References for: The function concept

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  1. J H Manheim, The genesis of point set topology (Pergamon Press, Oxford-Paris-Frankfurt; The Macmillan Co., New York, 1964).
  2. H N Jahnke (ed.), A history of analysis (American Mathematical Society, Providence, R.I., 2003).
  1. L Atkinson, Where do functions come from?, College Math. J. 33 (2) (2002), 107-112.
  2. R Bhatia, The development of the concept of a function, Math. Student 63 (1-4) (1994), 153-166.
  3. S Bochner, The rise of functions, Rice Univ. Studies 56 (2) (1970), 3-21.
  4. R Cantoral, Formation of the notion of analytic function (Spanish), Mathesis, Mathesis 7 (2) (1991), 223-239.
  5. S S Demidov, G W Leibniz's "continuity law" and Euler's concept of function continuity (Russian), Istor.-Mat. Issled. No. 32-33 (1990), 34-39.
  6. J Dhombres, The mathematics implied in the laws of nature and realism, or the role of functions around 1750, in The application of mathematics to the sciences of nature (Kluwer Acad. Publ., Dordrecht, 2002), 207-222.
  7. J Dhombres, Un texte d'Euler sur les fonctions continues et les fonctions discontinues, véritable programme d'organisation de l'analyse au 18e siècle, Cahiers du séminaire d'histoire des mathématiques 9 (Univ. Paris VI, Paris, 1988), 23-97.
  8. G Ferraro, Functions, functional relations, and the laws of continuity in Euler, Historia Math. 27 (2) (2000), 107-132.
  9. G Ferraro, Some aspects of Euler's theory of series: inexplicable functions and the Euler-Maclaurin summation formula, Historia Math. 25 (3) (1998), 290-317.
  10. I Kleiner, Functions : historical and pedagogical aspects, Sci. Ed. 2 (2) (1993), 183-209.
  11. Y Komatu, The change in the concept of functions(Japanese), in Essays in celebration of the 100th anniversary of Chuo University (Chuo Univ., Tokyo, 1985), 67-81.
  12. A Kopácková, Phylogenesis of the concept of a function (Czech), in Mathematics throughout the ages II (Czech), (Prometheus, Prague, 2001), 46-80.
  13. J Lützen, Between rigor and applications : developments in the concept of function in mathematical analysis, in The modern physical and mathematical sciences (Cambridge Univ. Press, Cambridge, 2003), 468-487.
  14. J Lützen, The development of the concept of function from Euler to Dirichlet. (Danish), Nordisk Mat. Tidskr. 25/26 (1) (1978), 5-32; 56.
  15. N Luzin, Function I, Amer. Math. Monthly 105 (1) (1998), 59-67.
  16. N Luzin, Function II, Amer. Math. Monthly 105 (3) (1998), 263-270.
  17. F A Medvedev, Lobacevskii's and Dirichlet's definition of the concept of function (Russian), Istor.-Mat. Issled. Vyp. 20 (1975), 232-245; 380.
  18. F A Medvedev, Newton's concept of function (Russian), in History and methodology of the natural sciences, No. XIV : Mathematics, mechanics (Russian) (Izdat. Moskov. Univ., Moscow, 1973), 153-158.
  19. M Panza, Concept of function, between quantity and form, in the 18th century, in History of mathematics and education: ideas and experiences, Essen, 1992 (Vandenhoeck & Ruprecht, Göttingen, 1996), 241-274.
  20. O Petersen, Logistics and the theory of functions, Arch. Internat. d'Hist. d. Sciences 24 (94) (1974), 29-50.
  21. J B Rosser, Boole and the concept of a function, Proc. Roy. Irish Acad. Sect. A. 57 (1955), 117-120.
  22. D Rüthing, Some definitions of the concept of function from Joh Bernoulli to N Bourbaki, Math. Intelligencer 6 (4) (1984), 72-77.
  23. M Schramm, Steps towards the idea of function: A comparison between Eastern and Western science of the Middle Ages. Some further remarks on A C Crombie's Augustine to Galileo, in Hist. of Sci. 4 (1965), 70-103.
  24. Siu, M K Concept of function - its history and teaching, in Learn from the masters!, Kristiansand, 1988 (Math. Assoc. America, Washington, DC, 1995), 105-121.
  25. D D Spalt, ... doch es gibt ihn nicht : Der Begriff der reellen Funktion im 19. Jahrhundert, Mathesis (Verl. Gesch. Nat.wiss. Tech., Berlin, 2000), 182-215.
  26. R Thiele, Frühe Variationsrechnung und Funktionsbegriff, Mathesis (Verl. Gesch. Nat.wiss. Tech., Berlin, 2000), 128-181.
  27. A P Youschkevitch, La notion de fonction chez Condorcet, in For Dirk Struik (Reidel, Dordrecht, 1974), 131-139.
  28. A P Youschkevitch, On the development of the concept of a function (Russian), Istor.-Mat. Issled. 17 (1966), 123-150.
  29. A P Youschkevitch, The concept of function in the works of Condorcet (Russian), in Studies in the history of mathematics, No. 19 (Russian), Izdat. "Nauka", Moscow, 1974), 158-166, 301.
  30. A P Youschkevitch, The concept of function up to the middle of the 19th century, Arch. History Exact Sci. 16 (1) (1976/77), 37-85.

JOC/EFR October 2005

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