Date: 08 Jan 2009
The infidel is innocent
- Adrian P. Simpson
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- 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!!
- 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. CrossRef
- 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. CrossRef
- 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).
- 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.
- 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.
- 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). CrossRef
- A. Robinson,Non-Standard Analysis, Amsterdam: North-Holland (1966).The original text upon which all of the theory is built.
- M. Spivak,Calculus, New York: Benjamin (1967).The introductory text to university-level analysis. The New English bible of the Quasi-religious Sect!
- I. Stewart,The Problems of Mathematics, Oxford: Oxford University Press (1987).Chapter 7 introduces the subject for the beginner.
- 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.
- 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.
- The infidel is innocent
The Mathematical Intelligencer
Volume 12, Issue 3 , pp 43-51
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