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 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 ...
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 ...
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, Savoi ...
. 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. It is located in Paris n ...
, 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, 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 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 matrice ...
* In
mathematical analysis
Analysis is the branch of mathematics dealing with continuous functions, limits, and related theories, such as differentiation, integration, measure, infinite sequences, series, and analytic functions.
These theories are usually studied ...
,
Jordan measure (or ''Jordan content'') is an area measure that predates
measure theory
In mathematics, the concept of a measure is a generalization and formalization of geometrical measures (length, area, volume) and other common notions, such as mass and probability of events. These seemingly distinct concepts have many simila ...
* In
group theory
In 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 ...
, 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, Galois theory, originally introduced by Évariste Galois, provides a connection between field theory and group theory. This connection, the fundamental theorem of Galois theory, allows reducing certain problems in field theory to ...
into the mainstream. He also investigated the
Mathieu group
In group theory, a topic in abstract algebra, the Mathieu groups are the five sporadic simple groups ''M''11, ''M''12, ''M''22, ''M''23 and ''M''24 introduced by . They are multiply transitive permutation groups on 11, 12, 22, 23 or 24 obje ...
s, the first examples of
sporadic groups. His ''Traité des substitutions'', on
permutation group
In mathematics, a permutation group is a group ''G'' whose elements are permutations of a given set ''M'' and whose group operation is the composition of permutations in ''G'' (which are thought of as bijective functions from the set ''M'' to ...
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, Strossburi , gsw, label= Haut Rhin Alsatian, Strossburig ) is the prefecture and largest city of the Grand Est region of eastern France and the official seat of the ...
.
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 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 matri ...
(
Jordan algebras).
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
*
Pochhammer contour
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