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 (Franco-Provençal: ''Liyon'') is a city in France. It is located at the confluence of the rivers Rhône and Saône, to the northwest of the French Alps, southeast of Paris, north of Marseille, southwest of Geneva, Switzerland, north ...
and educated at the
École polytechnique
(, ; also known as Polytechnique or l'X ) is a ''grande école'' located in Palaiseau, France. It specializes in science and engineering and is a founding member of the Polytechnic Institute of Paris.
The school was founded in 1794 by mat ...
. He was an engineer by profession; later in life he taught at the École polytechnique and the
Collège de 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, 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 functions of complex numbers. It is helpful in many branches of mathematics, including algebraic ...
* 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 matrix (mathemat ...
* 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 ( ...
,
Jordan measure
Jordan, officially the Hashemite Kingdom of Jordan, is a country in the Southern Levant region of West Asia. Jordan is bordered by Syria to the north, Iraq to the east, Saudi Arabia to the south, and Israel and the occupied Palestinian t ...
(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 magnitude (mathematics), magnitude, mass, and probability of events. These seemingl ...
* 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, Galois theory, originally introduced by Évariste Galois, provides a connection between field (mathematics), field theory and group theory. This connection, the fundamental theorem of Galois theory, allows reducing certain problems ...
into the mainstream. He also investigated the
Mathieu groups, the first examples of
sporadic groups. His ''Traité des substitutions'', on
permutation groups, 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 ( , ; ; ) is the Prefectures in France, prefecture and largest city of the Grand Est Regions of France, region of Geography of France, eastern France, in the historic region of Alsace. It is the prefecture of the Bas-Rhin Departmen ...
.
The
asteroid
An asteroid is a minor planet—an object larger than a meteoroid that is neither a planet nor an identified comet—that orbits within the Solar System#Inner Solar System, inner Solar System or is co-orbital with Jupiter (Trojan asteroids). As ...
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, 1882)
Cours d'analyse de l'Ecole Polytechnique; 2 Calcul intégral (Gauthier-Villars, 1883)
Cours d'analyse de l'Ecole Polytechnique; 3 Équations différentielles (Gauthier-Villars, 1887)
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 Paris - PSL alumni
Corps des mines
Scientists from Lyon
19th-century French mathematicians
Group theorists
Linear algebraists
Academic staff of the Collège de France
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