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隆重纪念鲁宾逊诞辰,不走样,不离谱

(2018-09-30 13:05:48)

    在数学界,鲁宾逊是无穷小的代名词。菲氏微积分徒子徒孙不喜欢无穷小,当然不会纪念鲁宾逊的诞辰,所以我们要特别隆重地纪念数学家鲁宾逊的100周年诞辰。

    当前,无穷小在中国高校数学教育界掀起一阵“风浪”,菲氏徒子徒孙心中发慌,害怕丢掉饭碗。

美国年轻数学家Joel A. Tropp1977- )发表论文“无穷小:历史与应用”,写作中参考许多关于无穷小的珍贵文献,本文附后,供读者参考。

隆重纪念鲁宾逊诞辰,不走样,不离谱,就是要突出无穷小的学术地位。无穷小是严格的数学概念,不是玄学。

    我们预祝大家国庆节愉快!

袁萌  陈启清  930

附:无穷小研究的参考文献

[1] Bell, E.T. Men of Mathematics: The Lives and Achievements of the Great Mathematicians from Zeno to Poincar´ e. Simon and Schuster, New York, 1937.

[2] Bell, J.L. A Primer of Innitesimal Analysis. Cambridge University Press, Cambridge, 1998

[3] Boyer, Carl B. The History of the Calculus and its Conceptual Development. Dover Publications, New York, 1949.

[4] “Luitzen Egbertus Jan Brouwer.” The MacTutor History of Mathematics Archive. http://www-history.mcs.st-andrews.ac.uk/history/Mathematicians/ Brouwer.html. 11 April 1999.

[5] Cutland, Nigel J. “Nonstandard Real Analysis.” Nonstandard Analysis: Theory and Applications. Eds. Lief O. Arkeryd et al. NATO ASI Series C 493. Kluwer Academic Publishers, Dordrecht, 1996.

[6] Dauben, Joseph Warren. Abraham Robinson: The Creation of Nonstandard Analysis; A Personal and Mathematical Odyssey. Princeton University Press, Princeton, 1995.

[7] Goldblatt, Robert. Lectures on the Hyperreals: An Introduction to Nonstandard Analysis. Graduate Texts in Mathematics #188. Springer-Verlag, New York, 1998.

[8] Henson, C. Ward. “Foundations of Nonstandard Analysis.” Nonstandard Analysis: Theory and Applications. Eds. Lief O. Arkeryd et al. NATO ASI Series C 493. Kluwer Academic Publishers, Dordrecht, 1996.

[9] Loeb, Peter A. “Nonstandard Analysis and Topology.” Nonstandard Analysis: Theory and Applications. Eds. Lief O. Arkeryd et al. NATO ASI Series C 493. Kluwer Academic Publishers, Dordrecht, 1996.

[10] Nonstandard Analysis: Theory and Applications. Eds. Lief O. Arkeryd et al. NATO ASI Series C 493. Kluwer Academic Publishers, Dordrecht, 1996.

[11] Robert, Alain. Nonstandard Analysis. John Wiley & Sons, Chichester, 1988.

[12] Rudin, Walter. Principles of Mathematical Analysis. 3rd ed. International Series in Pure and Applied Mathematics. McGraw-Hill, New York, 1976.

[13] Russell, Bertrand. Principles of Mathematics. 2nd ed. W.W. Norton & Company, New York, 1938.

[14] Russell, Bertrand. “Denition of Number.” The World of Mathematics. Vol. 1. Simon and Schuster, New York, 1956.

[15] Schechter, Eric. Handbook of Analysis and Its Foundations. Academic Press, San Diego, 1997.

[16] Varberg, Dale and Edwin J. Purcell. Calculus with Analytic Geometry. Prentice Hall, Englewood Clis, 1992.

 

 

 


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