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Author: Hans Freudenthal
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 201
ISBN-13: 9401036675
DOWNLOAD EBOOKProceedings of the Colloquium sponsored by the Division of Philosophy of Sciences of the International Union of History and Philosophy of Sciences organized at Utrecht, January 1960.
Author: J.W. Addison
Publisher: Elsevier
Published: 2014-05-27
Total Pages: 513
ISBN-13: 1483275345
DOWNLOAD EBOOKStudies in Logic and the Foundations of Mathematics: The Theory of Models covers the proceedings of the International Symposium on the Theory of Models, held at the University of California, Berkeley on June 25 to July 11, 1963. The book focuses on works devoted to the foundations of mathematics, generally known as "the theory of models." The selection first discusses the method of alternating chains, semantic construction of Lewis's systems S4 and S5, and continuous model theory. Concerns include ordered model theory, 2-valued model theory, semantics, sequents, axiomatization, formulas, axiomatic approach to hierarchies, alternating chains, and difference hierarchies. The text also ponders on Boolean notions extended to higher dimensions, elementary theories with models without automorphisms, and applications of the notions of forcing and generic sets. The manuscript takes a look at a hypothesis concerning the extension of finite relations and its verification for certain special cases, theories of functors and models, model-theoretic methods in the study of elementary logic, and extensions of relational structures. The text also reviews relatively categorical and normal theories, algebraic theories, categories, and functors, denumerable models of theories with extra predicates, and non-standard models for fragments of number theory. The selection is highly recommended for mathematicians and researchers interested in the theory of models.
Author: Urszula Strawinska-Zanko
Publisher: Springer
Published: 2018-06-07
Total Pages: 227
ISBN-13: 3319767658
DOWNLOAD EBOOKThis edited volume presents examples of social science research projects that employ new methods of quantitative analysis and mathematical modeling of social processes. This book presents the fascinating areas of empirical and theoretical investigations that use formal mathematics in a way that is accessible for individuals lacking extensive expertise but still desiring to expand their scope of research methodology and add to their data analysis toolbox. Mathematical Modeling of Social Relationships professes how mathematical modeling can help us understand the fundamental, compelling, and yet sometimes complicated concepts that arise in the social sciences. This volume will appeal to upper-level students and researchers in a broad area of fields within the social sciences, as well as the disciplines of social psychology, complex systems, and applied mathematics.
Author: National Research Council
Publisher: National Academies Press
Published: 2012-02-28
Total Pages: 400
ISBN-13: 0309214459
DOWNLOAD EBOOKScience, engineering, and technology permeate nearly every facet of modern life and hold the key to solving many of humanity's most pressing current and future challenges. The United States' position in the global economy is declining, in part because U.S. workers lack fundamental knowledge in these fields. To address the critical issues of U.S. competitiveness and to better prepare the workforce, A Framework for K-12 Science Education proposes a new approach to K-12 science education that will capture students' interest and provide them with the necessary foundational knowledge in the field. A Framework for K-12 Science Education outlines a broad set of expectations for students in science and engineering in grades K-12. These expectations will inform the development of new standards for K-12 science education and, subsequently, revisions to curriculum, instruction, assessment, and professional development for educators. This book identifies three dimensions that convey the core ideas and practices around which science and engineering education in these grades should be built. These three dimensions are: crosscutting concepts that unify the study of science through their common application across science and engineering; scientific and engineering practices; and disciplinary core ideas in the physical sciences, life sciences, and earth and space sciences and for engineering, technology, and the applications of science. The overarching goal is for all high school graduates to have sufficient knowledge of science and engineering to engage in public discussions on science-related issues, be careful consumers of scientific and technical information, and enter the careers of their choice. A Framework for K-12 Science Education is the first step in a process that can inform state-level decisions and achieve a research-grounded basis for improving science instruction and learning across the country. The book will guide standards developers, teachers, curriculum designers, assessment developers, state and district science administrators, and educators who teach science in informal environments.
Author: Lee Rudolph
Publisher: Routledge
Published: 2013-01-03
Total Pages: 494
ISBN-13: 1136232303
DOWNLOAD EBOOKIn this book Lee Rudolph brings together international contributors who combine psychological and mathematical perspectives to analyse how qualitative mathematics can be used to create models of social and psychological processes. Bridging the gap between the fields with an imaginative and stimulating collection of contributed chapters, the volume updates the current research on the subject, which until now has been rather limited, focussing largely on the use of statistics. Qualitative Mathematics for the Social Sciences contains a variety of useful illustrative figures, introducing readers from the social sciences to the rich contribution that modern mathematics has made to our knowledge of logic, structures, and dynamic systems. A beguiling array of conceptual systems, topological models and fractals are discussed which transcend the application of statistics, and bring a fresh perspective to the study of social representations. The wide selection of qualitative mathematical methodologies discussed in this volume will be hugely valuable to higher-level undergraduate and postgraduate students of psychology, sociology and mathematics. It will also be useful for researchers, academics and professionals from the social sciences who want a firmer grasp on the use of qualitative mathematics.
Author: Arthur C. Petersen
Publisher: CRC Press
Published: 2012-04-24
Total Pages: 227
ISBN-13: 146650062X
DOWNLOAD EBOOKComputer simulation has become an important means for obtaining knowledge about nature. The practice of scientific simulation and the frequent use of uncertain simulation results in public policy raise a wide range of philosophical questions. Most prominently highlighted is the field of anthropogenic climate change—are humans currently changing the climate? Referring to empirical results from science studies and political science, Simulating Nature: A Philosophical Study of Computer-Simulation Uncertainties and Their Role in Climate Science and Policy Advice, Second Edition addresses questions about the types of uncertainty associated with scientific simulation and about how these uncertainties can be communicated. The author, who participated in the United Nations’ Intergovernmental Panel on Climate Change (IPCC) plenaries in 2001 and 2007, discusses the assessment reports and workings of the IPCC. This second edition reflects the latest developments in climate change policy, including a thorough update and rewriting of sections that refer to the IPCC.
Author: Francisco Antonio Doria
Publisher: World Scientific
Published: 2017-05-30
Total Pages: 289
ISBN-13: 1786343177
DOWNLOAD EBOOKCurrent mathematical models are notoriously unreliable in describing the time evolution of unexpected social phenomena, from financial crashes to revolution. Can such events be forecast? Can we compute probabilities about them? Can we model them? This book investigates and attempts to answer these questions through Gödel's two incompleteness theorems, and in doing so demonstrates how influential Gödel is in modern logical and mathematical thinking. Many mathematical models are applied to economics and social theory, while Gödel's theorems are able to predict their limitations for more accurate analysis and understanding of national and international events.This unique discussion is written for graduate level mathematicians applying their research to the social sciences, including economics, social studies and philosophy, and also for formal logicians and philosophers of science.
Author: Richard J. Chorley
Publisher: Routledge
Published: 2013-10-14
Total Pages: 358
ISBN-13: 1136155848
DOWNLOAD EBOOKFirst published in 1968, this book explores the theme of geographical generalization, or model building. It is composed of seven of the chapters from the original Models in Geography, published in 1967. The first chapter broadly outlines this theme and examines the nature and function of generalized statements, ranging from conceptual models to scale models, in a geographical context. The following six chapters deal with socio-economic building in geography. They focus on demographic and sociological models as well as looking at special aspects of models in human geography in reference to economic development, urban geography and settlement location, industrial location, and agricultural activity. This book represents a robustly anti-idiographic statement of modern work in one of the major branches of geography.
Author: Michael Friedman
Publisher: Springer Nature
Published: 2022-08-08
Total Pages: 441
ISBN-13: 3030978338
DOWNLOAD EBOOKThis open access book collects the historical and medial perspectives of a systematic and epistemological analysis of the complicated, multifaceted relationship between model and mathematics, ranging from, for example, the physical mathematical models of the 19th century to the simulation and digital modelling of the 21st century. The aim of this anthology is to showcase the status of the mathematical model between abstraction and realization, presentation and representation, what is modeled and what models. This book is open access under a CC BY 4.0 license.
Author: Roderick Melnik
Publisher: John Wiley & Sons
Published: 2015-05-18
Total Pages: 340
ISBN-13: 1118853989
DOWNLOAD EBOOKMathematical and Computational Modeling Illustrates the application of mathematical and computational modeling in a variety of disciplines With an emphasis on the interdisciplinary nature of mathematical and computational modeling, Mathematical and Computational Modeling: With Applications in the Natural and Social Sciences, Engineering, and the Arts features chapters written by well-known, international experts in these fields and presents readers with a host of state-of-theart achievements in the development of mathematical modeling and computational experiment methodology. The book is a valuable guide to the methods, ideas, and tools of applied and computational mathematics as they apply to other disciplines such as the natural and social sciences, engineering, and technology. The book also features: Rigorous mathematical procedures and applications as the driving force behind mathematical innovation and discovery Numerous examples from a wide range of disciplines to emphasize the multidisciplinary application and universality of applied mathematics and mathematical modeling Original results on both fundamental theoretical and applied developments in diverse areas of human knowledge Discussions that promote interdisciplinary interactions between mathematicians, scientists, and engineers Mathematical and Computational Modeling: With Applications in the Natural and Social Sciences, Engineering, and the Arts is an ideal resource for professionals in various areas of mathematical and statistical sciences, modeling and simulation, physics, computer science, engineering, biology and chemistry, and industrial and computational engineering. The book also serves as an excellent textbook for graduate courses in mathematical modeling, applied mathematics, numerical methods, operations research, and optimization.
