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Mathematical Modelling by Help of Category Theory : Abstract Perspectives on Models and Coupling of Models / by Dmitrii Legatiuk

By: Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Mathematical EngineeringPublisher: Cham : Springer Nature Switzerland, 2025Edition: 1st ed. 2025Description: 1 Online-Ressource(XII, 178 p. 92 illus., 2 illus. in color.)ISBN:
  • 9783031849510
Subject(s): Additional physical formats: 9783031849503 | 9783031849527 | 9783031849534 | Erscheint auch als: Mathematical modelling by help of category theory. Druck-Ausgabe Cham : Springer Nature Switzerland, 2025. xii, 178 SeitenDDC classification:
  • 003.3 23
DOI: DOI: 10.1007/978-3-031-84951-0Online resources: Summary: - 1. Modelling process in engineering -- 2. Preliminaries from category theory -- 3. Categorical approach to mathematical modelling -- 4. Engineering perspectives and applications -- 5. Type-theoretic and abstract algebraic approaches to conceptual modelling -- 6. Epilogue.Summary: This monograph offers a novel structural perspective on the modelling of engineering problems, utilizing abstract mathematics in the form of category theory. Specifically, the book aims to enhance the understanding of mathematical modelling by developing a category theory-based framework. Category theory is employed to establish clear relationships between mathematical models and their complexities. The theory is then extended to encompass coupled mathematical models, incorporating more advanced categorical structures. To bridge theory and practice, the book presents engineering applications of the abstract categorical framework, providing various modelling examples from real-world engineering scenarios. Additionally, it introduces initial concepts for automatic model generation and error detection in modelling. The theory developed here demonstrates the practical utility of category theory, making this book a valuable resource for researchers in applied mathematics and engineering, particularly those focused on theoretical foundations of modelling.PPN: PPN: 1920502777Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SMA | ZDB-2-SXMS
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