Model and Mathematics by Friedman & Krauthausen

Book Contents :-
1. How to Grasp an Abstraction: Mathematical Models and Their Vicissitudes Between 1850 and 1950 PART-I HISTORICAL PERSPECTIVES AND CASE STUDIES 2. Knowing by Drawing: Geometric Material Models in Nineteenth Century France 3. Wilhelm Fiedler and His Models—The Polytechnic Side 4. Models from the Nineteenth Century Used for Visualizing Optical Phenomena and Line Geometry 5. Modeling Parallel Transport 6. The Great Yogurt Project: Models and Symmetry Principles in Early Particle Physics 7. Entanglements On and Models of Periodic Minimal Surfaces 8. The Dialectics Archetypes/Types (Universal Categorical Constructions/Concrete Models) in the Work of Alexander Grothendieck PART-II EPISTEMOLOGICAL AND CONCEPTUAL PERSPECTIVES 9. “Analogies,” “Interpretations,” “Images,” “Systems,” and “Models”: Remarks on the History of Abstract Representation in the Sciences Since the Nineteenth Century 10. Mappings, Models, Abstraction, and Imaging: Mathematical Contributions to Modern Thinking Circa 1900 11. Thinking with Notations: Epistemic Actions and Epistemic Activities in Mathematical Practice 12. Matrices—Compensating the Loss of Anschauung PART-III FROM PRODUCTION PROCESSES TO EXHIBITION PRACTICES 13. Between Viewing and Touching—Models and Their Materiality 14. Exhibitions and Mathematical Models in the Nineteenth and Twentieth Centuries 15. Real-Time Mathematics

About this book :-
"Model and Mathematics: From the 19th to the 21st Century" by Michael Friedman, Karin Krauthausen explores the evolution of "mathematical modeling" from the 19th century to the modern era. The book examines how "models" have shaped the development of "mathematics", bridging the gap between abstract theory and practical applications. By tracing historical milestones, the authors show how modeling influenced fields such as "geometry", "analysis", and applied mathematics, highlighting the interplay between real-world problems and mathematical ideas. The book emphasizes the role of models in both understanding and solving complex phenomena. Case studies illustrate how mathematical modeling has been used to tackle problems in physics, engineering, and other sciences, demonstrating the practical power of theoretical mathematics. Friedman and Krauthausen discuss the philosophical and methodological aspects of modeling, explaining how assumptions, simplifications, and abstractions contribute to building reliable and insightful mathematical frameworks. Designed for researchers, students, and mathematics enthusiasts, "Model and Mathematics" combines historical perspective with contemporary insights. It reveals how the practice of modeling continues to drive innovation, shape mathematical thought, and connect theory with application. This book is an essential resource for anyone interested in the evolution of "mathematics", the significance of "models", and the ongoing influence of modeling in science and education.

Book Detail :-
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 Author :-
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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