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The Philosophy of Mathematics Education
by Paul Ernest Ole Skovsmose Jean Paul van Bendegem Maria Bicudo Roger Miarka Ladislav Kvasz Regina MoellerAlthough many agree that all teaching rests on a theory of knowledge, there has been no in-depth exploration of the implications of the philosophy of mathematics for education. This is Paul Ernest's aim. Building on the work of Lakatos and Wittgenstein it challenges the prevalent notion that mathematical knowledge is certain, absolute and neutral, and offers instead an account of mathematics as a social construction. This has profound educational implications for social issues, including gender, race and multiculturalism; for pedagogy, including investigations and problem solving; and challenges hierarchical views of mathematics, learning and ability. Beyond this, the book offers a well-grounded model of five educational ideologies, each with its own epistemology, values, aims and social group of adherents. An analysis of the impact of these groups on the National Curriculum results in a powerful critique, revealing the questionable assumptions, values and interests upon which it rests. The book finishes on an optimistic note, arguing that pedagogy, left unspecified by the National Curriculum, is the way to achieve the radical aims of educating confident problem posers and solvers who are able to critically evaluate the social uses of mathematics.
The Philosophy of Mathematics Education Today (ICME-13 Monographs)
by Paul ErnestThis book offers an up-to-date overview of the research on philosophy of mathematics education, one of the most important and relevant areas of theory. The contributions analyse, question, challenge, and critique the claims of mathematics education practice, policy, theory and research, offering ways forward for new and better solutions. The book poses basic questions, including: What are our aims of teaching and learning mathematics? What is mathematics anyway? How is mathematics related to society in the 21st century? How do students learn mathematics? What have we learnt about mathematics teaching? Applied philosophy can help to answer these and other fundamental questions, and only through an in-depth analysis can the practice of the teaching and learning of mathematics be improved. The book addresses important themes, such as critical mathematics education, the traditional role of mathematics in schools during the current unprecedented political, social, and environmental crises, and the way in which the teaching and learning of mathematics can better serve social justice and make the world a better place for the future.
Philosophy of Mathematics in the Twentieth Century
by Charles ParsonsIn this illuminating collection, Charles Parsons surveys the contributions of philosophers and mathematicians who shaped the philosophy of mathematics over the course of the past century. Parsons begins with a discussion of the Kantian legacy in the work of L. E. J. Brouwer, David Hilbert, and Paul Bernays, shedding light on how Bernays revised his philosophy after his collaboration with Hilbert. He considers Hermann Weyl's idea of a "vicious circle" in the foundations of mathematics, a radical claim that elicited many challenges. Turning to Kurt Godel, whose incompleteness theorem transformed debate on the foundations of mathematics and brought mathematical logic to maturity, Parsons discusses his essay on Bertrand Russell's mathematical logic--Godel's first mature philosophical statement and an avowal of his Platonistic view. Philosophy of Mathematics in the Twentieth Century" insightfully treats the contributions of figures the author knew personally: W. V. Quine, Hilary Putnam, Hao Wang, and William Tait. Quine's early work on ontology is explored, as is his nominalistic view of predication and his use of the genetic method of explanation in the late work The Roots of Reference. " Parsons attempts to tease out Putnam's views on existence and ontology, especially in relation to logic and mathematics. Wang's contributions to subjects ranging from the concept of set, minds, and machines to the interpretation of Godel are examined, as are Tait's axiomatic conception of mathematics, his minimalist realism, and his thoughts on historical figures.
The Philosophy of Set Theory: An Historical Introduction to Cantor's Paradise
by Mary TilesA century ago, Georg Cantor demonstrated the possibility of a series of transfinite infinite numbers. His methods, unorthodox for the time, enabled him to derive theorems that established a mathematical reality for a hierarchy of infinities. Cantor's innovation was opposed, and ignored, by the establishment; years later, the value of his work was recognized and appreciated as a landmark in mathematical thought, forming the beginning of set theory and the foundation for most of contemporary mathematics. As Cantor's sometime collaborator, David Hilbert, remarked, "No one will drive us from the paradise that Cantor has created." This volume offers a guided tour of modern mathematics' Garden of Eden, beginning with perspectives on the finite universe and classes and Aristotelian logic. Author Mary Tiles further examines permutations, combinations, and infinite cardinalities; numbering the continuum; Cantor's transfinite paradise; axiomatic set theory; logical objects and logical types; and independence results and the universe of sets. She concludes with views of the constructs and reality of mathematical structure. Philosophers with only a basic grounding in mathematics, as well as mathematicians who have taken only an introductory course in philosophy, will find an abundance of intriguing topics in this text, which is appropriate for undergraduate-and graduate-level courses.
Philosophy of Stem Cell Biology
by Melinda Bonnie FaganThis examination of stem cell biology from a philosophy of science perspective clarifies the field's central concept, the stem cell, as well as its aims, methods, models, explanations and evidential challenges. Relations to systems biology and clinical medicine are also discussed.
Philosophy's Loss of Logic to Mathematics: An Inadequately Understood Take-Over (Studies in Applied Philosophy, Epistemology and Rational Ethics #43)
by Woosuk ParkThis book offers a historical explanation of important philosophical problems in logic and mathematics, which have been neglected by the official history of modern logic. It offers extensive information on Gottlob Frege’s logic, discussing which aspects of his logic can be considered truly innovative in its revolution against the Aristotelian logic. It presents the work of Hilbert and his associates and followers with the aim of understanding the revolutionary change in the axiomatic method. Moreover, it offers useful tools to understand Tarski’s and Gödel’s work, explaining why the problems they discussed are still unsolved. Finally, the book reports on some of the most influential positions in contemporary philosophy of mathematics, i.e., Maddy’s mathematical naturalism and Shapiro’s mathematical structuralism. Last but not least, the book introduces Biancani’s Aristotelian philosophy of mathematics as this is considered important to understand current philosophical issue in the applications of mathematics. One of the main purposes of the book is to stimulate readers to reconsider the Aristotelian position, which disappeared almost completely from the scene in logic and mathematics in the early twentieth century.
Phonon Thermal Transport in Silicon-Based Nanomaterials (SpringerBriefs in Physics)
by Hai-Peng Li Rui-Qin ZhangIn this Brief, authors introduce the advance in theoretical and experimental techniques for determining the thermal conductivity in nanomaterials, and focus on review of their recent theoretical studies on the thermal properties of silicon–based nanomaterials, such as zero–dimensional silicon nanoclusters, one–dimensional silicon nanowires, and graphenelike two–dimensional silicene. The specific subject matters covered include: size effect of thermal stability and phonon thermal transport in spherical silicon nanoclusters, surface effects of phonon thermal transport in silicon nanowires, and defects effects of phonon thermal transport in silicene. The results obtained are supplemented by numerical calculations, presented as tables and figures. The potential applications of these findings in nanoelectrics and thermoelectric energy conversion are also discussed. In this regard, this Brief represents an authoritative, systematic, and detailed description of the current status of phonon thermal transport in silicon–based nanomaterials. This Brief should be a highly valuable reference for young scientists and postgraduate students active in the fields of nanoscale thermal transport and silicon-based nanomaterials.
Photonic Neural Networks with Spatiotemporal Dynamics: Paradigms of Computing and Implementation
by Hideyuki Suzuki Jun Tanida Masanori HashimotoThis open access book presents an overview of recent advances in photonic neural networks with spatiotemporal dynamics. The computing and implementation paradigms presented in this book are outcomes of interdisciplinary studies by collaborative researchers from the three fields of nonlinear mathematical science, information photonics, and integrated systems engineering. This book offers novel multidisciplinary viewpoints on photonic neural networks, illustrating recent advances in three types of computing methodologies: fluorescence energy transfer computing, spatial-photonic spin system, and photonic reservoir computing. The book consists of four parts: Part I introduces the backgrounds of optical computing and neural network dynamics; Part II presents fluorescence energy transfer computing, a novel computing technology based on nanoscale networks of fluorescent particles; Parts III and IV review the models and implementation of spatial-photonic spin systems and photonic reservoir computing, respectively. These contents are beneficial to researchers in a broad range of fields, including information science, mathematical science, applied physics, and engineering, to better understand the novel computing concepts of photonic neural networks with spatiotemporal dynamics.
Photovoltaik
by Viktor Wesselak Sebastian VoswinckelWie funktioniert Photovoltaik? Welche Arten von Solarzellen gibt es? Wie wirtschaftlich sind Photovoltaik-Anlagen? Die Autoren erklären die wichtigsten Eigenschaften der Sonnenstrahlung und vermitteln die prinzipielle Funktionsweise einer Solarzelle. Sie gehen auf die Unterschiede heutiger und zukünftiger Technologien ein und diskutieren die Wirtschaftlichkeit unterschiedlicher Anlagenkonzepte. Dadurch finden Leser einen schnellen Einstieg ins Thema und lernen unterschiedliche Technologien und Anlagenvarianten einzuordnen und zu beurteilen.
Physical (A)Causality
by Karl SvozilThis open access book addresses the physical phenomenon of events that seem to occur spontaneously and without any known cause. These are to be contrasted with events that happen in a (pre-)determined, predictable, lawful, and causal way. All our knowledge is based on self-reflexive theorizing, as well as on operational means of empirical perception. Some of the questions that arise are the following: are these limitations reflected by our models? Under what circumstances does chance kick in? Is chance in physics merely epistemic? In other words, do we simply not know enough, or use too crude levels of description for our predictions? Or are certain events "truly", that is, irreducibly, random? The book tries to answer some of these questions by introducing intrinsic, embedded observers and provable unknowns; that is, observables and procedures which are certified (relative to the assumptions) to be unknowable or undoable. A (somewhat iconoclastic) review of quantum mechanics is presented which is inspired by quantum logic. Postulated quantum (un-)knowables are reviewed. More exotic unknowns originate in the assumption of classical continua, and in finite automata and generalized urn models, which mimic complementarity and yet maintain value definiteness. Traditional conceptions of free will, miracles and dualistic interfaces are based on gaps in an otherwise deterministic universe.
The Physical and Mathematical Foundations of the Theory of Relativity: A Critical Analysis
by Antonio Romano Mario Mango FurnariThis unique textbook offers a mathematically rigorous presentation of the theory of relativity, emphasizing the need for a critical analysis of the foundations of general relativity in order to best study the theory and its implications. The transitions from classical mechanics to special relativity and then to general relativity are explored in detail as well, helping readers to gain a more profound and nuanced understanding of the theory as a whole. After reviewing the fundamentals of differential geometry and classical mechanics, the text introduces special relativity, first using the physical approach proposed by Einstein and then via Minkowski’s mathematical model. The authors then address the relativistic thermodynamics of continua and electromagnetic fields in matter – topics which are normally covered only very briefly in other treatments – in the next two chapters. The text then turns to a discussion of general relativity by means of the authors’ unique critical approach, underlining the difficulty of recognizing the physical meaning of some statements, such as the physical meaning of coordinates and the derivation of physical quantities from those of space-time. Chapters in this section cover the model of space-time proposed by Schwarzschild; black holes; the Friedman equations and the different cosmological models they describe; and the Fermi-Walker derivative. Well-suited for graduate students in physics and mathematics who have a strong foundation in real analysis, classical mechanics, and general physics, this textbook is appropriate for a variety of graduate-level courses that cover topics in relativity. Additionally, it will interest physicists and other researchers who wish to further study the subtleties of these theories and understand the contemporary scholarly discussions surrounding them.
Physical Kinetics: Classical and Quantum Problems and Solutions
by Serguei N. BurmistrovThis book includes problems based on the material in the course of physical kinetics for the students of general and applied physics. It contains 60 problems with detailed solutions. The comments to the problems reflect the connection with the problems and methods of modern physical kinetics. A brief introduction gives the necessary information for solving and understanding the problems. The book is proposed for students and postgraduates studying the theoretical physics. The book is used as a supplement to the textbooks published on physical kinetics. The purpose of the book is to help students in training the practical skills and mastering the basic elements of physical kinetics. To understand the subject matter, it is sufficient to know the traditional courses of theoretical physics.
Physical Mathematics
by Kevin CahillUnique in its clarity, examples and range, Physical Mathematics explains as simply as possible the mathematics that graduate students and professional physicists need in their courses and research. The author illustrates the mathematics with numerous physical examples drawn from contemporary research. In addition to basic subjects such as linear algebra, Fourier analysis, complex variables, differential equations and Bessel functions, this textbook covers topics such as the singular-value decomposition, Lie algebras, the tensors and forms of general relativity, the central limit theorem and Kolmogorov test of statistics, the Monte Carlo methods of experimental and theoretical physics, the renormalization group of condensed-matter physics and the functional derivatives and Feynman path integrals of quantum field theory.
Physical Mathematics and Nonlinear Partial Differential Equations
by James H. LightbourneThis volume consists of the proceedings of the conference on Physical Mathematics and Nonlinear Partial Differential Equations held at West Virginia University in Morgantown. It describes some work dealing with weak limits of solutions to nonlinear systems of partial differential equations.
Physical Perspectives on Computation, Computational Perspectives on Physics
by Michael E. Cuffaro Samuel C. FletcherAlthough computation and the science of physical systems would appear to be unrelated, there are a number of ways in which computational and physical concepts can be brought together in ways that illuminate both. <P><P>This volume examines fundamental questions which connect scholars from both disciplines: is the universe a computer? Can a universal computing machine simulate every physical process? What is the source of the computational power of quantum computers? Are computational approaches to solving physical problems and paradoxes always fruitful? Contributors from multiple perspectives reflecting the diversity of thought regarding these interconnections address many of the most important developments and debates within this exciting area of research. Both a reference to the state of the art and a valuable and accessible entry to interdisciplinary work, the volume will interest researchers and students working in physics, computer science, and philosophy of science and mathematics.<P> Fills the gap in the book-length treatments of the interrelations between computation and physics, especially within philosophy.<P> Provides a reference point for the state of the art in important topics and research questions in this area.<P> Brings together scholars from a wide range of perspectives and disciplines.
Physical Principles of Electro-Mechano-Biology: Multiphysics and Supramolecular Approaches (Studies in Mechanobiology, Tissue Engineering and Biomaterials #25)
by Christian BrosseauThis book covers the recently developed understanding of Electro-Mechano-Biology (EMB) in which the focus is primarily on the couplings between the electric and mechanical fields. The emphasis lies on the analytical and computational aspects of EMB at the cellular level. The book is divided into two parts. In the first part, the author starts by defining and discussing the relevant basic aspects of the electrical and mechanical properties of cell membranes. He provides an overview of some of the ways analytical modelling of cell membrane electrodeformation (ED) and electroporation (EP) appears in a variety of contexts as well as a contemporary account of recent developments in computational approaches that can feature in the theory initiative, particularly in its attempt to describe the cohort of activities currently underway. Intended to serve as an introductory text and aiming to facilitate the understanding of the field to non-experts, this part does not dwell on the set of topics, such as cellular mechanosensing and mechanotransduction, irreversible EP, and atomistic molecular dynamics modelling of membrane EP. The second (and larger) part of the book is devoted to a presentation of the necessary analytical and computational tools to illustrate the ideas behind EMB and illuminate physical insights. Brief notes on the history of EMB and its many applications describing the variety of ideas and approaches are also included. In this part, the background of the first principles and practical calculation methods are discussed to highlight aspects that cannot be found in a single volume.
Physician Integration & Alignment: IPA, PHO, ACOs, and Beyond
by Maria K. ToddToday, with physician and hospital reimbursement being cut and tied to quality incentives, physicians and health plans are revisiting the concept of integration. Payers are demanding that the industry do more with less without sacrificing quality of care. As a result, physicians again find themselves integrating and aligning with hospitals that hav
The Physicists: The History of a Scientific Community in Modern America
by Daniel J. KevlesThis magnificent account of the coming of age of physics in America has been heralded as the best introduction to the history of science in the United States. Unsurpassed in its breadth and literary style, Kevles's account portrays the brilliant scientists who became a powerful force in bringing the world into a revolutionary new era. The book ranges widely as it links these exciting developments to the social, cultural, and political changes that occurred from the post-Civil War years to the present. Throughout, Kevles keeps his eye on the central question of how an avowedly elitist enterprise grew and prospered in a democratic culture. In this new edition, the author has brought the story up to date by providing an extensive, authoritative, and colorful account of the Superconducting Super Collider, from its origins in the international competition and intellectual needs of high-energy particle physics, through its establishment as a multibillion-dollar project, to its termination, in 1993, as a result of angry opposition within the American physics community and the Congress.
Physics: Volume 2
by David Halliday Robert Resnick Kenneth S. KraneWritten for the full year or three term Calculus-based University Physics course for science and engineering majors, the publication of the first edition of Physics in 1960 launched the modern era of Physics textbooks. It was a new paradigm at the time and continues to be the dominant model for all texts. Physics is the most realistic option for schools looking to teach a more demanding course. The entirety of Volume 2 of the 5th edition has been edited to clarify conceptual development in light of recent findings of physics education research. End-of-chapter problem sets are thoroughly over-hauled, new problems are added, outdated references are deleted, and new short-answer conceptual questions are added.
Physics and Finance (Undergraduate Lecture Notes in Physics)
by Volker ZiemannThis book introduces physics students to concepts and methods of finance. Despite being perceived as quite distant from physics, finance shares a number of common methods and ideas, usually related to noise and uncertainties. Juxtaposing the key methods to applications in both physics and finance articulates both differences and common features, this gives students a deeper understanding of the underlying ideas. Moreover, they acquire a number of useful mathematical and computational tools, such as stochastic differential equations, path integrals, Monte-Carlo methods, and basic cryptology. Each chapter ends with a set of carefully designed exercises enabling readers to test their comprehension.
Physics and Mathematics Behind Wave Dynamics (Synthesis Lectures on Wave Phenomena in the Physical Sciences)
by Sanichiro YoshidaMost physical phenomena exhibit spatiotemporal features interpreted as wave dynamics. Various diagnostic technologies use some waves such as light, sound, and microwaves. A proper understanding of wave dynamics is essential to interpret these physical phenomena and apply the technology efficiently. However, the physics underlying the wave-like behavior of real-world systems is not necessarily straightforward. Often the mathematical description of these physics is hard to understand. Consequently, the interpretation of diagnostic signals is not simple, which sometimes leads to an incorrect diagnosis. This book aims to solve these problems by describing the related topics on a sound physical basis and explaining them intuitively for easy digestion. Presents real-world examples of oscillatory and wave systems to help the reader understand wave dynamics while explaining numerical methods. Explains the physics and mathematics underlying wave dynamics in intuitive fashions.
Physics and Mathematics of Quantum Many-Body Systems (Graduate Texts in Physics)
by Hal TasakiThis book is a self-contained advanced textbook on the mathematical-physical aspects of quantum many-body systems, which begins with a pedagogical presentation of the necessary background information before moving on to subjects of active research, including topological phases of matter. The book explores in detail selected topics in quantum spin systems and lattice electron systems, namely, long-range order and spontaneous symmetry breaking in the antiferromagnetic Heisenberg model in two or higher dimensions (Part I), Haldane phenomena in antiferromagnetic quantum spin chains and related topics in topological phases of quantum matter (Part II), and the origin of magnetism in various versions of the Hubbard model (Part III). Each of these topics represents certain nontrivial phenomena or features that are invariably encountered in a variety of quantum many-body systems, including quantum field theory, condensed matter systems, cold atoms, and artificial quantum systems designed for future quantum computers. The book’s main focus is on universal properties of quantum many-body systems. The book includes roughly 50 problems with detailed solutions. The reader only requires elementary linear algebra and calculus to comprehend the material and work through the problems. Given its scope and format, the book is suitable both for self-study and as a textbook for graduate or advanced undergraduate classes.
Physics and Music: Essential Connections and Illuminating Excursions
by Stefan C. Müller Kinko TsujiThis book explores the fascinating and intimate relationship between music and physics. Over millennia, the playing of, and listening to music have stimulated creativity and curiosity in people all around the globe. Beginning with the basics, the authors first address the tonal systems of European-type music, comparing them with those of other, distant cultures. They analyze the physical principles of common musical instruments with emphasis on sound creation and particularly charisma. Modern research on the psychology of musical perception – the field known as psychoacoustics – is also described. The sound of orchestras in concert halls is discussed, and its psychoacoustic effects are explained. Finally, the authors touch upon the role of music for our mind and society. Throughout the book, interesting stories and anecdotes give insights into the musical activities of physicists and their interaction with composers and musicians.
The Physics Behind... (The Behind... series)
by Russ SwanCan you really lose weight by consuming nothing but ice cream and beer? How does the latest blockbuster movie get squeezed onto a disk, and how do they make the pictures seem 3D? How much does a selfie weigh? What's the science behind forensic investigations, body scans, and the dating of ancient artefacts?The Physics Behind... takes the reader on a fascinating journey through the scientific principles that that make the modern world work. Could there be life on Mars? Why is north really south? How do self-driving cars find their way around? These and many more topics are explored by starting with the basic science that makes them tick - examining the physics behind them. Packed with detailed original artwork and infographics, The Physics Behind... is perfect for anyone who has ever been curious about the science of life.Including:- The physics behind modern life: Wi-Fi, Facial recognition, touchscreens, microwave ovens, the ice cream and beer diet, taking a selfie, Flash memory, a bag of sugar, catching the train, calendars and clocks- The physics behind entertainment: optical discs, lasers, white water, executive toys, the electric guitar, music, 3D movies- The physics behind analysis: medical imaging, looking at little things, spectroscopy, crime scene investigation, tricorder, microfluidics, radiocarbon dating, proving the Earth is round- The physics behind space: rocket science, space weather, Planet Nine, space telescopes, is there anybody out there? life on Earth, life on Mars- The physics behind big science: what's the matter?, time travel, bomb or meltdown?, the Large Hadron Collider, the Human Genome Project, the Standard Model, gravity, everything- The physics behind the weird universe: strings, rings and other things, N-dimensional space, the hypercube, antimatter, the dark universe, quantum weirdness, quantum biology, time crystals and Majorana- The physics behind the environment: weather forecasts, climate change, renewable energy, migration, peacock feathers, sunburn, rainbows, spider silk- The physics behind transportation: autonomous autos, Hyperloop, Maglev, satellite navigation, motor sport, going rreeaallllyy fast, stealth- The physics behind everything else: curve balls, the Mpemba Effect, why north is really south, perpetual motion and the heat death of the universe, and the physics behind this book.
The Physics Behind...: Discover The Physics Of Everyday Life
by Russ SwanCan you really lose weight by consuming nothing but ice cream and beer? How does the latest blockbuster movie get squeezed onto a disk, and how do they make the pictures seem 3D? How much does a selfie weigh? What's the science behind forensic investigations, body scans, and the dating of ancient artefacts?The Physics Behind... takes the reader on a fascinating journey through the scientific principles that that make the modern world work. Could there be life on Mars? Why is north really south? How do self-driving cars find their way around? These and many more topics are explored by starting with the basic science that makes them tick - examining the physics behind them. Packed with detailed original artwork and infographics, The Physics Behind... is perfect for anyone who has ever been curious about the science of life.Including:- The physics behind modern life: Wi-Fi, Facial recognition, touchscreens, microwave ovens, the ice cream and beer diet, taking a selfie, Flash memory, a bag of sugar, catching the train, calendars and clocks- The physics behind entertainment: optical discs, lasers, white water, executive toys, the electric guitar, music, 3D movies- The physics behind analysis: medical imaging, looking at little things, spectroscopy, crime scene investigation, tricorder, microfluidics, radiocarbon dating, proving the Earth is round- The physics behind space: rocket science, space weather, Planet Nine, space telescopes, is there anybody out there? life on Earth, life on Mars- The physics behind big science: what's the matter?, time travel, bomb or meltdown?, the Large Hadron Collider, the Human Genome Project, the Standard Model, gravity, everything- The physics behind the weird universe: strings, rings and other things, N-dimensional space, the hypercube, antimatter, the dark universe, quantum weirdness, quantum biology, time crystals and Majorana- The physics behind the environment: weather forecasts, climate change, renewable energy, migration, peacock feathers, sunburn, rainbows, spider silk- The physics behind transportation: autonomous autos, Hyperloop, Maglev, satellite navigation, motor sport, going rreeaallllyy fast, stealth- The physics behind everything else: curve balls, the Mpemba Effect, why north is really south, perpetual motion and the heat death of the universe, and the physics behind this book.