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The Real Numbers
by John StillwellWhile most texts on real analysis are content to assume the real numbers, or to treat them only briefly, this text makes a serious study of the real number system and the issues it brings to light. Analysis needs the real numbers to model the line, and to support the concepts of continuity and measure. But these seemingly simple requirements lead to deep issues of set theory--uncountability, the axiom of choice, and large cardinals. In fact, virtually all the concepts of infinite set theory are needed for a proper understanding of the real numbers, and hence of analysis itself. By focusing on the set-theoretic aspects of analysis, this text makes the best of two worlds: it combines a down-to-earth introduction to set theory with an exposition of the essence of analysis--the study of infinite processes on the real numbers. It is intended for senior undergraduates, but it will also be attractive to graduate students and professional mathematicians who, until now, have been content to "assume" the real numbers. Its prerequisites are calculus and basic mathematics. Mathematical history is woven into the text, explaining how the concepts of real number and infinity developed to meet the needs of analysis from ancient times to the late twentieth century. This rich presentation of history, along with a background of proofs, examples, exercises, and explanatory remarks, will help motivate the reader. The material covered includes classic topics from both set theory and real analysis courses, such as countable and uncountable sets, countable ordinals, the continuum problem, the Cantor-Schröder-Bernstein theorem, continuous functions, uniform convergence, Zorn's lemma, Borel sets, Baire functions, Lebesgue measure, and Riemann integrable functions.
Real Options Illustrated
by Linda PetersThis book explains the standard Real Options Analysis (ROA) literature in a straightforward, step by step manner without the use of complex mathematics. A lot of ROA literature is described through partial differential equations, probabilitydensity functions and simulation techniques, all of which may be unconvincing in the applicable qualities ROA possesses. Using this book, the reader will have a better grasp about how ROA works and will be able to provide his or her judgment about ROA, since all the basics, as well as its positive and negative qualities, are discussed. Real Options Illustrated provides practitioners with a real options framework and encourages readers to study the methodology using the in-depth explanations. This introduction to ROA is sufficient to equip readers with ROA basics, enabling them to perform future independent research. From this book, readers can judge whether ROA is of any value to their field.
Real Quaternionic Calculus Handbook
by João Pedro Morais Svetlin Georgiev Wolfgang SprößigReal quaternion analysis is a multi-faceted subject. Created to describe phenomena in special relativity, electrodynamics, spin etc. , it has developed into a body of material that interacts with many branches of mathematics, such as complex analysis, harmonic analysis, differential geometry, and differential equations. It is also a ubiquitous factor in the description and elucidation of problems in mathematical physics. In the meantime real quaternion analysis has become a well established branch in mathematics and has been greatly successful in many different directions. This book is based on concrete examples and exercises rather than general theorems, thus making it suitable for an introductory one- or two-semester undergraduate course on some of the major aspects of real quaternion analysis in exercises. Alternatively, it may be used for beginning graduate level courses and as a reference work. With exercises at the end of each chapter and its straightforward writing style the book addresses readers who have no prior knowledge on this subject but have a basic background in graduate mathematics courses, such as real and complex analysis, ordinary differential equations, partial differential equations, and theory of distributions.
Real Spinorial Groups: A Short Mathematical Introduction (SpringerBriefs in Mathematics)
by Sebastià Xambó-DescampsThis book explores the Lipschitz spinorial groups (versor, pinor, spinor and rotor groups) of a real non-degenerate orthogonal geometry (or orthogonal geometry, for short) and how they relate to the group of isometries of that geometry.After a concise mathematical introduction, it offers an axiomatic presentation of the geometric algebra of an orthogonal geometry. Once it has established the language of geometric algebra (linear grading of the algebra; geometric, exterior and interior products; involutions), it defines the spinorial groups, demonstrates their relation to the isometry groups, and illustrates their suppleness (geometric covariance) with a variety of examples. Lastly, the book provides pointers to major applications, an extensive bibliography and an alphabetic index.Combining the characteristics of a self-contained research monograph and a state-of-the-art survey, this book is a valuable foundation reference resource on applications for both undergraduate and graduate students.
Real-Time Embedded Systems: Optimization, Synthesis, and Networking
by Meikang Qiu Jiayin LiUbiquitous in today's consumer-driven society, embedded systems use microprocessors that are hidden in our everyday products and designed to perform specific tasks. Effective use of these embedded systems requires engineers to be proficient in all phases of this effort, from planning, design, and analysis to manufacturing and marketing.Taking a sys
Real-Time Progressive Hyperspectral Image Processing
by Chein-I ChangThe book covers the most crucial parts of real-time hyperspectral image processing: causality and real-time capability. Recently, two new concepts of real time hyperspectral image processing, Progressive HyperSpectral Imaging (PHSI) and Recursive HyperSpectral Imaging (RHSI). Both of these can be used to design algorithms and also form an integral part of real time hyperpsectral image processing. This book focuses on progressive nature in algorithms on their real-time and causal processing implementation in two major applications, endmember finding and anomaly detection, both of which are fundamental tasks in hyperspectral imaging but generally not encountered in multispectral imaging. This book is written to particularly address PHSI in real time processing, while a book, Recursive Hyperspectral Sample and Band Processing: Algorithm Architecture and Implementation (Springer 2016) can be considered as its companion book.
Real Time Reduced Order Computational Mechanics: Parametric PDEs Worked Out Problems (SISSA Springer Series #5)
by Gianluigi Rozza Francesco Ballarin Leonardo Scandurra Federico PichiThe book is made up by several worked out problems concerning the application of reduced order modeling to different parametric partial differential equations problems with an increasing degree of complexity.This work is based on some experience acquired during lectures and exercises in classes taught at SISSA Mathematics Area in the Doctoral Programme “Mathematical Analysis, Modelling and Applications”, especially in computational mechanics classes, as well as regular courses previously taught at EPF Lausanne and during several summer and winter schools. The book is a companion for master and doctoral degree classes by allowing to go more deeply inside some partial differential equations worked out problems, examples and even exercises, but it is also addressed for researchers who are newcomers in computational mechanics with reduced order modeling. In order to discuss computational results for the worked out problems presented in this booklet, we will rely on the RBniCS Project. The RBniCS Project contains an implementation in FEniCS of the reduced order modeling techniques (such as certified reduced basis method and Proper Orthogonal Decomposition-Galerkin methods) for parametric problems that will be introduced in this booklet.
Real-Variable Theory of Hardy Spaces Associated with Generalized Herz Spaces of Rafeiro and Samko (Lecture Notes in Mathematics #2320)
by Dachun Yang Yinqin Li Long HuangThe real-variable theory of function spaces has always been at the core of harmonic analysis. In particular, the real-variable theory of the Hardy space is a fundamental tool of harmonic analysis, with applications and connections to complex analysis, partial differential equations, and functional analysis.This book is devoted to exploring properties of generalized Herz spaces and establishing a complete real-variable theory of Hardy spaces associated with local and global generalized Herz spaces via a totally fresh perspective. This means that the authors view these generalized Herz spaces as special cases of ball quasi-Banach function spaces.In this book, the authors first give some basic properties of generalized Herz spaces and obtain the boundedness and the compactness characterizations of commutators on them. Then the authors introduce the associated Herz–Hardy spaces, localized Herz–Hardy spaces, and weak Herz–Hardy spaces, and develop a complete real-variable theory of these Herz–Hardy spaces, including their various maximal function, atomic, molecular as well as various Littlewood–Paley function characterizations. As applications, the authors establish the boundedness of some important operators arising from harmonic analysis on these Herz–Hardy spaces. Finally, the inhomogeneous Herz–Hardy spaces and their complete real-variable theory are also investigated.With the fresh perspective and the improved conclusions on the real-variable theory of Hardy spaces associated with ball quasi-Banach function spaces, all the obtained results of this book are new and their related exponents are sharp. This book will be appealing to researchers and graduate students who are interested in function spaces and their applications.
Real-Variable Theory of Musielak-Orlicz Hardy Spaces
by Dachun Yang Yiyu Liang Luong Dang KyThe main purpose of this book is to give a detailed and complete survey of recent progress related to the real-variable theory of Musielak-Orlicz Hardy-type function spaces, and to lay the foundations for further applications. The real-variable theory of function spaces has always been at the core of harmonic analysis. Recently, motivated by certain questions in analysis, some more general Musielak-Orlicz Hardy-type function spaces were introduced. These spaces are defined via growth functions which may vary in both the spatial variable and the growth variable. By selecting special growth functions, the resulting spaces may have subtler and finer structures, which are necessary in order to solve various endpoint or sharp problems. This book is written for graduate students and researchers interested in function spaces and, in particular, Hardy-type spaces.
Real Variables: with Basic Metric Space Topology
by Prof. Robert B. AshDesigned for a first course in real variables, this text presents the fundamentals for more advanced mathematical work, particularly in the areas of complex variables, measure theory, differential equations, functional analysis, and probability. Geared toward advanced undergraduate and graduate students of mathematics, it is also appropriate for students of engineering, physics, and economics who seek an understanding of real analysis.The author encourages an intuitive approach to problem solving and offers concrete examples, diagrams, and geometric or physical interpretations of results. Detailed solutions to the problems appear within the text, making this volume ideal for independent study. Topics include metric spaces, Euclidean spaces and their basic topological properties, sequences and series of real numbers, continuous functions, differentiation, Riemann-Stieltjes integration, and uniform convergence and applications.
Real Variables (Pure And Applied Mathematics Ser. #Volume 123)
by Alberto TorchinskyA modern introduction to the theory of real variables and its applications to all areas of analysis and partial differential equations. The book discusses the foundations of analysis, including the theory of integration, the Lebesque and abstract integrals, the Radon-Nikodym Theorem, the Theory of Banach and Hilbert spaces, and a glimpse of Fourier series. All material is presented in a clear and motivational fashion.
The Real Work of Data Science: Turning data into information, better decisions, and stronger organizations
by Ron S. Kenett Thomas C. RedmanThe essential guide for data scientists and for leaders who must get more from their data science teams The Economist boldly claims that data are now "the world's most valuable resource." But, as Kenett and Redman so richly describe, unlocking that value requires far more than technical excellence. The Real Work of Data Science explores understanding the problems, dealing with quality issues, building trust with decision makers, putting data science teams in the right organizational spots, and helping companies become data-driven. This is the work that spells the difference between a good data scientist and a great one, between a team that makes marginal contributions and one that drives the business, between a company that gains some value from its data and one in which data truly is "the most valuable resource." "These two authors are world-class experts on analytics, data management, and data quality; they've forgotten more about these topics than most of us will ever know. Their book is pragmatic, understandable, and focused on what really counts. If you want to do data science in any capacity, you need to read it."—Thomas H. Davenport, Distinguished Professor, Babson College and Fellow, MIT Initiative on the Digital Economy "I like your book. The chapters address problems that have faced statisticians for generations, updated to reflect today's issues, such as computational Big Data."—Sir David Cox, Warden of Nuffield College and Professor of Statistics, Oxford University "Data science is critical for competitiveness, for good government, for correct decisions. But what is data science? Kenett and Redman give, by far, the best introduction to the subject I have seen anywhere. They address the critical questions of formulating the right problem, collecting the right data, doing the right analyses, making the right decisions, and measuring the actual impact of the decisions. This book should become required reading in statistics and computer science departments, business schools, analytics institutes and, most importantly, by all business managers." —A. Blanton Godfrey, Joseph D. Moore Distinguished University Professor, Wilson College of Textiles, North Carolina State University
Real World Ecology
by Susan Carstenn Martha Nungesser Shili MiaoEcological and environmental research has increased in scope and complexity in the last few decades, from simple systems with a few managed variables to complex ecosystems with many uncontrolled variables. These issues encompass problems that are inadequately addressed using the types of carefully controlled experiments that dominate past ecological research. Contemporary challenges facing ecologists include whole ecosystem responses to planned restoration activities and ecosystem modifications, as well as unplanned catastrophic events such as biological invasions, natural disasters, and global climate changes. Major perturbations implicated in large-scale ecological alterations share important characteristics that challenge traditional experimental design and statistical analyses. These include: * Lack of randomization, replication and independence * Multiple scales of spatial and temporal variability * Complex interactions and system feedbacks. In real world ecology, standard replicated designs are often neither practical nor feasible for large-scale experiments, yet ecologists continue to cling to these same standard designs and related statistical analyses. Case studies that fully elucidate the currently available techniques for conducting large-scale unreplicated analyses are lacking. Real World Ecology: Large-Scale and Long-Term Case Studies and Methods is the first to focus on case studies to demonstrate how ecologists can investigate complex contemporary problems using new and powerful experimental approaches. This collection of case studies showcases innovative experimental designs, analytical options, and interpretation possibilities currently available to theoretical and applied ecologists, practitioners, and biostatisticians. By illustrating how scientists have answered pressing questions about ecosystem restoration, impact and recovery, global warming, conservation, modeling, and biological invasions, this book will broaden the acceptance and application of modern approaches by scientists and encourage further methodological development.
Real-World Evidence in a Patient-Centric Digital Era (Chapman & Hall/CRC Biostatistics Series)
by Kelly H Zou Lobna A. Salem Amrit RayReal-world evidence is defined as evidence generated from real-world data outside randomized controlled trials. As scientific discoveries and methodologies continue to advance, real-world data and their companion technologies offer powerful new tools for evidence generation. Real-World Evidence in a Patient-Centric Digital Era provides perspectives, examples, and insights on the innovative application of real-world evidence to meet patient needs and improve healthcare, with a focus on the pharmaceutical industry. This book presents an overview of key analytical issues and best practices. Special attention is paid to the development, methodologies, and other salient features of the statistical and data science techniques that are customarily used to generate real-world evidence. It provides a review of key topics and emerging trends in cutting-edge data science and health innovation. Features: Provides an overview of statistical and analytic methodologies in real-world evidence to generate insights on healthcare, with a special focus on the pharmaceutical industry Examines timely topics of high relevance to industry such as bioethical considerations, regulatory standards, and compliance requirements Highlights emerging and current trends, and provides guidelines for best practices Illustrates methods through examples and use-case studies to demonstrate impact Provides guidance on software choices and digital applications for successful analytics Real-World Evidence in a Patient-Centric Digital Era will be a vital reference for medical researchers, health technology innovators, data scientists, epidemiologists, population health analysts, health economists, outcomes researchers, policymakers, and analysts in the healthcare industry.
Real-World Evidence in Drug Development and Evaluation (Chapman & Hall/CRC Biostatistics Series)
by Harry Yang Binbing YuReal-world evidence (RWE) has been at the forefront of pharmaceutical innovations. It plays an important role in transforming drug development from a process aimed at meeting regulatory expectations to an operating model that leverages data from disparate sources to aid business, regulatory, and healthcare decision making. Despite its many benefits, there is no single book systematically covering the latest development in the field.Written specifically for pharmaceutical practitioners, Real-World Evidence in Drug Development and Evaluation, presents a wide range of RWE applications throughout the lifecycle of drug product development. With contributions from experienced researchers in the pharmaceutical industry, the book discusses at length RWE opportunities, challenges, and solutions. Features Provides the first book and a single source of information on RWE in drug development Covers a broad array of topics on outcomes- and value-based RWE assessments Demonstrates proper Bayesian application and causal inference for real-world data (RWD) Presents real-world use cases to illustrate the use of advanced analytics and statistical methods to generate insights Offers a balanced discussion of practical RWE issues at hand and technical solutions suitable for practitioners with limited data science expertise
Real-World Evidence in Medical Product Development
by Weili He Yixin Fang Hongwei WangThis book provides state-of-art statistical methodologies, practical considerations from regulators and sponsors, logistics, and real use cases for practitioners for the uptake of RWE/D. Randomized clinical trials have been the gold standard for the evaluation of efficacy and safety of medical products. However, the cost, duration, practicality, and limited generalizability have incentivized many to look for alternative ways to optimize drug development. This book provides a comprehensive list of topics together to include all aspects with the uptake of RWE/D, including, but not limited to, applications in regulatory and non-regulatory settings, causal inference methodologies, organization and infrastructure considerations, logistic challenges, and practical use cases.
Real-World Math Projects for Gifted Learners, Grades 4-5
by Mark HessHelping bring mathematics and engineering to life, these challenging lessons give teachers an exciting tool for engaging advanced learners through creativity and hands-on products. Units are driven by standards and invite students to become baseball field architects, create flying jellyfish, make a gnome hat parachute, scale skyscrapers, and more! Each project includes step-by-step lesson plans with reproducible templates, time estimates, and a materials list. While centered on STEAM (science, technology, engineering, arts, and mathematics) competencies, true to real-world experiences, these hands-on projects span the curriculum—including writing and public speaking—and while they suit entire classrooms and smaller groups, they can also be easily adapted to individual projects for independent study and home school.
Real World Research
by Colin RobsonREAL WORLD RESEARCH Provides students and practitioner alike with clear and systematic guidance on performing social research in applied settings Real World Research supplies the multidisciplinary skills necessary to conduct social research projects inside and outside of the classroom or the workplace. Offering well-balanced coverage of qualitative, quantitative, and mixed methods, this highly practical resource incorporates approaches from different social science disciplines to help readers find answers to real-life research questions in healthcare, education, business and management, and in many other public and private settings. Detailed yet accessible chapters include step-by-step advice for developing a research question, choosing a research design strategy, collecting and analyzing the data, interpreting and reporting the results, and more. The fifth edition contains timely coverage of contemporary methodologies, key ethical issues, and ongoing debates within the field of social research. New and expanded sections address topics such as evidence‐based approaches to social research, ethical considerations when conducting research involving people, carrying out projects based solely on existing research, and the importance and implications of internet-based research. Featuring a wealth of up-to-date examples drawn from a wide range of disciplines, this classic textbook: Focuses on useful real-world research in applied settings such as homes, schools, businesses, and other workplaces Provides a concise overview and a well-defined example of each main step of the research process Highlights the importance of collaboration, cooperation, and active participation in social research Explains flexible research designs using largely qualitative methods, including additional coverage of ethnographic and grounded theory approaches Includes an extensive companion website with numerous research examples, links to journal articles, PowerPoint slides, and many other additional resources Real World Research, Fifth Edition, remains essential reading for those tasked with developing, performing, and reporting the findings of a research project, including students, academics and educators, social scientists, health practitioners, and professionals in a diverse range of fields.
A Realist Theory of Science (Radical Thinkers)
by Roy Bhaskar<i>A Realist Theory of Science</i> is one of the few books that have changed our understanding of the philosophy of science. In this analysis of the natural sciences, with a particular focus on the experimental process itself, Roy Bhaskar provides a definitive critique of the traditional, positivist conception of science and stakes out an alternative, realist position. Since it original publication in 1975, a movement known as ‘Critical Realism’, which is both intellectually diverse and international in scope, has developed on the basis of key concepts outlined in the text. The book has been hailed in many quarters as a ‘Copernican Revolution’ in the study of the nature of science, and the implications of its account have been far-reaching for many fields of the humanities and social sciences.
Realitätsbezogen Mathematik unterrichten: Ein Leitfaden für Lehrende (essentials)
by Jürgen MaaßIn diesem Essential wird an Beispielen erläutert, wie und mit welchen Herausforderungen gute realitätsbezogene Aufgaben und Unterrichtseinheiten gefunden und genutzt werden können. Dabei werden die Leserinnen und Leser immer wieder eingeladen, selbst etwas auszuprobieren.
Reality and Measurement in Algebraic Quantum Theory: Nagoya, Japan, March 9-13 2015 (Springer Proceedings in Mathematics & Statistics #261)
by Masanao Ozawa Jeremy Butterfield Hans Halvorson Miklós Rédei Yuichiro Kitajima Francesco BuscemiThis volume contains papers based on presentations at the “Nagoya Winter Workshop 2015: Reality and Measurement in Algebraic Quantum Theory (NWW 2015)”, held in Nagoya, Japan, in March 2015. The foundations of quantum theory have been a source of mysteries, puzzles, and confusions, and have encouraged innovations in mathematical languages to describe, analyze, and delineate this wonderland. Both ontological and epistemological questions about quantum reality and measurement have been placed in the center of the mysteries explored originally by Bohr, Heisenberg, Einstein, and Schrödinger. This volume describes how those traditional problems are nowadays explored from the most advanced perspectives. It includes new research results in quantum information theory, quantum measurement theory, information thermodynamics, operator algebraic and category theoretical foundations of quantum theory, and the interplay between experimental and theoretical investigations on the uncertainty principle. This book is suitable for a broad audience of mathematicians, theoretical and experimental physicists, and philosophers of science.
The Reality of Time Flow: Local Becoming in Modern Physics (The Frontiers Collection)
by Richard T. ArthurIt is commonly held that there is no place for the 'now’ in physics, and also that the passing of time is something subjective, having to do with the way reality is experienced but not with the way reality is. Indeed, the majority of modern theoretical physicists and philosophers of physics contend that the passing of time is incompatible with modern physical theory, and excluded in a fundamental description of physical reality. This book provides a forceful rebuttal of such claims. In successive chapters the author explains the historical precedents of the modern opposition to time flow, giving careful expositions of matters relevant to becoming in classical physics, the special and general theories of relativity, and quantum theory, without presupposing prior expertise in these subjects. Analysing the arguments of thinkers ranging from Aristotle, Russell, and Bergson to the proponents of quantum gravity, he contends that the passage of time, understood as a local becoming of events out of those in their past at varying rates, is not only compatible with the theories of modern physics, but implicit in them.
Reality Without Realism: Matter, Thought, and Technology in Quantum Physics
by Arkady PlotnitskyThis book presents quantum theory as a theory based on new relationships among matter, thought, and experimental technology, as against those previously found in physics, relationships that also redefine those between mathematics and physics in quantum theory. The argument of the book is based on its title concept, reality without realism (RWR), and in the corresponding view, the RWR view, of quantum theory. The book considers, from this perspective, the thinking of Bohr, Heisenberg, Schrödinger, and Dirac, with the aim of bringing together the philosophy and history of quantum theory. With quantum theory, the book argues, the architecture of thought in theoretical physics was radically changed by the irreducible role of experimental technology in the constitution of physical phenomena, accordingly, no longer defined independently by matter alone, as they were in classical physics or relativity. Or so it appeared. For, quantum theory, the book further argues, made us realize that experimental technology, beginning with that of our bodies, irreducibly shapes all physical phenomena, and thus makes us rethink the relationships among matter, thought, and technology in all of physics.
Realization and Model Reduction of Dynamical Systems: A Festschrift in Honor of the 70th Birthday of Thanos Antoulas
by Christopher Beattie Peter Benner Mark Embree Serkan Gugercin Sanda LefteriuThis book celebrates Professor Thanos Antoulas's 70th birthday, marking his fundamental contributions to systems and control theory, especially model reduction and, more recently, data-driven modeling and system identification. Model reduction is a prominent research topic with wide ranging scientific and engineering applications.
Realizing Rigor in the Mathematics Classroom
by Don S. Balka Ted H. Hull Ruth Harbin MilesRigor put within reach! Rigor: The Common Core has made it policy—and this first-of-its-kind guide takes math teachers and leaders through the process of making it reality. Using the Proficiency Matrix as a framework, the authors offer proven strategies and practical tools for successful implementation of the CCSS mathematical practices—with rigor as a central objective. You’ll learn how to Define rigor in the context of each mathematical practice Identify and overcome potential issues, including differentiating instruction and using data Relate specific roles and goals for all stakeholders Use assessment tools to guide work and monitor progress