Negative (electrical polarity), in electric circuits
Negative result (disambiguation)
Negative lenses, uses to describe diverging optics
Photography
Negative ... |
https://en.wikipedia.org/wiki/Positive | Positive is a property of positivity and may refer to:
Mathematics and science
Positive formula, a logical formula not containing negation
Positive number, a number that is greater than 0
Plus sign, the sign "+" used to indicate a positive number
Positive operator, a type of linear operator in mathematics
Positi... |
https://en.wikipedia.org/wiki/Extrema | Extrema may refer to:
Extrema (mathematics), maxima and minima values
Extremities (disambiguation)
Extrema, Minas Gerais, town in Brazil
Extrema, Rondônia, town in Brazil
Extrema (band), Antiprotestionarialconstructionaryism |
https://en.wikipedia.org/wiki/Hampshire%20College%20Summer%20Studies%20in%20Mathematics | The Hampshire College Summer Studies in Mathematics (HCSSiM) is an American residential program for mathematically talented high school students. The program has been conducted each summer since 1971, with the exceptions of 1981 and 1996, and has more than 1500 alumni. Due to the Coronavirus pandemic, the 2020 Summer ... |
https://en.wikipedia.org/wiki/Class%20field%20theory | In mathematics, class field theory (CFT) is the fundamental branch of algebraic number theory whose goal is to describe all the abelian Galois extensions of local and global fields using objects associated to the ground field.
Hilbert is credited as one of pioneers of the notion of a class field. However, this notion... |
https://en.wikipedia.org/wiki/List%20of%20mathematics%20reference%20tables | See also: List of reference tables
Mathematics
List of mathematical topics
List of statistical topics
List of mathematical functions
List of mathematical theorems
List of mathematical proofs
List of matrices
List of numbers
List of relativistic equations
List of small groups
Mathematical constants
Sporadic group
Tabl... |
https://en.wikipedia.org/wiki/Number%20%28disambiguation%29 | A number describes quantity and assesses multitude.
Number and numbers may also refer to:
Mathematics and language
Grammatical number, a morphological grammatical category indicating the quantity of referents
Number Forms, a Unicode block containing common fractions and Roman numerals
Nominal number, a label to id... |
https://en.wikipedia.org/wiki/Exp | Exp or EXP may stand for:
Exponential function, in mathematics
Expiry date of organic compounds like food or medicines
Experience points, in role-playing games
EXPTIME, a complexity class in computing
Ford EXP, a car manufactured in the 1980s
Exp (band), an Italian group in the 1990s
"EXP" (song), a song by The... |
https://en.wikipedia.org/wiki/Spectral%20method | Spectral methods are a class of techniques used in applied mathematics and scientific computing to numerically solve certain differential equations. The idea is to write the solution of the differential equation as a sum of certain "basis functions" (for example, as a Fourier series which is a sum of sinusoids) and the... |
https://en.wikipedia.org/wiki/Homogeneous%20coordinates | In mathematics, homogeneous coordinates or projective coordinates, introduced by August Ferdinand Möbius in his 1827 work , are a system of coordinates used in projective geometry, just as Cartesian coordinates are used in Euclidean geometry. They have the advantage that the coordinates of points, including points at i... |
https://en.wikipedia.org/wiki/Green%27s%20theorem | In vector calculus, Green's theorem relates a line integral around a simple closed curve to a double integral over the plane region bounded by . It is the two-dimensional special case of Stokes' theorem.
Theorem
Let be a positively oriented, piecewise smooth, simple closed curve in a plane, and let be the region b... |
https://en.wikipedia.org/wiki/Erlangen%20program | In mathematics, the Erlangen program is a method of characterizing geometries based on group theory and projective geometry. It was published by Felix Klein in 1872 as Vergleichende Betrachtungen über neuere geometrische Forschungen. It is named after the University Erlangen-Nürnberg, where Klein worked.
By 1872, non-... |
https://en.wikipedia.org/wiki/Cubic%20function | In mathematics, a cubic function is a function of the form that is, a polynomial function of degree three. In many texts, the coefficients , , , and are supposed to be real numbers, and the function is considered as a real function that maps real numbers to real numbers or as a complex function that maps complex numb... |
https://en.wikipedia.org/wiki/Projective%20geometry | In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that, compared to elementary Euclidean geometry, projective geometry has a different setting, projective space, and a selective set of basic geometric concepts. The basic in... |
https://en.wikipedia.org/wiki/Affine%20geometry | In mathematics, affine geometry is what remains of Euclidean geometry when ignoring (mathematicians often say "forgetting") the metric notions of distance and angle.
As the notion of parallel lines is one of the main properties that is independent of any metric, affine geometry is often considered as the study of para... |
https://en.wikipedia.org/wiki/Multilinear%20algebra | Multilinear algebra is the study of functions with multiple vector-valued arguments, which are linear maps with respect to each argument. Concepts such as matrices, vectors, systems of linear equations, higher-dimensional spaces, determinants, inner and outer products, and dual spaces emerge naturally in the mathematic... |
https://en.wikipedia.org/wiki/Singular%20%28software%29 | Singular (typeset Singular) is a computer algebra system for polynomial computations with special emphasis on the needs of commutative and non-commutative algebra, algebraic geometry, and singularity theory. Singular has been released under the terms of GNU General Public License. Problems in non-commutative algebra ca... |
https://en.wikipedia.org/wiki/Window%20function | In signal processing and statistics, a window function (also known as an apodization function or tapering function) is a mathematical function that is zero-valued outside of some chosen interval, normally symmetric around the middle of the interval, usually approaching a maximum in the middle, and usually tapering away... |
https://en.wikipedia.org/wiki/Matroid | In combinatorics, a branch of mathematics, a matroid is a structure that abstracts and generalizes the notion of linear independence in vector spaces. There are many equivalent ways to define a matroid axiomatically, the most significant being in terms of: independent sets; bases or circuits; rank functions; closure o... |
https://en.wikipedia.org/wiki/Improper%20rotation | In geometry, an improper rotation (also called rotation-reflection, rotoreflection, rotary reflection, or rotoinversion) is an isometry in Euclidean space that is a combination of a rotation about an axis and a reflection in a plane perpendicular to that axis. Reflection and inversion are each special case of improper ... |
https://en.wikipedia.org/wiki/Scalar%20multiplication | In mathematics, scalar multiplication is one of the basic operations defining a vector space in linear algebra (or more generally, a module in abstract algebra). In common geometrical contexts, scalar multiplication of a real Euclidean vector by a positive real number multiplies the magnitude of the vector without chan... |
https://en.wikipedia.org/wiki/Bipartite | Bipartite may refer to:
2 (number)
Bipartite (theology), a philosophical term describing the human duality of body and soul
Bipartite graph, in mathematics, a graph in which the vertices are partitioned into two sets and every edge has an endpoint in each set
Bipartite uterus, a type of uterus found in deer and mo... |
https://en.wikipedia.org/wiki/Total | Total may refer to:
Mathematics
Total, the summation of a set of numbers
Total order, a partial order without incomparable pairs
Total relation, which may also mean
connected relation (a binary relation in which any two elements are comparable).
Total function, a partial function that is also a total relation
Bu... |
https://en.wikipedia.org/wiki/Odd | Odd means unpaired, occasional, strange or unusual, or a person who is viewed as eccentric.
Odd may also refer to:
Mathematics
Even and odd numbers, an integer is odd if dividing by two does not yield an integer
Even and odd functions, a function is odd if f(−x) = −f(x) for all x
Even and odd permutations, a perm... |
https://en.wikipedia.org/wiki/Hodge%20conjecture | In mathematics, the Hodge conjecture is a major unsolved problem in algebraic geometry and complex geometry that relates the algebraic topology of a non-singular complex algebraic variety to its subvarieties.
In simple terms, the Hodge conjecture asserts that the basic topological information like the number of holes ... |
https://en.wikipedia.org/wiki/Rank%20of%20an%20abelian%20group | In mathematics, the rank, Prüfer rank, or torsion-free rank of an abelian group A is the cardinality of a maximal linearly independent subset. The rank of A determines the size of the largest free abelian group contained in A. If A is torsion-free then it embeds into a vector space over the rational numbers of dimensio... |
https://en.wikipedia.org/wiki/Injective%20cogenerator | In category theory, a branch of mathematics, the concept of an injective cogenerator is drawn from examples such as Pontryagin duality. Generators are objects which cover other objects as an approximation, and (dually) cogenerators are objects which envelope other objects as an approximation.
More precisely:
A gener... |
https://en.wikipedia.org/wiki/Higher-order%20function | In mathematics and computer science, a higher-order function (HOF) is a function that does at least one of the following:
takes one or more functions as arguments (i.e. a procedural parameter, which is a parameter of a procedure that is itself a procedure),
returns a function as its result.
All other functions are fi... |
https://en.wikipedia.org/wiki/Weil%20conjectures | In mathematics, the Weil conjectures were highly influential proposals by . They led to a successful multi-decade program to prove them, in which many leading researchers developed the framework of modern algebraic geometry and number theory.
The conjectures concern the generating functions (known as local zeta functi... |
https://en.wikipedia.org/wiki/Sphenic%20number | In number theory, a sphenic number (from , 'wedge') is a positive integer that is the product of three distinct prime numbers. Because there are infinitely many prime numbers, there are also infinitely many sphenic numbers.
Definition
A sphenic number is a product pqr where p, q, and r are three distinct prime numbers... |
https://en.wikipedia.org/wiki/L-function | In mathematics, an L-function is a meromorphic function on the complex plane, associated to one out of several categories of mathematical objects. An L-series is a Dirichlet series, usually convergent on a half-plane, that may give rise to an L-function via analytic continuation. The Riemann zeta function is an example... |
https://en.wikipedia.org/wiki/Jean%20Leray | Jean Leray (; 7 November 1906 – 10 November 1998) was a French mathematician, who worked on both partial differential equations and algebraic topology.
Life and career
He was born in Chantenay-sur-Loire (today part of Nantes). He studied at École Normale Supérieure from 1926 to 1929. He received his Ph.D. in 1933. In... |
https://en.wikipedia.org/wiki/Sheaf%20%28mathematics%29 | In mathematics, a sheaf (: sheaves) is a tool for systematically tracking data (such as sets, abelian groups, rings) attached to the open sets of a topological space and defined locally with regard to them. For example, for each open set, the data could be the ring of continuous functions defined on that open set. Such... |
https://en.wikipedia.org/wiki/Gaussian%20function | In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the base form
and with parametric extension
for arbitrary real constants , and non-zero . It is named after the mathematician Carl Friedrich Gauss. The graph of a Gaussian is a characteristic symmetric "bell curve" shape. T... |
https://en.wikipedia.org/wiki/Trigonometric%20integral | In mathematics, trigonometric integrals are a family of integrals involving trigonometric functions.
Sine integral
The different sine integral definitions are
Note that the integrand is the sinc function, and also the zeroth spherical Bessel function.
Since is an even entire function (holomorphic over the entire c... |
https://en.wikipedia.org/wiki/Convex%20function | In mathematics, a real-valued function is called convex if the line segment between any two distinct points on the graph of the function lies above the graph between the two points. Equivalently, a function is convex if its epigraph (the set of points on or above the graph of the function) is a convex set. A twice-diff... |
https://en.wikipedia.org/wiki/Euler%20integral | In mathematics, there are two types of Euler integral:
The Euler integral of the first kind is the beta function
The Euler integral of the second kind is the gamma function
For positive integers and , the two integrals can be expressed in terms of factorials and binomial coefficients:
See also
Leonhard Euler
Li... |
https://en.wikipedia.org/wiki/Beta%20function | In mathematics, the beta function, also called the Euler integral of the first kind, is a special function that is closely related to the gamma function and to binomial coefficients. It is defined by the integral
for complex number inputs
such that .
The beta function was studied by Leonhard Euler and Adrien-Marie ... |
https://en.wikipedia.org/wiki/Inverse%20Laplace%20transform | In mathematics, the inverse Laplace transform of a function F(s) is the piecewise-continuous and exponentially-restricted real function f(t) which has the property:
where denotes the Laplace transform.
It can be proven that, if a function F(s) has the inverse Laplace transform f(t), then f(t) is uniquely determined ... |
https://en.wikipedia.org/wiki/John%20Tate%20%28mathematician%29 | John Torrence Tate Jr. (March 13, 1925 – October 16, 2019) was an American mathematician distinguished for many fundamental contributions in algebraic number theory, arithmetic geometry, and related areas in algebraic geometry. He was awarded the Abel Prize in 2010.
Biography
Tate was born in Minneapolis, Minnesota. ... |
https://en.wikipedia.org/wiki/Elimination%20theory | In commutative algebra and algebraic geometry, elimination theory is the classical name for algorithmic approaches to eliminating some variables between polynomials of several variables, in order to solve systems of polynomial equations.
Classical elimination theory culminated with the work of Francis Macaulay on mult... |
https://en.wikipedia.org/wiki/Commutative%20algebra | Commutative algebra, first known as ideal theory, is the branch of algebra that studies commutative rings, their ideals, and modules over such rings. Both algebraic geometry and algebraic number theory build on commutative algebra. Prominent examples of commutative rings include polynomial rings; rings of algebraic int... |
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