Duality in 19th and 20th Century Mathematical Thinking
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...
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| Outros Autores: | , |
| Formato: | Recurso Electrónico livro electrónico |
| Idioma: | inglês |
| Publicado em: |
Cham :
Springer Nature Switzerland : Imprint: Birkhäuser,
2024.
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| Edição: | 1st ed. 2024. |
| Colecção: | Science Networks. Historical Studies,
63 |
| Assuntos: | |
| Acesso em linha: | https://doi.org/10.1007/978-3-031-59797-8 |
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Sumário:
- 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.