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E-raamat: Elementary Introduction to n-fold Groupoids: Contextualized by Elastic Composites and Metamaterials

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Elementary Introduction to n-fold Groupoids: Contextualized by Elastic Composites and MetamaterialsSuurem pilt
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This book introduces groupoids and n-fold groupoids as powerful mathematical tools that unify and generalize local and distant symmetries observed in physical systems. While these concepts are typically discussed in highly specialized literature, this volume makes them accessible to a broader audience by grounding them in concrete applications to solid mechanics, including composite materials and metamaterials. No prior knowledge of the theory or its applications is assumed. The chapters alternate between mathematical foundations and their realization in the behavior of elastic bodies, offering readers a guided and rewarding exploration. Throughout the book, examples and exercises support understanding and encourage hands-on engagement. This work opens a new perspective on symmetry in applied mathematics and physics, bridging abstract theory with practical modeling.

Chapter 1 What is a groupoid?.
Chapter 2 A surgical-mechanical
imagery.- Chapter 3 The material groupoid.- Chapter 4 Double
groupoids.-Chapter 5 Binary composites.- Chapter 6  Hypercubes abd
skeletons.
Chapter 7 Coarse n-groupoids.
Chapter 8 Material n-groupoids.
Marcelo Epstein is a professor at the University of Calgary, Canada, at the Department of Mechanical and Manufacturing Engineering.
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