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: Hardback
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, it delves into the diverse perspectives and applications of mathematical models. The primary objective of this anthology is to highlight the evolving status of the mathematical model, encompassing its relationship between abstraction and realization, presentation and representation, as well as the entities it models and the models that model them.

The book is freely accessible to all under a Creative Commons BY 4.0 license, fostering a collaborative and inclusive approach to understanding the complexities of the mathematical model. By compiling a diverse range of scholarly contributions, this volume serves as a valuable resource for researchers, educators, and practitioners interested in the fields of mathematics, engineering, computer science, and beyond.

The historical section of the book explores the origins and evolution of mathematical models, tracing their development from early abstractions to the precision and complexity of modern models. It examines the contributions of influential mathematicians, scientists, and engineers who have shaped the field, highlighting their groundbreaking theories, algorithms, and applications.

The media section showcases the diverse ways in which mathematical models are communicated and represented. It discusses the use of visualizations, graphics, animations, and interactive technologies to enhance understanding and facilitate decision-making. The book explores the challenges and opportunities associated with representing complex mathematical concepts and processes in a visually appealing and accessible manner, emphasizing the importance of effective communication in scientific and technical discourse.

The relationship between model and mathematics is examined from various perspectives, including theoretical, computational, and applied aspects. It explores the mathematical foundations of models, the algorithms used to simulate and analyze them, and the applications of models in fields such as physics, engineering, biology, and social sciences. The book discusses the advantages and limitations of different modeling approaches, the role of uncertainty and approximation in model validation, and the ethical considerations associated with the use of mathematical models.

In conclusion, this open-access book offers a comprehensive and interdisciplinary examination of the relationship between model and mathematics. It provides a rich tapestry of historical, theoretical, and applied perspectives, fostering a deeper understanding of the role of mathematical models in advancing scientific knowledge and solving real-world problems. By promoting open access and collaboration, it aims to inspire future research and innovation in the field.

Weight: 840g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030978327
Edition number: 1st ed. 2022