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An Interdisciplinary Perspective
Zero has been axial in human development, but the origin and discovery of zero has never been satisfactorily addressed by a comprehensive, systematic and above all interdisciplinary research program. In this volume, over 40 international scholars explore zero under four broad themes: history; religion, philosophy & linguistics; arts; and mathematics & the sciences. Some propose that the invention/discovery of zero may have been facilitated by the prior evolution of a sophisticated concept of Nothingness or Emptiness (as it is understood in non-European traditions); and conversely, inhibited by the absence of, or aversion to, such a concept of Nothingness in the West. But not all scholars agree. Join the debate.
An Interdisciplinary Perspective
Zero has been axial in human development, but the origin and discovery of zero has never been satisfactorily addressed by a comprehensive, systematic and above all interdisciplinary research program. In this volume, over 40 international scholars explore zero under four broad themes: history; religion, philosophy & linguistics; arts; and mathematics & the sciences. Some propose that the invention/discovery of zero may have been facilitated by the prior evolution of a sophisticated concept of Nothingness or Emptiness (as it is understood in non-European traditions); and conversely, inhibited by the absence of, or aversion to, such a concept of Nothingness in the West. But not all scholars agree. Join the debate.
A Graph-Theoretic Analysis of Sentence Structure
Author:
What is the most descriptively and explanatorily adequate format for syntactic structures and how are they constrained? Different theories of syntax have provided various answers: sets, feature structures, tree diagrams… Building on formal and empirical insights from a wide variety of approaches spanning more than 70 years (including Transformational Grammar, Relational Grammar, Lexical-Functional Grammar, and Tree Adjoining Grammar), this monograph develops a new, mathematically grounded, framework in which objects known as graphs, and the constraints that follow from them, are argued to provide the best characterisation of the system of expressions and relations that make up natural language grammars. This new approach is motivated and exemplified via detailed and formally explicit analyses of major syntactic phenomena in English and Spanish.
A Graph-Theoretic Analysis of Sentence Structure
Author:
What is the most descriptively and explanatorily adequate format for syntactic structures and how are they constrained? Different theories of syntax have provided various answers: sets, feature structures, tree diagrams… Building on formal and empirical insights from a wide variety of approaches spanning more than 70 years (including Transformational Grammar, Relational Grammar, Lexical-Functional Grammar, and Tree Adjoining Grammar), this monograph develops a new, mathematically grounded, framework in which objects known as graphs, and the constraints that follow from them, are argued to provide the best characterisation of the system of expressions and relations that make up natural language grammars. This new approach is motivated and exemplified via detailed and formally explicit analyses of major syntactic phenomena in English and Spanish.
The definition of a healthcare system evolves continuously, becoming broader and more complex with each rendering. Healthcare systems can consist of many different elements, including but not limited to: access to comprehensive medical care, health promotion, disease prevention, institutional framework, financing schemes, government responsibility over health, etc. In light of its broad classification of healthcare, this book focuses on a wide spectrum of health-related issues ranging from risk factors for disease to medical treatment and possible frameworks for healthcare systems. Aging populations, increasing costs of healthcare, advancing technology, and challenges created by the COVID-19 pandemic require an innovative conceptual and methodological framework. By combining the experience and effort of researchers from a variety of fields including mathematics, medicine and economics, this book offers an interdisciplinary approach to studying health-related issues. It contributes to the existing literature by integrating the perspective of treatment with the economic determinants of health care outcomes, such as population density, access to financial resources and institutional frameworks. It also provides new evidence regarding the pharmaceutical industry including innovation, international trade and company performance.
Contributors are: Sayansk Da Silva, Joe Feinglass, Scott W. Hegerty, Joseph E. Hibdon, Jr, Arkadiusz Michał Kowalski, Małgorzata Stefania Lewandowska, Dawid Majcherek, Ewelina Nojszewska, Izabela Pruchnicka-Grabias, Agata Sielska and Julian Smółka.
Contributors are: Sayansk Da Silva, Joe Feinglass, Scott W. Hegerty, Joseph E. Hibdon, Jr, Arkadiusz Michał Kowalski, Małgorzata Stefania Lewandowska, Dawid Majcherek, Ewelina Nojszewska, Izabela Pruchnicka-Grabias, Agata Sielska and Julian Smółka.
The definition of a healthcare system evolves continuously, becoming broader and more complex with each rendering. Healthcare systems can consist of many different elements, including but not limited to: access to comprehensive medical care, health promotion, disease prevention, institutional framework, financing schemes, government responsibility over health, etc. In light of its broad classification of healthcare, this book focuses on a wide spectrum of health-related issues ranging from risk factors for disease to medical treatment and possible frameworks for healthcare systems. Aging populations, increasing costs of healthcare, advancing technology, and challenges created by the COVID-19 pandemic require an innovative conceptual and methodological framework. By combining the experience and effort of researchers from a variety of fields including mathematics, medicine and economics, this book offers an interdisciplinary approach to studying health-related issues. It contributes to the existing literature by integrating the perspective of treatment with the economic determinants of health care outcomes, such as population density, access to financial resources and institutional frameworks. It also provides new evidence regarding the pharmaceutical industry including innovation, international trade and company performance.
Contributors are: Sayansk Da Silva, Joe Feinglass, Scott W. Hegerty, Joseph E. Hibdon, Jr, Arkadiusz Michał Kowalski, Małgorzata Stefania Lewandowska, Dawid Majcherek, Ewelina Nojszewska, Izabela Pruchnicka-Grabias, Agata Sielska and Julian Smółka.
Contributors are: Sayansk Da Silva, Joe Feinglass, Scott W. Hegerty, Joseph E. Hibdon, Jr, Arkadiusz Michał Kowalski, Małgorzata Stefania Lewandowska, Dawid Majcherek, Ewelina Nojszewska, Izabela Pruchnicka-Grabias, Agata Sielska and Julian Smółka.
Toward a Deep Reading of Texts and Minds
Author:
The old practices of interpretation have been exhausted, and the humanities and social sciences are facing a crisis. Is there a way out of the labyrinth of reading? In this book, Professor Neuman presents a challenging approach to interpreting texts and reading literature through the spectacles of conceptual mathematics. This approach strives to avoid the simplicity of a quantitative approach to the analysis of literature as well as both the relativistic and the ideological dangers facing a qualitative reading of a text. The approach is introduced in a rigorous and accessible manner and woven with insights gained from various fields. Taking us on a challenging journey from Ovid’s Metamorphoses to Nick Cave’s The Death of Bunny Munro, the book shows how we may gain a deeper understanding of literature and the aesthetic experience of reading.
Toward a Deep Reading of Texts and Minds
Author:
The old practices of interpretation have been exhausted, and the humanities and social sciences are facing a crisis. Is there a way out of the labyrinth of reading? In this book, Professor Neuman presents a challenging approach to interpreting texts and reading literature through the spectacles of conceptual mathematics. This approach strives to avoid the simplicity of a quantitative approach to the analysis of literature as well as both the relativistic and the ideological dangers facing a qualitative reading of a text. The approach is introduced in a rigorous and accessible manner and woven with insights gained from various fields. Taking us on a challenging journey from Ovid’s Metamorphoses to Nick Cave’s The Death of Bunny Munro, the book shows how we may gain a deeper understanding of literature and the aesthetic experience of reading.
Geometry as a Hermeneutic Science
Author:
In Pi (π) in Nature, Art, and Culture Marcel Danesi revisits the importance of π as a pattern in the structure of reality, fitting in with the Pythagorean view of Order. Pi has cropped up in formulas that describe natural and physical structures which, on the surface, seem to have nothing to do with a circle, but might harbor the archetype of circularity as a principle.
Through π, this book thus revisits the implicit ancient Greek view that geometry was a 'hermeneutic science,' a discipline aiming to investigate the connectivity among numbers, shapes, and natural phenomena. It also examines its manifestations in aesthetic, symbolic and cultural structures, which point to an abiding fascination with the circle as an unconscious archetype. Hermeneutic geometry is ultimately about the exploration of the meanings of geometric-mathematical notions to science and human life.
Through π, this book thus revisits the implicit ancient Greek view that geometry was a 'hermeneutic science,' a discipline aiming to investigate the connectivity among numbers, shapes, and natural phenomena. It also examines its manifestations in aesthetic, symbolic and cultural structures, which point to an abiding fascination with the circle as an unconscious archetype. Hermeneutic geometry is ultimately about the exploration of the meanings of geometric-mathematical notions to science and human life.
Geometry as a Hermeneutic Science
Author:
In Pi (π) in Nature, Art, and Culture Marcel Danesi revisits the importance of π as a pattern in the structure of reality, fitting in with the Pythagorean view of Order. Pi has cropped up in formulas that describe natural and physical structures which, on the surface, seem to have nothing to do with a circle, but might harbor the archetype of circularity as a principle.
Through π, this book thus revisits the implicit ancient Greek view that geometry was a 'hermeneutic science,' a discipline aiming to investigate the connectivity among numbers, shapes, and natural phenomena. It also examines its manifestations in aesthetic, symbolic and cultural structures, which point to an abiding fascination with the circle as an unconscious archetype. Hermeneutic geometry is ultimately about the exploration of the meanings of geometric-mathematical notions to science and human life.
Through π, this book thus revisits the implicit ancient Greek view that geometry was a 'hermeneutic science,' a discipline aiming to investigate the connectivity among numbers, shapes, and natural phenomena. It also examines its manifestations in aesthetic, symbolic and cultural structures, which point to an abiding fascination with the circle as an unconscious archetype. Hermeneutic geometry is ultimately about the exploration of the meanings of geometric-mathematical notions to science and human life.
The Mathematics Teacher Educator as a Developing Professional (Second Edition)
This second edition of the International Handbook of Mathematics Teacher Education builds on and extends the topics/ideas in the first edition while maintaining the themes for each of the volumes. Collectively, the authors looked back beyond and within the last 10 years to establish the state-of-the-art and continuing and new trends in mathematics teacher and mathematics teacher educator education, and looked forward regarding possible avenues for teachers, teacher educators, researchers, and policy makers to consider to enhance and/or further investigate mathematics teacher and teacher educator learning and practice, in particular. The volume editors provide introductions to each volume that highlight the subthemes used to group related chapters, which offer meaningful lenses to see important connections within and across chapters. Readers can also use these subthemes to make connections across the four volumes, which, although presented separately, include topics that have relevance across them since they are all situated in the common focus regarding mathematics teachers.
Volume 4, The Mathematics Teacher Educator as a Developing Professional, focuses on the professionalization of mathematics teacher educators, which, since the first Handbook, continues to grow as an important area for investigation and development. It addresses teacher educators’ knowledge, learning and practice with teachers/instructors of mathematics. Thus, as the fourth volume in the series, it appropriately attends to those who hold central roles in mathematics teacher education to provide an excellent culmination to the handbook.
Volume 4, The Mathematics Teacher Educator as a Developing Professional, focuses on the professionalization of mathematics teacher educators, which, since the first Handbook, continues to grow as an important area for investigation and development. It addresses teacher educators’ knowledge, learning and practice with teachers/instructors of mathematics. Thus, as the fourth volume in the series, it appropriately attends to those who hold central roles in mathematics teacher education to provide an excellent culmination to the handbook.
The Mathematics Teacher Educator as a Developing Professional (Second Edition)
This second edition of the International Handbook of Mathematics Teacher Education builds on and extends the topics/ideas in the first edition while maintaining the themes for each of the volumes. Collectively, the authors looked back beyond and within the last 10 years to establish the state-of-the-art and continuing and new trends in mathematics teacher and mathematics teacher educator education, and looked forward regarding possible avenues for teachers, teacher educators, researchers, and policy makers to consider to enhance and/or further investigate mathematics teacher and teacher educator learning and practice, in particular. The volume editors provide introductions to each volume that highlight the subthemes used to group related chapters, which offer meaningful lenses to see important connections within and across chapters. Readers can also use these subthemes to make connections across the four volumes, which, although presented separately, include topics that have relevance across them since they are all situated in the common focus regarding mathematics teachers.
Volume 4, The Mathematics Teacher Educator as a Developing Professional, focuses on the professionalization of mathematics teacher educators, which, since the first Handbook, continues to grow as an important area for investigation and development. It addresses teacher educators’ knowledge, learning and practice with teachers/instructors of mathematics. Thus, as the fourth volume in the series, it appropriately attends to those who hold central roles in mathematics teacher education to provide an excellent culmination to the handbook.
Volume 4, The Mathematics Teacher Educator as a Developing Professional, focuses on the professionalization of mathematics teacher educators, which, since the first Handbook, continues to grow as an important area for investigation and development. It addresses teacher educators’ knowledge, learning and practice with teachers/instructors of mathematics. Thus, as the fourth volume in the series, it appropriately attends to those who hold central roles in mathematics teacher education to provide an excellent culmination to the handbook.
Bridging Hegelian Dialectics and Marxian Models
Author:
In How Language Informs Mathematics Dirk Damsma shows how Hegel’s and Marx’s systematic dialectical analysis of mathematical and economic language helps us understand the structure and nature of mathematical and capitalist systems. More importantly, Damsma shows how knowledge of the latter can inform model assumptions and help improve models.
His book provides a blueprint for an approach to economic model building that does away with arbitrarily chosen assumptions and is sensitive to the institutional structures of capitalism. In light of the failure of mainstream economics to understand systemic failures like the financial crisis and given the arbitrary character of most assumptions in mainstream models, such an approach is desperately needed.
His book provides a blueprint for an approach to economic model building that does away with arbitrarily chosen assumptions and is sensitive to the institutional structures of capitalism. In light of the failure of mainstream economics to understand systemic failures like the financial crisis and given the arbitrary character of most assumptions in mainstream models, such an approach is desperately needed.
Bridging Hegelian Dialectics and Marxian Models
Author:
In How Language Informs Mathematics Dirk Damsma shows how Hegel’s and Marx’s systematic dialectical analysis of mathematical and economic language helps us understand the structure and nature of mathematical and capitalist systems. More importantly, Damsma shows how knowledge of the latter can inform model assumptions and help improve models.
His book provides a blueprint for an approach to economic model building that does away with arbitrarily chosen assumptions and is sensitive to the institutional structures of capitalism. In light of the failure of mainstream economics to understand systemic failures like the financial crisis and given the arbitrary character of most assumptions in mainstream models, such an approach is desperately needed.
His book provides a blueprint for an approach to economic model building that does away with arbitrarily chosen assumptions and is sensitive to the institutional structures of capitalism. In light of the failure of mainstream economics to understand systemic failures like the financial crisis and given the arbitrary character of most assumptions in mainstream models, such an approach is desperately needed.
An Expanded Glossary of Key Terms and Concepts in Mathematics Teaching and Learning
The Language of Mathematics Education: An Expanded Glossary of Key Terms and Concepts in Mathematics Teaching and Learning offers mathematics teachers, mathematics education professionals and students a valuable resource in which common terms are defined and expounded upon in short essay format. The shared vocabulary and terminology relating to mathematics teaching and learning, and used by mathematics educators is an essential component of work conducted in the field.
The authors provide an overview of more than 100 terms commonly used in mathematics teaching and learning. Each term is defined and is followed by a short overview of the concept under discussion that includes several bibliographic references the reader can use for further investigation. In addition to terms specific to the domain of mathematics education, select key terms common across all fields of education (e.g., curriculum, epistemology, metacognition) are included. The goal for this book is to serve as a resource for those entering the field as they navigate the language and terminology of mathematics education and as an asset for more established professionals who wish to gain additional insights into these ideas.
The authors provide an overview of more than 100 terms commonly used in mathematics teaching and learning. Each term is defined and is followed by a short overview of the concept under discussion that includes several bibliographic references the reader can use for further investigation. In addition to terms specific to the domain of mathematics education, select key terms common across all fields of education (e.g., curriculum, epistemology, metacognition) are included. The goal for this book is to serve as a resource for those entering the field as they navigate the language and terminology of mathematics education and as an asset for more established professionals who wish to gain additional insights into these ideas.
An Expanded Glossary of Key Terms and Concepts in Mathematics Teaching and Learning
The Language of Mathematics Education: An Expanded Glossary of Key Terms and Concepts in Mathematics Teaching and Learning offers mathematics teachers, mathematics education professionals and students a valuable resource in which common terms are defined and expounded upon in short essay format. The shared vocabulary and terminology relating to mathematics teaching and learning, and used by mathematics educators is an essential component of work conducted in the field.
The authors provide an overview of more than 100 terms commonly used in mathematics teaching and learning. Each term is defined and is followed by a short overview of the concept under discussion that includes several bibliographic references the reader can use for further investigation. In addition to terms specific to the domain of mathematics education, select key terms common across all fields of education (e.g., curriculum, epistemology, metacognition) are included. The goal for this book is to serve as a resource for those entering the field as they navigate the language and terminology of mathematics education and as an asset for more established professionals who wish to gain additional insights into these ideas.
The authors provide an overview of more than 100 terms commonly used in mathematics teaching and learning. Each term is defined and is followed by a short overview of the concept under discussion that includes several bibliographic references the reader can use for further investigation. In addition to terms specific to the domain of mathematics education, select key terms common across all fields of education (e.g., curriculum, epistemology, metacognition) are included. The goal for this book is to serve as a resource for those entering the field as they navigate the language and terminology of mathematics education and as an asset for more established professionals who wish to gain additional insights into these ideas.
Elementary School Mathematics Teachers’ Features of Education, Knowledge, Teaching and Personality
The issue of mathematics teaching and its impact on learners' attainments in this subject has continuously been on the public agenda. The anthology of chapters in this book consists of varied up-to-date studies of some of the best mathematics education researchers and mathematics teaching experts, exploring the varied aspects of this essential. The book depicts the elementary school mathematics teachers' world while relating to three aspects which comprise the professional environment of mathematics teachers: Teachers' education and teachers' knowledge, Teaching and Teachers' personality. The chapters are written on a level which addresses and might interest a wide readership: researchers, in-service teachers, pre-service teachers, parents and learners.
Elementary School Mathematics Teachers’ Features of Education, Knowledge, Teaching and Personality
The issue of mathematics teaching and its impact on learners' attainments in this subject has continuously been on the public agenda. The anthology of chapters in this book consists of varied up-to-date studies of some of the best mathematics education researchers and mathematics teaching experts, exploring the varied aspects of this essential. The book depicts the elementary school mathematics teachers' world while relating to three aspects which comprise the professional environment of mathematics teachers: Teachers' education and teachers' knowledge, Teaching and Teachers' personality. The chapters are written on a level which addresses and might interest a wide readership: researchers, in-service teachers, pre-service teachers, parents and learners.
Editor:
This is the first book to collect research on game-theoretic tools in the analysis of language with particular reference to semantics and pragmatics. Games are significant, because they pertain equally to pragmatics and semantics of natural language. The book provides an overview of the variety of ways in which game theory is used in the analysis of linguistic meaning and shows how games arise in pragmatic as well as semantic investigations. The book is a balanced combination of philosophical, linguistic, logical and mathematical argumentation. The book has an introductory and a concluding chapter, written by the editor, to give a gentle introduction to the topics covered in the book and to provide wider conclusions and prospects arising from the individual essays.
The major topics covering the field of game theory and linguistic meaning included in the book are: language games, Wittgenstein evolutionary language games communication games, Grice games of partial information equilibrium semantics game-theoretic semantics logical modelling, and generalised quantifiers the semantics/pragmatics distinction. It includes international contributions from known leaders in the field. It is part of the Current Research in Semantics/Pragmatics Interface series.
The major topics covering the field of game theory and linguistic meaning included in the book are: language games, Wittgenstein evolutionary language games communication games, Grice games of partial information equilibrium semantics game-theoretic semantics logical modelling, and generalised quantifiers the semantics/pragmatics distinction. It includes international contributions from known leaders in the field. It is part of the Current Research in Semantics/Pragmatics Interface series.
Editor:
This is the first book to collect research on game-theoretic tools in the analysis of language with particular reference to semantics and pragmatics. Games are significant, because they pertain equally to pragmatics and semantics of natural language. The book provides an overview of the variety of ways in which game theory is used in the analysis of linguistic meaning and shows how games arise in pragmatic as well as semantic investigations. The book is a balanced combination of philosophical, linguistic, logical and mathematical argumentation. The book has an introductory and a concluding chapter, written by the editor, to give a gentle introduction to the topics covered in the book and to provide wider conclusions and prospects arising from the individual essays.
The major topics covering the field of game theory and linguistic meaning included in the book are: language games, Wittgenstein evolutionary language games communication games, Grice games of partial information equilibrium semantics game-theoretic semantics logical modelling, and generalised quantifiers the semantics/pragmatics distinction. It includes international contributions from known leaders in the field. It is part of the Current Research in Semantics/Pragmatics Interface series.
The major topics covering the field of game theory and linguistic meaning included in the book are: language games, Wittgenstein evolutionary language games communication games, Grice games of partial information equilibrium semantics game-theoretic semantics logical modelling, and generalised quantifiers the semantics/pragmatics distinction. It includes international contributions from known leaders in the field. It is part of the Current Research in Semantics/Pragmatics Interface series.