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https://en.wikipedia.org/wiki/Torus | In geometry, a torus (: tori or toruses) is a surface of revolution generated by revolving a circle in three-dimensional space one full revolution about an axis that is coplanar with the circle. The main types of toruses include ring toruses, horn toruses, and spindle toruses. A ring torus is sometimes colloquially ref... |
https://en.wikipedia.org/wiki/Poker%20probability | In poker, the probability of each type of 5-card hand can be computed by calculating the proportion of hands of that type among all possible hands.
History
Probability and gambling have been ideas since long before the invention of poker. The development of probability theory in the late 1400s was attributed to gambl... |
https://en.wikipedia.org/wiki/Sum | Sum most commonly means the total of two or more numbers added together; see addition.
Sum can also refer to:
Mathematics
Sum (category theory), the generic concept of summation in mathematics
Sum, the result of summation, the addition of a sequence of numbers
3SUM, a term from computational complexity theory
B... |
https://en.wikipedia.org/wiki/Line | Line most often refers to:
Line (geometry), object that has zero thickness and curvature and stretches to infinity
Telephone line, a single-user circuit on a telephone communication system
Line, lines, The Line, or LINE may also refer to:
Arts, entertainment, and media
Films
Lines (film), a 2016 Greek film
The ... |
https://en.wikipedia.org/wiki/Multistage%20sampling | In statistics, multistage sampling is the taking of samples in stages using smaller and smaller sampling units at each stage.
Multistage sampling can be a complex form of cluster sampling because it is a type of sampling which involves dividing the population into groups (or clusters). Then, one or more clusters are c... |
https://en.wikipedia.org/wiki/Julius%20Petersen | Julius Peter Christian Petersen (16 June 1839, Sorø, West Zealand – 5 August 1910, Copenhagen) was a Danish mathematician. His contributions to the field of mathematics led to the birth of graph theory.
Biography
Petersen's interests in mathematics were manifold, including: geometry, complex analysis, number theory, m... |
https://en.wikipedia.org/wiki/Perpendicular | In elementary geometry, two geometric objects are perpendicular if their intersection forms right angles (angles that are 90 degrees or π/2 radians wide) at the point of intersection called a foot. The condition of perpendicularity may be represented graphically using the perpendicular symbol, ⟂. Perpendicular intersec... |
https://en.wikipedia.org/wiki/Parallel | Parallel may refer to:
Mathematics
Parallel (geometry), two lines in the Euclidean plane which never intersect
Parallel postulate, an axiom from Euclid's Elements establishing flat Euclidean geometry
Parallel transport, in differential geometry, a way of transporting geometrical data along smooth curves
Parallel ... |
https://en.wikipedia.org/wiki/Right%20angle | In geometry and trigonometry, a right angle is an angle of exactly 90 degrees or radians corresponding to a quarter turn. If a ray is placed so that its endpoint is on a line and the adjacent angles are equal, then they are right angles. The term is a calque of Latin angulus rectus; here rectus means "upright", referr... |
https://en.wikipedia.org/wiki/Gaspard%20Monge | Gaspard Monge, Comte de Péluse (9 May 1746 – 28 July 1818) was a French mathematician, commonly presented as the inventor of descriptive geometry, (the mathematical basis of) technical drawing, and the father of differential geometry. During the French Revolution he served as the Minister of the Marine, and was involve... |
https://en.wikipedia.org/wiki/Maple%20%28software%29 | Maple is a symbolic and numeric computing environment as well as a multi-paradigm programming language. It covers several areas of technical computing, such as symbolic mathematics, numerical analysis, data processing, visualization, and others. A toolbox, MapleSim, adds functionality for multidomain physical modeling ... |
https://en.wikipedia.org/wiki/Louis%20de%20Branges%20de%20Bourcia | Louis de Branges de Bourcia (born August 21, 1932) is a French-American mathematician. He is the Edward C. Elliott Distinguished Professor of Mathematics at Purdue University in West Lafayette, Indiana. He is best known for proving the long-standing Bieberbach conjecture in 1984, now called de Branges's theorem. He cla... |
https://en.wikipedia.org/wiki/Feigenbaum%20constants | In mathematics, specifically bifurcation theory, the Feigenbaum constants are two mathematical constants which both express ratios in a bifurcation diagram for a non-linear map. They are named after the physicist Mitchell J. Feigenbaum.
History
Feigenbaum originally related the first constant to the period-doubling b... |
https://en.wikipedia.org/wiki/Constant%20term | In mathematics, a constant term (sometimes referred to as a free term) is a term in an algebraic expression that does not contain any variables and therefore is constant. For example, in the quadratic polynomial
the 3 is a constant term.
After like terms are combined, an algebraic expression will have at most one co... |
https://en.wikipedia.org/wiki/Division%20by%20two | In mathematics, division by two or halving has also been called mediation or dimidiation. The treatment of this as a different operation from multiplication and division by other numbers goes back to the ancient Egyptians, whose multiplication algorithm used division by two as one of its fundamental steps.
Some mathema... |
https://en.wikipedia.org/wiki/Analytic%20continuation | In complex analysis, a branch of mathematics, analytic continuation is a technique to extend the domain of definition of a given analytic function. Analytic continuation often succeeds in defining further values of a function, for example in a new region where the infinite series representation which initially defined ... |
https://en.wikipedia.org/wiki/Zeros%20and%20poles | In complex analysis (a branch of mathematics), a pole is a certain type of singularity of a complex-valued function of a complex variable. It is the simplest type of non-removable singularity of such a function (see essential singularity). Technically, a point is a pole of a function if it is a zero of the function ... |
https://en.wikipedia.org/wiki/Proportionality%20%28mathematics%29 | In mathematics, two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a constant ratio. The ratio is called coefficient of proportionality (or proportionality constant) and its reciprocal is known as constant of normalization (or normalizing co... |
https://en.wikipedia.org/wiki/Coordinate%20system | In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space. The order of the coordinates is significant, and they are sometimes identified by their position in an ordered t... |
https://en.wikipedia.org/wiki/Factorization | In mathematics, factorization (or factorisation, see English spelling differences) or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind. For example, is an integer factorization of , and is a polynomial factorizat... |
https://en.wikipedia.org/wiki/Gram%E2%80%93Schmidt%20process | In mathematics, particularly linear algebra and numerical analysis, the Gram–Schmidt process or Gram-Schmidt algorithm is a method for orthonormalizing a set of vectors in an inner product space, most commonly the Euclidean space equipped with the standard inner product. The Gram–Schmidt process takes a finite, linear... |
https://en.wikipedia.org/wiki/Gnomon | A gnomon (; ) is the part of a sundial that casts a shadow. The term is used for a variety of purposes in mathematics and other fields.
History
A painted stick dating from 2300 BC that was excavated at the astronomical site of Taosi is the oldest gnomon known in China. The gnomon was widely used in ancient China from... |
https://en.wikipedia.org/wiki/Tychonoff%27s%20theorem | In mathematics, Tychonoff's theorem states that the product of any collection of compact topological spaces is compact with respect to the product topology. The theorem is named after Andrey Nikolayevich Tikhonov (whose surname sometimes is transcribed Tychonoff), who proved it first in 1930 for powers of the closed un... |
https://en.wikipedia.org/wiki/Euclidean%20planes%20in%20three-dimensional%20space | In Euclidean geometry, a plane is a flat two-dimensional surface that extends indefinitely.
Euclidean planes often arise as subspaces of three-dimensional space .
A prototypical example is one of a room's walls, infinitely extended and assumed infinitesimal thin.
While a pair of real numbers suffices to describe poin... |
https://en.wikipedia.org/wiki/Continuum | Continuum may refer to:
Continuum (measurement), theories or models that explain gradual transitions from one condition to another without abrupt changes
Mathematics
Continuum (set theory), the real line or the corresponding cardinal number
Linear continuum, any ordered set that shares certain properties of the re... |
https://en.wikipedia.org/wiki/Toma%C5%BE%20Pisanski | Tomaž (Tomo) Pisanski (born 24 May 1949 in Ljubljana, Yugoslavia, which is now in Slovenia) is a Slovenian mathematician working mainly in discrete mathematics and graph theory. He is considered by many Slovenian mathematicians to be the "father of Slovenian discrete mathematics."
Biography
As a high school student, P... |
https://en.wikipedia.org/wiki/Magnitude | Magnitude may refer to:
Mathematics
Euclidean vector, a quantity defined by both its magnitude and its direction
Magnitude (mathematics), the relative size of an object
Norm (mathematics), a term for the size or length of a vector
Order of magnitude, the class of scale having a fixed value ratio to the preceding clas... |
https://en.wikipedia.org/wiki/Vladimir%20Batagelj | Vladimir Batagelj (born June 14, 1948 in Idrija, Yugoslavia) is a Slovenian mathematician and an emeritus professor of mathematics at the University of Ljubljana. He is known for his work in discrete mathematics and combinatorial optimization, particularly analysis of social networks and other large networks (blockmod... |
https://en.wikipedia.org/wiki/Kite%20%28geometry%29 | In Euclidean geometry, a kite is a quadrilateral with reflection symmetry across a diagonal. Because of this symmetry, a kite has two equal angles and two pairs of adjacent equal-length sides. Kites are also known as deltoids, but the word deltoid may also refer to a deltoid curve, an unrelated geometric object sometim... |
https://en.wikipedia.org/wiki/HCN | HCN may refer to:
Science and mathematics
HCN channel, a cellular ion channel
Highly composite number, a type of integer
Hydrogen cyanide
Transportation
Halcyonair, a Cape Verdean airline
Headcorn railway station, in England
Hengchun Airport, in Taiwan
Other
Health Communication Network, an Australian soft... |
https://en.wikipedia.org/wiki/Lah%20number | In mathematics, the (signed and unsigned) Lah numbers are coefficients expressing rising factorials in terms of falling factorials and vice versa. They were discovered by Ivo Lah in 1954. Explicitly, the unsigned Lah numbers are given by the formula involving the binomial coefficient
for .
Unsigned Lah numbers ha... |
https://en.wikipedia.org/wiki/Winding%20number | In mathematics, the winding number or winding index of a closed curve in the plane around a given point is an integer representing the total number of times that curve travels counterclockwise around the point, i.e., the curve's number of turns. For certain open plane curves, the number of turns may be non-integer. The... |
https://en.wikipedia.org/wiki/Dann | Dann is an English surname. It is a toponymic surname which came from Middle English and Old English , "valley". Variant spellings include Dan and Dane.
According to statistics compiled by Patrick Hanks on the basis of the 2011 United Kingdom census and the Census of Ireland 2011, 2,666 people on the island of Great ... |
https://en.wikipedia.org/wiki/Glottochronology | Glottochronology (from Attic Greek γλῶττα tongue, language and χρόνος time) is the part of lexicostatistics which involves comparative linguistics and deals with the chronological relationship between languages.
The idea was developed by Morris Swadesh in the 1950s in his article on Salish internal relationships. He d... |
https://en.wikipedia.org/wiki/Snake%20lemma | The snake lemma is a tool used in mathematics, particularly homological algebra, to construct long exact sequences. The snake lemma is valid in every abelian category and is a crucial tool in homological algebra and its applications, for instance in algebraic topology. Homomorphisms constructed with its help are gener... |
https://en.wikipedia.org/wiki/Connectedness | In mathematics, connectedness is used to refer to various properties meaning, in some sense, "all one piece". When a mathematical object has such a property, we say it is connected; otherwise it is disconnected. When a disconnected object can be split naturally into connected pieces, each piece is usually called a comp... |
https://en.wikipedia.org/wiki/Naive%20Bayes%20classifier | In statistics, naive Bayes classifiers are a family of linear "probabilistic classifiers" based on applying Bayes' theorem with strong (naive) independence assumptions between the features (see Bayes classifier). They are among the simplest Bayesian network models, but coupled with kernel density estimation, they can a... |
https://en.wikipedia.org/wiki/Graph%20of%20a%20function | In mathematics, the graph of a function is the set of ordered pairs , where In the common case where and are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.
In the case of functions of two variables, that is functions whose domain consist... |
https://en.wikipedia.org/wiki/Additive%20function | In number theory, an additive function is an arithmetic function f(n) of the positive integer variable n such that whenever a and b are coprime, the function applied to the product ab is the sum of the values of the function applied to a and b:
Completely additive
An additive function f(n) is said to be completely ad... |
https://en.wikipedia.org/wiki/List%20of%20U.S.%20states%20and%20territories%20by%20population | The states and territories included in the United States Census Bureau's statistics for the United States population, ethnicity, religion, and most other categories include the 50 states and Washington, D.C. Separate statistics are maintained for the five permanently inhabited territories of the United States: Puerto R... |
https://en.wikipedia.org/wiki/G.%20H.%20Hardy | Godfrey Harold Hardy (7 February 1877 – 1 December 1947) was an English mathematician, known for his achievements in number theory and mathematical analysis. In biology, he is known for the Hardy–Weinberg principle, a basic principle of population genetics.
G. H. Hardy is usually known by those outside the field of m... |
https://en.wikipedia.org/wiki/Ratio | In mathematics, a ratio () shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). Similarly, the ratio of lemons to oranges is 6:8 (or 3:4) and ... |
https://en.wikipedia.org/wiki/Sharkovskii%27s%20theorem | In mathematics, Sharkovskii's theorem (also spelled Sharkovsky's theorem, Sharkovskiy's theorem, Šarkovskii's theorem or Sarkovskii's theorem), named after Oleksandr Mykolayovych Sharkovsky, who published it in 1964, is a result about discrete dynamical systems. One of the implications of the theorem is that if a disc... |
https://en.wikipedia.org/wiki/Safe%20and%20Sophie%20Germain%20primes | In number theory, a prime number p is a Sophie Germain prime if 2p + 1 is also prime. The number 2p + 1 associated with a Sophie Germain prime is called a safe prime. For example, 11 is a Sophie Germain prime and 2 × 11 + 1 = 23 is its associated safe prime. Sophie Germain primes are named after French mathematician So... |
https://en.wikipedia.org/wiki/Curve | In mathematics, a curve (also called a curved line in older texts) is an object similar to a line, but that does not have to be straight.
Intuitively, a curve may be thought of as the trace left by a moving point. This is the definition that appeared more than 2000 years ago in Euclid's Elements: "The [curved] line is... |
https://en.wikipedia.org/wiki/Frustum | In geometry, a ; (: frusta or frustums) is the portion of a solid (normally a pyramid or a cone) that lies between two parallel planes cutting the solid. In the case of a pyramid, the base faces are polygonal and the side faces are trapezoidal. A right frustum is a right pyramid or a right cone truncated perpendicularl... |
https://en.wikipedia.org/wiki/Inequation | In mathematics, an inequation is a statement that an inequality holds between two values. It is usually written in the form of a pair of expressions denoting the values in question, with a relational sign between them indicating the specific inequality relation. Some examples of inequations are:
In some cases... |
https://en.wikipedia.org/wiki/Inequality%20%28mathematics%29 | In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size. There are several different notations used to represent different kinds of inequalities:
The notation a < ... |
https://en.wikipedia.org/wiki/Primitive | Primitive may refer to:
Mathematics
Primitive element (field theory)
Primitive element (finite field)
Primitive cell (crystallography)
Primitive notion, axiomatic systems
Primitive polynomial (disambiguation), one of two concepts
Primitive function or antiderivative, = f
Primitive permutation group
Primitive ... |
https://en.wikipedia.org/wiki/Equality%20%28mathematics%29 | In mathematics, equality is a relationship between two quantities or, more generally two mathematical expressions, asserting that the quantities have the same value, or that the expressions represent the same mathematical object. The equality between and is written , and pronounced " equals ". The symbol "" is called... |
https://en.wikipedia.org/wiki/Geodesic | In geometry, a geodesic () is a curve representing in some sense the shortest path (arc) between two points in a surface, or more generally in a Riemannian manifold. The term also has meaning in any differentiable manifold with a connection. It is a generalization of the notion of a "straight line".
The noun geodesic... |
https://en.wikipedia.org/wiki/Angle%20trisection | Angle trisection is a classical problem of straightedge and compass construction of ancient Greek mathematics. It concerns construction of an angle equal to one third of a given arbitrary angle, using only two tools: an unmarked straightedge and a compass.
In 1837, Pierre Wantzel proved that the problem, as stated, is... |
https://en.wikipedia.org/wiki/Fermat%20number | In mathematics, a Fermat number, named after Pierre de Fermat, the first known to have studied them, is a positive integer of the form
where n is a non-negative integer. The first few Fermat numbers are:
3, 5, 17, 257, 65537, 4294967297, 18446744073709551617, ... .
If 2k + 1 is prime and , then k itself must be a po... |
https://en.wikipedia.org/wiki/Andrey%20Kolmogorov | Andrey Nikolaevich Kolmogorov (, 25 April 1903 – 20 October 1987) was a Soviet mathematician who contributed to the mathematics of probability theory, topology, intuitionistic logic, turbulence, classical mechanics, algorithmic information theory and computational complexity.
Biography
Early life
Andrey Kolmogorov wa... |
https://en.wikipedia.org/wiki/Bartel%20Leendert%20van%20der%20Waerden | Bartel Leendert van der Waerden (; 2 February 1903 – 12 January 1996) was a Dutch mathematician and historian of mathematics.
Biography
Education and early career
Van der Waerden learned advanced mathematics at the University of Amsterdam and the University of Göttingen, from 1919 until 1926. He was much influenced b... |
https://en.wikipedia.org/wiki/Linearity | In mathematics, the term linear is used in two distinct senses for two different properties:
linearity of a function (or mapping);
linearity of a polynomial.
An example of a linear function is the function defined by that maps the real line to a line in the Euclidean plane R2 that passes through the origin. An examp... |
https://en.wikipedia.org/wiki/Lambert%20W%20function | In mathematics, the Lambert function, also called the omega function or product logarithm, is a multivalued function, namely the branches of the converse relation of the function , where is any complex number and is the exponential function.
For each integer there is one branch, denoted by , which is a complex-val... |
https://en.wikipedia.org/wiki/Omar%20Khayyam | Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm Nīsābūrī (18 May 1048 – 4 December 1131), commonly known as Omar Khayyam ( ; ), was a polymath, known for his contributions to mathematics, astronomy, philosophy, and poetry. He was born in Nishapur, the initial capital of the Seljuk Empire. As a scholar, he was contemporar... |
https://en.wikipedia.org/wiki/Solid%20angle | In geometry, a solid angle (symbol: ) is a measure of the amount of the field of view from some particular point that a given object covers. That is, it is a measure of how large the object appears to an observer looking from that point.
The point from which the object is viewed is called the apex of the solid angle, a... |
https://en.wikipedia.org/wiki/Stirling%20number | In mathematics, Stirling numbers arise in a variety of analytic and combinatorial problems. They are named after James Stirling, who introduced them in a purely algebraic setting in his book Methodus differentialis (1730). They were rediscovered and given a combinatorial meaning by Masanobu Saka in 1782.
Two different... |
https://en.wikipedia.org/wiki/Maxima%20%28software%29 | Maxima () is a computer algebra system (CAS) based on a 1982 version of Macsyma. It is written in Common Lisp and runs on all POSIX platforms such as macOS, Unix, BSD, and Linux, as well as under Microsoft Windows and Android. It is free software released under the terms of the GNU General Public License (GPL).
Histor... |
https://en.wikipedia.org/wiki/Isaac%20Barrow | Isaac Barrow (October 1630 – 4 May 1677) was an English Christian theologian and mathematician who is generally given credit for his early role in the development of infinitesimal calculus; in particular, for proof of the fundamental theorem of calculus. His work centered on the properties of the tangent; Barrow was th... |
https://en.wikipedia.org/wiki/Jules%20Richard%20%28mathematician%29 | Jules Richard (12 August 1862 – 14 October 1956) was a French mathematician who worked mainly in geometry but his name is most commonly associated with Richard's paradox.
Life and works
Richard was born in Blet, in the Cher département.
He taught at the lycées of Tours, Dijon and Châteauroux. He obtained his doctora... |
https://en.wikipedia.org/wiki/Richard%27s%20paradox | In logic, Richard's paradox is a semantical antinomy of set theory and natural language first described by the French mathematician Jules Richard in 1905. The paradox is ordinarily used to motivate the importance of distinguishing carefully between mathematics and metamathematics.
Kurt Gödel specifically cites Richar... |
https://en.wikipedia.org/wiki/Row%20and%20column%20spaces | In linear algebra, the column space (also called the range or image) of a matrix A is the span (set of all possible linear combinations) of its column vectors. The column space of a matrix is the image or range of the corresponding matrix transformation.
Let be a field. The column space of an matrix with components ... |
https://en.wikipedia.org/wiki/Flexagon | In geometry, flexagons are flat models, usually constructed by folding strips of paper, that can be flexed or folded in certain ways to reveal faces besides the two that were originally on the back and front.
Flexagons are usually square or rectangular (tetraflexagons) or hexagonal (hexaflexagons). A prefix can be add... |
https://en.wikipedia.org/wiki/Magma%20%28computer%20algebra%20system%29 | Magma is a computer algebra system designed to solve problems in algebra, number theory, geometry and combinatorics. It is named after the algebraic structure magma. It runs on Unix-like operating systems, as well as Windows.
Introduction
Magma is produced and distributed by the Computational Algebra Group within the... |
https://en.wikipedia.org/wiki/Coset | In mathematics, specifically group theory, a subgroup of a group may be used to decompose the underlying set of into disjoint, equal-size subsets called cosets. There are left cosets and right cosets. Cosets (both left and right) have the same number of elements (cardinality) as does . Furthermore, itself is both a... |
https://en.wikipedia.org/wiki/Spanning%20Tree%20Protocol | The Spanning Tree Protocol (STP) is a network protocol that builds a loop-free logical topology for Ethernet networks. The basic function of STP is to prevent bridge loops and the broadcast radiation that results from them. Spanning tree also allows a network design to include backup links providing fault tolerance if ... |
https://en.wikipedia.org/wiki/Lagrange%20%28disambiguation%29 | Joseph-Louis Lagrange was an Italian mathematician, physicist and astronomer.
Lagrange or La Grange may also refer to:
Lagrange (surname), list of people with this name
Mathematics and physics
Lagrange multiplier, a mathematical technique
Lagrange's theorem (group theory), or Lagrange's lemma, an important result ... |
https://en.wikipedia.org/wiki/J%C3%A1nos%20Bolyai | János Bolyai (; 15 December 1802 – 27 January 1860) or Johann Bolyai, was a Hungarian mathematician who developed absolute geometry—a geometry that includes both Euclidean geometry and hyperbolic geometry. The discovery of a consistent alternative geometry that might correspond to the structure of the universe helped t... |
https://en.wikipedia.org/wiki/Algebraic%20integer | In algebraic number theory, an algebraic integer is a complex number which is integral over the integers. That is, an algebraic integer is a complex root of some monic polynomial (a polynomial whose leading coefficient is 1) whose coefficients are integers. The set of all algebraic integers is closed under addition, s... |
https://en.wikipedia.org/wiki/Shape%20of%20the%20universe | In physical cosmology, the shape of the universe refers to both its local and global geometry. Local geometry is defined primarily by its curvature, while the global geometry is characterised by its topology (which itself is constrained by curvature). General relativity explains how spatial curvature (local geometry) i... |
https://en.wikipedia.org/wiki/Convergent | Convergent is an adjective for things that converge. It is commonly used in mathematics and may refer to:
Convergent boundary, a type of plate tectonic boundary
Convergent (continued fraction)
Convergent evolution
Convergent series
Convergent may also refer to:
Convergent Books, an imprint of Crown Publishing Gro... |
https://en.wikipedia.org/wiki/Exponentiation | In mathematics, exponentiation is an operation involving two numbers, the base and the exponent or power. Exponentiation is written as , where is the base and is the power; this is pronounced as " (raised) to the (power of) ". When is a positive integer, exponentiation corresponds to repeated multiplication of the b... |
https://en.wikipedia.org/wiki/Presentation%20of%20a%20group | In mathematics, a presentation is one method of specifying a group. A presentation of a group G comprises a set S of generators—so that every element of the group can be written as a product of powers of some of these generators—and a set R of relations among those generators. We then say G has presentation
Informally... |
https://en.wikipedia.org/wiki/Hyperplane | In geometry, a hyperplane is a subspace whose dimension is one less than that of its ambient space. For example, if a space is 3-dimensional then its hyperplanes are the 2-dimensional planes, while if the space is 2-dimensional, its hyperplanes are the 1-dimensional lines. This notion can be used in any general space... |
https://en.wikipedia.org/wiki/Generating%20set%20of%20a%20group | In abstract algebra, a generating set of a group is a subset of the group set such that every element of the group can be expressed as a combination (under the group operation) of finitely many elements of the subset and their inverses.
In other words, if is a subset of a group , then , the subgroup generated by , is... |
https://en.wikipedia.org/wiki/Dihedral%20group | In mathematics, a dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections. Dihedral groups are among the simplest examples of finite groups, and they play an important role in group theory, geometry, and chemistry.
The notation for the dihedral group differs in geometry... |
https://en.wikipedia.org/wiki/List%20of%20group%20theory%20topics | In mathematics and abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms. Groups recu... |
https://en.wikipedia.org/wiki/Legendre%20polynomials | In mathematics, Legendre polynomials, named after Adrien-Marie Legendre (1782), are a system of complete and orthogonal polynomials with a vast number of mathematical properties and numerous applications. They can be defined in many ways, and the various definitions highlight different aspects as well as suggest genera... |
https://en.wikipedia.org/wiki/Khan%20Yunis | Khan Yunis (, also spelled Khan Younis or Khan Yunus; translation: "Caravansary [of] Jonah") is a city in the southern Gaza Strip. According to the Palestinian Central Bureau of Statistics, Khan Yunis had a population of 205,125 in 2017. Khan Yunis, which lies only 4 kilometers (about 2.5 miles) east of the Mediterrane... |
https://en.wikipedia.org/wiki/Euler%E2%80%93Jacobi%20pseudoprime | In number theory, an odd integer n is called an Euler–Jacobi probable prime (or, more commonly, an Euler probable prime) to base a, if a and n are coprime, and
where is the Jacobi symbol.
If n is an odd composite integer that satisfies the above congruence, then n is called an Euler–Jacobi pseudoprime (or, more com... |
https://en.wikipedia.org/wiki/Dirichlet%27s%20theorem%20on%20arithmetic%20progressions | In number theory, Dirichlet's theorem, also called the Dirichlet prime number theorem, states that for any two positive coprime integers a and d, there are infinitely many primes of the form a + nd, where n is also a positive integer. In other words, there are infinitely many primes that are congruent to a modulo d. Th... |
https://en.wikipedia.org/wiki/MMT | MMT may refer to:
Economics
Modern Monetary Theory, a branch of economic theory
Geography
4QMMT (or MMT), one of the Dead Sea Scrolls
Myanmar Standard Time (UTC+6:30)
Mathematics
MacMahon Master theorem, a result in enumerative combinatorics and linear algebra
Technology
MMT (Eclipse), a software proje... |
https://en.wikipedia.org/wiki/Diophantine%20set | In mathematics, a Diophantine equation is an equation of the form P(x1, ..., xj, y1, ..., yk) = 0 (usually abbreviated P(, ) = 0) where P(, ) is a polynomial with integer coefficients, where x1, ..., xj indicate parameters and y1, ..., yk indicate unknowns.
A Diophantine set is a subset S of , the set of all j-tuples... |
https://en.wikipedia.org/wiki/Degenerate%20distribution | In mathematics, a degenerate distribution is, according to some, a probability distribution in a space with support only on a manifold of lower dimension, and according to others a distribution with support only at a single point. By the latter definition, it is a deterministic distribution and takes only a single valu... |
https://en.wikipedia.org/wiki/Perturbation%20theory | In mathematics and applied mathematics, perturbation theory comprises methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. A critical feature of the technique is a middle step that breaks the problem into "solvable" and "perturbative" parts. In pe... |
https://en.wikipedia.org/wiki/Orthogonality | In mathematics, orthogonality is the generalization of the geometric notion of perpendicularity.
Orthogonality is also used with various meanings that are often weakly related or not related at all with the mathematical meanings.
Etymology
The word comes from the Ancient Greek (), meaning "upright", and (), meaning... |
https://en.wikipedia.org/wiki/Log-normal%20distribution | In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. Thus, if the random variable is log-normally distributed, then has a normal distribution. Equivalently, if has a normal distribution, then the exponen... |
https://en.wikipedia.org/wiki/John%20Forbes%20Nash%20Jr. | John Forbes Nash, Jr. (June 13, 1928 – May 23, 2015), known and published as John Nash, was an American mathematician who made fundamental contributions to game theory, real algebraic geometry, differential geometry, and partial differential equations. Nash and fellow game theorists John Harsanyi and Reinhard Selten we... |
https://en.wikipedia.org/wiki/Bernoulli%20process | In probability and statistics, a Bernoulli process (named after Jacob Bernoulli) is a finite or infinite sequence of binary random variables, so it is a discrete-time stochastic process that takes only two values, canonically 0 and 1. The component Bernoulli variables Xi are identically distributed and independent. Pr... |
https://en.wikipedia.org/wiki/Bernoulli%20trial | In the theory of probability and statistics, a Bernoulli trial (or binomial trial) is a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted. It is named after Jacob Bernoulli, a 17th-century Swiss mathemati... |
https://en.wikipedia.org/wiki/Graded%20ring | In mathematics, in particular abstract algebra, a graded ring is a ring such that the underlying additive group is a direct sum of abelian groups such that . The index set is usually the set of nonnegative integers or the set of integers, but can be any monoid. The direct sum decomposition is usually referred to as gr... |
https://en.wikipedia.org/wiki/Outer%20product | In linear algebra, the outer product of two coordinate vectors is the matrix whose entries are all products of an element in the first vector with an element in the second vector. If the two coordinate vectors have dimensions n and m, then their outer product is an n × m matrix. More generally, given two tensors (multi... |
https://en.wikipedia.org/wiki/Distributive%20property | In mathematics, the distributive property of binary operations is a generalization of the distributive law, which asserts that the equality
is always true in elementary algebra.
For example, in elementary arithmetic, one has
Therefore, one would say that multiplication distributes over addition.
This basic property ... |
https://en.wikipedia.org/wiki/Vladimir%20Voevodsky | Vladimir Alexandrovich Voevodsky (, ; 4 June 1966 – 30 September 2017) was a Russian-American mathematician. His work in developing a homotopy theory for algebraic varieties and formulating motivic cohomology led to the award of a Fields Medal in 2002. He is also known for the proof of the Milnor conjecture and motivic... |
https://en.wikipedia.org/wiki/Laurent%20Lafforgue | Laurent Lafforgue (; born 6 November 1966) is a French mathematician. He has made outstanding contributions to Langlands' program in the fields of number theory and analysis, and in particular proved the Langlands conjectures for the automorphism group of a function field. The crucial contribution by Lafforgue to solve... |
https://en.wikipedia.org/wiki/Partition%20%28number%20theory%29 | In number theory and combinatorics, a partition of a non-negative integer , also called an integer partition, is a way of writing as a sum of positive integers. Two sums that differ only in the order of their summands are considered the same partition. (If order matters, the sum becomes a composition.) For example, ... |
https://en.wikipedia.org/wiki/Solvable%20group | In mathematics, more specifically in the field of group theory, a solvable group or soluble group is a group that can be constructed from abelian groups using extensions. Equivalently, a solvable group is a group whose derived series terminates in the trivial subgroup.
Motivation
Historically, the word "solvable" ar... |
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