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Durer, Albrecht (1471-1528)

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Loci: Convergence

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

by Anthony J. Del Latto (Adelphi University) and Salvatore J. Petrilli, Jr. (Adelphi University)

References

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[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.

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

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[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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Del Latto, Anthony J. and Salvatore J. Petrilli, Jr., "Algebraic Formalism within the Works of Servois and Its Influence on the Development of Linear Operator Theory," Loci (January 2012), DOI: 10.4169/loci003802


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