Currently, economics and cognitive science are heavily rooted in Newtonian physics, successfully borrowing a great deal of modeling tools from it. This is a great achievement. You do not need quantum mechanics or theories of relativity to build a house or bridge. Nevertheless, no one would deny the importance of modern theoretical physics. I believe many intellectuals have realized the need to go beyond the limitations of the Newtonian tradition for means of social science research. The big question is how to do it and how to do it right. This book aims to integrate economics and cognitive science by applying theoretical physics from a modeling perspective. During the course of this book, necessary background knowledge preparations for understanding the content topics are also briefl y provided. Thus, this book is designed to be conceptually and instrumentally self-contained. Everyone interested should be able to read it.

A new and comprehensive examination of the history of the modern physical and mathematical sciences.

The major creations and developments in mathematics from the beginnings in Babylonia and Egypt through the first few decades of the twentieth century are presented with clarity and precision in this comprehensive historical study.

The Mathematical Principles of Scale Relativity Physics: The Concept of Interpretation explores and builds upon the principles of Laurent Nottale’s scale relativity. The authors address a variety of problems encountered by researchers studying the dynamics of physical systems. It explores Madelung fluid from a wave mechanics point of view, showing that confinement and asymptotic freedom are the fundamental laws of modern natural philosophy. It then probes Nottale’s scale transition description, offering a sound mathematical principle based on continuous group theory. The book provides a comprehensive overview of the matter to the reader via a generalization of relativity, a theory of colors, and classical electrodynamics. Key Features: Develops the concept of scale relativity interpreted according to its initial definition enticed by the birth of wave and quantum mechanics Provides the fundamental equations necessary for interpretation of matter, describing the ensembles of free particles according to the concepts of confinement and asymptotic freedom Establishes a natural connection between the Newtonian forces and the Planck’s law from the point of view of space and time scale transition: both are expressions of invariance to scale transition The work will be of great interest to graduate students, doctoral candidates, and academic researchers working in mathematics and physics.

The field of education is in constant flux as new theories and practices emerge to engage students and improve the learning experience. Globalization has created new challenges for mathematics educators as they are compelled to respond to the shifting patterns and practices of everyday life and stay abreast of the latest research in education, curriculum, development, and technologies. Globalized Curriculum Methods for Modern Mathematics Education is a comprehensive and timely publication that contains the latest research in mathematics education and modern globalized curriculum development and technologies. The book examines subjects such as teaching competencies, digital games for teaching and learning mathematics, and the challenges and prospects of globalized science curriculum. This is an ideal resource for educators, academicians, teachers, policy makers, researchers, and graduate-level students seeking to further their research in mathematics education.

Philanthropic societies funded by the Rockefeller family were prominent in the social history of the twentieth century, for their involvement in medicine and applied science. This book provides the first detailed study of their relatively brief but nonetheless influential foray into the field of mathematics.

The separation of science and religion in modern secular culture can easily obscure the fact that in sixteenth- and seventeenth-century Europe ideas about nature were intimately related to ideas about God. Readers of this book will find fresh and exciting accounts of a phenomenon common to both science and religion: deviation from orthodox belief. How is heterodoxy to be measured? How might the scientific heterodoxy of particular thinkers impinge on their religious views? Would heterodoxy in religion create a predisposition towards heterodoxy in science? Might there be a homology between heterodox views in both domains? Such major protagonists as Galileo and Newton are re-examined together with less familiar figures in order to bring out the extraordinary richness of scientific and religious thought in the pre-modern world.

This book is not a conventional history of mathematics as such, a museum of documents and scientific curiosities. Instead, it identifies this vital science with the thought of those who constructed it and in its relation to the changing cultural context in which it evolved. Particular emphasis is placed on the philosophic and logical systems, from Aristotle onward, that provide the basis for the fusion of mathematics and logic in contemporary thought.