Model and Mathematics: From the 19th to the 21st Century

This open-access book explores the historical and media perspectives of the relationship between model and mathematics, covering physical mathematical models to simulation and digital modeling in the 21st century. It aims to showcase the status of mathematical models between abstraction and realization, presentation and representation, and what is modeled and what models.

Format: Paperback / softback
Length: 445 pages
Publication date: 09 August 2022
Publisher: Springer Nature Switzerland AG

This comprehensive open-access book presents a systematic and epistemological exploration of the intricate and multifaceted relationship between model and mathematics, spanning a vast historical and media spectrum. From the physical mathematical models of the 19th century to the simulation and digital modeling of the 21st century, this anthology seeks to showcase the evolving status of the mathematical model in terms of abstraction, realization, presentation, and representation. It delves into the core concepts of what is modeled and what models, shedding light on the diverse applications and implications of mathematical models across various fields.

The book is organized into several chapters, each dedicated to exploring different aspects of the model-mathematics relationship. Contributors from diverse disciplines contribute their expertise, providing insights and perspectives that contribute to a comprehensive understanding of this complex subject.

One of the key themes explored in the book is the balance between abstraction and realization. Mathematical models can be abstract, representing complex systems with simplified mathematical structures, or they can be realized, using specific computational techniques and data. The authors discuss the advantages and challenges of both approaches, highlighting the need for a judicious choice depending on the specific problem at hand.

Another important aspect of the book is the relationship between presentation and representation. Mathematical models can be presented in various forms, such as graphical representations, mathematical equations, or computer simulations. The authors explore the strengths and limitations of different presentation methods, discussing how they can enhance understanding and communication of mathematical concepts.

Furthermore, the book examines the role of mathematical models in capturing and simulating real-world phenomena. From physical systems to social networks, mathematical models provide a powerful tool for understanding and predicting complex behavior. The authors discuss the challenges and opportunities associated with modeling, highlighting the importance of interdisciplinary collaboration and the need for rigorous validation and verification of models.

In conclusion, this open-access book offers a valuable resource for researchers, students, and practitioners interested in the study of the model-mathematics relationship. It provides a comprehensive and interdisciplinary perspective, covering a wide range of historical and contemporary topics. By exploring the abstraction, realization, presentation, and representation of mathematical models, the book contributes to our understanding of the role of mathematics in shaping our world.

Weight: 688g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030978358
Edition number: 1st ed. 2022