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Titlebook: Duality in 19th and 20th Century Mathematical Thinking; Ralf Kr?mer,Emmylou Haffner Book 2024 The Editor(s) (if applicable) and The Author

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樓主
發(fā)表于 2025-3-21 16:05:52 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書目名稱Duality in 19th and 20th Century Mathematical Thinking
編輯Ralf Kr?mer,Emmylou Haffner
視頻videohttp://file.papertrans.cn/285/284837/284837.mp4
概述Provides an extensive and multidisciplinary investigation of the history of duality.Discusses in depth the uses and circulation of various notions of duality.Offers a comprehensive overview of duality
叢書名稱Science Networks. Historical Studies
圖書封面Titlebook: Duality in 19th and 20th Century Mathematical Thinking;  Ralf Kr?mer,Emmylou Haffner Book 2024 The Editor(s) (if applicable) and The Author
描述.This volume brings together scholars across various domains of the history and philosophy of mathematics, investigating duality as a multi-faceted phenomenon. Encompassing both systematic analysis and historical examination, the book endeavors to elucidate the status, roles, and dynamics of duality within the realms of 19th and 20th-century mathematics. Eschewing .a priori. notions, the contributors embrace the diverse interpretations and manifestations of duality, thus presenting a nuanced and comprehensive perspective on this intricate subject...Spanning a broad spectrum of mathematical topics and historical periods, the book uses detailed case studies to investigate the different forms in which duality appeared and still appears in mathematics, to study their respective histories, and to analyze interactions between the different forms of duality. The chapters inquire into questions such as the contextual occurrences of duality in mathematics, the influence of chosen forms of representation, the impact of investigations of duality on mathematical practices, and the historical interconnections among various instances of duality. Together, they aim to answer a core question: Is t
出版日期Book 2024
關(guān)鍵詞Duality in Mathematics; HIstory of Mathematics; 19th century; 20th century; Philosophy of mathematics; De
版次1
doihttps://doi.org/10.1007/978-3-031-59797-8
isbn_softcover978-3-031-59799-2
isbn_ebook978-3-031-59797-8Series ISSN 1421-6329 Series E-ISSN 2296-6080
issn_series 1421-6329
copyrightThe Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl
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沙發(fā)
發(fā)表于 2025-3-21 23:31:45 | 只看該作者
Alfred Karl Louis,Peter Maa?,Andreas Riederearch. On the other hand, a close link between Hodge’s theory and the Maxwell equation has been claimed not only from a systematic point of view but also historically by Hodge’s former student M. Atiyah in his talks on dualities in mathematics and physics.
板凳
發(fā)表于 2025-3-22 04:26:46 | 只看該作者
Advanced Lectures in Mathematicsduality. Let us give a first example: Lautman speaks of duality when two points of view, sometimes distinct, sometimes opposed, sometimes complementary, can be adopted to study the same mathematical entity.
地板
發(fā)表于 2025-3-22 08:03:35 | 只看該作者
5#
發(fā)表于 2025-3-22 09:17:34 | 只看該作者
6#
發(fā)表于 2025-3-22 15:48:22 | 只看該作者
Philosophical and mathematical duality in Albert Lautman’s workduality. Let us give a first example: Lautman speaks of duality when two points of view, sometimes distinct, sometimes opposed, sometimes complementary, can be adopted to study the same mathematical entity.
7#
發(fā)表于 2025-3-22 19:21:30 | 只看該作者
Duality and Distributions: An Application of Topological Vector Spacesto the main proponent of the latter, Bourbaki (1960 and 1955), the development of the theory of normed spaces came to a temporary halt after the appearance of Stefan Banach’s book . (1932). Instead, functional analysis went in the direction of more general spaces such as locally convex spaces in particular Frechet spaces.
8#
發(fā)表于 2025-3-23 00:02:54 | 只看該作者
,Technischer Hochwasserschutz – Bauvorsorge,ality” was coined (although “reciprocity” or “polarity” were also used). With the emergence of modern mathematics during the 19th and 20th centuries, the number of phenomena labelled “duality” exploded.
9#
發(fā)表于 2025-3-23 01:47:57 | 只看該作者
10#
發(fā)表于 2025-3-23 06:29:41 | 只看該作者
Die kontinuierliche Wavelet-Transformation, and elsewhere, from various biographic and autobiographical accounts concerning Pontrjagin himself or some of his contemporaries, from archival material available at the ETH Zurich (in particular, Heinz Hopf’s correspondence with Paul Alexandroff and other colleagues) and at the IAS Princeton, and from secondary literature.
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