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Research in Data Science (Association for Women in Mathematics Series #17)
by Ellen Gasparovic Carlotta DomeniconiThis edited volume on data science features a variety of research ranging from theoretical to applied and computational topics. Aiming to establish the important connection between mathematics and data science, this book addresses cutting edge problems in predictive modeling, multi-scale representation and feature selection, statistical and topological learning, and related areas. Contributions study topics such as the hubness phenomenon in high-dimensional spaces, the use of a heuristic framework for testing the multi-manifold hypothesis for high-dimensional data, the investigation of interdisciplinary approaches to multi-dimensional obstructive sleep apnea patient data, and the inference of a dyadic measure and its simplicial geometry from binary feature data. Based on the first Women in Data Science and Mathematics (WiSDM) Research Collaboration Workshop that took place in 2017 at the Institute for Compuational and Experimental Research in Mathematics (ICERM) in Providence, Rhode Island, this volume features submissions from several of the working groups as well as contributions from the wider community. The volume is suitable for researchers in data science in industry and academia.
Micro to MACRO Mathematical Modelling in Soil Mechanics (Trends in Mathematics)
by Pasquale Giovine Paolo Maria Mariano Giuseppe MortaraThis special issue collects selected contributions (excluding general lectures) of a Symposium on "Micro to MACRO Mathematical Modelling in Soil Mechanics", which took place at the University of Reggio Calabria, Italy, from May 29th to June 1st, 2018.The Symposium provided an opportunity to enhance the scientific debate on the construction of mathematical models for the description of the physical behaviour of soils, as well as on the suggestions provided by the micro-mechanical observation of the matter. The focus was on the comparison between the appropriateness of models and the need of mathematics to obtain rigorous results, which involves know-how from applied mathematical physics, geotechnical engineering and mechanics of solids.The contributions were selected by the Editors and the other Members of the Scientific Committee of the Symposium: Gianfranco Capriz (Pisa, Roma), Claudio di Prisco (Milan), Wolfgang Ehlers (Stuttgart), James T. Jenkins (Cornell), Stefan Luding (Twente), David Muir Wood (Dundee), Kenichi Soga (Berkeley).
Mehrsprachige Vorstellungsentwicklungsprozesse: Lernprozessstudie zum Anteilskonzept bei deutsch-türkischen Lernenden (Dortmunder Beiträge zur Entwicklung und Erforschung des Mathematikunterrichts #42)
by Taha Ertuğrul KuzuTaha Ertuğrul Kuzu untersucht Formen und Funktionen der Aktivierung mehrsprachiger Ressourcen im Rahmen mathematischer Verstehensprozesse im vorrangig monolingualen deutschen Schulkontext. Dazu kombiniert er in einem interdisziplinären Forschungszugriff mathematikdidaktische und linguistische Perspektiven auf die Mehrsprachigkeit, um in qualitativen Fallanalysen individuelle Lernpfade und Sprachnutzungsmuster zu rekonstruieren. Als zentrale Erkenntnis zeigt der Autor, dass sich die mehrsprachigen Ressourcen der Lernenden sukzessive vernetzen und im Lernprozess wichtige Funktionen, wie die Schaffung von konzeptueller Multiperspektivität sowie der Konsolidierung von Vorstellungen, einnehmen.
Mathematik zum Studieneinstieg: Grundwissen der Analysis für Wirtschaftswissenschaftler, Ingenieure, Naturwissenschaftler und Informatiker
by Gabriele Adams Hermann-Josef Kruse Diethelm Sippel Udo PfeifferStudierende in den Fächern Wirtschaftswissenschaften, Technik, Naturwissenschaften und Informatik benötigen zum Studienbeginn bestimmte Grundkenntnisse in der Mathematik, die im vorliegenden Buch sehr ausführlich dargestellt werden. Es behandelt die Grundlagen der Analysis im Sinne einer Wiederholung/Vertiefung des gymnasialen Oberstufenstoffes. Der Stoff wird schrittweise erklärt und anhand vieler Beispiele aus verschiedenen Disziplinen illustriert. Aufgaben (mit Lösungen) dienen der Einübung. Wiederholtes Aufgreifen der Anwendungsbeispiele regen zur Auseinandersetzung mit den verschiedenen Themen an. Durch die breite Darstellung ist das Buch insbesondere für die Wiederholung oder den Erwerb des Wissens im Selbststudium (auch für Schüler im Leistungskurs Mathematik) geeignet.
Survival Analysis with Correlated Endpoints: Joint Frailty-Copula Models (SpringerBriefs in Statistics)
by Takeshi Emura Shigeyuki Matsui Virginie RondeauThis book introduces readers to advanced statistical methods for analyzing survival data involving correlated endpoints. In particular, it describes statistical methods for applying Cox regression to two correlated endpoints by accounting for dependence between the endpoints with the aid of copulas. The practical advantages of employing copula-based models in medical research are explained on the basis of case studies. In addition, the book focuses on clustered survival data, especially data arising from meta-analysis and multicenter analysis. Consequently, the statistical approaches presented here employ a frailty term for heterogeneity modeling. This brings the joint frailty-copula model, which incorporates a frailty term and a copula, into a statistical model. The book also discusses advanced techniques for dealing with high-dimensional gene expressions and developing personalized dynamic prediction tools under the joint frailty-copula model. To help readers apply the statistical methods to real-world data, the book provides case studies using the authors’ original R software package (freely available in CRAN). The emphasis is on clinical survival data, involving time-to-tumor progression and overall survival, collected on cancer patients. Hence, the book offers an essential reference guide for medical statisticians and provides researchers with advanced, innovative statistical tools. The book also provides a concise introduction to basic multivariate survival models.
Stochastic Flows and Jump-Diffusions (Probability Theory and Stochastic Modelling #92)
by Hiroshi KunitaThis monograph presents a modern treatment of (1) stochastic differential equations and (2) diffusion and jump-diffusion processes. The simultaneous treatment of diffusion processes and jump processes in this book is unique: Each chapter starts from continuous processes and then proceeds to processes with jumps.In the first part of the book, it is shown that solutions of stochastic differential equations define stochastic flows of diffeomorphisms. Then, the relation between stochastic flows and heat equations is discussed. The latter part investigates fundamental solutions of these heat equations (heat kernels) through the study of the Malliavin calculus. The author obtains smooth densities for transition functions of various types of diffusions and jump-diffusions and shows that these density functions are fundamental solutions for various types of heat equations and backward heat equations. Thus, in this book fundamental solutions for heat equations and backward heat equations are constructed independently of the theory of partial differential equations.Researchers and graduate student in probability theory will find this book very useful.
Time Use and Transfers in the Americas: Producing, Consuming, and Sharing Time Across Generations and Genders
by B. Piedad Urdinola Jorge A. TovarThis book provides a comparison of the measurement in time and monetary units of unpaid domestic work in Colombia, Costa Rica, Uruguay, and the Hispanic ethnicity in the United States. A standardized technique allows the development of comparable estimates across countries per age and gender which reveal specific behavioral patterns over the life cycle. A mixture of economic conditions, social norms, and demographic trends provide insightful explanations for the unequal burden that women and girls carry when dealing with unpaid domestic activities, an economically significant but traditionally neglected activity. As such, the book is of interested to practitioners in all social sciences, particularly sociologists, demographers, economists, and policymakers.
Old and New Perspectives on Mortality Forecasting (Demographic Research Monographs)
by Tommy Bengtsson Nico KeilmanThis open access book describes methods of mortality forecasting and discusses possible improvements. It contains a selection of previously unpublished and published papers, which together provide a state-of-the-art overview of statistical approaches as well as behavioural and biological perspectives. The different parts of the book provide discussions of current practice, probabilistic forecasting, the linearity in the increase of life expectancy, causes of death, and the role of cohort factors. The key question in the book is whether it is possible to project future mortality accurately, and if so, what is the best approach. This makes the book a valuable read to demographers, pension planners, actuaries, and all those interested and/or working in modelling and forecasting mortality.
Introducing the Stars: Formation, Structure and Evolution (Undergraduate Lecture Notes in Physics)
by Martin BeechThis textbook introduces the reader to the basic concepts and equations that describe stellar structure. Various approximation techniques are used to solve equations, and an intuitive rather than rigorous approach is employed to interpret the properties of the stars. The book provides step-by-step instructions, helpful exercises and relevant historical lessons to familiarize students with key concepts and mathematical theories.Based upon a series of one-semester (12 weeks) elective undergraduate courses offered at the University of Regina, this book is intended for students who are interested in seeing how basic calculus and introductory physics can be applied to the understanding of the stars from their formation to their death. The text provides an intermediate stepping stone between lower-level undergraduate classes and more specialized postgraduate texts on the subject of stellar structure.
Tutorium Algebra: Mathematik von Studenten für Studenten erklärt und kommentiert
by Florian Modler Martin KrehIn einer Algebra-Vorlesung beschäftigt man sich nicht mehr mit Linearer Algebra, sondern es wird abstrakter. Um die Studierenden beim Verständnis für diesen abstrakten Stoff zu unterstützen, erscheint nun mit "Tutorium Algebra" ein weiterer Band der Tutoriums-Reihe der Autoren Modler und Kreh.In dem Buch erläutern die beiden Autoren den Stoff der Algebra. Dabei liegt das Hauptaugenmerk auf der Körpertheorie, genauer der Galoistheorie. Die Inhalte werden an verständlichen und ausführlichen vorgerechneten Beispielen erklärt. Das Konzept bleibt wieder das bewährte: Jedes Kapitel ist zwei geteilt in einen mathematischen Teil, in dem die Definitionen, Sätze und Beweise stehen, und einen erklärenden Teil, in dem die schwierigen Definitionen und Sätze auf gewohnt lockere und lustige Art und Weise mit mehr als 120 Beispielen und etwa 30 Abbildungen mit Leben gefüllt werden.So erhält der Leser einerseits einen Blick für mathematisch exakte Formulierungen und andererseits Hilfen und Anschauungen, die wichtig sind, um den Stoff zu verstehen.Das Buch ist in der 3. Auflage vollständig durchgesehen, verbessert und ergänzt worden. Insbesondere finden sich im Kapitel über Ringe und Ideale einige neue Beispiele (z.B. über den Ring der holomorphen Funktionen) und die Lokalisierung von Ringen wird behandelt. Zudem wurden weitere Kriterien zur Irreduzibilität von Polynomen ergänzt.
Nonsmooth Optimization and Its Applications (International Series of Numerical Mathematics #170)
by Seyedehsomayeh Hosseini Boris S. Mordukhovich André UschmajewSince nonsmooth optimization problems arise in a diverse range of real-world applications, the potential impact of efficient methods for solving such problems is undeniable. Even solving difficult smooth problems sometimes requires the use of nonsmooth optimization methods, in order to either reduce the problem’s scale or simplify its structure. Accordingly, the field of nonsmooth optimization is an important area of mathematical programming that is based on by now classical concepts of variational analysis and generalized derivatives, and has developed a rich and sophisticated set of mathematical tools at the intersection of theory and practice.This volume of ISNM is an outcome of the workshop "Nonsmooth Optimization and its Applications," which was held from May 15 to 19, 2017 at the Hausdorff Center for Mathematics, University of Bonn. The six research articles gathered here focus on recent results that highlight different aspects of nonsmooth and variational analysis, optimization methods, their convergence theory and applications.
Holomorphic Curves and Global Questions in Contact Geometry (Birkhäuser Advanced Texts Basler Lehrbücher)
by Casim Abbas Helmut HoferThis book explains the foundations of holomorphic curve theory in contact geometry. By using a particular geometric problem as a starting point the authors guide the reader into the subject. As such it ideally serves as preparation and as entry point for a deeper study of the analysis underlying symplectic field theory.An introductory chapter sets the stage explaining some of the basic notions of contact geometry and the role of holomorphic curves in the field. The authors proceed to the heart of the material providing a detailed exposition about finite energy planes and periodic orbits (chapter 4) to disk filling methods and applications (chapter 9).The material is self-contained. It includes a number of technical appendices giving the geometric analysis foundations for the main results, so that one may easily follow the discussion. Graduate students as well as researchers who want to learn the basics of this fast developing theory will highly appreciate this accessible approach taken by the authors.
Algebra ausführlich erklärt in Aufgaben und Lösungen
by Matthias LehnerDieses Lehrbuch unterstützt Sie beim individuellen Studium der Algebra. Es ist die perfekte Ergänzung zu Ihrer Vorlesung sowie zum klassischen Lehrbuch. Die Inhalte, die Sie aus diesen Formaten kennen, werden zu Beginn jedes Kapitels zusammengefasst. Der Schwerpunkt dieses Werkes liegt auf zahlreichen Beispielaufgaben. Durch eine detaillierte Aufgabenstellung sowie konkrete Lösungshinweise wird das individuelle Erlernen der Algebra unterstützt. Ausführliche Lösungsbeispiele helfen Ihnen beim Erarbeiten eigener Lösungswege oder ermöglichen Ihnen Ihre eigenen Überlegungen zu überprüfen. Das Aufgabenbuch folgt der klassischen Dreiteilung Gruppen - Ringe - Körper, die Sie in den meisten einführenden Algebrakursen vorfinden und ist daher vielfach einsetzbar. Aufgrund des übersichtlichen Aufbaus mit vielen Aufgaben und einer übersichtlichen Zusammenfassung der Theorie eignet es sich für ein tiefgreifendes Verständnis ebenso wie für die kurzfristige Klausurvorbereitung.
Many Agent Games in Socio-economic Systems: Corruption, Inspection, Coalition Building, Network Growth, Security (Springer Series in Operations Research and Financial Engineering)
by Vassili N. Kolokoltsov Oleg A. MalafeyevThere has been an increase in attention toward systems involving large numbers of small players, giving rise to the theory of mean field games, mean field type control and nonlinear Markov games. Exhibiting various real world problems involving major and minor agents, this book presents a systematic continuous-space approximation approach for mean-field interacting agents models and mean-field games models. After describing Markov-chain methodology and a modeling of mean-field interacting systems, the text presents various structural conditions on the chain to yield respective socio-economic models, focusing on migration models via binary interactions. The specific applications are wide-ranging – including inspection and corruption, cyber-security, counterterrorism, coalition building and network growth, minority games, and investment policies and optimal allocation – making this book relevant to a wide audience of applied mathematicians interested in operations research, computer science, national security, economics, and finance.
Computer-Based Analysis of the Stochastic Stability of Mechanical Structures Driven by White and Colored Noise (SpringerBriefs in Applied Sciences and Technology)
by Aydin Azizi Poorya Ghafoorpoor YazdiThis book provides a concise introduction to the behavior of mechanical structures and testing their stochastic stability under the influence of noise. It explains the physical effects of noise and in particular the concept of Gaussian white noise. In closing, the book explains how to model the effects of noise on mechanical structures, and how to nullify / compensate for it by designing effective controllers.
Flash Computation and EoS Modelling for Compositional Thermal Simulation of Flow in Porous Media (Springer Theses)
by Duncan PatersonThis book investigates a wide range of phase equilibrium modelling and calculation problems for compositional thermal simulation. Further, it provides an effective solution for multiphase isenthalpic flash under the classical framework, and it also presents a new flash calculation framework for multiphase systems, which can handle phase equilibrium and chemical reaction equilibrium simultaneously. The framework is particularly suitable for systems with many phases and reactions. In this book, the author shows how the new framework can be generalised for different flash specifications and different independent variables. Since the flash calculation is at the heart of various types of compositional simulation, the findings presented here will promote the combination of phase equilibrium and chemical equilibrium calculations in future simulators, aiming at improving their robustness and efficiency.
R For College Mathematics and Statistics
by Thomas PfaffR for College Mathematics and Statistics encourages the use of R in mathematics and statistics courses. Instructors are no longer limited to ``nice'' functions in calculus classes. They can require reports and homework with graphs. They can do simulations and experiments. R can be useful for student projects, for creating graphics for teaching, as well as for scholarly work. This book presents ways R, which is freely available, can enhance the teaching of mathematics and statistics. R has the potential to help students learn mathematics due to the need for precision, understanding of symbols and functions, and the logical nature of code. Moreover, the text provides students the opportunity for experimenting with concepts in any mathematics course. Features: Does not require previous experience with R Promotes the use of R in typical mathematics and statistics course work Organized by mathematics topics Utilizes an example-based approach Chapters are largely independent of each other
Im Banne der Mathematik: Die kulturellen Aspekte der Mathematik in Zivilisation, Kunst und Natur
by Rik VerhulstDieses Buch wendet sich an interessierte Laien sowie professionelle Mathematiker und spricht zahlreiche Aspekte dieser Wissenschaft an. Das Werk zeigt insbesondere, wie die Mathematik aufgebaut ist und wie sie arbeitet. Beispiele aus der Praxis werden dabei ebenso besprochen wie die allgemeine Rolle der Mathematik in Kultur und Kunst, in der Natur und im täglichen Leben. Hierbei reicht die Bandbreite der behandelten Themen von Sprachbildung über Anwendungen in antiken wie auch modernen Kulturen und den Goldenen Schnitt bis hin zu mathematischen Kuriositäten. Dieses Buch vermittelt einen verständlichen Einblick in das faszinierende Panorama der Mathematik und hebt ihre Bedeutung in der Menschheitsgeschichte hervor. Dabei werden nur die grundlegenden Begriffe der Schulmathematik vorausgesetzt, um jedem Leser Zugang zur spannenden Welt der Mathematik zu ermöglichen. Zahlreiche Beispiele und Abbildungen veranschaulichen den Text.
Experimetrics: Econometrics For Experimental Economics (PDF)
by Peter G. MoffattThis advanced textbook is an essential guide to discovering new and more illuminating ways to analyse the econometric modelling of experimental data. Peter Moffatt, one of the world's experts in the field, covers a range of techniques: from the familiar, such as treatment testing, to lesser known ones such as finite mixture models and the method of maximum simulated likelihood. The book takes a hands-on approach by explaining STATA commands in detail. In addition, difficult problems inherent in the methodology are addressed, such as the parametric estimation of social preference models, quantal response models, and learning models. An indispensable book for researchers and advanced students in experimental and behavioural economics who want to come to grips with the field of Experimetrics. The companion website www.palgrave.com/moffatt contains: - all data sets (in Stata format) used as examples in the book; - an executable Stata 'do-file' containing stata commands and programs used in examples; and - an Excel file containing some Excel calculations presented in the text
Edexcel A Level Mathematics Year 1 (AS) (PDF)
by Sophie Goldie Susan Whitehouse Val Hanrahan Cath Moore Jean-Paul Muscat Keith PledgerHelp students to develop their knowledge and apply their reasoning to mathematical problems with worked examples, stimulating activities and assessment support tailored to the 2017 Edexcel specification. The content benefits from the expertise of subject specialist Keith Pledger and the support of MEI (Mathematics in Education and Industry). -Prepare students for assessment with skills-building activities, worked examples and practice questions tailored to the changed criteria. -Develop a fuller understanding of mathematical concepts with real world examples that help build connections between topics and develop mathematical modelling skills. -Cement understanding of problem-solving, proof and modelling with dedicated sections on these key areas. -Confidently teach the new statistics requirements with five dedicated statistics chapters and questions around the use of large data sets. -Cover the use of technology in Mathematics with a variety of questions based around the use of spreadsheets, graphing software and graphing calculators. -Provide clear paths of progression that combine pure and applied maths into a coherent whole.
Gravity: A Ladybird Expert Book
by Jim Al-KhaliliPart of the new Ladybird Expert series, Gravity is an accessible and authoritative introduction to a force as familiar to us as breathing. What is gravity?How does it work?And why are there extreme gravitational environments?Written by celebrated physicist and broadcaster Jim Al-Khalili, Gravity proves to be so much more than the adage: 'what goes up must come down'. Stuck to the surface of our planet we experience gravity merely as a force pulling us down to the ground, but we will discover that it is far richer than that. Inside, you'll learn that gravity is not really a 'force' at all, but something altogether more profound. In fact, gravity controls the very shape of space and the passage of time themselves and, as such, the history and destiny of the entire Universe. Written by the leading lights and most outstanding communicators in their fields, the Ladybird Expert books provide clear, accessible and authoritative introductions to subjects drawn from science, history and culture.For an adult readership, the Ladybird Expert series is produced in the same iconic small hardback format pioneered by the original Ladybirds. Each beautifully illustrated book features the first new illustrations produced in the original Ladybird style for nearly forty years.
A Dynamical Perspective on the ɸ4 Model: Past, Present and Future (Nonlinear Systems and Complexity #26)
by Panayotis G. Kevrekidis Jesús Cuevas-MaraverThis book presents a careful selection of the most important developments of the \phi^4 model, offering a judicious summary of this model with a view to future prospects and the challenges ahead. Over the past four decades, the \phi^4 model has been the basis for a broad array of developments in the physics and mathematics of nonlinear waves. From kinks to breathers, from continuum media to discrete lattices, from collisions of solitary waves to spectral properties, and from deterministic to stochastic models of \phi^4 (and \phi^6, \phi^8, \phi^12 variants more recently), this dynamical model has served as an excellent test bed for formulating and testing the ideas of nonlinear science and solitary waves.
Contributions to Partial Differential Equations and Applications (Computational Methods in Applied Sciences #47)
by O. Pironneau J. Periaux P. Neittaanmäki Y. A. Kuznetsov W. Fitzgibbon B. N. ChetverushkinThis book treats Modelling of CFD problems, Numerical tools for PDE, and Scientific Computing and Systems of ODE for Epidemiology, topics that are closely related to the scientific activities and interests of Prof. William Fitzgibbon, Prof. Yuri Kuznetsov, and Prof. O. Pironneau, whose outstanding achievements are recognised in this volume. It contains 20 contributions from leading scientists in applied mathematics dealing with partial differential equations and their applications to engineering, ab-initio chemistry and life sciences. It includes the mathematical and numerical contributions to PDE for applications presented at the ECCOMAS thematic conference "Contributions to PDE for Applications" held at Laboratoire Jacques Louis Lions in Paris, France, August 31- September 1, 2015, and at the Department of Mathematics, University of Houston, Texas, USA, February 26-27, 2016. This event brought together specialists from universities and research institutions who are developing or applying numerical PDE or ODE methods with an emphasis on industrial and societal applications. This volume is of interest to researchers and practitioners as well as advanced students or engineers in applied and computational mathematics. All contributions are written at an advanced scientific level with no effort made by the editors to make this volume self-contained. It is assumed that the reader is a specialist already who knows the basis of this field of research and has the capability of understanding and appreciating the latest developments in this field.
Simulationen und Randomisierungstests mit der Software TinkerPlots: Theoretische Werkzeuganalyse und explorative Fallstudie (Studien zur Hochschuldidaktik und zum Lehren und Lernen mit digitalen Medien in der Mathematik und in der Statistik)
by Susanne PodwornyAusgangspunkt dieser Arbeit ist die weitverbreitete Ansicht, dass Lernprozesse von computergestützten Simulationen profitieren können. Susanne Podworny untersucht das Unterstützungspotential der Software TinkerPlots zur stochastischen Simulation und entwickelt daraus eine Lerneinheit zum statistischen Schließen mit Randomisierungstests nach dem Design-Based-Research-Ansatz. In einer anschließenden Fallstudie werden mit Mitteln der Interaktionsanalyse die Bearbeitungsprozesse von sechs Studierenden untersucht und daraus Hinweise für die Didaktik der Stochastik abgeleitet.
Diversity of Experimental Methods in Economics
by Hirokazu Takizawa Toshiji KawagoeThis is the first book that examines the diverse range of experimental methods currently being used in the social sciences, gathering contributions by working economists engaged in experimentation, as well as by a political scientist, psychologists and philosophers of the social sciences. Until the mid-twentieth century, most economists believed that experiments in the economic sciences were impossible. But that’s hardly the case today, as evinced by the fact that Vernon Smith, an experimental economist, and Daniel Kahneman, a behavioral economist, won the Nobel Prize in Economics in 2002. However, the current use of experimental methods in economics is more diverse than is usually assumed. As the concept of experimentation underwent considerable abstraction throughout the twentieth century, the areas of the social sciences in which experiments are applied are expanding, creating renewed interest in, and multifaceted debates on, the way experimental methods are used. This book sheds new light on the diversity of experimental methodologies used in the social sciences. The topics covered include historical insights into the evolution of experimental methods; the necessary “performativity” of experiments, i.e., the dynamic interaction with the social contexts in which they are embedded; the application of causal inferences in the social sciences; a comparison of laboratory, field, and natural experiments; and the recent use of randomized controlled trials (RCTs) in development economics. Several chapters also deal with the latest heated debates, such as those concerning the use of the random lottery method in laboratory experiments.