Camille Jordan
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Marie Ennemond Camille Jordan (; 5 January 1838 – 22 January 1922) was a French mathematician, known both for his foundational work in
group theory In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ...
and for his influential ''Cours d'analyse''.


Biography

Jordan was born in
Lyon Lyon,, ; Occitan: ''Lion'', hist. ''Lionés'' also spelled in English as Lyons, is the third-largest city and second-largest metropolitan area of France. It is located at the confluence of the rivers Rhône and Saône, to the northwest of t ...
and educated at the
École polytechnique École may refer to: * an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée) * École (river), a tributary of the Seine flowing in région Île-de-France * École, ...
. He was an engineer by profession; later in life he taught at the École polytechnique and the
Collège de France The Collège de France (), formerly known as the ''Collège Royal'' or as the ''Collège impérial'' founded in 1530 by François I, is a higher education and research establishment ('' grand établissement'') in France France (), ...
, where he had a reputation for eccentric choices of notation. He is remembered now by name in a number of results: * The
Jordan curve theorem In topology, the Jordan curve theorem asserts that every ''Jordan curve'' (a plane simple closed curve) divides the plane into an "interior (topology), interior" region Boundary (topology), bounded by the curve and an "exterior (topology), exteri ...
, a topological result required in
complex analysis Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates Function (mathematics), functions of complex numbers. It is helpful in many branches of mathemati ...
* The
Jordan normal form In linear algebra Linear algebra is the branch of mathematics concerning linear equations such as: :a_1x_1+\cdots +a_nx_n=b, linear maps such as: :(x_1, \ldots, x_n) \mapsto a_1x_1+\cdots +a_nx_n, and their representations in vector spaces and ...
and the Jordan matrix in
linear algebra Linear algebra is the branch of mathematics concerning linear equations such as: :a_1x_1+\cdots +a_nx_n=b, linear maps such as: :(x_1, \ldots, x_n) \mapsto a_1x_1+\cdots +a_nx_n, and their representations in vector spaces and through matrix (mat ...
* In
mathematical analysis Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series (m ...
,
Jordan measure In mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in mode ...
(or ''Jordan content'') is an area measure that predates
measure theory In mathematics, the concept of a measure is a generalization and formalization of Geometry#Length, area, and volume, geometrical measures (length, area, volume) and other common notions, such as mass and probability of events. These seemingly ...
* In
group theory In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ...
, the Jordan–Hölder theorem on composition series is a basic result. * Jordan's theorem on finite linear groups Jordan's work did much to bring
Galois theory In mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in mo ...
into the mainstream. He also investigated the
Mathieu group In group theory In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathemati ...
s, the first examples of sporadic groups. His ''Traité des substitutions'', on
permutation group In mathematics, a permutation group is a group (mathematics), group ''G'' whose elements are permutations of a given Set (mathematics), set ''M'' and whose group operation is the composition of permutations in ''G'' (which are thought of as bijec ...
s, was published in 1870; this treatise won for Jordan the 1870 ''prix Poncelet''. He was an Invited Speaker of the ICM in 1920 in
Strasbourg Strasbourg (, , ; german: Straßburg ; gsw, label=Bas Rhin Alsatian dialect, Alsatian, Strossburi , gsw, label=Haut Rhin Alsatian dialect, Alsatian, Strossburig ) is the Prefectures in France, prefecture and largest city of the Grand Est Re ...
. The
asteroid An asteroid is a minor planet of the inner Solar System. Sizes and shapes of asteroids vary significantly, ranging from 1-meter rocks to a dwarf planet almost 1000 km in diameter; they are rocky, metallic or icy bodies with no atmosphere ...
25593 Camillejordan and are named in his honour. Camille Jordan is not to be confused with the
geodesist Geodesy ( ) is the Earth science of accurately measuring and understanding Earth's figure ( geometric shape and size), orientation in space, and gravity. The field also incorporates studies of how these properties change over time and equi ...
Wilhelm Jordan ( Gauss–Jordan elimination) or the physicist
Pascual Jordan Ernst Pascual Jordan (; 18 October 1902 – 31 July 1980) was a German theoretical and mathematical physicist who made significant contributions to quantum mechanics and quantum field theory. He contributed much to the mathematical form of matrix ...
(
Jordan algebra In abstract algebra, a Jordan algebra is a nonassociative algebra algebra over a field, over a field whose Product (mathematics), multiplication satisfies the following axioms: # xy = yx (commutative law) # (xy)(xx) = x(y(xx)) (). The product of ...
s).


Bibliography

* Cours d'analyse de l'Ecole Polytechnique ; 1 Calcul différentiel (Gauthier-Villars, 1909) * Cours d'analyse de l'Ecole Polytechnique ; 2 Calcul intégral (Gauthier-Villars, 1909) * Cours d'analyse de l'Ecole Polytechnique ; 3 équations différentielles (Gauthier-Villars, 1909)
Mémoire sur le nombre des valeurs des fonctions
(1861–1869)
Recherches sur les polyèdres
(Gauthier-Villars, 1866) * * * The collected works of Camille Jordan were published 1961–1964 in four volumes at Gauthier-Villars, Paris.


See also

* Centered tree *
Frenet–Serret formulas In differential geometry, the Frenet–Serret formulas describe the kinematic properties of a particle moving along a differentiable curve in three-dimensional Euclidean space \mathbb^, or the geometric properties of the curve itself irrespective ...
*
Pochhammer contour In mathematics, the Pochhammer contour, introduced by Jordan (1887), pp. 243–244 and , is a contour in the complex plane In mathematics, the complex plane is the plane (geometry), plane formed by the complex numbers, with a Cartesian coordi ...


References


External links

* * {{DEFAULTSORT:Jordan, Camille 1838 births 1922 deaths École Polytechnique alumni Mines ParisTech alumni Corps des mines Scientists from Lyon 19th-century French mathematicians Group theorists Linear algebraists Collège de France faculty Corresponding members of the Saint Petersburg Academy of Sciences Members of the French Academy of Sciences Foreign Members of the Royal Society Foreign associates of the National Academy of Sciences Members of the Ligue de la patrie française