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Original Articles

The British development of the theory of invariants (1841–1895)

Pages 186-199 | Published online: 23 Feb 2007

Bibliography

  • Anonymous . 1859 . ‘The Rev. G. Salmon's Lessons introductory to the modern higher algebra’ . Philosophical Magazine , 18 : 67 – 68 .
  • Boole , George . 1841--1842 . ‘Exposition of a general theory of linear transformations’ . Cambridge Mathematical Journal , 3 1--20 and 106--119
  • Cayley , Arthur . 1845 . ‘On the theory of linear transformations’ . Cambridge Mathematical Journal , 4 : 193 – 209 .
  • Cayley , Arthur . 1846 . ‘On linear transformations’ . Cambridge and Dublin Mathematical Journal , 1 : 104 – 122 .
  • Cayley , Arthur . 1854 . ‘An introductory memoir upon quantics’ . Philosophical Transactions of the Royal Society of London , 144 : 244 – 258 .
  • Cayley , Arthur . 1856 . ‘A second memoir upon quantics’ . Philosophical Transactions of the Royal Society of London , 146 : 101 – 126 .
  • Cayley , Arthur . 1871 . ‘A ninth memoir on quantics’ . Philosophical Transactions of the Royal Society of London , 161 : 17 – 50 .
  • Cayley , Arthur . 1889 . ‘On the finite number of covariants of a binary form’ . Mathematische Annalen , 34 : 319 – 320 .
  • Cayley , Arthur and Forsyth , AR . 1889–1898 . The collected mathematical papers of Arthur Cayley , 14 vols , Cambridge : Cambridge University Press .
  • Crilly , Tony . 1981 . “ ‘The mathematics of Arthur Cayley with particular reference to linear algebra’ ” . In unpublished doctoral dissertation , Middlesex Polytechnic Institute .
  • Crilly , Tony . 1986 . ‘The rise of Cayley's invariant theory (1841--1862)’ . Historia Mathematica , 13 : 241 – 254 .
  • Crilly , Tony . 1988 . ‘The decline of Cayley's invariant theory (1863--1895)’ . Historia Mathematica , 15 : 332 – 347 .
  • Crilly , Tony . 2004 . ‘The Cambridge Mathematical Journal and its descendents: 1830--1870’ . Historia Mathematica , 31 : 255 – 297 .
  • Crilly , Tony . 2005 . Arthur Cayley: mathematician laureate of the Victorian age , Baltimore : The Johns Hopkins University Press .
  • Despeaux , Sloan Evans . 2002 . “ ‘The development of a publication community: nineteenth-century mathematics in British scientific journals’ ” . In unpublished doctoral dissertation , University of Virginia .
  • Elliott , Edwin Bailey . 1895 . An introduction to the algebra of quantics , Oxford : Oxford University Press .
  • Gordan , Paul . 1868 . ‘Beweis, dass jede Covariante und Invariante einer binären Form eine ganze Function mit numerische Coeficienten einer endlichen Anzahl solchen Formen ist’ . Journal für die reine und angewandte Mathematik , 69 : 323 – 354 .
  • Hesse , Otto . 1844 . Üeber die Elimination der Variabeln aus drei algebraischen Gleichungen vom zweiten Grade mit zwei Variabeln’ . Journal für die reine und angewandte Mathematik , 28 : 68 – 96 .
  • Hilbert , David . 1889 . Über die Endlichkeit des Invariantensystems für binäre Grundformen’ . Mathematische Annalen , 34 : 223 – 226 .
  • Hilbert , David . 1890 . ‘Ueber die Theorie des algebraischen Formen’ . Mathematische Annalen , 36 : 473 – 534 .
  • Hilbert , David . 1893 . ‘Ueber die vollen Invariantensysteme’ . Mathematische Annalen , 42 : 313 – 373 .
  • Hilbert , David . 1896 . “ ‘Ueber die Theorie der algebraischen Invarianten’ ” . In Mathematical papers read at the International Mathematical Congress held in connection with the World's Columbian Exposition, Chicago 1893 , Edited by: Eliakim Hastings , Moore , Oskar , Bolza , Heinrich , Maschke and Henry , S. White . 116 – 124 . New York : Macmillan and Co. .
  • Koppelman , Elaine . 1971--1972 . ‘The calculus of operations and the rise of abstract algebra’ . Archive for History of Exact Sciences , 8 : 155 – 242 .
  • Meyer , W Franz . 1897 . Sur les progrés de la théorie des invariants projectifs , Paris : Gauthier-Villers .
  • Parshall , Karen . 1988 . ‘America's first school of mathematical research: James Joseph Sylvester at The Johns Hopkins University’ . Archive for History of Exact Sciences , 38 : 153 – 196 .
  • Parshall , Karen . 1989 . “ ‘Toward a history of nineteenth-century invariant theory’ ” . In The History of Modern Mathematics , Edited by: David , E Rowe and John , McCleary . 2 vols , Boston : Academic Press, Inc. .
  • Parshall , Karen . 1998 . James Joseph Sylvester: life and work in letters , Oxford : Clarendon Press .
  • Parshall , Karen . 1999 . ‘The mathematical legacy of James Joseph Sylvester’ . Nieuw Archief voor Wiskunde , 17 : 247 – 267 .
  • Parshall , Karen Hunger . 2006 . James Joseph Sylvester: Jewish mathematician in a Victorian world , Baltimore : The Johns Hopkins University Press .
  • Parshall , Karen and Rowe , David E . 1994 . The emergence of the American mathematical research community, 1876--1900: , Edited by: Sylvester , JJ , Felix , Klein and Moore , EH . Providence : American Mathematical Society and London: London Mathematical Society .
  • Salmon , George . 1848 . A treatise on conic sections, containing an account of some of the most important modern algebraic and geometric methods , 1st edition , Dublin : Hodges & Smith .
  • Salmon , George . 1859 . Lessons introductory to the modern higher algebra , Dublin : Hodges & Smith .
  • Sylvester , JJ . 1850a . to Arthur Cayley , 3 February 1850, Sylvester Papers , Cambridge : St. John's College . Box 9
  • Sylvester , JJ . 1850b . ‘On the intersections, contacts, and other correlations of two conics expressed by indeterminate coordinates’ . Cambridge and Dublin Mathematical Journal , 5 : 262 – 282 .
  • Sylvester , JJ . 1851a . ‘Sketch of a memoir on elimination, transformation, and canonical forms’ . Cambridge and Dublin Mathematical Journal , 6 : 186 – 200 .
  • Sylvester , JJ . 1851b . ‘On the general theory of associated algebraical forms’ . Cambridge and Dublin Mathematical Journal , 6 : 289 – 293 .
  • Sylvester , JJ . 1851c . ‘On certain general properties of homogeneous functions’ . Cambridge and Dublin , 6 : 1 – 17 .
  • Sylvester , JJ . 1852a . ‘On the principles of the calculus of forms’ . Cambridge and Dublin Mathematical Journal , 7 52--97 and 179--217
  • Sylvester , JJ . 1852b . ‘A demonstration of the theorem that every homogeneous quadratic polynomial is reducible by real orthogonal substitutions to the form of a sum of positive and negative squares’ . Philosophical Magazine , 4 : 138 – 142 .
  • Sylvester , JJ . 1853 . ‘On a theory of the syzygetic relations of two rational integral functions, comprising an application to the theory of Sturm's functions, and that of the greatest algebraical measure’ . Philosophical Transactions of the Royal Society of London , 143 : 407 – 548 .
  • Sylvester , JJ . 1870 . The laws of verse or principles of versification exemplified in metrical translations: together with an annotated reprint of the inaugural presidential address to the Mathematical and Physical Section of the British Association at Exeter , London : Longmans, Green, and Co. .
  • Sylvester , JJ . 1879 . (assisted by Fabian Franklin), ‘Tables of the generating functions and groundforms for the binary quantics of the first ten orders’ . American Journal of Mathematics , 2 : 223 – 251 .
  • Sylvester , JJ . 1904–1912 . The collected mathematical papers of James Joseph Sylvester , Edited by: Baker , HF . 4 vols , Cambridge : Cambridge University Press .

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