The Mathematical Intelligencer

, Volume 12, Issue 3, pp 43–51 | Cite as

The infidel is innocent

  • Adrian P. Simpson
Article

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Annotated Bibliography

  1. Bishop Berkeley, The analyst: A discourse addressed to an infidel mathematician,The World of Mathematics, vol. 1 (J. R. Newman, ed.), London: Allen and Unwin (1956), 288–293.A thin succulent layer of mathematics with a strong sprinkling of invective, steeped in a vitriolic sauce of sarcasm. Brilliant!!Google Scholar
  2. M. Diener, The canard unchainedor how fast/slow dynamical systems bifurcate,Mathematical Intelligencer 6, no. 3 (1984), 38–49.A canny introduction to duck-hunting. CrossRefMATHMathSciNetGoogle Scholar
  3. S. Haack,Philosophy of Logics, Cambridge: Cambridge University Press (1978).Discusses some of the problems with second-order logic and gives the basis for the language used in Section 3. CrossRefGoogle Scholar
  4. A. E. Hurd (ed.),Nonstandard Analysis-RecentDevelopments, New York: Springer-Verlag (1983).A series of papers (all quite technical) on recent uses of Robinson’s work. Includes a paper by Richter and Szabo on program verification (cf. Section 5). MATHGoogle Scholar
  5. A. E. Hurd and P. A. Loeb,An Introduction to Nonstandard Real Analysis, London: Academic Press (1985).Chapter 1 contains the construction on which Section 3 was based. MATHGoogle Scholar
  6. H. J. Keisler,Foundations of Infinitesimal Calculus, Boston: Prindle, Weber and Schmidt (1976).The definitive book on the teaching and understanding of non- standard analysis. MATHGoogle Scholar
  7. R. Lutz and M. Goze,Nonstandard Analysis: A Practical Guide with Applications, New York: Springer-Verlag (1981).A chirpy, if technical, exploration of non-standard analysis. Good humour let down by poor English!Chapter IV.8 discusses canards (cf. Section 5). CrossRefMATHGoogle Scholar
  8. A. Robinson,Non-Standard Analysis, Amsterdam: North-Holland (1966).The original text upon which all of the theory is built.MATHGoogle Scholar
  9. M. Spivak,Calculus, New York: Benjamin (1967).The introductory text to university-level analysis. The New English bible of the Quasi-religious Sect!Google Scholar
  10. I. Stewart,The Problems of Mathematics, Oxford: Oxford University Press (1987).Chapter 7 introduces the subject for the beginner. MATHGoogle Scholar
  11. K. D. Stroyan and W. A. J. Luxemburg,An Introduction to the Theory of Infinitesimals, New York: Academic Press (1976).Pitched highly, but contains a good ultrafilter construction in chapter 1. Google Scholar
  12. D. O. Tall,Infinitesimals Constructed Algebraically and Interpreted Geometrically, Coventry: University of Warwick, preprint (1979).Gives a construction of another extension containing infinitesimals with a neat way of visualising them.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 1990

Authors and Affiliations

  • Adrian P. Simpson
    • 1
  1. 1.Tudor CourtSuffolkUK

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