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How Language Informs Mathematics

Bridging Hegelian Dialectics and Marxian Models

Series:

Dirk Damsma

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.

The Narrative of Mathematics Teachers

Elementary School Mathematics Teachers’ Features of Education, Knowledge, Teaching and Personality

Edited by Dorit Patkin and Avikam Gazit

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.

Series:

John McNutt, Chao Guo, Lauri Goldkind and Seongho An

Information and communication technologies (ICT) are major forces shaping our current age. ICT affects many areas of human existence and influences the both human wellbeing and human evil. The nonprofit sector is already heavily involved in technology both as a way to pursue its mission and as an influential factor in the evolution of the sector. This article examines how technology affects the sector and how the sector uses technology in its work.
The article begins with a discussion of how the emerging information society will change the nonprofit sector. The sector that we know is grounded on our experience in the agrarian and industrial periods in the United States and Europe. We then explore how technology evolved in the sector. This is followed by an examination of technology and nonprofit organizational behavior. Technology changes the organizations that make use of its capacities. Next is a discussion of the types of technology that nonprofit organizations use. The final three sections deal with technology and social change, technology in nonprofit settings, and issues and trends. This article provides the reader with a current appreciation of the scholarly and professional literature on ICT in the nonprofit sector.

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Edited by Ahti-Veikko Pietarinen

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 Commentary of al-Nayrizi on Book I of Euclid's Elements of Geometry

with an Introduction on the Transmission of Euclid's Elements in the Middle Ages

Series:

Edited by Anthony Lo Bello

For more than two millennia, the Elements of Geometry by the Greek mathematician Euclid of Alexandria (ca. 300 B.C.E. ) was held to be “the supreme example of the exercise of human reason” and “a paradigm of rational certainty” (from the preface, after Simon Blackburn). The Commentary of al-Nayrizi on Book I of Euclid’s Elements of Geometry introduces readers to the transmission of Euclid’s Elements from the Middle East to the Latin West in the medieval period and then offers the first English translation of al-Nayrizi’s (d. ca. 922) Arabic commentary on Book I.

The Three Volumes are also available as set (ISBN 0 391 04197 5)

Series:

Edited by Anthony Lo Bello

The Commentary of Albertus Magnus on Book I of Euclid’s Elements of Geometry is the third in Lo Bello’s series on the Elements. Lo Bello provides the first modern translation of a key Latin text of the Elements in the Middle Ages, the commentary of the Dominican scholastic philosopher Albertus Magnus (d. 1280), the teacher of Thomas Aquinas. The volume includes a translation, notes on the translation, and a critical examination of the mathematical content of the three commentaries on Euclid’s Elements of Geometry thus far treated in this series.

The Three Volumes are also available as set (ISBN 0 391 04197 5)

Gerard of Cremona’s Translation of the Commentary of al-Nayrizi on Book I of Euclid’s Elements of Geometry

With an Introductory Account of the Twenty-Two Early Extant Arabic Manuscripts of the Elements

Series:

Edited by Anthony Lo Bello

Anthony Lo Bello’s Gerard of Cremona’s Translation of Book I of the Commentary of al-Nayrizi on Euclid’s Elements of Geometry is the first modern translation of Gerard of Cremona’s (1114–1187) Latin version of al-Nayrizi’s famous Arabic commentary. Lo Bello gives an introductory account of the twenty-two early extant Arabic manuscripts of the Elements, an annotated English translation of Gerard’s translation of al-Nayrizi’s commentary, and finally a critical analysis of the idiosyncrasies of Gerard’s method of translation.

The Three Volumes are also available as set (ISBN 0 391 04197 5)