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Cardinalities of Fuzzy Sets (Studies in Fuzziness and Soft Computing #118)
by Maciej WygralakCounting is one of the basic elementary mathematical activities. It comes with two complementary aspects: to determine the number of elements of a set - and to create an ordering between the objects of counting just by counting them over. For finite sets of objects these two aspects are realized by the same type of num bers: the natural numbers. That these complementary aspects of the counting pro cess may need different kinds of numbers becomes apparent if one extends the process of counting to infinite sets. As general tools to determine numbers of elements the cardinals have been created in set theory, and set theorists have in parallel created the ordinals to count over any set of objects. For both types of numbers it is not only counting they are used for, it is also the strongly related process of calculation - especially addition and, derived from it, multiplication and even exponentiation - which is based upon these numbers. For fuzzy sets the idea of counting, in both aspects, looses its naive foundation: because it is to a large extent founded upon of the idea that there is a clear distinc tion between those objects which have to be counted - and those ones which have to be neglected for the particular counting process.
Cardiovascular Fluid Mechanics (CISM International Centre for Mechanical Sciences #446)
by Gianni Pedrizzetti Karl PerktoldThe book presents the state of the art in the interdisciplinary field of fluid mechanics applied to cardiovascular modelling. It is neither a monograph nor a collection of research papers, rather an extended review in the field. It is arranged in 4 scientific chapters each presenting thoroughly the approach of a leading research team; two additional chapters prepared by biomedical scientists present the topic by the applied perspective. A unique feature is a substantial (approx. one fourth of the book) medical introductory part, written by clinical researchers for scientific readers, that would require a large effort to be collected otherwise.
Cardiovascular Mathematics: Modeling and simulation of the circulatory system (MS&A #1)
by Luca Formaggia Alfio Quarteroni Allesandro VenezianiMathematical models and numerical simulations can aid the understanding of physiological and pathological processes. This book offers a mathematically sound and up-to-date foundation to the training of researchers and serves as a useful reference for the development of mathematical models and numerical simulation codes.
Care in Mathematics Education: Alternative Educational Spaces and Practices (Palgrave Studies in Alternative Education)
by Anne WatsonThis book investigates the process of care in mathematics teaching. The author proposes transformative educational spaces in which learning mathematics, rather than consisting of a repetitive grind of exercises and facts, can become a part of learner identity. This book describes examples of mathematics teachings in a wide range of contexts and pedagogies, coordinated to identify common features where care for mathematical learning and thinking is combined with care for learners. Along with detailing caring mathematics education practices in alternative spaces, the author demonstrates similar practices alive even with the current mainstream spaces of acquisition and performance. Care is integrated through listening, and developing responsive and trusting relationships. It will be of interest to scholars of mathematics education, as well as pre-service and in-service teachers and teacher educators.
A Career in Statistics: Beyond the Numbers
by Gerald J. Hahn Necip DoganaksoyA valuable guide to a successful career as a statistician A Career in Statistics: Beyond the Numbers prepares readers for careers in statistics by emphasizing essential concepts and practices beyond the technical tools provided in standard courses and texts. This insider's guide from internationally recognized applied statisticians helps readers decide whether a career in statistics is right for them, provides hands-on guidance on how to prepare for such a career, and shows how to succeed on the job. The book provides non-technical guidance for a successful career. The authors' extensive industrial experience is supplemented by insights from contributing authors from government and academia, Carol Joyce Blumberg, Leonard M. Gaines, Lynne B. Hare, William Q. Meeker, and Josef Schmee. Following an introductory chapter that provides an overview of the field, the authors discuss the various dimensions of a career in applied statistics in three succinct parts: The Work of a Statistician describes the day-to-day activities of applied statisticians in business and industry, official government, and various other application areas, highlighting the work environment and major on-the-job challenges Preparing for a Successful Career in Statistics describes the personal traits that characterize successful statisticians, the education that they need to acquire, and approaches for securing the right job Building a Successful Career as a Statistician offers practical guidance for addressing key challenges that statisticians face on the job, such as project initiation and execution, effective communication, publicizing successes, ethical considerations, and gathering good data; alternative career paths are also described The book concludes with an in-depth examination of careers for statisticians in academia as well as tips to help them stay on top of their field throughout their careers. Each chapter includes thought-provoking discussion questions and a Major Takeaways section that outlines key concepts. Real-world examples illustrate key points, and an FTP site provides additional information on selected topics. A Career in Statistics is an invaluable guide for individuals who are considering or have decided on a career in statistics as well as for statisticians already on the job who want to accelerate their path to success. It also serves as a suitable book for courses on statistical consulting, statistical practice, and statistics in the workplace at the undergraduate and graduate levels.
A Career in Statistics: Beyond the Numbers
by Gerald J. Hahn Necip DoganaksoyA valuable guide to a successful career as a statistician A Career in Statistics: Beyond the Numbers prepares readers for careers in statistics by emphasizing essential concepts and practices beyond the technical tools provided in standard courses and texts. This insider's guide from internationally recognized applied statisticians helps readers decide whether a career in statistics is right for them, provides hands-on guidance on how to prepare for such a career, and shows how to succeed on the job. The book provides non-technical guidance for a successful career. The authors' extensive industrial experience is supplemented by insights from contributing authors from government and academia, Carol Joyce Blumberg, Leonard M. Gaines, Lynne B. Hare, William Q. Meeker, and Josef Schmee. Following an introductory chapter that provides an overview of the field, the authors discuss the various dimensions of a career in applied statistics in three succinct parts: The Work of a Statistician describes the day-to-day activities of applied statisticians in business and industry, official government, and various other application areas, highlighting the work environment and major on-the-job challenges Preparing for a Successful Career in Statistics describes the personal traits that characterize successful statisticians, the education that they need to acquire, and approaches for securing the right job Building a Successful Career as a Statistician offers practical guidance for addressing key challenges that statisticians face on the job, such as project initiation and execution, effective communication, publicizing successes, ethical considerations, and gathering good data; alternative career paths are also described The book concludes with an in-depth examination of careers for statisticians in academia as well as tips to help them stay on top of their field throughout their careers. Each chapter includes thought-provoking discussion questions and a Major Takeaways section that outlines key concepts. Real-world examples illustrate key points, and an FTP site provides additional information on selected topics. A Career in Statistics is an invaluable guide for individuals who are considering or have decided on a career in statistics as well as for statisticians already on the job who want to accelerate their path to success. It also serves as a suitable book for courses on statistical consulting, statistical practice, and statistics in the workplace at the undergraduate and graduate levels.
The Career of a Research Statistician: From Consulting to Theoretical Development (Statistics for Industry, Technology, and Engineering)
by Shelemyahu ZacksThis monograph highlights the connection between the theoretical work done by research statisticians and the impact that work has on various industries. Drawing on decades of experience as an industry consultant, the author details how his contributions have had a lasting impact on the field of statistics as a whole. Aspiring statisticians and data scientists will be motivated to find practical applications for their knowledge, as they see how such work can yield breakthroughs in their field.Each chapter highlights a consulting position the author held that resulted in a significant contribution to statistical theory. Topics covered include tracking processes with change points, estimating common parameters, crossing fields with absorption points, military operations research, sampling surveys, stochastic visibility in random fields, reliability analysis, applied probability, and more. Notable advancements within each of these topics are presented by analyzing the problems facing various industries, and how solving those problems contributed to the development of the field.The Career of a Research Statistician is ideal for researchers, graduate students, or industry professionals working in statistics. It will be particularly useful for up-and-coming statisticians interested in the promising connection between academia and industry.
Carefree calculations for healthcare students
by Elizabeth Atere-Roberts Diana CobenThis is a maths book with a difference. Based in the healthcare context, it is designed to help healthcare students to tackle the maths they need in their work and to become more independent learners in the process. The book is particularly intended to help those who may be anxious about their maths, and strategies are included to help students to calculate under pressure of time and stress.
Caribbean Primary Mathematics Book 3 6th edition
by Karen MorrisonMake teaching and learning mathematics relevant and enjoyable with the best-known Primary mathematics series in the Caribbean updated and revised for the 21st Century by practising teachers, with a new focus on self-directed learning, problem -solving and raising standards.- Ensure all requirements of primary schools in all Caribbean territories from kindergarten to primary school exit examination level are covered. - Engage students and make maths more relevant with real-life situations used throughout the book, including the front cover, showing Mathematics in action.- Reinforce knowledge and encourage progression with Assessment Bank, available separately to compliment the topics covered in this series.- Encourage students to understand and build their own learning with all key skills and concepts clearly introduced in sequence, demonstrating links between mathematical strands and other curriculum subjects.
Caribbean Primary Mathematics Book 3 (6th edition) (PDF)
by Jonella GiffardMake teaching and learning mathematics relevant and enjoyable with the best-known Primary mathematics series in the Caribbean updated and revised for the 21st Century by practising teachers, with a new focus on self-directed learning, problem -solving and raising standards. - Ensure all requirements of primary schools in all Caribbean territories from kindergarten to primary school exit examination level are covered. - Engage students and make maths more relevant with real-life situations used throughout the book, including the front cover, showing Mathematics in action. - Reinforce knowledge and encourage progression with Assessment Bank, available separately to compliment the topics covered in this series. - Encourage students to understand and build their own learning with all key skills and concepts clearly introduced in sequence, demonstrating links between mathematical strands and other curriculum subjects.
Caribbean Primary Mathematics Book 3 (6th edition) (PDF)
by Karen MorrisonMake teaching and learning mathematics relevant and enjoyable with the best-known Primary mathematics series in the Caribbean updated and revised for the 21st Century by practising teachers, with a new focus on self-directed learning, problem -solving and raising standards. - Ensure all requirements of primary schools in all Caribbean territories from kindergarten to primary school exit examination level are covered. - Engage students and make maths more relevant with real-life situations used throughout the book, including the front cover, showing Mathematics in action. - Reinforce knowledge and encourage progression with Assessment Bank, available separately to compliment the topics covered in this series. - Encourage students to understand and build their own learning with all key skills and concepts clearly introduced in sequence, demonstrating links between mathematical strands and other curriculum subjects.
Caribbean Primary Mathematics Book 4 6th edition
by Karen MorrisonMake teaching and learning mathematics relevant and enjoyable with the best-known Primary mathematics series in the Caribbean updated and revised for the 21st Century by practising teachers, with a new focus on self-directed learning, problem -solving and raising standards. - Ensure all requirements of primary schools in all Caribbean territories from kindergarten to primary school exit examination level are covered. - Engage students and make maths more relevant with real-life situations used throughout the book, including the front cover, showing Mathematics in action.- Reinforce knowledge and encourage progression with Assessment Bank, available separately to compliment the topics covered in this series.- Encourage students to understand and build their own learning with all key skills and concepts clearly introduced in sequence, demonstrating links between mathematical strands and other curriculum subjects.
Caribbean Primary Mathematics Book 5 6th edition
by Karen MorrisonMake teaching and learning mathematics relevant and enjoyable with the best-known Primary mathematics series in the Caribbean updated and revised for the 21st Century by practising teachers, with a new focus on self-directed learning, problem-solving and raising standards. - Ensure all requirements of primary schools in all Caribbean territories from kindergarten to primary school exit examination level are covered. - Engage students and make maths more relevant with real-life situations used throughout the book, including the front cover, showing Mathematics in action.- Reinforce knowledge and encourage progression with Assessment Bank, available separately to compliment the topics covered in this series.- Encourage students to understand and build their own learning with all key skills and concepts clearly introduced in sequence, demonstrating links between mathematical strands and other curriculum subjects.
Caribbean Primary Mathematics Book 6 6th edition
by Karen MorrisonMake teaching and learning mathematics relevant and enjoyable with the best-known Primary mathematics series in the Caribbean updated and revised for the 21st Century by practising teachers, with a new focus on self-directed learning, problem-solving and raising standards. - Ensure all requirements of primary schools in all Caribbean territories from kindergarten to primary school exit examination level are covered. - Engage students and make maths more relevant with real-life situations used throughout the book, including the front cover, showing Mathematics in action.- Reinforce knowledge and encourage progression with Assessment Bank, available separately to compliment the topics covered in this series.- Encourage students to understand and build their own learning with all key skills and concepts clearly introduced in sequence, demonstrating links between mathematical strands and other curriculum subjects.
Caribbean Primary Mathematics Level 5 6th Edition (PDF)
by Karen MorrisonMake teaching and learning mathematics relevant and enjoyable with the best-known Primary mathematics series in the Caribbean updated and revised for the 21st Century by practising teachers, with a new focus on self-directed learning, problem-solving and raising standards. - Ensure all requirements of primary schools in all Caribbean territories from kindergarten to primary school exit examination level are covered. - Engage students and make maths more relevant with real-life situations used throughout the book, including the front cover, showing Mathematics in action. - Reinforce knowledge and encourage progression with Assessment Bank, available separately to compliment the topics covered in this series.
Carl Adam Petri: Eine Biographie
by Einar SmithDer Autor präsentiert Leben, Werk und Wirken eines der weltweit bekanntesten deutschen Informatiker: Carl Adam Petri. Die Stadien seiner Entwicklung sind lebendig und kurzweilig beschrieben, gehen aber so weit in die Tiefe, dass der Leser ein gutes Verständnis für die Hintergründe von Petris wichtigstem Beitrag zur Informatik bekommt, die nach ihm benannten Petrinetze. Das Buch kann so als Einführung in die Petrinetze gelesen werden, erörtert aber auch die theoretischen, physikalischen und philosophischen Grundlagen der Netze, die erst einen umfassenden Zugang zu Petris Werk ermöglichen. Das Buch wendet sich dank seiner verständlichen Darstellung aber auch an Leser, die einfach nur eine bemerkenswerte Persönlichkeit der Zeitgeschichte kennenlernen möchten.
Carl Adam Petri: Life and Science
by Einar SmithThe book presents the life and works of one of Germany's most famous computer scientists, Carl Adam Petri. It is written in a vivid and entertaining manner, providing an in-depth discussion of the background behind Petri's best-known contribution to computer science, the Petri net. In this way the book can be read as a first introduction to nets, but it also covers the theoretical, physical and philosophical foundations behind nets, thus facilitating a comprehensive understanding of the wider range of Petri's works. The book is intended for readers with a previous knowledge in computer science, as well as for “interested non-professionals”, who want to get to know a remarkable personality of contemporary science.
Carleman Estimates and Applications to Inverse Problems for Hyperbolic Systems (Springer Monographs in Mathematics)
by Mourad Bellassoued Masahiro YamamotoThis book is a self-contained account of the method based on Carleman estimates for inverse problems of determining spatially varying functions of differential equations of the hyperbolic type by non-overdetermining data of solutions. The formulation is different from that of Dirichlet-to-Neumann maps and can often prove the global uniqueness and Lipschitz stability even with a single measurement. These types of inverse problems include coefficient inverse problems of determining physical parameters in inhomogeneous media that appear in many applications related to electromagnetism, elasticity, and related phenomena. Although the methodology was created in 1981 by Bukhgeim and Klibanov, its comprehensive development has been accomplished only recently. In spite of the wide applicability of the method, there are few monographs focusing on combined accounts of Carleman estimates and applications to inverse problems. The aim in this book is to fill that gap. The basic tool is Carleman estimates, the theory of which has been established within a very general framework, so that the method using Carleman estimates for inverse problems is misunderstood as being very difficult. The main purpose of the book is to provide an accessible approach to the methodology. To accomplish that goal, the authors include a direct derivation of Carleman estimates, the derivation being based essentially on elementary calculus working flexibly for various equations. Because the inverse problem depends heavily on respective equations, too general and abstract an approach may not be balanced. Thus a direct and concrete means was chosen not only because it is friendly to readers but also is much more relevant. By practical necessity, there is surely a wide range of inverse problems and the method delineated here can solve them. The intention is for readers to learn that method and then apply it to solving new inverse problems.
Carleman Estimates and Applications to Uniqueness and Control Theory (Progress in Nonlinear Differential Equations and Their Applications #46)
by Feruccio Colombini Claude Zuily
Carleman Estimates for Second Order Partial Differential Operators and Applications: A Unified Approach (SpringerBriefs in Mathematics)
by Xiaoyu Fu Qi Lü Xu ZhangThis book provides a brief, self-contained introduction to Carleman estimates for three typical second order partial differential equations, namely elliptic, parabolic, and hyperbolic equations, and their typical applications in control, unique continuation, and inverse problems. There are three particularly important and novel features of the book. First, only some basic calculus is needed in order to obtain the main results presented, though some elementary knowledge of functional analysis and partial differential equations will be helpful in understanding them. Second, all Carleman estimates in the book are derived from a fundamental identity for a second order partial differential operator; the only difference is the choice of weight functions. Third, only rather weak smoothness and/or integrability conditions are needed for the coefficients appearing in the equations. Carleman Estimates for Second Order Partial Differential Operators and Applications will be of interest to all researchers in the field.
Carleman Inequalities: An Introduction and More (Grundlehren der mathematischen Wissenschaften #353)
by Nicolas LernerOver the past 25 years, Carleman estimates have become an essential tool in several areas related to partial differential equations such as control theory, inverse problems, or fluid mechanics. This book provides a detailed exposition of the basic techniques of Carleman Inequalities, driven by applications to various questions of unique continuation.Beginning with an elementary introduction to the topic, including examples accessible to readers without prior knowledge of advanced mathematics, the book's first five chapters contain a thorough exposition of the most classical results, such as Calderón's and Hörmander's theorems. Later chapters explore a selection of results of the last four decades around the themes of continuation for elliptic equations, with the Jerison-Kenig estimates for strong unique continuation, counterexamples to Cauchy uniqueness of Cohen and Alinhac & Baouendi, operators with partially analytic coefficients with intermediate results between Holmgren's and Hörmander's uniqueness theorems, Wolff's modification of Carleman's method, conditional pseudo-convexity, and more.With examples and special cases motivating the general theory, as well as appendices on mathematical background, this monograph provides an accessible, self-contained basic reference on the subject, including a selection of the developments of the past thirty years in unique continuation.
Carleman’s Formulas in Complex Analysis: Theory and Applications (Mathematics and Its Applications #244)
by L.A. AizenbergIntegral representations of holomorphic functions play an important part in the classical theory of functions of one complex variable and in multidimensional com plex analysis (in the later case, alongside with integration over the whole boundary aD of a domain D we frequently encounter integration over the Shilov boundary 5 = S(D)). They solve the classical problem of recovering at the points of a do main D a holomorphic function that is sufficiently well-behaved when approaching the boundary aD, from its values on aD or on S. Alongside with this classical problem, it is possible and natural to consider the following one: to recover the holomorphic function in D from its values on some set MeaD not containing S. Of course, M is to be a set of uniqueness for the class of holomorphic functions under consideration (for example, for the functions continuous in D or belonging to the Hardy class HP(D), p ~ 1).
Carleson Curves, Muckenhoupt Weights, and Toeplitz Operators (Progress in Mathematics #154)
by Albrecht Böttcher Yuri I. KarlovichAward-winning monograph of the Ferran Sunyer i Balaguer Prize 1997. This book is a self-contained exposition of the spectral theory of Toeplitz operators with piecewise continuous symbols and singular integral operators with piecewise continuous coefficients. It includes an introduction to Carleson curves, Muckenhoupt weights, weighted norm inequalities, local principles, Wiener-Hopf factorization, and Banach algebras generated by idempotents. Some basic phenomena in the field and the techniques for treating them came to be understood only in recent years and are comprehensively presented here for the first time.The material has been polished in an effort to make advanced topics accessible to a broad readership. The book is addressed to a wide audience of students and mathematicians interested in real and complex analysis, functional analysis and operator theory.