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Schramm–Loewner Evolution
by Antti KemppainenThis book is a short, but complete, introduction to the Loewner equation and the SLEs, which are a family of random fractal curves, as well as the relevant background in probability and complex analysis. The connection to statistical physics is also developed in the text in an example case. The book is based on a course (with the same title) lectured by the author. First three chapters are devoted to the background material, but at the same time, give the reader a good understanding on the overview on the subject and on some aspects of conformal invariance. The chapter on the Loewner equation develops in detail the connection of growing hulls and the differential equation satisfied by families of conformal maps. The Schramm-Loewner evolutions are defined and their basic properties are studied in the following chapter, and the regularity properties of random curves as well as scaling limits of discrete random curves are investigated in the final chapter. The book is aimed at graduate students or researchers who want to learn the subject fairly quickly.
Schriftliche Begründungskompetenzen in stochastischen Aufgabenkontexten: Eine Evaluations- und Interventionsstudie im 4. Schuljahr
by Marieke VogtKinder sollen bereits im Mathematikunterricht der Grundschule mathematische Zusammenhänge erklären und begründen. Fraglich ist, wie dieses Thema erfolgreich unterrichtet werden kann. Das vorliegende Buch liefert empirisch überprüfte Ansätze zur Förderung mathematischer Begründungskompetenzen und zeigt auf, wie diese mit dem innermathematischen Themenbereich der Stochastik verknüpft werden können. Die Autorin Marieke Vogt arbeitet derzeit als Grundschullehrerin in Niedersachsen.
Schrödinger Operators, Spectral Analysis and Number Theory: In Memory of Erik Balslev (Springer Proceedings in Mathematics & Statistics #348)
by Sergio Albeverio Anindita Balslev Ricardo WederThis book gives its readers a unique opportunity to get acquainted with new aspects of the fruitful interactions between Analysis, Geometry, Quantum Mechanics and Number Theory. The present book contains a number of contributions by specialists in these areas as an homage to the memory of the mathematician Erik Balslev and, at the same time, advancing a fascinating interdisciplinary area still full of potential. Erik Balslev has made original and important contributions to several areas of Mathematics and its applications. He belongs to the founders of complex scaling, one of the most important methods in the mathematical and physical study of eigenvalues and resonances of Schrödinger operators, which has been very essential in advancing the solution of fundamental problems in Quantum Mechanics and related areas. He was also a pioneer in making available and developing spectral methods in the study of important problems in Analytic Number Theory.
The Schrödinger-Virasoro Algebra
by Claude Roger Jérémie UnterbergerThis monograph provides the first up-to-date and self-contained presentation of a recently discovered mathematical structure--the Schrödinger-Virasoro algebra. Just as Poincaré invariance or conformal (Virasoro) invariance play a key rôle in understanding, respectively, elementary particles and two-dimensional equilibrium statistical physics, this algebra of non-relativistic conformal symmetries may be expected to apply itself naturally to the study of some models of non-equilibrium statistical physics, or more specifically in the context of recent developments related to the non-relativistic AdS/CFT correspondence. The study of the structure of this infinite-dimensional Lie algebra touches upon topics as various as statistical physics, vertex algebras, Poisson geometry, integrable systems and supergeometry as well as representation theory, the cohomology of infinite-dimensional Lie algebras, and the spectral theory of Schrödinger operators.
Schrodinger's Killer App: Race to Build the World's First Quantum Computer
by Jonathan P. DowlingWritten by a renowned quantum physicist closely involved in the U.S. government's development of quantum information science, this book presents an inside look at the government's quest to build a quantum computer capable of solving complex mathematical problems and hacking the public-key encryption codes used to secure the Internet. The "killer app" refers to Shor's quantum factoring algorithm, which would unveil the encrypted communications of the entire Internet if a quantum computer could be built to run the algorithm. Schrodinger's notion of quantum entanglement-and his infamous cat-is at the heart of it all.
Schrödinger’s Web: Race to Build the Quantum Internet
by Jonathan P. DowlingAs the race to build the world&’s first quantum computer is coming to an end, the race to build the quantum internet has just started. This book leverages the author&’s unique insights into both the Chinese and American quantum programs. It begins with the physics and history of the quantum internet and ends with the latest results in quantum computing and quantum networks. The Chinese quantum Sputnik moment. The U.S. National Quantum Initiative. What&’s up with Quantum Computing Supremacy? The Race to Build the Quantum Internet. Where will Quantum Technology be Tomorrow? Written by a renowned quantum physicist, this book is for everyone who is interested in the rapidly advancing field of Quantum Technology — The Second Quantum Revolution. The 2016 launch of the Chinese quantum satellite Mozi was a quantum Sputnik moment. The United States went from thinking it was ten years ahead of the Chinese to the realization that it was ten years behind them. This quantum gap led to the U.S. National Quantum Initiative, launched in 2018. Since then, the race to build the quantum internet has taken off at breakneck speed.
Schubert Calculus and Its Applications in Combinatorics and Representation Theory: Guangzhou, China, November 2017 (Springer Proceedings in Mathematics & Statistics #332)
by Jianxun Hu Changzheng Li Leonardo C. MihalceaThis book gathers research papers and surveys on the latest advances in Schubert Calculus, presented at the International Festival in Schubert Calculus, held in Guangzhou, China on November 6–10, 2017. With roots in enumerative geometry and Hilbert's 15th problem, modern Schubert Calculus studies classical and quantum intersection rings on spaces with symmetries, such as flag manifolds. The presence of symmetries leads to particularly rich structures, and it connects Schubert Calculus to many branches of mathematics, including algebraic geometry, combinatorics, representation theory, and theoretical physics. For instance, the study of the quantum cohomology ring of a Grassmann manifold combines all these areas in an organic way. The book is useful for researchers and graduate students interested in Schubert Calculus, and more generally in the study of flag manifolds in relation to algebraic geometry, combinatorics, representation theory and mathematical physics.
Schulcurriculares Fachwissen von Mathematiklehramtsstudierenden: Struktur, Entwicklung und Einfluss auf den Studienerfolg (Studien zur theoretischen und empirischen Forschung in der Mathematikdidaktik)
by Jennifer LungJennifer Lung entwickelte ein Testinstrument, mithilfe dessen sie das Schulcurriculare Fachwissen von 703 Mathematiklehramtsstudierenden zu unterschiedlichen Zeitpunkten im Studienverlauf erhebt. Diese Trendstudie erlaubt es, die Struktur des Schulcurricularen Fachwissens, dessen Entwicklung im Studienverlauf sowie den Zusammenhang mit dem Studienerfolg zu beschreiben. Die Befunde zeigen, dass sich zwar Teilbereiche des Schulcurricularen Fachwissens im Studienverlauf weiterentwickeln, die Testleistungen jedoch aus Sicht von Hochschullehrenden insgesamt als unzureichend zu bewerten sind. Regressionsanalysen verdeutlichen die Rolle des Schulcurricularen Fachwissens sowohl als Prädiktor als auch als eigenständiger Aspekt von Studienerfolg.
Schülervorstellungen zu Geradengleichungen in der vektoriellen Analytischen Geometrie (Studien zur theoretischen und empirischen Forschung in der Mathematikdidaktik)
by Stefan-Harald KaufmannDie vorliegende qualitative Interviewstudie geht der Frage nach, welche Vorstellungen Schülerinnen und Schüler mit einer Geradengleichung in Vektorform verbinden. Insgesamt 22 Schülerinnen und Schüler der gymnasialen Oberstufe werden mit Hilfe eines leitfadengestützten, problemzentrierten Interviews zu Geradengleichungen in Vektorform aus unterschiedlichen Perspektiven befragt. Die Auswertung der Interviews erfolgt mit einer an die Grounded Theory angelehnten Kategoriengenerierung und einer typenbildenden qualitativen Inhaltsanalyse, die die Bildung von 6 verschiedenen Typen ermöglicht.
Schulische Kabinettprojektion: Räumliches Zeichnen im Raster (essentials)
by Berthold HeinrichBerthold Heinrich stellt die mathematischen und zeichnerischen Grundlagen für die Darstellung von Objekten im Raum auf kariertem Papier vor. Dabei präsentiert er auch die Nutzung von Software. In der Schule wird oft kariertes Papier als Raster zur Darstellung von Flächen und Körpern genutzt. Allerdings werden, selbst in einigen Druckwerken, z. B. die entstehenden Ellipsen und Winkelbögen ungenau gezeichnet oder eine Kugelkontur falsch als Kreis dargestellt. Im vorliegenden Essential werden die korrekten Verfahren sowohl theoretisch als auch an konkreten Beispielen vorgestellt und können meist direkt umgesetzt werden. Einige aufwändigere Abläufe stellt der Autor anschaulich an Beispielen dar.
The Schwarz Lemma (Dover Books on Mathematics)
by Sean DineenThe Schwarz lemma is among the simplest results in complex analysis that capture the rigidity of holomorphic functions. This self-contained volume provides a thorough overview of the subject; it assumes no knowledge of intrinsic metrics and aims for the main results, introducing notation, secondary concepts, and techniques as necessary. Suitable for advanced undergraduates and graduate students of mathematics, the two-part treatment covers basic theory and applications. Starting with an exploration of the subject in terms of holomorphic and subharmonic functions, the treatment proves a Schwarz lemma for plurisubharmonic functions and discusses the basic properties of the Poincaré distance and the Schwarz-Pick systems of pseudodistances. Additional topics include hyperbolic manifolds, special domains, pseudometrics defined using the (complex) Green function, holomorphic curvature, and the algebraic metric of Harris. The second part explores fixed point theorems and the analytic Radon-Nikodym property.
The Science and Art of Simulation: Trust in Science
by Michael M. Resch Nico Formánek Ammu Joshy Andreas KaminskiTrust is a central pillar of the scientific enterprise. Much work in the philosophy of science can be seen as coping with the problem of establishing trust in a certain theory, a certain model, or even science as a whole. However, trust in science is threatened by various developments. With the advent of more complex models and the increasing usage of computer methods such as machine learning and computer simulation, it seems increasingly challenging to establish trust in science. How and on what basis can an appropriate trust in science be built? We are interested in how trust is established in such cases of increasing complexity (of models and communication) and what could be appropriate measures to alleviate doubt.
Science and Mathematics: From Primitive to Modern Times
by Jayant V. NarlikarThis book offers an engaging and comprehensive introduction to scientific theories and the evolution of science and mathematics through the centuries. It discusses the history of scientific thought and ideas and the intricate dynamic between new scientific discoveries, scientists, culture and societies. Through stories and historical accounts, the volume illustrates the human engagement and preoccupation with science and the interpretation of natural phenomena. It highlights key scientific breakthroughs from the ancient to later ages, giving us accounts of the work of ancient Greek and Indian mathematicians and astronomers, as well as of the work of modern scientists like Descartes, Newton, Planck, Mendel and many more. The author also discusses the vast advancements which have been made in the exploration of space, matter and genetics and their relevance in the advancement of the scientific tradition. He provides great insights into the process of scientific experimentation and the relationship between science and mathematics. He also shares amusing anecdotes of scientists and their interactions with the world around them. Detailed and accessible, this book will be of great interest to students and researchers of science, mathematics, the philosophy of science, science and technology studies and history. It will also be useful for general readers who are interested in the history of scientific discoveries and ideas.
Science and Mathematics for Engineering
by John BirdA practical introduction to the engineering science and mathematics required for engineering study and practice.Science and Mathematics for Engineering is an introductory textbook that assumes no prior background in engineering. This new edition covers the fundamental scientific knowledge that all trainee engineers must acquire in order to pass their examinations and has been brought fully in line with the compulsory science and mathematics units in the new engineering course specifications. A new chapter covers present and future ways of generating electricity, an important topic.John Bird focuses upon engineering examples, enabling students to develop a sound understanding of engineering systems in terms of the basic laws and principles. This book includes over 580 worked examples, 1300 further problems, 425 multiple choice questions (with answers), and contains sections covering the mathematics that students will require within their engineering studies, mechanical applications, electrical applications and engineering systems.This book is supported by a companion website of materials that can be found at www.routledge/cw/bird. This resource includes fully worked solutions of all the further problems for students to access, and the full solutions and marking schemes for the revision tests found within the book for instructor use. In addition, all 447 illustrations will be available for downloading by lecturers.
Science and Method
by Henri PoincaréThis classic by the famous mathematician defines the basic methodology and psychology of scientific discovery, particularly regarding mathematics and mathematical physics. Drawing on examples from many fields, it explains how scientists analyze and choose their working facts, and it explores the nature of experimentation, theory, and the mind. 1914 edition.
Science Communication in the World
by Michel Claessens Shunke Shi Bernard SchieleThis volume is aimed at all those who wonder about the mechanisms and effects of the disclosure of knowledge. Whether they have a professional interest in understanding these processes generally, or they wish to conduct targeted investigations in the PCST field, it will be useful to anyone involved in science communication, including researchers, academics, students, journalists, science museum staff, scientists high public profiles, and information officers in scientific institutions.
Science for Humans: Mind, Life, The Formal-&-Natural Sciences, and A New Concept of Nature
by Robert HannaThis book presents and defends an original and paradigm-shifting conception of formal science, natural science, and the natural universe alike, that’s fully pro-science, but at the same time neither theological or God-centered, nor solipsistic or self-centered, nor communitarian or social-institution-centered, nor scientistic or science-valorizing, nor materialist/physicalist or reductive, nor—above all—mechanistic. It does this by presenting and defending what Robert Hanna calls the neo-organicist turn, including manifest realism and the three sub-parts of metaphysical organicism: liberal naturalism, mind-life continuity, and explanatory inversion, whereby mechanical systems are explained by grounding them in organic systems, and not the other way around. Or more briefly and simply put, the purpose of this book is to present and defend science for humans. As such, it will be highly interesting and profoundly relevant to graduate students and specialist researchers in philosophy and the formal-&-natural sciences.
The Science Girls
by AkiGrab your goggles and join the Science Girls! We’re science girls! We love to learn.We gather, test, assess, discern!From the lab to the meadow to the greenhouse—the science girls have lots to see, lots to do, and lots to explore. Follow this troupe of busy girls as they have fun hypothesizing and analyzing in a day full of curiosity and excitement.
Science in the City: Culturally Relevant STEM Education (Race And Education Ser.)
by Bryan A. Brown Christopher EmdinScience in the City examines how language and culture matter for effective science teaching. Author Bryan A. Brown argues that, given the realities of our multilingual and multicultural society, teachers must truly understand how issues of culture intersect with the fundamental principles of learning. This book links an exploration of contemporary research on urban science teaching to a more generative instructional approach in which students develop mastery by discussing science in culturally meaningful ways. <P><P> The book starts with a trenchant analysis of the “black tax,” a double standard at work in science language and classrooms that forces students of color to appropriate and express their science knowledge solely in ways that accord with the dominant culture and knowledge regime. Because we are in an interactive, multimedia world, the author also posits the necessity of applying what is known about best practices in science teaching to best practices in technology. <P><P> The book then turns to instruction, illustrating how science education can flourish if it is connected to students’ backgrounds, identities, language, and culture. In this empowered—and inclusive—form of science classroom, the role of narrative is key: educators use stories and anecdotes to induct students into the realm of scientific thinking; introduce big ideas in easy, familiar terms; and prioritize explanation over mastery of symbolic systems. The result is a classroom that showcases how the use of more familiar, culturally relevant modes of communication can pave the way for improved science learning.
Science Interrupted: Rethinking Research Practice with Bureaucracy, Agroforestry, and Ethnography (Expertise: Cultures and Technologies of Knowledge)
by Timothy G. McLellanScience Interrupted examines how scientists in China pursue environmental sustainability within the constraints of domestic and international bureaucracies. Timothy G. McLellan offers a theoretical framework for analyzing the formal procedural work of Chinese bureaucracy—work that is overlooked when China scholars restrict their gaze to the informal and interpersonal channels through which bureaucracy is often navigated. Homing in on an agroforestry research organization in southwest China, the author takes the experiences of the organization's staff in navigating diverse international funding regimes and authoritarian state institutions as entry points for understanding the pervasiveness of bureaucracy in contemporary science. He asks: What if we take the tools, sensibilities, and practices of bureaucracies seriously not only as objects of critique but as resources for re-thinking scientific practice? Extending a mode of anthropological research in which ethnography serves as source of theory as well as source of data, Science Interrupted thinks with, and not only against, bureaucracy. McLellan shows that ethnographic engagement with bureaucracy enables us to imagine more democratic and more collaborative modes of scientific practice.
Science Mysteries Explained: In-Depth Explorations of Natural Science’s Most Fascinating Facts (Idiot's Guides)
by Anthony FordhamIdeal for the armchair science enthusiast, Idiot's Guides: Science Mysteries Explained takes a question/answer-based approach to teach readers a wide variety of topics in Earth Science, Life Science, Chemistry, Physics, and Cosmology. Using helpful full-color illustrations and expert information, this book features 130 fascinating questions and answers to satisfy any scientist wannabe.
Science, Numbers and Politics
by Markus J. PrutschThis study explores the dynamic relationship between science, numbers and politics. What can scientific evidence realistically do in and for politics? The volume contributes to that debate by focusing on the role of “numbers” as a means by which knowledge is expressed and through which that knowledge can be transferred into the political realm. Based on the assumption that numbers are constantly being actively created, translated, and used, and that they need to be interpreted in their respective and particular contexts, it examines how numbers and quantifications are made ‘politically workable’, examining their production, their transition into the sphere of politics and their eventual use therein. Key questions that are addressed include: In what ways does scientific evidence affect political decision-making in the contemporary world? How and why did quantification come to play such an important role within democratic politics? What kind of work do scientific evidence and numbers do politically?
The Science of Cities and Regions: Lectures on Mathematical Model Design
by Alan WilsonA 'science of cities and regions' is critical for meeting future challenges. The world is urbanising: huge cities are being created and are continuing to grow rapidly. There are many planning and development issues arising in different manifestations in countries across the globe. These developments can, in principle, be simulated through mathematical computer models which provide tools for forecasting and testing future scenarios and plans. These models can represent the functioning of cities and regions, predicting the spatial demography and the economy, the main flows such as journey to work or to services, and the mechanisms of future evolution. In this book, the main principles involved in the design of this range of models are articulated, providing an account of the current state of the art as well as future research challenges. Alan Wilson has over forty years working with urban and regional models and has contributed important discoveries. He has distilled this experience into what serves as both an introduction and a review of the research frontier. Topics covered include the Lowry model, the retail model, principles of account-based models and the methods rooted in Boltzmann-style statistical modelling and the Lotka-Volterra approach to system evolution. Applications range from urban and regional planning to wars and epidemics.
The Science of Conjecture: Evidence and Probability before Pascal
by James FranklinHow did we make reliable predictions before Pascal and Fermat's discovery of the mathematics of probability in 1654? What methods in law, science, commerce, philosophy, and logic helped us to get at the truth in cases where certainty was not attainable? In The Science of Conjecture, James Franklin examines how judges, witch inquisitors, and juries evaluated evidence; how scientists weighed reasons for and against scientific theories; and how merchants counted shipwrecks to determine insurance rates.The Science of Conjecture provides a history of rational methods of dealing with uncertainty and explores the coming to consciousness of the human understanding of risk.
Science of Cyber Security: 6th International Conference, SciSec 2024, Copenhagen, Denmark, August 14–16, 2024, Proceedings (Lecture Notes in Computer Science #15441)
by Jun Zhao Weizhi MengThis book constitutes the refereed proceedings of the 6th International Conference on Science of Cyber Security, SciSec 2024, held in Copenhagen, Denmark, during August 14–16, 2024. The 25 full papers presented here were carefully selected and reviewed from 79 submissions. These papers focus on the recent research, trends and challenges in the emerging field of Cyber Security.