| Description |
1 online resource |
| Series |
Mathematics in Mind Series |
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Mathematics in Mind
|
| Contents |
Intro -- Foreword -- Preface -- References -- Introduction -- References -- Contents -- Part I Algebraic Thinking and Modeling -- Problematic of Mathematics, Social Sciences, and Arts: A Ubiquitous Constructive Interaction in Algebraic Modeling -- 1 Introduction -- 2 Mathematics and Society -- 3 Algebra, Algebraic Modeling, and Sciences -- 4 Mathematics and Arts -- 5 Concluding Remarks -- References -- Algebra as a Semiotic Modeling System -- 1 Introduction -- 2 Modeling Systems Theory: An Outline -- 3 Principles -- 4 Algebra as a Modeling System -- 5 Concluding Remarks -- Glossary |
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3.3 The Number Line in School Mathematics -- 3.4 Complexities in Using a Number Line in School Mathematics -- 3.5 Example: A Train Problem -- 4 Conclusions -- Appendix: Glossary of Notation and Definitions -- References -- Gödel's Incompleteness as an Argument for Dualism -- 1 Introduction -- 2 Naturalism vs. Dualism -- 3 Bare Bones of Incompleteness -- 4 Gödel's First Incompleteness Theorem -- 5 Gödel's Second Incompleteness Theorem -- 6 Gödelian Dualist Arguments and Their Refutations -- Appendix: Glossary of Notation and Definitions -- References |
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Vetoing: Social, Logical and Mathematical Aspects -- 1 Introduction -- 2 Impossibility through History -- 3 Social Decision: Practice and Theory -- 4 Social Choice: Traditional Theory -- 5 A Method of Axioms Simplification -- 6 Impossibilities with Vetoing, Dictatorship and Pareto Rule -- 7 Measuring the Veto Power in Voting Systems -- 8 A Note on Possible Further Research -- 9 Concluding Remarks -- Appendix: Glossary of Notation and Definitions -- References -- Part II Semigroups and Other Algebraic Structures in Social Sciences -- Constructive Semigroups with Apartness: A State of the Art |
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1 Introduction -- 2 The CLASS Case -- 2.1 Sets and Relations -- 2.1.1 Basic Concepts and Important Examples -- 2.1.2 Quotient Sets: Homomorphism and Isomorphism Theorems -- 2.1.3 Ordered Sets -- 2.2 Semigroups Within CLASS -- 2.2.1 Basic Concepts: Definitions, Examples, and Embedding Theorems -- 2.2.2 General Structure Results: Quotient Semigroups, Homomorphism, and Isomorphism Theorems -- 2.2.3 Ordered Semigroups: Definitions, Ordered Homomorphism and Ordered Isomorphism Theorems -- 2.3 Applications and Possible Applications -- 2.4 Notes -- 3 Within BISH -- 3.1 Set with Apartness |
| Summary |
This book addresses interconnections between contemporary advances in mathematics, especially algebra, with applications in the social sciences and the arts. It promotes the idea that knowledge cannot remain in disciplinary silos, rather, it belongs to all people, and is dedicated to associative relationships in a variety of mathematics applications, from sociology to linguistics, including anthropology, semiotics, education, and cognitive science. Contributions illuminate some of the ways in which algebra is developed, learned, understood, communicated, and applied in the social sciences and the humanities. The content in this book has its origins in a conference, Mathematics for Social Sciences and ArtsAlgebraic Modelling, virtually hosted by the Faculty of Mechanical Engineering, University of Ni, Serbia, from the 24th to the 26th of May, 2021. This conference brought together scholars from various disciplines and geographic regions and focused on the juxtaposition of algebra and social science applications. The conference organizers, higher education institutes from four different continents, invited leading scientists in social sciences and algebra, to contribute to this volume. The first part of this book addresses algebraic and mathematical thinking, specifically learning and practicing mathematics from a cognitive science perspective, as well as illustrative applications to distinctly human concerns, like education and semiotics. The second part focuses on algebraic semigroups and some of their generalizations. This book and the conference that engendered it provide an example of a fruitful collaboration, in which the skills and deep knowledge of algebraic structures, modeling, social sciences and arts brought in by the authors from different countries and continents merge in harmonious ways. These expositions are a rich resource and are of interest both to mathematicians and non-mathematicians |
| Bibliography |
References -- The "Unreasonable" Effectiveness of Mathematical Modeling -- 1 Introduction -- 2 Conceptual Integration (Blending) Theory: The Basic Architecture -- 3 The Concept of Mathematical Mapping and Small Spatial Stories -- 3.1 Small Spatial Stories and the Mathematical Classroom -- 4 Concluding Remarks -- Appendix: Glossary of Notation and Definitions -- References -- Algebra and Modeling in Mathematics School Curricula -- 1 Introduction -- 2 Algebra in the Curriculum -- 3 Algebra and Modeling -- 3.1 Number Line: A Powerful Model -- 3.2 Number Line in Mathematics |
| Notes |
Print version record |
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Online resource; title from PDF title page (SpringerLink, viewed February 23, 2024) |
| Subject |
Social sciences -- Mathematical models
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Arts -- Mathematical models
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| Genre/Form |
Electronic books
|
| Form |
Electronic book
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| Author |
Hounkonnou, M. Norbert.
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Martinovic, Dragana.
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Mitrović, Melanija
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Pattison, Philippa.
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| ISBN |
9783031377921 |
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3031377923 |
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