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Author: Marcel Danesi
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.
Bridging Hegelian Dialectics and Marxian Models
Author: 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.
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.
Elementary School Mathematics Teachers’ Features of Education, Knowledge, Teaching and Personality
Editors: 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.
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.
Editors: Kim Beswick and Olive Chapman
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.

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.

One method successfully employed to denoise digital images is the diffusive iterative filtering. An important point of this technique is the estimation of the stopping time of the diffusion process. In this paper, we propose a stopping time criterion based on the evolution of the negentropy of the ’noise signal’ with the diffusion parameter. The nonlinear diffusive filter implemented with this stopping criterion is evaluated by using several noisy test images with different statistics. Assuming that images are corrupted by additive Gaussian noise, a statistical measure of the Gaussianity can be used to estimate the amount of noise removed from noisy images. In particular, the differential entropy function or, equivalently, the negentropy are robust measures of the Gaussianity. Because of computational complexity of the negentropy function, it is estimated by using an approximation of the negentropy introduced by Hyv¨arinen in the context of independent component analysis.

In: Computing Letters
Author: T.E. Simos

In this paper we investigate the connection between closed Newton-Cotes formulae, trigonometrically-fitted differential methods, symplectic integrators and efficient solution of the Schr¨odinger equation. Several one step symplectic integrators have been produced based on symplectic geometry, as one can see from the literature. However, the study of multistep symplectic integrators is very poor. Zhu et. al. [1] has studied the symplectic integrators and the well known open Newton-Cotes differential methods and as a result has presented the open Newton-Cotes differential methods as multilayer symplectic integrators. The construction of multistep symplectic integrators based on the open Newton-Cotes integration methods was investigated by Chiou and Wu [2]. In this paper we investigate the closed Newton-Cotes formulae and we write them as symplectic multilayer structures. We also develop trigonometrically-fitted symplectic methods which are based on the closed Newton-Cotes formulae. We apply the symplectic schemes to the well known one-dimensional Schr¨odinger equation in order to investigate the efficiency of the proposed method to these type of problems.

In: Computing Letters
Authors: F. Costabile and A. Napoli

For the numerical solution of the second order nonlinear two-point boundary value problems a family of polynomial global methods is derived.

Numerical examples provide favorable comparisons with other existing methods.

In: Computing Letters