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Full Description
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 Arts-Algebraic Modelling, virtually hosted by the Faculty of Mechanical Engineering, University of Niš, Serbia, from the 24th to the 26th of May, 2021. This conference brought together scholars from various disciplines and geographic regions and focused on thejuxtaposition 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.
Contents
Preface.- Foreword.- Introduction.- Problematic of mathematics and social sciences and arts: An ubiquitous constructive interaction in algebraic modeling.- Algebra as a semiotic modeling system.- The "unreasonable" effectiveness of mathematical modeling.- Algebra and modeling in mathematics school curricula.- Gödel's incompleteness as an argument for dualism.- Vetoing--social, logical and mathematical aspects.- Constructive semigrou0p with apartness--a state of the art.- Algebraic approaches to the analysis of social networks.- Relational systems of transport network and providences in ancient Rome.- Time and sequence in networks of social interactions.- Algebraic structures and social processes.- Index.
