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Reviving Ancient Chinese Mathematics: Mathematics, History and Politics in the Work of Wu Wen-Tsun (Needham Research Institute Series)
by Jiri HudecekTwentieth-century China has been caught between a desire to increase its wealth and power in line with other advanced nations, which, by implication, means copying their institutions, practices and values, whilst simultaneously seeking to preserve China’s independence and historically formed identity. Over time, Chinese philosophers, writers, artists and politicians have all sought to reconcile these goals and this book shows how this search for a Chinese way penetrated even the most central, least contested area of modernity: science. Reviving Ancient Chinese Mathematics is a study of the life of one of modern China’s most admired scientific figures, the mathematician Wu Wen-Tsun. Negotiating the conflict between progress and tradition, he found a path that not only ensured his political and personal survival, but which also brought him renown as a mathematician of international status who claimed that he stood outside the dominant western tradition of mathematics. Wu Wen-Tsun’s story highlights crucial developments and contradictions in twentieth -century China, the significance of which extends far beyond the field of mathematics. On one hand lies the appeal of radical scientific modernity, "mechanisation" in all its forms, and competitiveness within the international scientific community. On the other is an anxiety to preserve national traditions and make them part of the modernisation project. Moreover, Wu’s intellectual development also reflects the complex relationship between science and Maoist ideology, because his turn to history was powered by his internalisation of certain aspects of Maoist ideology, including its utilitarian philosophy of science. This book traces how Wu managed to combine political success and international scientific eminence, a story that has wider implications for a new century of increasing Chinese activity in the sciences. As such, it will be of great interest to students and scholars of Chinese history, the history of science and the history and philosophy of mathematics.
Revolutionary Mathematics: Artificial Intelligence, Statistics and the Logic of Capitalism
by Justin JoqueTraces the revolution in statistics that gave rise to artificial intelligence and predictive algorithms refiguring contemporary capitalism.Our finances, politics, media, opportunities, information, shopping and knowledge production are mediated through algorithms and their statistical approaches to knowledge; increasingly, these methods form the organizational backbone of contemporary capitalism. Revolutionary Mathematics traces the revolution in statistics and probability that has quietly underwritten the explosion of machine learning, big data and predictive algorithms that now decide many aspects of our lives. Exploring shifts in the philosophical understanding of probability in the late twentieth century, Joque shows how this was not merely a technical change but a wholesale philosophical transformation in the production of knowledge and the extraction of value. This book provides a new and unique perspective on the dangers of allowing artificial intelligence and big data to manage society. It is essential reading for those who want to understand the underlying ideological and philosophical changes that have fueled the rise of algorithms and convinced so many to blindly trust their outputs, reshaping our current political and economic situation.
Revolutionizing Fashion and Retail: Proceedings of the Fifth fashionXrecsys Workshop at the Recommender Systems Conference, Singapore, 18th-22nd September 2023 (Lecture Notes in Electrical Engineering #1299)
by Nima Dokoohaki Reza Shirvany Julia LaserreThis book presents the proceedings from the Fifth Workshop on Recommender Systems in Fashion and Retail (2023), highlighting the latest advances in AI-driven technologies for e-commerce, retail, and fashion. With contributions from leading academic and industry researchers, it explores how AI-powered recommender systems address key challenges and enable innovations in personalization and beauty, size and fit recommendations, and helping brands deliver more tailored and engaging shopping experiences.
Revolutionizing Youth Mental Health with Ethical AI: Transform Youth Mental Well-being by Exploring Responsible AI and GenAI Applications
by Sharmistha Chatterjee Azadeh Dindarian Usha RengarajuThis book is your comprehensive guide into the dynamic intersection of artificial intelligence (AI) and youth mental health. It aims to bridge the gap between cutting-edge AI technology and its transformative potential in addressing youth mental health challenges. The book's content is structured into three key parts, each focusing on different facets of AI applications in youth mental health. The first part provides a comprehensive background on the current state of youth mental health, analyzing the prevalence of mental health issues and identifying the unique challenges faced by the digital generation. In the second part, we explore the foundational principles of AI and its potential for revolutionizing mental health care, including natural language processing, machine learning, and predictive analytics. In this section, you will find in-depth case studies and real-world applications that showcase how AI-driven interventions have already transformed mental health care for youth across diverse contexts. Finally, the third part delves into ethical considerations, fairness, privacy concerns, and the responsible integration of AI in youth mental health care to design long-term sustainable solutions. This book offers a unique and holistic perspective, making it an indispensable resource for anyone passionate about leveraging AI for the betterment of youth mental health. Through this book, you will gain the knowledge and tools needed to design and implement effective AI-driven solutions that have the potential to transform the mental health landscape for the benefit of future generations. What You Will Learn Understand the current state of youth mental health, exploring the prevalence of mental health issues among the digital generation Understand natural language processing, machine learning, and predictive analytics Know how AI interventions are already transforming mental health care for youth in diverse contexts Be aware of fairness, privacy concerns, and the responsible integration of AI in youth mental health care Get familiar with the role of GenAI in the mental health domain and how AI agents can be a game-changer Who This Book Is For To equip academics and researchers in the AI, computer science, and digital mental health domain as well as AI application developers with a deeper understanding of how AI-powered innovations can enhance the well-being of youth; and innovation managers and policymakers who are interested in exploring the AI use cases
Rewriting Logic and Its Applications: 12th International Workshop, Wrla 2018, Held As A Satellite Event Of Etaps, Thessaloniki, Greece, June 14-15, 2018, Proceedings (Lecture Notes in Computer Science #11152)
by Vlad RusuThis book constitutes revised selected papers from the 12th International Workshop on Rewriting Logic and Its Applications, WRLA 2018, held in Thessaloniki, Greece, in June 2018. The 12 full papers presented in this volume were carefully reviewed and selected from 21 submissions. They deal with rewriting, a natural model of computation and an expressive semantic framework for concurrency, parallelism, communication, and interaction, and its applications.
Rewriting Logic and Its Applications: 15th International Workshop, WRLA 2024, Luxembourg City, Luxembourg, April 6–7, 2024, Revised Selected Papers (Lecture Notes in Computer Science #14953)
by Narciso Martí-Oliet Kazuhiro OgataThis book constitutes revised selected papers from the refereed proceedings of the 15th International Workshop on Rewriting Logic and Its Applications, WRLA 2024, held in Luxembourg City, Luxembourg, during April 6–7, 2024. The 11 full papers included in this book were carefully reviewed and selected from 16 submissions. They focus on several topics, e.g., foundations; rewriting as a logical and semantic framework; rewriting languages; verification techniques; applications; and education.
Rewriting the History of School Mathematics in North America 1607-1861
by M. A. Ken Clements Nerida EllertonThe focus of this book is the fundamental influence of the cyphering tradition on mathematics education in North American colleges, schools, and apprenticeship training classes between 1607 and 1861. It is the first book on the history of North American mathematics education to be written from that perspective. The principal data source is a set of 207 handwritten cyphering books that have never previously been subjected to careful historical analysis.
Rhetorical Ways of Thinking
by Lillie R. Albert Danielle Corea Vittoria MacadinoRhetorical Ways of Thinking focuses on how the co-construction of learning models the interpretation of a mathematical situation. It is a comprehensive examination of the role of sociocultural-historical theory developed by Vygotsky. This book puts forward the supposition that the major assumptions of sociocultural-historic theory are essential to understanding the theory's application to mathematical pedagogy, which explores issues relevant to learning and teaching mathematics-in-context, thus providing a valuable practical tool for general mathematics education research. The most important goal, then, is to exemplify the merging of the theory with practice and the subsequent applications to mathematics teaching and learning. This monograph contains five chapters, including a primer to Vygotsky's sociocultural historic theory, three comprehensive empirical studies examining: prospective teachers' perception of mathematics teaching and learning and the practice of scaffolded instruction to assist practicing teachers in developing their understanding of pedagogical content knowledge. Finally, the book concludes with a contextualization of the theory, linking it to best practices in the classroom.
Rhythmische Vorteile in Big Data und Machine Learning
by Kanad Ray Anirban BandyopadhyayDas Buch behandelt verschiedene Aspekte der Biophysik, beginnend mit einem populären Artikel über Neurobiologie und erstreckt sich bis zur Quantenbiologie, um letztendlich das Bewusstsein sowohl von Menschen als auch des Universums zu erforschen. Die Autoren haben neun verschiedene Facetten der natürlichen Intelligenz behandelt, angefangen bei der Entdeckung von Zeitkristallen in der chemischen Biologie bis hin zu den Schwingungen und Resonanzen von Proteinen. Sie haben ein breites Spektrum hierarchischer Kommunikation unter verschiedenen biologischen Systemen abgedeckt. Besonderes Augenmerk wurde darauf gelegt, sicherzustellen, dass der Inhalt selbst für Schülerinnen und Schüler zugänglich ist, wodurch die Biophysik wie ein Lehrbuch erscheint, das die Leser in die Bereiche der Biologie und Physik wie nie zuvor entführt. Die Autoren, die größtenteils erfahrene Akademiker sind, haben klare und einfache Sprache verwendet, um sicherzustellen, dass der Inhalt für alle Leser ansprechend und verständlich ist.
Ricci Flow and Geometric Applications
by Michel Boileau Gerard Besson Carlo Sinestrari Gang Tianriccardo Benedetti Carlo MantegazzaPresenting some impressive recent achievements in differential geometry and topology, this volume focuses on results obtained using techniques based on Ricci flow. These ideas are at the core of the study of differentiable manifolds. Several very important open problems and conjectures come from this area and the techniques described herein are used to face and solve some of them. The book's four chapters are based on lectures given by leading researchers in the field of geometric analysis and low-dimensional geometry/topology, respectively offering an introduction to: the differentiable sphere theorem (G. Besson), the geometrization of 3-manifolds (M. Boileau), the singularities of 3-dimensional Ricci flows (C. Sinestrari), and Kähler-Ricci flow (G. Tian). The lectures will be particularly valuable to young researchers interested in differential manifolds.
Ricci Flow for Shape Analysis and Surface Registration
by Wei Zeng Xianfeng David GuRicci Flow for Shape Analysis and Surface Registration introduces the beautiful and profound Ricci flow theory in a discrete setting. By using basic tools in linear algebra and multivariate calculus, readers can deduce all the major theorems in surface Ricci flow by themselves. The authors adapt the Ricci flow theory to practical computational algorithms, apply Ricci flow for shape analysis and surface registration, and demonstrate the power of Ricci flow in many applications in medical imaging, computer graphics, computer vision and wireless sensor network. Due to minimal pre-requisites, this book is accessible to engineers and medical experts, including educators, researchers, students and industry engineers who have an interest in solving real problems related to shape analysis and surface registration.
Riddle-iculous Math
by Joan Holub Regan Dunnick"What's the number of states in the U.S.A. minus the number of days in the month of May minus the number of paws on a grizzly bear minus the number of legs on the spider in your hair? Spider!?! Eeeek!" The answer to this and other math questions can be found in this funny book of riddles and jokes. Children can learn basic math skills while reading about animal sleepover parties, cafeteria food fights, and a boy who made more than 5 million dollars in one month!
Ridge Functions
by Allan PinkusRidge functions are a rich class of simple multivariate functions which have found applications in a variety of areas. These include partial differential equations (where they are sometimes termed 'plane waves'), computerised tomography, projection pursuit in the analysis of large multivariate data sets, the MLP model in neural networks, Waring's problem over linear forms, and approximation theory. Ridge Functions is the first book devoted to studying them as entities in and of themselves. The author describes their central properties and provides a solid theoretical foundation for researchers working in areas such as approximation or data science. He also includes an extensive bibliography and discusses some of the unresolved questions that may set the course for future research in the field.
Riemann Surfaces and Algebraic Curves
by Renzo Cavalieri Eric MilesHurwitz theory, the study of analytic functions among Riemann surfaces, is a classical field and active research area in algebraic geometry. The subject's interplay between algebra, geometry, topology and analysis is a beautiful example of the interconnectedness of mathematics. This book introduces students to this increasingly important field, covering key topics such as manifolds, monodromy representations and the Hurwitz potential. Designed for undergraduate study, this classroom-tested text includes over 100 exercises to provide motivation for the reader. Also included are short essays by guest writers on how they use Hurwitz theory in their work, which ranges from string theory to non-Archimedean geometry. Whether used in a course or as a self-contained reference for graduate students, this book will provide an exciting glimpse at mathematics beyond the standard university classes.
Riemannian Geometry
by Peter PetersenIntended for a one year course, this text serves as a single source, introducing readers to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian geometry. This is one of the few Works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory. The book will appeal to a readership that have a basic knowledge of standard manifold theory, including tensors, forms, and Lie groups. Important revisions to the third edition include: a substantial addition of unique and enriching exercises scattered throughout the text; inclusion of an increased number of coordinate calculations of connection and curvature; addition of general formulas for curvature on Lie Groups and submersions; integration of variational calculus into the text allowing for an early treatment of the Sphere theorem using a proof by Berger; incorporation of several recent results about manifolds with positive curvature; presentation of a new simplifying approach to the Bochner technique for tensors with application to bound topological quantities with general lower curvature bounds. From reviews of the first edition: "The book can be highly recommended to all mathematicians who want to get a more profound idea about the most interesting achievements in Riemannian geometry. It is one of the few comprehensive sources of this type. " ―Bernd Wegner, ZbMATH
Riemannian Geometry and Geometric Analysis
by Jürgen JostThis established reference work continues to lead its readers to some of the hottest topics of contemporary mathematical research. The previous edition already introduced and explained the ideas of the parabolic methods that had found a spectacular success in the work of Perelman at the examples of closed geodesics and harmonic forms. It also discussed further examples of geometric variational problems from quantum field theory, another source of profound new ideas and methods in geometry. The 6th edition includes a systematic treatment of eigenvalues of Riemannian manifolds and several other additions. Also, the entire material has been reorganized in order to improve the coherence of the book. From the reviews: "This book provides a very readable introduction to Riemannian geometry and geometric analysis. . . . With the vast development of the mathematical subject of geometric analysis, the present textbook is most welcome. " Mathematical Reviews ". . . the material . . . is self-contained. Each chapter ends with a set of exercises. Most of the paragraphs have a section 'Perspectives', written with the aim to place the material in a broader context and explain further results and directions. " Zentralblatt MATH
Riemannian Optimization and Its Applications (SpringerBriefs in Electrical and Computer Engineering)
by Hiroyuki SatoThis brief describes the basics of Riemannian optimization—optimization on Riemannian manifolds—introduces algorithms for Riemannian optimization problems, discusses the theoretical properties of these algorithms, and suggests possible applications of Riemannian optimization to problems in other fields.To provide the reader with a smooth introduction to Riemannian optimization, brief reviews of mathematical optimization in Euclidean spaces and Riemannian geometry are included. Riemannian optimization is then introduced by merging these concepts. In particular, the Euclidean and Riemannian conjugate gradient methods are discussed in detail. A brief review of recent developments in Riemannian optimization is also provided. Riemannian optimization methods are applicable to many problems in various fields. This brief discusses some important applications including the eigenvalue and singular value decompositions in numerical linear algebra, optimal model reduction in control engineering, and canonical correlation analysis in statistics.
Riemannsche Zahlensphäre und Möbius-Transformationen
by Maximilian WiechaIn diesem Buch wird der Punkt Unendlich zum Greifen nahe! Mit seiner berühmten Zahlenkugel fand Riemann eine Darstellung, in die der „unendlich ferne Punkt“ völlig gleichberechtigt zu den Punkten steht, die durch endliche Zahlenwerte beschrieben werden. Neben der Konstruktionsanleitung dieser Kugel widmen wir uns ausführlich den topologischen Grundlagen der erweiterten komplexen Ebene und den Eigenschaften der stereographischen Projektion. Zudem wird der Bezug zu einem wichtigen Abbildungstypen der Funktionentheorie hergestellt: den Möbius-Transformationen. Möbius-Transformationen bilden die Automorphismen der erweiterten Eben und kommen beispielsweise in der speziellen Relativitätstheorie und der Elektrotechnik („Smith-Diagramm“) zur Anwendung. Die als Lehrskript verfasste Lektüre umfasst das Fundament für das Verständnis beider Themen und beleuchtet ihre Verbindung. Sie enthält den ausführlich ausgearbeiteten Beweis zum berühmten YouTube-Video „Möbius Transformations Revealed“ (2008) von Arnold und Rogness und richtet sich an Interessierte der Mathematik, die bereits mit den Grundlagen der reellen Analysis, linearen Algebra und Differentialgeometrie vertraut sind. Der Autor Maximilian Wiecha studierte an der TU Braunschweig Chemie und Mathematik auf gymnasiales Lehramt. Im Laufe seines Studiums vertiefte er beide Fachrichtungen und beschäftigte sich u. a. mit der selektiven Synthese unsymmetrischer Diboran(IV)-Derivate. Neben seiner Leidenschaft für anorganische und physikalische Chemie, gehören die höhere Mathematik. Sein Interesse liegt auf Forschung und universitärer Lehre.
Riemann–Stieltjes Integral Inequalities for Complex Functions Defined on Unit Circle: with Applications to Unitary Operators in Hilbert Spaces
by Silvestru Sever DragomirThe main aim of this book is to present several results related to functions of unitary operators on complex Hilbert spaces obtained, by the author in a sequence of recent research papers. The fundamental tools to obtain these results are provided by some new Riemann-Stieltjes integral inequalities of continuous integrands on the complex unit circle and integrators of bounded variation. Features All the results presented are completely proved and the original references where they have been firstly obtained are mentioned Intended for use by both researchers in various fields of Linear Operator Theory and Mathematical Inequalities, as well as by postgraduate students and scientists applying inequalities in their specific areas Provides new emphasis to mathematical inequalities, approximation theory and numerical analysis in a simple, friendly and well-digested manner. About the Author Silvestru Sever Dragomir is Professor and Chair of Mathematical Inequalities at the College of Engineering & Science, Victoria University, Melbourne, Australia. He is the author of many research papers and several books on Mathematical Inequalities and their Applications. He also chairs the international Research Group in Mathematical Inequalities and Applications (RGMIA). For details, see https://rgmia.org/index.php.
Rigging Math Made Simple
by Delbert HallThis book breaks down complex entertainment rigging (theatre and arena) calculations and makes them easy to understand. It also provides hints for remembering many rigging formulas. It is a great resource for anyone studying for either ETCP rigging exam, and includes an explanation of the equations found on the ETCP Certified Rigger - Formula Table. The third edition has a greatly expanded section on arena rigging, as well as more material and appendices for theatrical rigging. Also, this edition has links to even more free downloads of Excel workbooks for arena rigging. Beginning riggers will find this an excellent textbook and experience riggers will find it as a great reference book.
Rigid Cohomology over Laurent Series Fields
by Christopher Lazda Ambrus PálIn this monograph, the authors develop a new theory of p-adiccohomology for varieties over Laurent series fields in positive characteristic,based on Berthelot's theory of rigid cohomology. Many major fundamentalproperties of these cohomology groups are proven, such as finite dimensionalityand cohomological descent, as well asinterpretations in terms of Monsky-Washnitzer cohomology and Le Stum'soverconvergent site. Applications of this new theory to arithmetic questions, such as l-independenceand the weight monodromy conjecture, are also discussed. The construction of these cohomology groups, analogous to theGalois representations associated tovarieties over local fields in mixed characteristic, fills a major gap in the study of arithmetic cohomology theoriesover function fields. By extending the scope of existing methods, the results presented here also serve as a firststep towards a more general theory of p-adic cohomology overnon-perfect ground fields. Rigid Cohomology over Laurent Series Fields will provide a useful tool for anyone interested in thearithmetic of varieties over local fields of positive characteristic. Appendices on important background material such as rigid cohomology and adicspaces make it as self-contained as possible, and an ideal starting point forgraduate students looking to explore aspects of the classical theory of rigidcohomology and with an eye towards future research in the subject.
Rigid Geometry of Curves and Their Jacobians
by Werner LütkebohmertThis book presents some of the most important aspects of rigid geometry, namely its applications to the study of smooth algebraic curves, of their Jacobians, and of abelian varieties - all of them defined over a complete non-archimedean valued field. The text starts with a survey of the foundation of rigid geometry, and then focuses on a detailed treatment of the applications. In the case of curves with split rational reduction there is a complete analogue to the fascinating theory of Riemann surfaces. In the case of proper smooth group varieties the uniformization and the construction of abelian varieties are treated in detail. Rigid geometry was established by John Tate and was enriched by a formal algebraic approach launched by Michel Raynaud. It has proved as a means to illustrate the geometric ideas behind the abstract methods of formal algebraic geometry as used by Mumford and Faltings. This book should be of great use to students wishing to enter this field, as well as those already working in it.
Rigidity and Symmetry
by Robert Connelly Asia Ivić Weiss Walter WhiteleyThis book contains recent contributions to the fields of rigidity and symmetry with two primary focuses: to present the mathematically rigorous treatment of rigidity of structures and to explore the interaction of geometry, algebra and combinatorics. Contributions present recent trends and advances in discrete geometry, particularly in the theory of polytopes. The rapid development of abstract polytope theory has resulted in a rich theory featuring an attractive interplay of methods and tools from discrete geometry, group theory, classical geometry, hyperbolic geometry and topology. Overall, the book shows how researchers from diverse backgrounds explore connections among the various discrete structures with symmetry as the unifying theme The volume will be a valuable source as an introduction to the ideas of both combinatorial and geometric rigidity theory and its applications, incorporating the surprising impact of symmetry. It will appeal to students at both the advanced undergraduate and graduate levels, as well as post docs, structural engineers and chemists.
Rigor in the 6–12 Math and Science Classroom: A Teacher Toolkit
by Barbara R. Blackburn Abbigail ArmstrongLearn how to incorporate rigorous activities in your math or science classroom and help students reach higher levels of learning. Expert educators and consultants Barbara R. Blackburn and Abbigail Armstrong offer a practical framework for understanding rigor and provide specialized examples for middle and high school math and science teachers. Topics covered include: Creating a rigorous environment High expectations Support and scaffolding Demonstration of learning Assessing student progress Collaborating with colleagues The book comes with classroom-ready tools, offered in the book and as free eResources on our website at www.routledge.com/9781138302716.
Rigor in the K–5 Math and Science Classroom: A Teacher Toolkit
by Barbara R. Blackburn Abbigail ArmstrongLearn how to incorporate rigorous activities in your math or science classroom and help students reach higher levels of learning. Expert educators and consultants Barbara R. Blackburn and Abbigail Armstrong offer a practical framework for understanding rigor and provide specialized examples for elementary math and science teachers. Topics covered include: Creating a rigorous environment High expectations Support and scaffolding Demonstration of learning Assessing student progress Collaborating with colleagues The book comes with classroom-ready tools, offered in the book and as free eResources on our website at www.routledge.com/9780367343194.