Zobrazeno 1 - 10
of 20
pro vyhledávání: '"Karin U. Katz"'
Publikováno v:
Journal of Humanistic Mathematics. 8:108-119
Felix Klein and Abraham Fraenkel each formulated a criterion for a theory of infinitesimals to be successful, in terms of the feasibility of implementation of the Mean Value Theorem. We explore the evolution of the idea over the past century, and the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a7079e4007670c2410e28a418957f85b
https://doi.org/10.5642/jhummath.201801.07
https://doi.org/10.5642/jhummath.201801.07
Autor:
Tiziana Bascelli, Piotr Błaszczyk, Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz, Semen S. Kutateladze, Tahl Nowik, David M. Schaps, David Sherry
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c2627b1b073968a7dfd0759b7da226bc
https://doi.org/10.2307/j.ctvggx33b.18
https://doi.org/10.2307/j.ctvggx33b.18
Autor:
Piotr Błaszczyk, Karin U. Katz, Vladimir Kanovei, Mikhail G. Katz, David M. Schaps, Tiziana Bascelli, Tahl Nowik, David Sherry, Semen S. Kutateladze
Publikováno v:
Foundations of Science. 23:133-144
In relation to a thesis put forward by Marx Wartofsky, we seek to show that a historiography of mathematics requires an analysis of the ontology of the part of mathematics under scrutiny. Following Ian Hacking, we point out that in the history of mat
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f62d6fd22c094674d6c8edf1e263ca23
https://doi.org/10.1007/s10699-016-9512-9
https://doi.org/10.1007/s10699-016-9512-9
Publikováno v:
Experimental Mathematics. 25:399-415
We give a detailed description of the arithmetic Fuchsian group of the Bolza surface and the associated quaternion order. This description enables us to show that the corresponding principal congruence covers satisfy the bound sys(X) > 4/3 log g(X) o
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::19dee10f0f57fcafe3e397f11f341bfa
https://doi.org/10.1080/10586458.2015.1073642
https://doi.org/10.1080/10586458.2015.1073642
Autor:
Tiziana Bascelli, Vladimir Kanovei, David M. Schaps, David Sherry, Mikhail G. Katz, Piotr Błaszczyk, Karin U. Katz
Publikováno v:
HOPOS: The Journal of the International Society for the History of Philosophy of Science. 6:117-147
Did Leibniz exploit infinitesimals and infinities `a la rigueur, or only as shorthand for quantified propositions that refer to ordinary Archimedean magnitudes? Chapter 5 in (Ishiguro 1990) is a defense of the latter position, which she reformulates
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d7a4c4aa5df5156e352865937234a469
https://doi.org/10.1086/685645
https://doi.org/10.1086/685645
Publikováno v:
The Mathematical Intelligencer. 37:48-51
In a piece published in 1981, H. M. Edwards touts the benefits of reading the masters. A quarter-century later, Edwards takes seriously his own advice by publishing an encomium on Euler's Institutiones (1755). While we agree with Edwards that we shal
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9d3fff496aff9c38d37ecd0b5bbf88c7
https://doi.org/10.1007/s00283-015-9565-6
https://doi.org/10.1007/s00283-015-9565-6
Autor:
Piotr Błaszczyk, Karin U. Katz, Mikhail G. Katz, Thomas Mormann, David Sherry, Vladimir Kanovei, Taras Kudryk
To explore the extent of embeddability of Leibnizian infinitesimal calculus in first-order logic (FOL) and modern frameworks, we propose to set aside ontological issues and focus on procedural questions. This would enable an account of Leibnizian pro
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ddab7387421c250ab15234fc8db9e765
http://arxiv.org/abs/1605.03501
http://arxiv.org/abs/1605.03501
The space of matrices of positive determinant GL^+_n inherits an extrinsic metric space structure from R^{n^2}. On the other hand, taking the infimum of the lengths of all paths connecting two points in GL^+_n gives an intrinsic metric. We prove bili
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ab4406ba46768c6d77e413f5e0bffebb
http://arxiv.org/abs/1602.01227
http://arxiv.org/abs/1602.01227
Autor:
Mikhail G. Katz, David Sherry, Semen S. Kutateladze, Vladimir Kanovei, Piotr Błaszczyk, Karin U. Katz
Abraham Robinson's framework for modern infinitesimals was developed half a century ago. It enables a re-evaluation of the procedures of the pioneers of mathematical analysis. Their procedures have been often viewed through the lens of the success of
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::67f7f8c444666adc72f34f977cd6e9bd
Autor:
Mikhail G. Katz, Karin U. Katz
Publikováno v:
Foundations of Science. 17:109-123
We explore the potential of Simon Stevin's numbers, obscured by shifting foundational biases and by 19th century developments in the arithmetisation of analysis.
Comment: 22 pages, 4 figures. arXiv admin note: text overlap with arXiv:1104.0375,
Comment: 22 pages, 4 figures. arXiv admin note: text overlap with arXiv:1104.0375,
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a3571ab477b1841f1a1a6960dffd8737
https://doi.org/10.1007/s10699-011-9228-9
https://doi.org/10.1007/s10699-011-9228-9