From discrete arithmetic to arithmetic of the continuum
暂无分享,去创建一个
[1] J. Bell. A primer of infinitesimal analysis , 1998 .
[2] F. William Lawvere,et al. Toward the description in a smooth topos of the dynamically possible motions and deformations of a continuous body , 1980 .
[3] T. Skolem. Über die Nicht-charakterisierbarkeit der Zahlenreihe mittels endlich oder abzählbar unendlich vieler Aussagen mit ausschliesslich Zahlenvariablen , 1934 .
[4] Howard Eves,et al. An Introduction To The Foundations And Fundamental Concepts Of Mathematics , 1965 .
[5] Edwin Hewitt,et al. Rings of real-valued continuous functions. I , 1948 .
[6] Jérôme Havenel. Peirce's Clarifications of Continuity , 2008 .
[7] Robert Goldblatt,et al. Lectures on the hyperreals , 1998 .
[8] David Tall,et al. The transition to formal thinking in mathematics , 2008 .
[9] A. Robinson. Non-standard analysis , 1966 .
[10] Karin U. Katz,et al. When is .999... less than 1? , 2010, The Mathematics Enthusiast.
[11] R. Ely. Nonstandard Student Conceptions About Infinitesimals , 2010 .
[12] D. Tall,et al. THE TENSION BETWEEN INTUITIVE INFINITESIMALS AND FORMAL MATHEMATICAL ANALYSIS , 2011, 1110.5747.
[13] John P. Burgess,et al. A Subject with No Object: Strategies for Nominalistic Interpretation of Mathematics , 2001 .
[14] A. Cauchy. Cours d'analyse de l'École royale polytechnique , 1821 .
[15] D. Fowler. Dedekind's Theorem: , 1992 .
[17] J. Dauben. C. S. Peirce's Philosophy of Infinite Sets , 1977 .
[18] Numbers and models, standard and nonstandard , 2010 .
[19] Geoffrey Hellman,et al. Mathematics without Numbers: Towards a Modal-Structural Interpretation , 1989 .
[20] J. Naets. How to Define a Number? A General Epistemological Account of Simon Stevin’s Art of Defining , 2010 .
[21] Lorenzo Magnani,et al. Perceiving the Infinite and the Infinitesimal World: Unveiling and Optical Diagrams in Mathematics , 2005 .
[22] Leif Arkeryd,et al. Intermolecular forces of infinite range and the Boltzmann equation , 1981 .
[23] Mikhail G. Katz,et al. Leibniz's laws of continuity and homogeneity , 2012, 1211.7188.
[24] D. J. Winter. A History of Algebra. , 1988 .
[25] Heinrich Rust. Operational Semantics for Timed Systems: A Non-standard Approach to Uniform Modeling of Timed and Hybrid Systems , 2005, Lecture Notes in Computer Science.
[26] S. Shapiro,et al. Mathematics without Numbers , 1993 .
[27] D. Tall. Looking at graphs through infinitesimal microscopes, windows and telescopes , 1980, The Mathematical Gazette.
[28] E. Seneta. Cauchy, Augustin–Louis , 2006 .
[29] David Sherry,et al. The wake of Berkeley's analyst: Rigor mathematicae? , 1987 .
[30] G. Lakoff,et al. Where Mathematics Comes From , 2000 .
[31] Detlef Laugwitz. Infinitely small quantities in Cauchy's textbooks , 1987 .
[32] P. Zsombor-Murray,et al. Elementary Mathematics from an Advanced Standpoint , 1940, Nature.
[33] Augusto Hasman,et al. Comments on the paper , 2012 .
[34] A. Tarski,et al. Une contribution à la théorie de la mesure , 1930 .
[35] C. Peirce. How to Make Our Ideas Clear , 2011, The Nature of Truth.
[36] René Taton,et al. The Principal Works of Simon Stevin , 1959 .
[37] H. Keisler. Elementary Calculus: An Infinitesimal Approach , 1976 .
[38] Mikhail G. Katz,et al. Cauchy's Continuum , 2011, Perspectives on Science.
[39] Mikhail G. Katz,et al. Zooming in on infinitesimal 1–.9.. in a post-triumvirate era , 2010, 1003.1501.
[40] J. Dauben. Peirce's place in mathematics , 1982 .
[41] Martin Davis,et al. Applied Nonstandard Analysis , 1977 .
[42] G. Lakoff,et al. Where mathematics comes from : how the embodied mind brings mathematics into being , 2002 .
[43] Augustin-Louis Cauchy. Oeuvres complètes: LEÇONS SUR LE CALCUL DIFFÉRENTIEL , 2009 .
[44] Christoph J. Scriba,et al. B. L. van der Waerden: A History of Algebra. From al‐Khwarizmi to Emmy Noether. Berlin/Heidelberg/New York/Tokyo: Springer‐Verlag 1985. xi, 271 Seiten, 28 Figuren. Leinen, DM 98,‐. , 1987 .
[45] Solomon Gandz,et al. The Invention of the Decimal Fractions and the Application of the Exponential Calculus by Immanuel Bonfils of Tarascon (c. 1350) , 1936, Isis.
[46] Mikhail G. Katz,et al. Ten Misconceptions from the History of Analysis and Their Debunking , 2012, 1202.4153.
[47] S. Albeverio. Nonstandard Methods in Stochastic Analysis and Mathematical Physics , 1986 .
[48] M. E. Moore. The completeness of the real line , 2007 .
[49] Implicit Differentiation with Microscopes , 2010 .
[50] Detlef Laugwitz,et al. Comments on the paper “Two letters by N. N. Luzin to M. Ya. Vygodskiῐ” , 2000, Am. Math. Mon..
[51] Desmond Fearnley-Sander,et al. Hermann Grassmann and the Creation of Linear Algebra , 1979 .
[52] Ekkehard Kopp,et al. On Cauchy's Notion of Infinitesimal , 1988, The British Journal for the Philosophy of Science.
[53] H. Jerome Keisler,et al. The Hyperreal Line , 1994 .
[54] C. Allen,et al. Stanford Encyclopedia of Philosophy , 2011 .
[55] Lorenzo Magnani,et al. Mathematics through Diagrams: Microscopes in Non-Standard and Smooth Analysis , 2007, Model-Based Reasoning in Science, Technology, and Medicine.
[56] Augustin-Louis Cauchy. Oeuvres complètes: Mémoire sur les développements des fonctions en séries périodiques , 2009 .
[57] Mikhail G. Katz,et al. Meaning in Classical Mathematics: Is it at Odds with Intuitionism? , 2011, 1110.5456.
[58] Charles Coulston Gillispie,et al. Dictionary of scientific biography , 1970 .
[59] Antoni Malet,et al. Renaissance notions of number and magnitude , 2006 .
[60] Alexandre Borovik,et al. Who Gave You the Cauchy–Weierstrass Tale? The Dual History of Rigorous Calculus , 2011, 1108.2885.
[61] D. Laugwitz. Early delta functions and the use of infinitesimals in research , 1992 .
[62] Philip Ehrlich,et al. The Rise of non-Archimedean Mathematics and the Roots of a Misconception I: The Emergence of non-Archimedean Systems of Magnitudes , 2006 .
[63] Gert Schubring,et al. Conflicts between Generalization, Rigor and Intuition. Number Concepts Underlying the Development of Analysis in 17th-19th Century France and Germany , 2005 .
[64] Carl B. Boyer,et al. The Concepts of the Calculus , 1940 .
[65] J. Burgess,et al. A Subject with no Object , 1999 .
[66] Kajsa Bråting,et al. A new look at E.G. Björling and the Cauchy sum theorem , 2007 .
[67] Jerzy Loś,et al. Quelques Remarques, Théorèmes Et Problèmes Sur Les Classes Définissables D'algèbres , 1955 .
[68] Augustin-Louis Cauchy. Oeuvres complètes: ANALYSE MATHÉMATIQUE. — Note sur les séries convergentes dont les divers termes sont des fonctions continues d'une variable réelle ou imaginaire, entre des limites données , 2009 .
[69] D. Laugwitz. Definite values of infinite sums: Aspects of the foundations of infinitesimal analysis around 1820 , 1989 .
[70] K. D. Stroyan. Uniform Continuity and Rates of Growth of Meromorphic Functions1) , 1972 .
[71] Mikhail G. Katz,et al. A Burgessian Critique of Nominalistic Tendencies in Contemporary Mathematics and its Historiography , 2011, 1104.0375.
[72] R. Goldblatt. Lectures on the hyperreals : an introduction to nonstandard analysis , 1998 .