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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 Anirban Bandyopadhyay Kanad RayDas 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.
A Richer Picture of Mathematics: The Göttingen Tradition and Beyond
by David E. RoweHistorian David E. Rowe captures the rich tapestry of mathematical creativity in this collection of essays from the “Years Ago” column of The Mathematical Intelligencer. With topics ranging from ancient Greek mathematics to modern relativistic cosmology, this collection conveys the impetus and spirit of Rowe’s various and many-faceted contributions to the history of mathematics. Centered on the Göttingen mathematical tradition, these stories illuminate important facets of mathematical activity often overlooked in other accounts. Six sections place the essays in chronological and thematic order, beginning with new introductions that contextualize each section. The essays that follow recount episodes relating to the section’s overall theme. All of the essays in this collection, with the exception of two, appeared over the course of more than 30 years in The Mathematical Intelligencer. Based largely on archival and primary sources, these vignettes offer unusual insights into behind-the-scenes events. Taken together, they aim to show how Göttingen managed to attract an extraordinary array of talented individuals, several of whom contributed to the development of a new mathematical culture during the first decades of the twentieth century.
The Richness of the History of Mathematics: A Tribute to Jeremy Gray (Archimedes #66)
by Karine Chemla José Ferreirós Lizhen Ji Erhard Scholz Chang WangThis book, a tribute to historian of mathematics Jeremy Gray, offers an overview of the history of mathematics and its inseparable connection to philosophy and other disciplines. Many different approaches to the study of the history of mathematics have been developed. Understanding this diversity is central to learning about these fields, but very few books deal with their richness and concrete suggestions for the “what, why and how” of these domains of inquiry. The editors and authors approach the basic question of what the history of mathematics is by means of concrete examples. For the “how” question, basic methodological issues are addressed, from the different perspectives of mathematicians and historians. Containing essays by leading scholars, this book provides a multitude of perspectives on mathematics, its role in culture and development, and connections with other sciences, making it an important resource for students and academics in the history and philosophy of mathematics.
Riddle-iculous Math
by Regan Dunnick Joan Holub"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.
The Riemann Hypothesis: The Greatest Unsolved Problem in Mathematics
by Karl SabbaghHistorical discussion of the still unsolved problem of the Riemann Hypothesis.
The Riemann Hypothesis for Function Fields
by Machiel Van FrankenhuijsenThis book provides a lucid exposition of the connections between non-commutative geometry and the famous Riemann Hypothesis, focusing on the theory of one-dimensional varieties over a finite field. The reader will encounter many important aspects of the theory, such as Bombieri's proof of the Riemann Hypothesis for function fields, along with an explanation of the connections with Nevanlinna theory and non-commutative geometry. The connection with non-commutative geometry is given special attention, with a complete determination of the Weil terms in the explicit formula for the point counting function as a trace of a shift operator on the additive space, and a discussion of how to obtain the explicit formula from the action of the idele class group on the space of adele classes. The exposition is accessible at the graduate level and above, and provides a wealth of motivation for further research in this area.
The Riemann Hypothesis in Characteristic p in Historical Perspective (Lecture Notes in Mathematics #2222)
by Peter RoquetteThis book tells the story of the Riemann hypothesis for function fields (or curves) starting with Artin's 1921 thesis, covering Hasse's work in the 1930s on elliptic fields and more, and concluding with Weil's final proof in 1948. The main sources are letters which were exchanged among the protagonists during that time, found in various archives, mostly the University Library in Göttingen. The aim is to show how the ideas formed, and how the proper notions and proofs were found, providing a particularly well-documented illustration of how mathematics develops in general. The book is written for mathematicians, but it does not require any special knowledge of particular mathematical fields.
The Riemann Problem in Continuum Physics (Applied Mathematical Sciences #219)
by Philippe G. LeFloch Mai Duc ThanhThis monograph provides a comprehensive study of the Riemann problem for systems of conservation laws arising in continuum physics. It presents the state-of-the-art on the dynamics of compressible fluids and mixtures that undergo phase changes, while remaining accessible to applied mathematicians and engineers interested in shock waves, phase boundary propagation, and nozzle flows. A large selection of nonlinear hyperbolic systems is treated here, including the Saint-Venant, van der Waals, and Baer-Nunziato models. A central theme is the role of the kinetic relation for the selection of under-compressible interfaces in complex fluid flows. This book is recommended to graduate students and researchers who seek new mathematical perspectives on shock waves and phase dynamics.
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.
The Riemann Zeta-Function: Theory and Applications (Dover Books on Mathematics)
by Aleksandar IvicThis extensive survey presents a comprehensive and coherent account of Riemann zeta-function theory and applications. Starting with elementary theory, it examines exponential integrals and exponential sums, the Voronoi summation formula, the approximate functional equation, the fourth power moment, the zero-free region, mean value estimates over short intervals, higher power moments, and omega results. Additional topics include zeros on the critical line, zero-density estimates, the distribution of primes, the Dirichlet divisor problem and various other divisor problems, and Atkinson's formula for the mean square. End-of-chapter notes supply the history of each chapter's topic and allude to related results not covered by the book. 1985 edition.
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.