Change and Invariance
Change and Invariance

Author: Ilya Sinitsky

Publisher: Springer

Published: 2016-11-25

Total Pages: 389

ISBN-13: 9463006990

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"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."

Theory of Technical Change and Economic Invariance
Theory of Technical Change and Economic Invariance

Author: Ryuzo Sato

Publisher: Academic Press

Published: 2014-05-10

Total Pages: 458

ISBN-13: 148327649X

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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.

Scale Invariance
Scale Invariance

Author: Annick LESNE

Publisher: Springer Science & Business Media

Published: 2011-11-04

Total Pages: 406

ISBN-13: 364215123X

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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.

Quarrel Between Invariance and Flux
Quarrel Between Invariance and Flux

Author: Joseph Margolis

Publisher: Penn State Press

Published: 2010-11-01

Total Pages: 284

ISBN-13: 9780271042503

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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.

Exploring Mathematics
Exploring Mathematics

Author: Daniel Grieser

Publisher: Springer

Published: 2018-05-21

Total Pages: 308

ISBN-13: 3319903217

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Have you ever faced a mathematical problem and had no idea how to approach it? Or perhaps you had an idea but got stuck halfway through? This book guides you in developing your creativity, as it takes you on a voyage of discovery into mathematics. Readers will not only learn strategies for solving problems and logical reasoning, but they will also learn about the importance of proofs and various proof techniques. Other topics covered include recursion, mathematical induction, graphs, counting, elementary number theory, and the pigeonhole, extremal and invariance principles. Designed to help students make the transition from secondary school to university level, this book provides readers with a refreshing look at mathematics and deep insights into universal principles that are valuable far beyond the scope of this book. Aimed especially at undergraduate and secondary school students as well as teachers, this book will appeal to anyone interested in mathematics. Only basic secondary school mathematics is required, including an understanding of numbers and elementary geometry, but no calculus. Including numerous exercises, with hints provided, this textbook is suitable for self-study and use alongside lecture courses.

Invariance Principles and the Structure of Technology
Invariance Principles and the Structure of Technology

Author: R. Sato

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 104

ISBN-13: 364245545X

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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.

Intuition in Science and Mathematics
Intuition in Science and Mathematics

Author: Efraim Fischbein

Publisher: Springer Science & Business Media

Published: 2005-12-19

Total Pages: 234

ISBN-13: 0306472376

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In writing the present book I have had in mind the following objectives: - To propose a theoretical, comprehensive view of the domain of intuition. - To identify and organize the experimental findings related to intuition scattered in a wide variety of research contexts. - To reveal the educational implications of the idea, developed for science and mathematics education. Most of the existing monographs in the field of intuition are mainly concerned with theoretical debates - definitions, philosophical attitudes, historical considerations. (See, especially the works of Wild (1938), of Bunge (1 962) and of Noddings and Shore (1 984).) A notable exception is the book by Westcott (1968), which combines theoretical analyses with the author’s own experimental studies. But, so far, no attempt has been made to identify systematically those findings, spread throughout the research literature, which could contribute to the deciphering of the mechanisms of intuition. Very often the relevant studies do not refer explicitly to intuition. Even when this term is used it occurs, usually, as a self-evident, common sense term.

Transformations
Transformations

Author: Wilfred R. Bion

Publisher: Routledge

Published: 2020-10-28

Total Pages: 221

ISBN-13: 0429923236

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Transformations continues the investigation of various aspects of psychoanalytic theory and practice which the author commenced with Learning from Experience (1962) and pursued in Elements of Psychoanalysis (1963). In this third work published in 1965, the author examines the ways in which the analyst's description of the original analytic experience, mediated by theory, necessarily transforms it in the course of effecting an interpretation.

New Methods for the Analysis of Change
New Methods for the Analysis of Change

Author: Linda M. Collins

Publisher: Amer Psychological Assn

Published: 2001-01-01

Total Pages: 442

ISBN-13: 9781557987549

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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).

Robust Python
Robust Python

Author: Patrick Viafore

Publisher: "O'Reilly Media, Inc."

Published: 2021-07-12

Total Pages: 365

ISBN-13: 1098100611

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Does it seem like your Python projects are getting bigger and bigger? Are you feeling the pain as your codebase expands and gets tougher to debug and maintain? Python is an easy language to learn and use, but that also means systems can quickly grow beyond comprehension. Thankfully, Python has features to help developers overcome maintainability woes. In this practical book, author Patrick Viafore shows you how to use Python's type system to the max. You'll look at user-defined types, such as classes and enums, and Python's type hinting system. You'll also learn how to make Python extensible and how to use a comprehensive testing strategy as a safety net. With these tips and techniques, you'll write clearer and more maintainable code. Learn why types are essential in modern development ecosystems Understand how type choices such as classes, dictionaries, and enums reflect specific intents Make Python extensible for the future without adding bloat Use popular Python tools to increase the safety and robustness of your codebase Evaluate current code to detect common maintainability gotchas Build a safety net around your codebase with linters and tests