Model and Mathematics by Friedman & Krauthausen
Model and Mathematics - Table of Contents
- 1. How to Grasp an Abstraction
- 2. Knowing by Drawing: Geometric Models
- 3. Wilhelm Fiedler and His Models
- 4. Models for Optical Phenomena & Line Geometry
- 5. Modeling Parallel Transport
- 6. Models & Symmetry in Particle Physics
- 7. Periodic Minimal Surfaces
- 8. Archetypes/Types in Grothendieck's Work
- 9. History of Abstract Representation
- 10. Mappings, Models, Abstraction, and Imaging
- 11. Thinking with Notations in Practice
- 12. Matrices—Compensating Loss of Anschauung
- 13. Models and Their Materiality
- 14. Exhibitions and Mathematical Models
- 15. Real-Time Mathematics
What You Will Learn in Model and Mathematics
Model and Mathematics by Michael Friedman and Karin Krauthausen is an authoritative, multi-author volume published by Birkhäuser that explores the historical, epistemological, and material role of models in mathematical thinking from 1850 to 1950. This comprehensive work guides readers through nineteenth-century geometric models, optical phenomena visualization, parallel transport modeling, periodic minimal surfaces, Grothendieck's categorical constructions, epistemic notations, and exhibition practices with exceptional scholarly depth.
Designed for historians of mathematics, philosophers of science, design theorists, exhibition curators, and mathematical researchers, this foundational text bridges physical material artifacts with abstract structural representation. Friedman, Krauthausen, and leading contributors analyze step-by-step how tactile models, drawings, matrices, and spatial notations compensated for the loss of visual intuition (Anschauung) as modern mathematics grew increasingly abstract. Whether you are investigating the history of geometric pedagogy, researching material culture in science, or studying mathematical epistemology, this book offers an indispensable roadmap.
Recognized globally as a landmark publication on material mathematics and visual culture, it stands as one of the best scholarly works on mathematical representation and modeling. By connecting physical models to formal abstraction and museum display practices, it serves as an essential tool for mastering the history and philosophy of mathematical modeling with confidence.
Book Details & Specifications
Title:
Model and Mathematics by Friedman & Krauthausen
Publisher:
Birkhäuser
Year:
2022
Pages:
441
Type:
PDF
Language:
English
ISBN-10 #:
3030978354
ISBN-13 #:
978-3030978358
License:
CC BY 4.0
Amazon:
Amazon
About the Author: Michael Friedman and Karin Krauthausen
The author Michael Friedman and Karin Krauthausen
are mathematicians and authors specializing in the "history of mathematics", "mathematical modeling", and the philosophy of the discipline. Their work explores how mathematics develops through "theory", abstraction, and practical application. In "Model and Mathematics: From the 19th to the 21st Century", they examine how "mathematical models" have shaped various fields over time. The book highlights the evolution of "mathematical reasoning", showing the interaction between ideas and real-world problems.
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