Duality in 19th and 20th Century Mathematical Thinking (Record no. 61263)
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| 001 - CONTROL NUMBER | |
| control field | 978-3-031-59797-8 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | DE-He213 |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20251030112608.0 |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
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| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
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| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9783031597978 |
| -- | 978-3-031-59797-8 |
| 024 7# - OTHER STANDARD IDENTIFIER | |
| Standard number or code | 10.1007/978-3-031-59797-8 |
| Source of number or code | doi |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA21-27 |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | PBX |
| Source | bicssc |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | MAT015000 |
| Source | bisacsh |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | PBX |
| Source | thema |
| 245 10 - TITLE STATEMENT | |
| Title | Duality in 19th and 20th Century Mathematical Thinking |
| Medium | [electronic resource] / |
| Statement of responsibility, etc. | edited by Ralf Krömer, Emmylou Haffner. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. 2024. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Cham : |
| Name of producer, publisher, distributor, manufacturer | Springer Nature Switzerland : |
| -- | Imprint: Birkhäuser, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2024. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | XVI, 960 p. |
| Other physical details | online resource. |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 347 ## - DIGITAL FILE CHARACTERISTICS | |
| File type | text file |
| Encoding format | |
| Source | rda |
| 490 1# - SERIES STATEMENT | |
| Series statement | Science Networks. Historical Studies, |
| International Standard Serial Number | 2296-6080 ; |
| Volume/sequential designation | 63 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Preface -- Chapter 1. Ralf Krömer, Emmylou Haffner: Introduction -- Part I. The 19th century heritage -- Chapter 2. Michael Friedman: On “contour apparent”, “courbe de contact” and ramification curves: Duality between a principle and a tool -- Chapter 3. Juan Luis Gastaldi: De Morgan’s De Morgan’s Laws: Duality in the Emergence of Formal Logic -- Chapter 4. Dirk Schlimm: The emergence of duality in 19th-century algebra of logic -- Chapter 5. Emmylou Haffner: Duality as a guiding light in the genesis of Dedekind’s Dualgruppen -- Chapter 6. Erhard Scholz: From Grassmann complements to Hodge-duality -- Part II. From topology to groups -- Chapter 7. Stephan Oltmanns, Ralf Krömer, Klaus Volkert: Duality theorems in topology -- Chapter 8. Ralf Krömer: The historical development of Pontrjagin duality -- Chapter 9. Harald Kümmerle: Tannaka Tadao’s 1938 paper on the duality of noncommutative topological groups and its historical background -- Chapter 10. Christophe Eckes: Philosophical and mathematical duality in Albert Lautman’s work -- Part III. Functional analysis and related fields -- Chapter 11. Alessa Waldvogel: The development of dual spaces in functional analysis -- Chapter 12. Frédéric Jaëck: Duality in Banach’s 1929 work on functionals -- Chapter 13. Ralf Krömer: Marshall Stone and duality: from differential equations to Boolean algebras -- Chapter 14. Ralf Krömer: Duality à la Bourbaki -- Chapter 15. Jesper Lützen: Duality and Distributions: An Application of Topological Vector Spaces -- Part IV. The post-war outlook -- Chapter 16. Tinne Hoff Kjeldsen: From duality in mathematical programming to Fenchel duality and convex analysis: Duality as a force of inspiration in the creation of new mathematics -- Chapter 17. Jean-Pierre Marquis: An Historical Perspective on Duality and Category Theory -- List of abbreviations -- Bibliography -- Author index. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | 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 there such a thing as duality in mathematics, or are there just several things called by the same name and similar in some respect? What emerges is that duality can be considered as a basic structure of mathematical thinking, thereby opening new horizons for the research on the history and the philosophy of mathematics and the reflection on mathematics in general. The volume will appeal not only to experts in the discipline but also to advanced students of mathematics, history, and philosophy intrigued by the complexities of this captivating subject matter. |
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| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Krömer, Ralf. |
| Relator term | editor. |
| Relator code | edt |
| -- | http://id.loc.gov/vocabulary/relators/edt |
| 9 (RLIN) | 79870 |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Haffner, Emmylou. |
| Relator term | editor. |
| Relator code | edt |
| -- | http://id.loc.gov/vocabulary/relators/edt |
| 9 (RLIN) | 79871 |
| 710 2# - ADDED ENTRY--CORPORATE NAME | |
| Corporate name or jurisdiction name as entry element | SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY | |
| Title | Springer Nature eBook |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Printed edition: |
| International Standard Book Number | 9783031597961 |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Printed edition: |
| International Standard Book Number | 9783031597985 |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Printed edition: |
| International Standard Book Number | 9783031597992 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Science Networks. Historical Studies, |
| International Standard Serial Number | 2296-6080 ; |
| Volume number/sequential designation | 63 |
| 9 (RLIN) | 79872 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://doi.org/10.1007/978-3-031-59797-8">https://doi.org/10.1007/978-3-031-59797-8</a> |
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