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Algebraic Formalism within the Works of Servois and Its Influence on the Development of Linear Operator Theory - References

Author(s): 
Anthony J. Del Latto (Adelphi University) and Salvatore J. Petrilli, Jr. (Adelphi University)

[Aebischer and Languereau 2010] Aebischer, A. and Languereau, H. (2010). Servois ou la géométrie á l'école de l'artillerie. Besançon Cedex: Presses universitaires de Franche-Comté.

[Allaire and Bradley 2002] Allaire, P. and Bradley, R. (2002). “Symbolic Algebra as a Foundation for Calculus: D.F. Gregory's Contribution,” Historia Mathematica 29, 395-426.

[Boole 1860] Boole, G. (1860). A Treatise on the Calculus of Finite Differences. London: Cambridge: Macmillian and Co.

[Boyer 1895] Boyer, J. (1895). “Le mathematicien franc-comtois François-Joseph Servois,” Mémoires de la Société d'émulation de Doubs 9, 305-313.

[Boyer 1989] Boyer, C. B. (1989). A History of Mathematics. New York: John Wiley and Sons.

[Bradley 2002] Bradley, R. E. (2002). “The Origins of Linear Operator Theory in the Work of François-Joseph Servois,” Proceedings of Canadian Society for History and Philosophy of Mathematics 14, 1 - 21.

[Bradley and Petrilli 2010] Bradley, R. E. and Petrilli, S. J. (2010). “Servois' 1814 Essay on the Principles of the Differential Calculus, with an English Translation,” Loci: Convergence 7. DOI: 10.4169/loci003487 http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=3597

[Cardano 1545] Cardano, G. (1545). Ars Magna. English translation by R. Witmer (1968): The Rules of Algebra. New York: Dover.

[Cauchy 1821] Cauchy, A.-L. (1821). Cours d'analyse. Paris: de Bure. English translation by R. E. Bradley and C. E. Sandifer (2009): Cauchy's Cours d'analyse: An Annotated Translation. New York: Springer.

[Crilly 2006] Crilly, Tony. (2006). Authur Cayley: Mathematician laureate of the Victorian age. New York: Johns Hopkins Press.

[De Morgan 1849] De Morgan, A. (1849). Trigonometry and Double Algebra. London: Cambridge.

[Dunham 1990] Dunham, W. (1990). Journey Through Genius: The Great Theorem of Mathematics. New York: Penguin Books.

[Epsteen and Maclagan-Wedderburn 1905] Epsteen, S. and Maclagan-Wedderburn, J. H. (1905). “On the Structure of Hypercomplex Number Systems,” Transactions of the American Mathematical Society 6, No. 2, 172-178.

[Français 1814] Français, J. F. (1814). “Sur la théorie des imaginaries," Annales de mathématiques pures et appliquées 4 (1814-1815), 61-71.

[Gauss 1801] Gauss, C. F. (1801). Disquisitiones Arithmeticae. English translation by Clarke et al, New York: Springer, 1986.

[Gregory 1865] Gregory, D. F. (1865). The Mathematical Writings. W. Walton (Ed.). London: Cambridge.     

[Jarrett 1831] Jarrett, T. (1831). An Essay on Algebraic Development Containing the Principle Expansion in Common Algebra, in the Differential and Integral Calculus, and in the Calculus of Finite Differences; the General Term Being in Each Case Immediately Obtained by Means of a New and Comprehensive Notation. London: Cambridge University.

[Katz 2009] Katz, V. (2009). A History of Mathematics: An Introduction. Boston, MA: Addison-Wesley.

[Koppleman 1971] Koppleman, E. (1971). “The Calculus of Operations and the Rise of Abstract Algebra,” Archive for History of Exact Sciences 8, 155-242.

[Lacroix 1802] Lacroix, S. F., 1802. Traité élémentaire de calcul différentiel et de calcul intégral. Duprat, Paris.

[Miller 2010] Miller, J. (2010). Earliest Known Uses of Some of the Words of Mathematics. Retrieved July 14, 2011, from http://jeff560.tripod.com/mathword.html.

[Murphy 1837] Murphy, R. (1837). “First Memoir on the Theory of Analytic Operations,” Philosophical Transactions of the Royal Society of London, 127, 179-210.

[O'Connor and Robertson 1996] O'Connor, J. and Robertson, E. (1996). “George Peacock.” Retrieved August 11, 2011, from MacTutor History of Mathematics Archive: http://www.gap-system.org/ history/Biographies/Peacock.html.

[Peacock 1820] Peacock, G. (1820). Collection of Examples of the Applications of the Differential and Integral Calculus. London: Cambridge.

[Petrilli 2010] Petrilli S. J. (2010). “François-Joseph Servois: Priest, Artillery Officer, and Professor of Mathematics,” Loci: Convergence 7. DOI: 10.4169/loci003498 http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=3498

[Petrova 1978] Petrova, S. S. (1978). “The Origin of Linear Operator Theory in the Works of Servois and Murphy.” History and Methodology of the Natural Sciences 20, 122-128. (Unpublished translation by Valery Krupkin.)

[Piccolino 1984] Piccolino, A. V. (1984). A Study of the Contributions of Early Nineteenth Century British Mathematicians to the Development of Abstract Algebra and Their Influence on Later Algebraists and Modern Secondary Curricula. Doctoral thesis: Columbia University Teachers College.

[Rapson 1892] Rapson, E. J. (1892). "Jarrett, Thomas," in Dictionary of National Biography, L. Stephen and S. Lee, eds. New York: Macmillian and Co., XXIX. 253-254. Also available at http://en.wikisource.org/wiki/Jarrett,_Thomas_(DNB00)

[Servois 1814a] Servois, F. J. (1814). “Essai sur un nouveau mode d'exposition des principes du calcul différentiel," Annales de mathématiques pures et appliqués 5 (1814-1815), 93-140.

[Servois 1814b] Servois, F. J. (1814). “Sur la théorie des imaginaries, Lettre de M. Servois," Annales de mathématiques pures et appliquées 5 (1814-1815), 228-235.

[Smith 1951] Smith, D. E. (1951). History of Mathematics, Volume I. London, UK: Constable and Company, Ltd.

[Smith 1958] Smith, D. E. (1958). History of Mathematics, Volume II. New York: Dover Publications.

[Taton 1972a] Taton, R. (1972). “Français," in Dictionary of Scientific Biography, 1972, C. C. Gillespie, Ed., New York: Scribner, V. 110-112.

[Taton 1972b] Taton, R. (1972). “Servois," in Dictionary of Scientific Biography, 1972, C. C. Gillespie, Ed., New York: Scribner, XII. 325-326.

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