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Author: Ilya Sinitsky
Publisher: Springer
ISBN: 9463006990
Category : Education
Languages : en
Pages : 389
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Book Description
"What is the connection between finding the amount of acid needed to reach the desired concentration of a chemical solution, checking divisibility by a two-digit prime number, and maintaining the perimeter of a polygon while reducing its area? The simple answer is the title of this book.The world is an interplay of variation and constancy – a medley of differences and similarities – and this change and invariance is, largely, a language of science and mathematics. This book proposes a unique approach for developing mathematical insight through the perspective of change and invariance as it applies to the properties of numbers and shapes.After a short introductory chapter, each of the following chapters presents a series of evolving activities for students that focus on a specific aspect of interplay between change and invariance. Each activity is accompanied by detailed mathematical explanations and a didactic discussion. The assignments start with tasks familiar from the school curriculum, but progress beyond the menial to lead to sophisticated generalizations. Further activities are suggested to augment the chapter’s theme. Some examples: “How to represent all the integers from zero to 1000 using ten fingers?”, “How to win at the game of Nim?”, “Why do different square lattice polygons with the same area often have the same perimeter?” This book can be used as a textbook for pre-service mathematics teachers and is primarily intended for their academic instructors. Essentially, students, teachers and anyone interested in elementary mathematics will enjoy the elegant solutions provided for the plethora of problems in elementary mathematics through the systematic approach of invariance and change."
Author: Ilya Sinitsky
Publisher: Springer
ISBN: 9463006990
Category : Education
Languages : en
Pages : 389
Get Book Here
Book Description
"What is the connection between finding the amount of acid needed to reach the desired concentration of a chemical solution, checking divisibility by a two-digit prime number, and maintaining the perimeter of a polygon while reducing its area? The simple answer is the title of this book.The world is an interplay of variation and constancy – a medley of differences and similarities – and this change and invariance is, largely, a language of science and mathematics. This book proposes a unique approach for developing mathematical insight through the perspective of change and invariance as it applies to the properties of numbers and shapes.After a short introductory chapter, each of the following chapters presents a series of evolving activities for students that focus on a specific aspect of interplay between change and invariance. Each activity is accompanied by detailed mathematical explanations and a didactic discussion. The assignments start with tasks familiar from the school curriculum, but progress beyond the menial to lead to sophisticated generalizations. Further activities are suggested to augment the chapter’s theme. Some examples: “How to represent all the integers from zero to 1000 using ten fingers?”, “How to win at the game of Nim?”, “Why do different square lattice polygons with the same area often have the same perimeter?” This book can be used as a textbook for pre-service mathematics teachers and is primarily intended for their academic instructors. Essentially, students, teachers and anyone interested in elementary mathematics will enjoy the elegant solutions provided for the plethora of problems in elementary mathematics through the systematic approach of invariance and change."
Author: Ryuzo Sato
Publisher: Academic Press
ISBN: 148327649X
Category : Business & Economics
Languages : en
Pages : 458
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Book Description
Theory of Technical Change and Economic Invariance: Application of Lie Groups presents the economic invariance problems observable behavior under general transformations such as taste change or technical change. This book covers a variety of topics in economic theory, ranging from the analysis of production functions to the general recoverability problem of optimal dynamic behavior. Organized into nine chapters, this book begins with an overview of the theory of observable behavior by analyzing the invariant relationships among economic variables. This text then examines the Lie group theory which provides one of the most efficient methods of studying invariance properties. Other chapters consider the analysis of exogenous technical change, a process partly due to dynamic market forces of supply and demand. This book discusses as well the topics closely related to parametric changes under Lie groups and related transformations. The final chapter deals with mathematical foundations of the theory of observable market behavior. This book is a valuable resource for economists.
Author: Annick LESNE
Publisher: Springer Science & Business Media
ISBN: 364215123X
Category : Science
Languages : en
Pages : 406
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Book Description
During a century, from the Van der Waals mean field description (1874) of gases to the introduction of renormalization group (RG techniques 1970), thermodynamics and statistical physics were just unable to account for the incredible universality which was observed in numerous critical phenomena. The great success of RG techniques is not only to solve perfectly this challenge of critical behaviour in thermal transitions but to introduce extremely useful tools in a wide field of daily situations where a system exhibits scale invariance. The introduction of scaling, scale invariance and universality concepts has been a significant turn in modern physics and more generally in natural sciences. Since then, a new "physics of scaling laws and critical exponents", rooted in scaling approaches, allows quantitative descriptions of numerous phenomena, ranging from phase transitions to earthquakes, polymer conformations, heartbeat rhythm, diffusion, interface growth and roughening, DNA sequence, dynamical systems, chaos and turbulence. The chapters are jointly written by an experimentalist and a theorist. This book aims at a pedagogical overview, offering to the students and researchers a thorough conceptual background and a simple account of a wide range of applications. It presents a complete tour of both the formal advances and experimental results associated with the notion of scaling, in physics, chemistry and biology.
Author: Joseph Margolis
Publisher: Penn State Press
ISBN: 9780271042503
Category : Philosophy
Languages : en
Pages : 284
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Book Description
Rather than just offer background readings or a survey of views on a subject, as traditional anthologies do, this volume tries to engage the reader's active participation in understanding how philosophy came to be split between analytic and continental approaches and in finding ways to reconcile the two. It does so by tracing the history of philosophy as a perennial contest between two opposing world views: one that relates change to an underlying structure of invariance, and another that sees change itself ("flux") as the basic condition of existence. The seven chapters cover the full range of major topics of philosophy, from metaphysics to epistemology to ethics, and present carefully selected readings from key thinkers--Plato, Aristotle, Locke, Hegel, and Peirce up to Heidegger, Husserl, Kuhn, Kripke, and Putnam, among others--juxtaposed and introduced by the editors so as to stimulate active thinking about how the debate between these competing visions plays out in each arena. A bibliography of additional sources ends each chapter. The result is a new and inspiring tool for teaching philosophy to both beginning and advanced students. Even seasoned professionals will have much to learn about the development of philosophy and its current predicament from accepting the challenge to rethink the tradition from the perspective presented here.
Author: Ryuzo Sato
Publisher: Edward Elgar Publishing
ISBN:
Category : Economics, Mathematical
Languages : en
Pages : 466
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Book Description
This edition of Sato's 20-year-old work illustrates his contribution to economics. Under the heading transformation and invariance, the book deals with a number of topics in economic theory, from production functions to the general recoverability problem of optimal dynamic behaviour.
Author: Linda M. Collins
Publisher: Amer Psychological Assn
ISBN: 9781557987549
Category : Medical
Languages : en
Pages : 442
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Book Description
Annotation Psychologists update the Association's 1991 with 12 studies, many from a conference held at Pennsylvania State University in 1998, and some with comments attached. The topics include differential structural equation modeling of intra-individual variability, combining auto-regressive and latent curve models, and planned missing-data designs for analyzing change. Annotation c. Book News, Inc., Portland, OR (booknews.com).
Author: R. Sato
Publisher: Springer Science & Business Media
ISBN: 364245545X
Category : Business & Economics
Languages : en
Pages : 104
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Book Description
The theory of Lie groups has proven to be a most powerful analytical tool in many areas of modern scientific endeavors. It was only a few years ago that economists discovered the usefulness of this approach in their study of the frontiers of modern economic theory. These frontiers include the areas of technical change and productivity, technology and preference, economic conservation laws, comparative statics and integrability conditions, index number problems, and the general theory of ~ observable market behavior (Sato [1980, 1981], Nono [1971], Sato and N~no [1983], Russell [1983]). 1 In Nono [1971] and Sa to [1981, Chapter 4] the concept of "G-neutral" (group neutral) technical change was first introduced as a natural extension of the well-known concepts of Hicks, Harrod, Solow and Sato-Beckmann-Rose neutrality. The present monograph contains a further extension of the G-neutral technical change to the case of non-constant-returns-to-scale technology and to the case of multiple factor inputs. The methodology of total productivity estimation by means of Lie group transformations is also developed in this monograph. We would like to express our sincere thanks to many individuals notably to Professor M. J. Beckmann, Professor F. Mimura, Professor G. Suzawa, T. Mitchell, K. Mino and P. Calem, for their numerous contributions at various stages of this work. We are also grateful to Marion Wathey for her usual superb typing of this difficult manuscript. Providence, R. I. , U. S. A.
Author: Michael Eid
Publisher: Guilford Publications
ISBN: 1462555721
Category : Social Science
Languages : en
Pages : 379
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Book Description
The use of multiple raters can improve the validity of conclusions made on self- (and other) reports of emotions, attitudes, goals, and self-perceptions of personality. Yet analyzing these ratings requires special psychometric models that take into account the specific nature of these data. From leading authorities, this book offers the first comprehensive introduction to structural equation modeling (SEM) of multiple rater data. Rather than taking a one-size-fits-all approach, the book shows how the choice of a model should be guided by measurement design and purpose. Practical recommendations are provided for selecting suitable measurement designs, raters, and psychometric models. Models for different combinations of rater types and for cross-sectional as well as longitudinal research designs are described step by step, with a strong emphasis on the substantive meaning of the latent variables in the models. User-friendly features include equation boxes, application boxes, and a companion website with Mplus and lavaan code for the book’s examples.
Author: Hanjo Berressem
Publisher: Edinburgh University Press
ISBN: 1474450784
Category : Philosophy
Languages : en
Pages : 273
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Book Description
Hanjo Berressem establishes the notion of a schizoanalytic ecology as the most consistent conceptual spine of Félix Guattari's work. He covers the whole range of Guattari's solo work and the books co-authored with Gilles Deleuze, primarily a rigorous explication and analysis of 'Schizoanalytic Cartographies'.
Author: G. Cristescu
Publisher: Springer Science & Business Media
ISBN: 1461500036
Category : Mathematics
Languages : en
Pages : 375
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Book Description
Lectori salutem! The kind reader opens the book that its authors would have liked to read it themselves, but it was not written yet. Then, their only choice was to write this book, to fill a gap in the mathematicalliterature. The idea of convexity has appeared in the human mind since the antiquity and its fertility has led to a huge diversity of notions and of applications. A student intending a thoroughgoing study of convexity has the sensation of swimming into an ocean. It is due to two reasons: the first one is the great number of properties and applications of the classical convexity and second one is the great number of generalisations for various purposes. As a consequence, a tendency of writing huge books guiding the reader in convexity appeared during the last twenty years (for example, the books of P. M. Gruber and J. M. Willis (1993) and R. J. Webster (1994)). Another last years' tendency is to order, from some point of view, as many convexity notions as possible (for example, the book of I. Singer (1997)). These approaches to the domain of convexity follow the previous point of view of axiomatizing it (A. Ghika (1955), W. Prenowitz (1961), D. Voiculescu (1967), V. W. Bryant and R. J. Webster (1969)). Following this last tendency, our book proposes to the reader two classifications of convexity properties for sets, both of them starting from the internal mechanism of defining them.
