Mathematical Modelling by Help of Category Theory: Abstract Perspectives on Models and Coupling of Models
暫譯: 透過範疇論的數學建模：模型及模型耦合的抽象視角

Legatiuk, Dmitrii

Mathematical Modelling by Help of Category Theory: Abstract Perspectives on Models and Coupling of Models
  • 出版商: Springer
  • 出版日期: 2025-03-20
  • 售價: $6,700
  • 貴賓價: 9.5 折 $6,365
  • 語言: 英文
  • 頁數: 178
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3031849507
  • ISBN-13: 9783031849503
  • 相關分類: 離散數學 Discrete-mathematics

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商品描述

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.

商品描述(中文翻譯)

這本專著提供了一種新穎的結構性視角，用於工程問題的建模，利用類別理論的抽象數學形式。

具體而言，本書旨在通過發展基於類別理論的框架來增強對數學建模的理解。類別理論被用來建立數學模型及其複雜性之間的清晰關係。然後，該理論擴展到涵蓋耦合的數學模型，並納入更高級的類別結構。為了橋接理論與實踐，本書展示了抽象類別框架的工程應用，提供來自現實工程場景的各種建模範例。此外，它還介紹了自動模型生成和建模中的錯誤檢測的初步概念。

這裡發展的理論展示了類別理論的實用性，使本書成為應用數學和工程領域研究人員的寶貴資源，特別是那些專注於建模理論基礎的研究者。

作者簡介

Dimitrii Legatiuk is a mathematician working at the University of Erfurt, Germany. The main research interests of Dr. Legatiuk are related to Clifford analysis in continuous and discrete setting, discrete octonionic analysis, numerical analysis of partial differential equations, classical complex function theory and its applications, as well as the formalisation of mathematical modelling by the help of category theory and type theory. For his outstanding contribution to the field of Clifford analysis, Dr. Legatiuk was awarded the W.K. Clifford prize in 2020.

作者簡介(中文翻譯)

Dimitrii Legatiuk 是一位在德國厄爾福特大學工作的數學家。Legatiuk 博士的主要研究興趣與克利福德分析（Clifford analysis）在連續和離散環境中的應用、離散八元數分析（discrete octonionic analysis）、偏微分方程的數值分析、經典複變函數理論及其應用，以及通過範疇理論（category theory）和類型理論（type theory）來形式化數學建模有關。因為他對克利福德分析領域的傑出貢獻，Legatiuk 博士於2020年獲得了W.K. Clifford獎。

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