Search Results for Jordan

Biographies

  1. Jordan biography
    • Marie Ennemond Camille Jordan .
    • Camille Jordan's father, Esprit-Alexandre Jordan (1800-1888), was an engineer who had been educated at the Ecole Polytechnique.
    • Camille's father's family were also quite well known; a grand-uncle also called Ennemond-Camille Jordan (1771-1821) achieved a high political position while a cousin Alexis Jordan (1814-1897) was a famous botanist.
    • Jordan studied at the Lycee de Lyon and at the College d'Oullins.
    • This establishment provided training to be an engineer and Jordan, like many other French mathematicians of his time, qualified as an engineer and took up that profession.
    • Cauchy in particular had been one to take this route and, like Cauchy, Jordan was able to work as an engineer and still devote considerable time to mathematical research.
    • Jordan's doctoral thesis was in two parts with the first part Sur le nombre des valeurs des foncyions being on algebra.
    • Jordan was examined on 14 January 1861 by Duhamel, Serret and Puiseux.
    • In fact the topic of the second part of Jordan's thesis had been proposed by Puiseux and it was this second part which the examiners preferred.
    • Jordan married Marie-Isabelle Munet, the daughter of the deputy mayor of Lyon, in 1862.
    • Jordan was a mathematician who worked in a wide variety of different areas essentially contributing to every mathematical topic which was studied at that time.
    • The references [Oeuvres de Camille Jordan I (Paris 1961).',3)">3], [Oeuvres de Camille Jordan II (Paris 1961).',4)">4], [Oeuvres de Camille Jordan III (Paris 1962).',5)">5], [Oeuvres de Camille Jordan IV (Paris 1964).',6)">6] are to the four volumes of his complete works and the range of topics is seen from the contents of these.
    • Volumes 1 and 2 contain Jordan's papers on finite groups, Volume 3 contains his papers on linear and multilinear algebra and on the theory of numbers, while Volume 4 contains papers on the topology of polyhedra, differential equations, and mechanics.
    • Jordan introduced the notion of homotopy of paths looking at the deformation of paths one into the other.
    • Jordan was particularly interested in the theory of finite groups.
    • In fact this is not really an accurate statement, for it would be reasonable to argue that before Jordan began his research in this area there was no theory of finite groups.
    • It was Jordan who was the first to develop a systematic approach to the topic.
    • Serret, Bertrand and Hermite had attended Liouville's lectures on Galois theory and had begun to contribute to the topic but it was Jordan who was the first to formulate the direction the subject would take.
    • To Jordan a group was what we would call today a permutation group; the concept of an abstract group would only be studied later.
    • Indeed Jordan introduced the concept of a composition series (a series of subgroups each normal in the preceding with the property that no further terms could be added to the series so that it retains that property).
    • Jordan proved the Jordan-Holder theorem, namely that although groups can have different composition series, the set of composition factors is an invariant of the group.
    • Jordan, however, clearly saw this as an aim of the subject, even if it was not one which might ever be solved.
    • The treatise contains the 'Jordan normal form' theorem for matrices, not over the complex numbers but over a finite field.
    • It would also be fair to say that group theory was one of the major areas of mathematical research for 100 years following Jordan's fundamental publication.
    • Jordan's use of the group concept in geometry in 1869 was motivated by studies of crystal structure.
    • Jordan's interest in groups of Euclidean transformations in three dimensional space influenced Lie and Klein in their own theories of continuous and discontinuous groups.
    • The publication of Traite des substitutions et des equations algebraique did not mark the end of Jordan's contribution to group theory.
    • Generalising a result of Fuchs on linear differential equations, Jordan was led to study the finite subgroups of the general linear group of n × n matrices over the complex numbers.
    • Although there are infinite families of such finite subgroups, Jordan found that they were of a very specific group theoretic structure which he was able to describe.
    • Another generalisation, this time of work by Hermite on quadratic forms with integral coefficients, led Jordan to consider the special linear group of n × n matrices of determinant 1 over the complex numbers acting on the vector space of complex polynomials in n indeterminates of degree m.
    • Jordan is best remembered today among analysts and topologists for his proof that a simply closed curve divides a plane into exactly two regions, now called the Jordan curve theorem.
    • The second edition appeared in 1893 while the Jordan curve theorem appeared in the third edition of the text which appeared between 1909 and 1915.
    • Of course by 1882, when the first volume was published, Jordan was lecturing at the Ecole Polytechnique and the book was written as a text for the students there.
    • Jordan was aware that his work was at a level that would be somewhat inappropriate for engineering students for he once said to Lebesgue that he called it "Ecole Polytechnique analysis course" since:- .
    • Gispert-Chambaz in [Camille Jordan et les fondements de l\'analyse : Comparaison de la 1ere edition (1882-1887) et de la 2eme (1893) de son cours d\'analyse de l\'ecole Polytechnique (Orsay, 1982).',7)">7] contrasts the way that topological concepts are treated by Jordan in the first and second editions of the book.
    • However between the editions Jordan had taught more advanced courses on analysis at the College de France and this may have influenced him to put set topology right up front in the second edition.
    • Among Jordan's many contributions to analysis we should also mention his generalisation of the criteria for the convergence of a Fourier series.
    • Liouville died in 1882 and in 1885 Jordan became editor of the Journal, a role he kept for over 35 years until his death.
    • In 1912 Jordan retired from his positions.
    • Among the honours given to Jordan was his election to the Academie des Sciences on 4 April 1881.
    • Although given Jordan's work on matrices and the fact that the Jordan normal form is named after him, the Gauss-Jordan pivoting elimination method for solving the matrix equation Ax= b is not.
    • The Jordan of Gauss-Jordan is Wilhelm Jordan (1842 to 1899) who applied the method to finding squared errors to work on surveying.
    • Jordan algebras are called after the German physicist and mathematician Pascual Jordan (1902 to 1980).
    • Honours awarded to Camille Jordan .
    • http://www-history.mcs.st-andrews.ac.uk/Biographies/Jordan.html .

  2. Jacobson biography
    • Florie did not give up mathematics for she was a joint author with her husband on their 1949 paper Classification and representation of semi-simple Jordan algebras.
    • I also wrote my first paper on Jordan rings during this period.
    • I [EFR] attended Jacobson's course that he gave on Quadratic Jordan algebras at the Colloquium and learnt much, not only about Jordan algebras, but also on how to lecture combining both excitement and clarity.
    • He also made very substantial contributions to nonassociative algebras, in particular Lie algebras and Jordan algebras.
    • On Jordan algebras he wrote Structure and representations of Jordan algebras (1968) and another major work on algebra was PI-algebras : an introduction (1975).

  3. Springer biography
    • The first was Jordan algebras and algebraic groups (1973).
    • In his review of the book Jordan-Algebren by H Braun and M Koecher (1966), the present author took those authors to task for not sufficiently emphasizing the structure group as a linear algebraic group.
    • For the associatively-inclined this book expunges the dread word "nonassociative" from Jordan theory, since there is nothing nonassociative about inversion; most importantly, it makes Jordan structure theory accessible to the growing audience of persons familiar with root systems.
    • By placing the classification of Jordan algebras in the perspective of classification of certain root systems, the book demonstrates that the structure theories of associative, Lie, and Jordan algebras are not separate creations, but rather instances of the one all-encompassing miracle of root systems.
    • The fourth of Springer's books, Octonions, Jordan algebras and exceptional groups (2000), was also based on lectures given by Springer, but these were given in 1963 in German at the University of Gottingen.

  4. Zelmanov biography
    • In particular his work completely changed the whole of the subject of Jordan algebras by extending results from the classical theory of finite dimensional Jordan algebras to infinite dimensional Jordan algebras.
    • Zelmanov described this work on Jordan algebras in his invited lecture to the International Congress of Mathematicians at Warsaw in 1983.
    • The results mentioned above on Jordan algebras and Lie algebras would have guaranteed Zelmanov a place as one of the great algebraists of the 20th century.
    • The proof uses a deep structure theory for (quadratic) Jordan algebras, previously developed by McCrimmon and Zelmanov, as well as divided powers and other tools; it also relies on the joint work of Kostrikin and Zelmanov, which establishes the local nilpotency of the so-called sandwich algebras.
    • While Lie algebras have long been considered a natural playground in the context of the Restricted Burnside problem, the appearance of Jordan algebras is unprecedented and quite surprising.

  5. Nicomachus biography
    • Born: about 60 in Gerasa, Roman Syria (now Jarash, Jordan) .

  6. Klein Oskar biography
    • In 1927, Klein was appointed Lektor in Copenhagen but nonetheless continued his research working with Pascual Jordan on the second quantization in quantum mechanics.
    • In his work with Jordan, he demonstrated the close connection between quantum fields and quantum statistics.
    • He and Jordan showed that one can quantize the non-relativistic Schrodinger equation and, in honour of this work, he was the recipient of yet another named mathematical tool, the Jordan-Klein matrices.

  7. Albert Abraham biography
    • Lectures by Weyl on Lie algebras were particularly stimulating but perhaps even more important was his introduction to Jordan algebras.
    • These algebras had been introduced by Pascual Jordan as being related to quantum theory.
    • Jordan had worked with von Neumann and Wigner on the structure of these algebras but they had left open certain fundamental questions.
    • His work on Jordan algebras did not end there for he published three further fundamental papers on their structure in 1946, 1947 and 1950.

  8. Lie biography
    • There they met Darboux, Chasles and Camille Jordan.
    • Jordan seems to have succeeded in a way that Sylow did not, for Jordan made Lie realise how important group theory was for the study of geometry.

  9. Dieudonne biography
    • In addition to the historical texts, Dieudonne edited the works of Camille Jordan.
    • In the first volume Dieudonne has contributed an article on Jordan's work on finite groups and in the second volume an interesting 116-page introduction to Jordan's work on linear and multilinear algebra and on the theory of numbers.

  10. Dickson biography
    • Dickson then spent some time with Lie at Leipzig and later with Jordan in Paris.
    • The book here announced proposes to treat of linear congruence groups, or more generally, of linear groups in a Galois field, a subject enriched by the labors of Galois, Betti, Mathieu [Emile Mathieu], Jordan and many recent writers.
    • Dickson presented a unified, complete, and general theory of the classical linear groups - not merely over the prime field GF(p) as Jordan had done - but over the general finite field GF(pn), and he did this against the backdrop of a well-developed theory of these underlying fields.

  11. Wilder biography
    • The best known example of such a positional invariant is embodied in the Jordan curve theorem: A simple closed curve in the 2-sphere has precisely two complementary domains and is the boundary of each of them.
    • A converse to the Jordan curve theorem, proved by Schonflies, states that a subset of the 2-sphere is a simple closed curve if it has two complementary domains, is the boundary of each of them, and is accessible from each of these domains.
    • He continued to undertake research with this aim and in 1930, in A converse of the Jordan-Brouwer separation theorem in three dimensions, Wilder showed that a subset of Euclidean 3-space whose complementary domains satisfied certain homology conditions was a 2-sphere.

  12. Vallee Poussin biography
    • It was [Jordan's Cours d'Analyse] which, as is recorded by Hardy and other mathematicians of his generation, opened their eyes to what analysis really was.
    • If Jordan's is the most noble of the Cours d'Analyse and perhaps Goursat's (helped by its translation by Hedrick) the most widely read, it can hardly be doubted that Vallee Poussin's is the most elegant and lucid.
    • Most of the additional material appeared in small type and covered topics such as set theory, in particular the Schroder-Bernstein theorem, the Lebesgue integral, functions of bounded variation, the Jordan curve theorem, polynomial approximation, Parseval's theorem on trigonometric series, results of Fejer, etc.

  13. Douglas biography
    • He published One-sided minimal surfaces with a given boundary (1932) and A Jordan space curve no arc of which can form part of a contour which bounds a finite area (1934).
    • In the first of these Douglas looked at the following form of the problem: Given an aggregate G of k non-intersecting Jordan curves in n-space, to find a minimal surface bounded by G and having a prescribed genus h and a prescribed orientability character (one-sided or two-sided).

  14. Humbert Georges biography
    • He became Jordan's assistant at the College de France in 1904 succeeding to Jordan's chair in 1912.

  15. Alexander biography
    • Soon after arriving in Princeton, Alexander generalised the Jordan curve theorem and continued his work, now exclusively on topology, with an important paper on the Jordan-Brouwer separation theorem.

  16. Goldie Alfred biography
    • This led Goldie to the results in universal algebra which he published in The Jordan-Holder theorem for general abstract algebras (1950) and The scope of the Jordan-Holder theorem in abstract algebra (1952).

  17. Heisenberg biography
    • It was Max Born and Pascual Jordan in Gottingen who recognised this non-commutative algebra to be a matrix algebra.
    • Matrix mechanics was further developed in a three author paper by Heisenberg, Born and Jordan published in 1926.

  18. Lebesgue biography
    • Building on the work of others, including that of Emile Borel and Camille Jordan, Lebesgue formulated the theory of measure in 1901 and in his famous paper Sur une generalisation de l'integrale definie, which appeared in the Comptes Rendus on 29 April 1901, he gave the definition of the Lebesgue integral that generalises the notion of the Riemann integral by extending the concept of the area below a curve to include many discontinuous functions.
    • In 1905 Lebesgue gave a deep discussion of the various conditions Lipschitz and Jordan had used in order to ensure that a function f (x) is the sum of its Fourier series.

  19. Frattini biography
    • The route that Frattini had taken to undertake research in group theory had been to study Camille Jordan's papers on the topic.

  20. Miller biography
    • Miller spent the years from 1895 to 1897 in Europe attending lectures on group theory by Lie in Leipzig and Jordan in Paris.

  21. Waring biography
    • This is, in essence, the first result in the theory of symmetric functions (beyond the basic building blocks which appeared in Chapter 1), a theory whose systematic development was not to appear until the 19th century (Lagrange, Gauss, and others) and was ultimately followed by the theory of permutation groups (Galois, Jordan, ..

  22. Wall biography
    • The book builds up to a proof of the Alexander duality theorem in the plane; a result which generalises the Jordan curve theorem.

  23. Schreier biography
    • Schreier (1928) found an important refinement of the fundamental Jordan-Holder theorem, 39 years after the publication of Holder's paper.

  24. Osgood biography
    • Some papers over the next few years included: Sufficient conditions in the calculus of variations (1900), On a fundamental property of a minimum in the calculus of variations and the proof of a theorem of Weierstrass's (1901), A Jordan curve of positive area (1903), On Cantor's theorem concerning the coefficients of a convergent trigonometric series, with generalizations (1909), On the gyroscope (1922), and On normal forms of differential equations (1925).

  25. Brouwer biography
    • He also introduced the idea of the degree of a mapping, generalised the Jordan curve theorem to n-dimensional space, and defined topological spaces in 1913.

  26. Hahn biography
    • He wrote papers on the theory of curves including one which gave a rigorous proof of the Jordan's theorem for simple closed polygons which he based on Veblen's geometrical axioms.

  27. Dyson biography
    • Not only did he have one of the finest mathematics teachers in the country, namely C V Durell, but he was in the same class as James Lighthill and the two studied advanced mathematics together such as Jordan's Cours d'Analyse.

  28. Fox Leslie biography
    • It contains chapters on: Matrix algebra; Elimination methods of Gauss, Jordan, and Aitken; Compact elimination methods of Doolittle, Crout, Banachiewicz and Cholesky; Orthogonalization methods; Condition, accuracy and precision; Comparison of methods, measure of work; Iterative and gradient methods; Iterative methods for latent roots and vectors; and Notes on error analysis for latent roots and vectors.

  29. Hadamard biography
    • Then in 1912 he was appointed as professor of analysis at the Ecole Polytechnique where he succeed Jordan.

  30. Schmidt biography
    • He found a new proof of the Jordan curve theorem which quickly became a classic.

  31. Tietze biography
    • Among the topics in topology which Tietze worked on were knot theory, Jordan curves and continuous mappings of areas.

  32. Arf biography
    • [Jordan] found all the groups that could be solved.

  33. Cohn biography
    • From 1958 he published papers on Jordan algebras, Lie division rings, skew fields, free ideal rings and non-commutative unique factorisation domains.

  34. Kerekjarto biography
    • The material in the book may be essentially classified into three groups: (a) Topology of the plane and its curves, centering around the Jordan curve theorems and including such questions as invariance of dimensionality and regionality, structure of regions and their boundaries, the general closed curve, etc.

  35. Betti biography
    • Although Jordan, in his Traite des substitutions et des equations algebriques (1870) credits Betti with having filled the gaps in Galois' arguments and with having been the first to establish the sequence of Galois' theorems rigorously, the fact is that Betti's work contains substantial obscurities and errors.

  36. Stormer biography
    • He spent two academic years, from 1898 to 1900, at the Sorbonne studying with Emile Picard, Henri Poincare, Paul Painleve, Camille Jordan, Gaston Darboux, and Edouard Goursat.

  37. Burnside biography
    • Special cases of this result had been proved by Sylow (the case n = 0 in 1872), Frobenius (the case n = 1 in 1895) and Jordan (the case n = 2 in 1898).

  38. Stoilow biography
    • After a fairly standard introduction to the general theory, beginning with power series, he goes on, in volume 1, to look at topics such as entire and meromorphic functions, doubly periodic functions, conformal mapping on the boundary of a Jordan region, multiple-valued functions, and applications of modular functions to the Picard circle of ideas.

  39. Holder biography
    • Holder proved the uniqueness of the factor groups in a composition series, the theorem now called the Jordan-Holder theorem.

  40. Kirkman biography
    • Three memoirs were submitted, the other two by Emile Mathieu and Jordan.

  41. Thompson John biography
    • Early contributions were made by Galois, Jordan and Emile Mathieu.

  42. Ledermann biography
    • The little book (152 pages) discusses the group axioms, isomorphisms, cyclic groups, coset decompositions, Lagrange's theorem, permutation groups, normal subgroups, quotient groups, homomorphisms, the first and second isomorphism theorems, and the Jordan-Holder theorem.

  43. Albertus biography
    • After studying liberal arts at the University of Padua he joined the Dominican Order at Padua in 1223 being attracted by the teachings of Jordan of Saxony who was the head of the Order.

  44. Borel biography
    • Later Borel spoke about the mathematicians who had influenced him most in his early years mentioning, among others, Camille Jordan, Emile Picard, Paul Appell, Edouard Goursat, Paul Painleve and Marcel Brillouin.

  45. Lindemann biography
    • In England he made visits to Oxford, Cambridge and London, while in France he spent time at Paris where he was influenced by Chasles, Bertrand, Jordan and Hermite.

  46. Tits biography
    • Jordan, in his famous Traite des substitutions et des equations algebriques, published in 1870, promoted Galois' work and put the theory of groups on a firm foundation.

  47. Herstein biography
    • The book largely concerns Herstein's work on Lie and Jordan structure of simple associative rings which he published in various papers in the early 1950s.

  48. Hardy biography
    • But the great debt which I owe to him was his advice to read Jordan's "Cours d'analyse"; and I shall never forget the astonishment with which I read that remarkable work, the first inspiration for so many mathematicians of my generation, and learnt for the first time as I read it what mathematics really meant.

  49. Zassenhaus biography
    • During this time he proved Zassenhaus's lemma, a beautiful result on subgroups which can be used to give a simple proof of the Jordan-Holder theorem.

  50. Janiszewski biography
    • He gave a topological characterisation of the plane which simplified considerably the Jordan curve theorem.

  51. Flato biography
    • He led a small group of soldiers into Jordan in 1955 but they were ambushed and seven of the ten were killed.

  52. Frechet biography
    • The topics discussed are: the Jordan curve theorem, the map colouring problem, the Euler characteristic and the classification of surfaces.

  53. Hirsch biography
    • However he kept up his mathematics attending a study group where he studied Emmy Noether's work and read Schreier's paper on the Jordan-Holder theorem.

  54. Cholesky biography
    • His professors at l'Ecole Polytechnique included Camille Jordan, and Henri Becquerel the famous physicist who discovered radioactivity.

  55. Fatou biography
    • Although not giving a complete solution, Fatou's work also made a major contribution to finding a solution to the related question of whether conformal mapping of Jordan regions onto the open disc can be extended continuously to the boundary.

  56. Couturat biography
    • He continued to study mathematics at the Ecole Normale Superieure, being taught by Jules Tannery in academic year 1890-91, then studying with Emile Picard and Camille Jordan during 1891-92.

  57. Shoda biography
    • develops generalized theories of normal chains, composition series, of direct and subdirect products, and generalizations of the Jordan-Holder and the Remak-Schmidt-Ore theorems.

  58. Blumenthal biography
    • After this he went to Paris where he spent the winter of 1899-1900 studying under Borel and Jordan.

  59. Fuchs biography
    • (N.S.) 10 (1) (1984), 1-26.',3)">3] where Gray also describes how this work influenced Klein, Jordan, Poincare and others.

  60. Kaluznin biography
    • Despite the fact that the earliest applications of wreath products of permutation groups was due to C Jordan, W Specht and G Polya, it was Kaluznin who first developed special computational tools for this purpose.

  61. Caratheodory biography
    • During periods when construction work had to stop due to floods, he studied mathematics from some textbooks he had with him, such as Jordan's Cours d'Analyse and Salmon's text on the analytic geometry of conic sections.

  62. Klein biography
    • It is fair to add that Camille Jordan also played a part in teaching Klein about groups.

History Topics

  1. Matrices and determinants
    • In 1870 the Jordan canonical form appeared in Treatise on substitutions and algebraic equations by Jordan.

  2. Abstract groups
    • However, from 1863 when Jordan wrote a commentary on Galois' work in which he used "group", it became the standard term.
    • This was reinforced when Jordan published his major group theory text Traite des substitutions et des equations algebraique in 1870.

  3. Topology history

  4. Group theory

  5. Wave versus matrix
    • These amplitudes formed a non-commutative algebra and only later did Max Born and Pascual Jordan recognise this non-commutative algebra to be a matrix algebra.

  6. Modern light
    • Two mathematical models of quantum mechanics were presented, that of matrix mechanics, proposed by Werner Heisenberg, Max Born, and Pascual Jordan, and that of wave mechanics proposed by Erwin Schrodinger.

  7. Weil family
    • When Andre was awarded a school prize he asked Hadamard to help him choose some mathematics books and as a result he became the proud owner of Jordan's Cours d'Analyse and Thomson and Tait's Treatise of Natural Philosophy.

Famous Curves

  1. Straight
    • In fact nobody attempted a general definition of a curve until Jordan in his Cours d'Analysein 1893.

Societies etc

  1. St Andrews Colloquium 2003
    • BACK ROW: Colin Campbell, Almut Veraart, Manuel Stadlbaeur, Brian Winn, Jonathan Jordan, Tommy Charles, Bjorn Bottcher, Guler Ergun, Andrew Wade, Thomas Jordan, John Harris, Paul Hjorth, Matthieu Rickly, Owen Jones, Alexander Cox, Steven Johnstone, Tony Mullholland, Steffen Winter, Yu Koyama, Zoltan Balogh, Hiso Kimura, Tamas Matrai, Ivan Werner .

  2. EMS 1976
    • SECOND ROW, Dr M J Crabb, Dr I Anderson, Dr D Jordan, Dr C R Jordan, Prof C W Kilmister, Miss S J Kilmister, Mr A C Kilmister, Dr T S Blyth, Dr J J O'Connor, Dr R M F Moss, Dr A Wulfsohn, Dr J S N Elvey, Mrs D Singmaster, Prof R W Carter, Dr A C Thompson, Mr D Deriziotis, Dr T J Laffey, Ms N B Tinberg, Prof F D Parker, Mr B Mortimer, Mr N H Grieg-Smith, Dr J Van Casteren, Miss E M Elton, Mrs M Van Casteren, Dr E Scourfield, Dr J B Wilker, Miss K Wilker, .

  3. EMS 1964
    • SECOND ROW, A J Crilly, C E Rogers, M Baines, J Sanders, J D King, T A Peng, B W Bugden, B T Hassen, M S Morsy, T A Antone, 1 M H Etherington, W D Munn, D M Jordan, J M Jackson, D C Pack, N Wilson, W L Wilson, Mrs Sprague, L M Brown, J A Lloyd, A C Baker .

  4. BMC 1982
    • Neumann, P MSimple groups from Galois to Jordan .

  5. BMC 1994
    • Jordan, D Skew polynomial rings from Hilbert to quantum groups .

  6. BMC speakers
    • Jordan, D : 1994 .

  7. BMC 1972
    • Springer, T A Jordan algebras and algebraic groups .

  8. BMC Morning speakers
    • Jordan, D : 1994 .

  9. BMC 2008
    • Thalmeier, ABrownian motion of Jordan curves and stochastic calculus on the diffeomorphism group of the circle .

  10. BMC 1997
    • Macpherson, H D Infinite Jordan permutation groups .

  11. BMC 1964

  12. Paris Academy of Sciences
    • The 1860 prize on group theory was not awarded despite submissions from Kirkman, Emile Mathieu and Jordan.

  13. LMS Honorary Member
    • 1907 C Jordan .

  14. French Mathematical Society
    • 1880 C Jordan .

  15. Fellow of the Royal Society
    • Camille Jordan 1919 .

References

  1. References for Jordan
    • References for Camille Jordan .
    • J Dieudonne (ed.), Oeuvres de Camille Jordan I (Paris 1961).
    • J Dieudonne (ed.), Oeuvres de Camille Jordan II (Paris 1961).
    • J Dieudonne (ed.), Oeuvres de Camille Jordan III (Paris 1962).
    • J Dieudonne (ed.), Oeuvres de Camille Jordan IV (Paris 1964).
    • H Gispert-Chambaz, Camille Jordan et les fondements de l'analyse : Comparaison de la 1ere edition (1882-1887) et de la 2eme (1893) de son cours d'analyse de l'ecole Polytechnique (Orsay, 1982).
    • C Billoux, La 'correspondance mathematique' de Camille Jordan dans les archives de l'ecole Polytechnique, Historia Math.
    • Camille Jordan, Proc.
    • Y Hirano, Note sur la seconde these de Camille Jordan, Rev.
    • D M Johnson, The correspondence of Camille Jordan, Historia Math.
    • H Lebesgue, Camille Jordan, Memoires de l'Academie des sciences de l'Institut de France 58 (1923), 29-66.
    • http://www-history.mcs.st-andrews.ac.uk/References/Jordan.html .

  2. References for Pauli
    • E L Schucking, Jordan, Pauli, politics, Brecht ..

  3. References for Darboux
    • H Gispert, Sur les fondements de l'analyse en France (a partir de lettres inedites de G Darboux et de l'etude des differentes editions du Cours d'analyse de C Jordan), Archive for History of Exact Science 28 (1) (1983), 37-106.

  4. References for Dehn
    • H Guggenheimer, The Jordan curve theorem and an unpublished manuscript by Max Dehn, Archive for History of Exact Science 17 (2) (1977), 193-200.

Additional material

  1. W Burnside: 'Theory of Groups of Finite Order
    • This was followed in 1870 by M Jordan's "Traite des substitutions et des equations algebriques." The greater part of M Jordan's treatise is devoted to a development of the ideas of Galois and to their application to the theory of equations.
    • In 1882 appeared Herr Netto's "Substitutionentheorie und ihre Anwendungen auf die Algebra," in which, as in M Serret's and M Jordan's works, the subject is treated entirely from the point of view of groups of substitutions.
    • In addition to the works by Serret, Jordan, Netto and Weber [Heinrich Weber] already referred to, I have while writing this book consulted many original memoirs.

  2. Born Inaugural
    • But when it became known, theoretical physics was already prepared to treat it by proper mathematical methods, the so-called quantum mechanics, initiated by Heisenberg, worked out in collaboration with Jordan and myself, and quite independently by Dirac; and another form of the same theory, the wave-mechanics, worked out by Schrodinger in close connection with de Broglie's suggestion.
    • Their standpoint (Jordan, 1936) is even more radical than that of Dirac mentioned above.
    • Jordan, P., 1936.

  3. H F Baker: 'A locus with 25920 linear self-transformations' Introduction
    • In his monumental volume on the theory of substitutions (Traite des substitutions, Paris, 1870), Jordan considers the group of the lines of a cubic surface in ordinary space, which he regards primarily as the group of the substitutions of the tritangent planes of the surface.
    • One remark should perhaps be added here to make the general statements of this introduction more precise: The group of the lines of a cubic surface is of order 24× 34× 40; this group has a subgroup of order 1/2 (24× 34× 40) or 23× 34× 40, which, as Jordan proved, is simple [it is PSp(4,3), the projective symplectic group of 4 × 4 matrices over the field of 3 elements].
    • This subgroup, regarded, as by Jordan, as a group of substitutions of the tritangent planes, contains only even substitutions of these.

  4. H F Baker's locus with 25920 linear self-transformations - Introduction
    • In his monumental volume on the theory of substitutions (Traite des substitutions, Paris, 1870), Jordan considers the group of the lines of a cubic surface in ordinary space, which he regards primarily as the group of the substitutions of the tritangent planes of the surface.
    • One remark should perhaps be added here to make the general statements of this introduction more precise: The group of the lines of a cubic surface is of order 24 cross 34 cross 40; this group has a subgroup of order 1/2 (24 cross 34 cross 40) or 23 cross 34 cross 40, which, as Jordan proved, is simple [it is PSp(4,3), the projective symplectic group of 4 cross 4 matrices over the field of 3 elements].
    • This subgroup, regarded, as by Jordan, as a group of substitutions of the tritangent planes, contains only even substitutions of these.

  5. Oskar Bolza: 'Calculus of Variations
    • In order, however, to make the book accessible to a larger circle of readers, I have systematically given references to the following standard works: Encyclopaedie der mathematischen Wissenschaften, especially the articles on "Allgemeine Functionslehre" (Pringsheim) and "Differential- und Integralrechnung" (Voss); Jordan, Cours d'Analyse, second edition); Genocchi-Peano, Differentialrechnung und Grundzuge der Integralrechnung, translated by Bohlmann and Schepp; occasionally also to Dini, Theorie der Functionen einer veraaderlichen reelen Grosse, translated by Lutroth and Schepp; Stolz, Grundzuge der Differential- und Integralrechnung.
    • In concluding, I wish to express my thanks to Professor G A Bliss for valuable suggestions and criticisms, and to Dr H E Jordan for his assistance in the revision of the proof-sheets.

  6. H Weyl: 'Theory of groups and quantum mechanics'Preface to Second Edition
    • I may mention in this connection the derivation of the Clebsch-Gordan series, which is of fundamental importance for the whole of spectroscopy and for the applications of quantum theory to chemistry, the section on the Jordan-Holder theorem and its analogues, and above all the careful investigation of the connection between the algebra of symmetric transformations and the symmetric permutation group.

  7. Max Born's matrices
    • In 1925 Heisenberg put forward a decisive idea; this was seized on by Jordan and myself, who worked out the appropriate mathematics, the so-called matrix mechanics.

  8. Herstein: Preface to 'Topics in algebra
    • The subject matter chosen for discussion has been picked not only because it has become standard to present it at this level or because it is important in the whole general development but also with an eye to this "concreteness." For this reason I chose to omit the Jordan-Holder theorem, which certainly could have easily been included in the results derived about groups.

  9. Rédei: Algebra
    • The concept of an algebraic structure (a set equipped with some operations, usually binary), semigroups, rings, skew fields, homomorphism, quotient with respect to an equivalence relation, the Jordan-Holder-Schreier theorem.

  10. Born's matrices.html
    • In 1925 Heisenberg put forward a decisive idea; this was seized on by Jordan and myself, who worked out the appropriate mathematics, the so-called matrix mechanics.

  11. Malcev: 'Foundations of Linear Algebra' Introduction
    • Results which appeared near the end of the 19th century included the normal form of a matrix of a linear transformation (Jordan), elementary divisors (Weierstrass), pairs of quadratic forms (Weierstrass, Kronecker), and Hermitian forms (Hermite).

  12. Kurosh's book The theory of groups 1st edition
    • Arising from the needs of Galois theory, it developed at first as the theory of finite substitution groups (Cauchy, Jordan, Sylow).

  13. EMS obituary
    • This group, of order 25920, had been found 20 years before by Camille Jordan; but Burkhardt constructed 5 theta-functions that were linearly transformed by it and so was able to display it as a group G of linear substitutions on 5 variables.

  14. Andrew Russell Forsyth by Leonard Roth
    • Hardy has recorded that he himself first saw the light when he read the volumes of Jordan's Cours d'Analyse; and many other young men of his generation must have done likewise.

  15. Kuratowski: 'Introduction to Topology
    • Here is given a detailed proof of the Jordan theorem which is a classical theorem of analysis.

  16. Todd: 'Basic Numerical Mathematics
    • We use repeatedly the existence of an orthogonal matrix which diagonalizes a real symmetric matrix; we make considerable use of partitioned or block matrices, but we need the Jordan normal form only incidentally.

  17. Kurosh: 'The theory of groups' 1st edition
    • Arising from the needs of Galois theory, it developed at first as the theory of finite substitution groups (Cauchy, Jordan, Sylow).

  18. Felix Klein on intuition
    • [If a work like] Cours d'analyse of Camille Jordan is placed in the hands of a beginner a large part of the subject will remain unintelligible, and at a later stage, the student will not have gained the power of making use of the principles in the simple cases occurring in the applied sciences ..

  19. Wave versus matrix mechanics
    • These amplitudes formed a non-commutative algebra and only later did Max Born and Pascual Jordan recognise this non-commutative algebra to be a matrix algebra.

Quotations

  1. A quotation by Jordan
    • A quotation by Camille Jordan .
    • http://www-history.mcs.st-andrews.ac.uk/Quotations/Jordan.html .

Chronology

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