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Jean Dieudonné
Jean Alexandre Eugène Dieudonné (; 1 July 1906 – 29 November 1992) was a French mathematician, notable for research in abstract algebra, algebraic geometry, and functional analysis, for close involvement with the Nicolas Bourbaki pseudonymous group and the ''Éléments de géométrie algébrique'' project of Alexander Grothendieck, and as a historian of mathematics, particularly in the fields of functional analysis and algebraic topology. His work on the classical groups (the book ''La Géométrie des groupes classiques'' was published in 1955), and on formal groups, introducing what now are called Dieudonné modules, had a major effect on those fields. He was born and brought up in Lille, with a formative stay in England where he was introduced to algebra. In 1924 he was admitted to the École Normale Supérieure, where André Weil was a classmate. He began working in complex analysis. In 1934 he was one of the group of ''normaliens'' convened by Weil, which would become ' B ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lille
Lille (, ; ; ; ; ) is a city in the northern part of France, within French Flanders. Positioned along the Deûle river, near France's border with Belgium, it is the capital of the Hauts-de-France Regions of France, region, the Prefectures in France, prefecture of the Nord (French department), Nord Departments of France, department, and the main city of the Métropole Européenne de Lille, European Metropolis of Lille. The city of Lille proper had a population of 236,234 in 2020 within its small municipal territory of , but together with its French suburbs and exurbs the Lille metropolitan area (French part only), which extends over , had a population of 1,515,061 that same year (January 2020 census), the fourth most populated in France after Paris, Lyon, and Marseille. The city of Lille and 94 suburban French municipalities have formed since 2015 the Métropole Européenne de Lille, European Metropolis of Lille, an Indirect election, indirectly elected Métropole, metropolitan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dieudonné Determinant
In linear algebra, the Dieudonné determinant is a generalization of the determinant of a matrix to matrices over division rings and local rings. It was introduced by . If ''K'' is a division ring, then the Dieudonné determinant is a group homomorphism from the group GL''n''(''K'') of invertible ''n''-by-''n'' matrices over ''K'' onto the abelianization ''K''×/ 'K''×, ''K''×of the multiplicative group ''K''× of ''K''. For example, the Dieudonné determinant for a 2-by-2 matrix is the residue class, in ''K''×/ 'K''×, ''K''× of :\det \left(\right) = \left\lbrace\right. Properties Let ''R'' be a local ring. There is a determinant map from the matrix ring GL(''R'') to the abelianised unit group ''R''×ab with the following properties:Rosenberg (1994) p.64 * The determinant is invariant under elementary row operations * The determinant of the identity matrix is 1 * If a row is left multiplied by ''a'' in ''R''× then the determinant is left multiplied by ''a'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pseudonym
A pseudonym (; ) or alias () is a fictitious name that a person assumes for a particular purpose, which differs from their original or true meaning ( orthonym). This also differs from a new name that entirely or legally replaces an individual's own. Many pseudonym holders use them because they wish to remain anonymous and maintain privacy, though this may be difficult to achieve as a result of legal issues. Scope Pseudonyms include stage names, user names, ring names, pen names, aliases, superhero or villain identities and code names, gamertags, and regnal names of emperors, popes, and other monarchs. In some cases, it may also include nicknames. Historically, they have sometimes taken the form of anagrams, Graecisms, and Latinisations. Pseudonyms should not be confused with new names that replace old ones and become the individual's full-time name. Pseudonyms are "part-time" names, used only in certain contexts: to provide a more clear-cut separation between one's privat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nicolas Bourbaki
Nicolas Bourbaki () is the collective pseudonym of a group of mathematicians, predominantly French alumni of the École normale supérieure (Paris), École normale supérieure (ENS). Founded in 1934–1935, the Bourbaki group originally intended to prepare a new textbook in mathematical analysis, analysis. Over time the project became much more ambitious, growing into a large series of textbooks published under the Bourbaki name, meant to treat modern pure mathematics. The series is known collectively as the ''Éléments de mathématique'' (''Elements of Mathematics''), the group's central work. Topics treated in the series include set theory, abstract algebra, topology, analysis, Lie groups, and Lie algebras. Bourbaki was founded in response to the effects of the First World War which caused the death of a generation of French mathematicians; as a result, young university instructors were forced to use dated texts. While teaching at the University of Strasbourg, Henri Cartan co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Functional Analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (for example, Inner product space#Definition, inner product, Norm (mathematics)#Definition, norm, or Topological space#Definitions, topology) and the linear transformation, linear functions defined on these spaces and suitably respecting these structures. The historical roots of functional analysis lie in the study of function space, spaces of functions and the formulation of properties of transformations of functions such as the Fourier transform as transformations defining, for example, continuous function, continuous or unitary operator, unitary operators between function spaces. This point of view turned out to be particularly useful for the study of differential equations, differential and integral equations. The usage of the word ''functional (mathematics), functional'' as a noun goes back to the calculus of v ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Geometry
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; the modern approach generalizes this in a few different aspects. The fundamental objects of study in algebraic geometry are algebraic variety, algebraic varieties, which are geometric manifestations of solution set, solutions of systems of polynomial equations. Examples of the most studied classes of algebraic varieties are line (geometry), lines, circles, parabolas, ellipses, hyperbolas, cubic curves like elliptic curves, and quartic curves like lemniscate of Bernoulli, lemniscates and Cassini ovals. These are plane algebraic curves. A point of the plane lies on an algebraic curve if its coordinates satisfy a given polynomial equation. Basic questions involve the study of points of special interest like singular point of a curve, singular p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abstract Algebra
In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are set (mathematics), sets with specific operation (mathematics), operations acting on their elements. Algebraic structures include group (mathematics), groups, ring (mathematics), rings, field (mathematics), fields, module (mathematics), modules, vector spaces, lattice (order), lattices, and algebra over a field, algebras over a field. The term ''abstract algebra'' was coined in the early 20th century to distinguish it from older parts of algebra, and more specifically from elementary algebra, the use of variable (mathematics), variables to represent numbers in computation and reasoning. The abstract perspective on algebra has become so fundamental to advanced mathematics that it is simply called "algebra", while the term "abstract algebra" is seldom used except in mathematical education, pedagogy. Algebraic structures, with their associated homomorphisms, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peccot Lectures
The Peccot Lecture (''Cours Peccot'' in French) is a semester-long mathematics course given at the Collège de France. Each course is given by a mathematician under 30 years old who has distinguished themselves by their promising work. The course consists in a series of conferences during which the laureate exposes their recent research works. Being a Peccot lecturer is a distinction that often foresees an exceptional scientific career. Several future recipients of the Fields Medal, Abel Prize, members of the French Academy of Sciences, and professors at the Collège de France are among the laureates. Some of the most illustrious recipients include Émile Borel and the Fields medalists Laurent Schwartz, Jean-Pierre Serre, or Alain Connes. Some Peccot lectures may additionally be granted – exceptionally and irregularly – the Peccot prize or the Peccot–Vimont prize. History The Peccot lectures are among several manifestations organized at the Collège de France which are fu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prix Francoeur
The Prix Francoeur, or Francoeur Prize, was an award granted by the Institut de France, Academie des Sciences, Fondation Francoeur to authors of works useful to the progress of pure and applied mathematics. Preference was given to young scholars or to geometricians not yet established. It was established in 1882 and has been discontinued. Prize winners * 1882–1888 — Emile Barbier * 1889–1890 — Maximilien Marie * 1891–1892 — Augustin Mouchot * 1893 — Guy Robin * 1894 — J. Collet * 1895 — Jules Andrade * 1896 — Alphonse Valson * 1897 — Guy Robin * 1898 — Aimé Vaschy * 1899 — Le Cordier * 1900 — Edmond Maillet * 1901 — Léonce Laugel * 1902–1904 — Emile Lemoine * 1905 — Xavier Stouff * 1906–1912 — Emile Lemoine * 1913–1914 — A. Claude * 1915 — Joseph Marty * 1916 — René Gateaux * 1917 — Henri Villat * 1918 — Paul Montel * 1919 — Georges Giraud * 1920–1921 — René Baire * 1922 — Louis Antoine * 1923 — Gaston Bertran ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paul R
Paul may refer to: People * Paul (given name), a given name, including a list of people * Paul (surname), a list of people * Paul the Apostle, an apostle who wrote many of the books of the New Testament * Ray Hildebrand, half of the singing duo Paul & Paula * Paul Stookey, one-third of the folk music trio Peter, Paul and Mary * Billy Paul, stage name of American soul singer Paul Williams (1934–2016) * Vinnie Paul, drummer for American Metal band Pantera * Paul Avril, pseudonym of Édouard-Henri Avril (1849–1928), French painter and commercial artist * Paul, pen name under which Walter Scott wrote ''Paul's letters to his Kinsfolk'' in 1816 * Jean Paul, pen name of Johann Paul Friedrich Richter (1763–1825), German Romantic writer Places *Paul, Cornwall, a village in the civil parish of Penzance, United Kingdom *Paul (civil parish), Cornwall, United Kingdom *Paul, Alabama, United States, an unincorporated community *Paul, Idaho, United States, a city *Paul, Nebraska, United Sta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paracompact Space
In mathematics, a paracompact space is a topological space in which every open cover has an open refinement that is locally finite. These spaces were introduced by . Every compact space is paracompact. Every paracompact Hausdorff space is normal, and a Hausdorff space is paracompact if and only if it admits partitions of unity subordinate to any open cover. Sometimes paracompact spaces are defined so as to always be Hausdorff. Every closed subspace of a paracompact space is paracompact. While compact subsets of Hausdorff spaces are always closed, this is not true for paracompact subsets. A space such that every subspace of it is a paracompact space is called hereditarily paracompact. This is equivalent to requiring that every open subspace be paracompact. The notion of paracompact space is also studied in pointless topology, where it is more well-behaved. For example, the product of any number of paracompact locales is a paracompact locale, but the product of two paracomp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
