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Directions in Number Theory
by Ellen E. Eischen Ling Long Rachel Pries Katherine E. StangeExploring the interplay between deep theory and intricate computation, this volume is a compilation of research and survey papers in number theory, written by members of the Women In Numbers (WIN) network, principally by the collaborative research groups formed at Women In Numbers 3, a conference at the Banff International Research Station in Banff, Alberta, on April 21-25, 2014. The papers span a wide range of research areas: arithmetic geometry; analytic number theory; algebraic number theory; and applications to coding and cryptography. The WIN conference series began in 2008, with the aim of strengthening the research careers of female number theorists. The series introduced a novel research-mentorship model: women at all career stages, from graduate students to senior members of the community, joined forces to work in focused research groups on cutting-edge projects designed and led by experienced researchers. The goals for Women In Numbers 3 were to establish ambitious new collaborations between women in number theory, to train junior participants about topics of current importance, and to continue to build a vibrant community of women in number theory. Forty-two women attended the WIN3 workshop, including 15 senior and mid-level faculty, 15 junior faculty and postdocs, and 12 graduate students.
Dirichlet Forms Methods for Poisson Point Measures and Lévy Processes
by Nicolas Bouleau Laurent DenisA simplified approach to Malliavin calculus adapted to Poisson random measures is developed and applied in this book. Called the "lent particle method" it is based on perturbation of the position of particles. Poisson random measures describe phenomena involving random jumps (for instance in mathematical finance) or the random distribution of particles (as in statistical physics). Thanks to the theory of Dirichlet forms, the authors develop a mathematical tool for a quite general class of random Poisson measures and significantly simplify computations of Malliavin matrices of Poisson functionals. The method gives rise to a new explicit calculus that they illustrate on various examples: it consists in adding a particle and then removing it after computing the gradient. Using this method, one can establish absolute continuity of Poisson functionals such as Lévy areas, solutions of SDEs driven by Poisson measure and, by iteration, obtain regularity of laws. The authors also give applications to error calculus theory. This book will be of interest to researchers and graduate students in the fields of stochastic analysis and finance, and in the domain of statistical physics. Professors preparing courses on these topics will also find it useful. The prerequisite is a knowledge of probability theory.
Dirichlet and Related Distributions
by Man-Lai Tang Kai Wang Ng Guo-Liang TianThe Dirichlet distribution appears in many areas of application, which include modelling of compositional data, Bayesian analysis, statistical genetics, and nonparametric inference. This book provides a comprehensive review of the Dirichlet distribution and two extended versions, the Grouped Dirichlet Distribution (GDD) and the Nested Dirichlet Distribution (NDD), arising from likelihood and Bayesian analysis of incomplete categorical data and survey data with non-response.The theoretical properties and applications are also reviewed in detail for other related distributions, such as the inverted Dirichlet distribution, Dirichlet-multinomial distribution, the truncated Dirichlet distribution, the generalized Dirichlet distribution, Hyper-Dirichlet distribution, scaled Dirichlet distribution, mixed Dirichlet distribution, Liouville distribution, and the generalized Liouville distribution.Key Features:Presents many of the results and applications that are scattered throughout the literature in one single volume.Looks at the most recent results such as survival function and characteristic function for the uniform distributions over the hyper-plane and simplex; distribution for linear function of Dirichlet components; estimation via the expectation-maximization gradient algorithm and application; etc.Likelihood and Bayesian analyses of incomplete categorical data by using GDD, NDD, and the generalized Dirichlet distribution are illustrated in detail through the EM algorithm and data augmentation structure.Presents a systematic exposition of the Dirichlet-multinomial distribution for multinomial data with extra variation which cannot be handled by the multinomial distribution.S-plus/R codes are featured along with practical examples illustrating the methods.Practitioners and researchers working in areas such as medical science, biological science and social science will benefit from this book.
Dirichlet: A Mathematical Biography
by Uta C. MerzbachThis is the first extensive biography of the influential German mathematician, Peter Gustav Lejeune Dirichlet (1805 – 1859). Dirichlet made major contributions to number theory in addition to clarifying concepts such as the representation of functions as series, the theory of convergence, and potential theory. His mathematical methodology was explicitly based on a thorough knowledge of the work of his predecessors and his belief in the underlying unity of the branches of mathematics. This unified approach is exemplified in a paper that effectively launched the field of analytic number theory. The same orientation pervaded his teaching, which had a profound influence on the work of many mathematicians of subsequent generations. Chapters dealing with his mathematical work alternate with biographical chapters that place Dirichlet’s life and those of some of his notable associates in the context of the political, social, and artistic culture of the period. This book will appeal not only to mathematicians but also to historians of mathematics and sciences, and readers interested in the cultural and intellectual history of the nineteenth century.
Disability and Qualitative Inquiry: Methods for Rethinking an Ableist World (Interdisciplinary Disability Studies)
by Ronald J. Berger Laura S. LorenzThis groundbreaking text makes an intervention on behalf of disability studies into the broad field of qualitative inquiry. Ronald Berger and Laura Lorenz introduce readers to a range of issues involved in doing qualitative research on disabilities by bringing together a collection of scholarly work that supplements their own contributions and covers a variety of qualitative methods: participant observation, interviewing and interview coding, focus groups, autoethnography, life history, narrative analysis, content analysis, and participatory visual methods. The chapters are framed in terms of the relevant methodological issues involved in the research, bringing in substantive findings to illustrate the fruits of the methods. In doing so, the book covers a range of physical, sensory, and cognitive impairments. This work resonates with themes in disability studies such as emancipatory research, which views research as a collaborative effort with research subjects whose lives are enhanced by the process and results of the work. It is a methodological approach that requires researchers to be on guard against exploiting informants for the purpose of professional aggrandizement and to engage in a process of ongoing self-reflection to clear themselves of personal and professional biases that may interfere with their ability to hear and empathize with others.
Disaster Law: Emerging Thresholds
by Amita SinghThis book looks at how legal frameworks can and do reduce risks arising out of disasters. The volume: analyses existing disaster laws and the challenges on the ground; brings together case studies from some of the most vulnerable regions; and proposes solutions to avert existing and possible future crises. The book offers appropriate legal frameworks for disaster management which could not only offer sustainable institutional reforms towards community resilience and preparedness but also reduce risk within the frameworks of justice, equity and accountability. It examines the intricacies of governance within which governments function and discusses how recent trends in infrastructure development and engineering technology could be balanced within the legal principles of ethics, transparency and integrity. The chapters in the volume suggest that legal frameworks ought to resonate with new challenges of resource management and climate change. Further, these frameworks could help secure citizens’ trust, institutional accountability and effective implementation through an unceasing partnership which keeps the community better prepared and more resilient. This volume will be indispensable to scholars and researchers of disaster management, law, public policy, environment and development studies as well as policymakers and those in administrative, governmental, judicial and development sectors.
Disasters of Technology
by Sheila Sweeny HigginsonFind out about the Titanic's maiden voyage, Hindenburg's fiery demise and the Challenger explosions.
Disciplinary Literacy and Gamified Learning in Elementary Classrooms: Questing Through Time and Space (Springer Texts in Education)
by Leslie Haas Michelle Metzger Jill T. TusseyThis textbook provides real world examples of how disciplinary literacy can incorporate gamified learning opportunities in elementary classrooms (grades K-5 or ages 5-11). It also presents concrete examples of how to seamlessly integrate literacy within other subjects in engaging and unique ways. Furthermore, this text offers practical information related to pedagogy, content, and differentiation for each lesson. Preservice teachers, practicing teachers, instructional coaches, and administrators can benefit from this user-friendly text and its companion digital components, allowing for replication of lessons based on national standards, backed by best-practices, and supported by differentiated pedagogy.This unique volume begins with engineering marvels that span across centuries and locations. The eight chapters focus on the following marvels in chronological order: Great Pyramid of Giza, Stonehenge, Leaning Tower of Pisa, Great Wall of China, Machu Picchu, Panama Canal, Golden Gate Bridge, and International Space Station. By focusing on these specific examples of human ingenuity, opportunities are created to delve into the historical and social aspects of each chapter’s focus. There are also occasions to explore the artistic merit and the art created about and around each focus. Additional teaching opportunities lie in understanding the science, engineering, technology, and math embedded in all featured marvels.Each chapter features an adventure roadmap in the form of a narrative quest set against the chapter’s marvel that guides teachers and student players through embedded activities. Activities are designed for lower elementary school (grades K-2 or ages 5-8) and upper elementary school (grades 3-5 or ages 8-11). Instructional support for both novice and career teachers is provided through differentiation strategies, resource materials, and teaching tips.
Disciplinary Literacy and Gamified Learning in Middle School Classrooms: Questing Through Time and Space (Springer Texts in Education)
by Leslie Haas Michelle Metzger Jill T. TusseyThis textbook prepares teachers to incorporate gamified learning experiences into middle school classrooms. Its focus provides concrete examples of how to seamlessly integrate literacy across disciplines in a fun, engaging, and unique way for all learners. Furthermore, this book offers practical information related to pedagogy, content, and differentiation for each lesson. Preservice teachers, practicing teachers, instructional coaches, and administrators can benefit from this user-friendly text and its companion digital components, allowing for replication of lessons based on national standards, backed by best-practices, and supported by differentiated pedagogy.This unique book begins with engineering marvels that span across centuries and locations. The ten chapters, in chronological order, are titled: Acropolis, Petra, Colosseum, Chichen Itza, Moai, Red Square, Taj Mahal, Neuschwanstein, Eiffel Tower, and Sydney Opera House. By focusing on specific examples of human ingenuity, opportunities are created to delve into the historical and social aspects of each chapter’s focus. There are also chances to explore the artistic merit and the art created about and around each marvel. Additional teaching moments lie in understanding the science, engineering, technology, and math embedded in all featured marvels. Each chapter offers material lists, resource materials, and visual/graphic images to support understanding. Teaching tips and differentiation strategies are also provided to support novice and career teachers alike.
Disciplinary and Interdisciplinary Education in STEM: Changes and Innovations (Advances in STEM Education)
by Yeping Li Zheng Zeng Naiqing SongThis book provides an international platform for educators from different STEM disciplines to present, discuss, connect, and develop collaborations in two inter-related ways: (1) sharing and discussing changes and innovations in individual discipline-based education in STEM/STEAM, and (2) sharing and discussing the development of interdisciplinary STEM/STEAM education. Possible relationships and connections between individual disciplines (like mathematics or physics) and STEM education remain under explored and the integration of traditionally individual discipline-based education in STEM education is far from balanced. Efforts to pursue possible connections among traditionally separated individual disciplines in STEM are not only necessary for the importance of deepening and expanding interdisciplinary research and education in STEM, but also for the ever-increasing need of reflecting on and changing how traditional school subjects (like mathematics or physics) can and should be viewed, taught, and learned. Scholars from eight countries/regions provide diverse perspectives and approaches on changes and innovations in STEM disciplinary and interdisciplinary education. Disciplinary and Interdisciplinary Education in STEM will be a great resource to students and researchers in STEM education as well as STEM curriculum developers and teacher educators internationally.
Disciplining Statistics: Demography And Vital Statistics In France And England, 1830-1885
by Libby SchweberIn Disciplining Statistics Libby Schweber compares the science of population statistics in England and France during the nineteenth century, demonstrating radical differences in the interpretation and use of statistical knowledge. Through a comparison of vital statistics and demography, Schweber describes how the English government embraced statistics, using probabilistic interpretations of statistical data to analyze issues related to poverty and public health. The French were far less enthusiastic. Political and scientific lites in France struggled with the "reality" of statistical populations, wrestling with concerns about the accuracy of figures that aggregated heterogeneous groups such as the rich and poor and rejecting probabilistic interpretations. Tracing the introduction and promotion of vital statistics and demography, Schweber identifies the institutional conditions that account for the contrasting styles of reasoning. She shows that the different reactions to statistics stemmed from different criteria for what counted as scientific knowledge. The French wanted certain knowledge, a one-to-one correspondence between observations and numbers. The English adopted an instrumental approach, using the numbers to influence public opinion and evaluate and justify legislation. Schweber recounts numerous attempts by vital statisticians and demographers to have their work recognized as legitimate scientific pursuits. While the British scientists had greater access to government policy makers, and were able to influence policy in a way that their French counterparts were not, ultimately neither the vital statisticians nor the demographers were able to institutionalize their endeavors. By 1885, both fields had been superseded by new forms of knowledge. Disciplining Statistics highlights how the development of "scientific" knowledge was shaped by interrelated epistemological, political, and institutional considerations.
Discontinuity and Complexity in Nonlinear Physical Systems
by Dumitru Baleanu J. A. Tenreiro Machado Albert C J LuoDiscontinuity in Nonlinear Physical Systems explores recent developments in experimental research in this broad field, organized in four distinct sections. Part I introduces the reader to the fractional dynamics and Lie group analysis for nonlinear partial differential equations. Part II covers chaos and complexity in nonlinear Hamiltonian systems, important to understand the resonance interactions in nonlinear dynamical systems, such as Tsunami waves and wildfire propagations; as well as Lev flights in chaotic trajectories, dynamical system synchronization and DNA information complexity analysis. Part III examines chaos and periodic motions in discontinuous dynamical systems, extensively present in a range of systems, including piecewise linear systems, vibro-impact systems and drilling systems in engineering. And in Part IV, engineering and financial nonlinearity are discussed. The mechanism of shock wave with saddle-node bifurcation and rotating disk stability will be presented, and the financial nonlinear models will be discussed.
Discontinuous Dynamics and System Synchronization (Nonlinear Systems and Complexity #39)
by Fuhong MinThis book provides a systematic introduction to the dynamical behaviors of discontinuous dynamical systems and system synchronization. The first part of the book presents the theory of flow switching in discontinuous dynamical systems as well as the switching dynamics in such discontinuous systems. The second part presents a theory for interaction discontinuities between distinct dynamical systems, from which partial and complete chaotic synchronizations in such systems are studied analytically and experimentally.
Discontinuous Galerkin Method
by Vít Dolejší Miloslav FeistauerThe subject of the book is the mathematical theory of the discontinuous Galerkin method (DGM), which is a relatively new technique for the numerical solution of partial differential equations. The book is concerned with the DGM developed for elliptic and parabolic equations and its applications to the numerical simulation of compressible flow. It deals with the theoretical as well as practical aspects of the DGM and treats the basic concepts and ideas of the DGM, as well as the latest significant findings and achievements in this area. The main benefit for readers and the book's uniqueness lie in the fact that it is sufficiently detailed, extensive and mathematically precise, while at the same time providing a comprehensible guide through a wide spectrum of discontinuous Galerkin techniques and a survey of the latest efficient, accurate and robust discontinuous Galerkin schemes for the solution of compressible flow.
Discourse on the Method of Rightly Conducting One's Reason and of Seeking Truth in the Sciences
by René DescartesIn this work, René Descartes (1596-1650) outlines his "Method," which attempts to apply mathematical reasoning to all fields of inquiry. Starting with universal doubt, Descartes passes via his celebrated "I think, therefore I am," to the certainty of the existence of God.
Discourse on the Method of Rightly Conducting One's Reason and of Seeking Truth in the Sciences
by René DescartesIn this work,René Descartes (1596-1650) outlines his "Method," which attempts to apply mathematical reasoning to all fields of inquiry. Starting with universal doubt, Descartes passes via his celebrated "I think, therefore I am," to the certainty of the existence of God.
Discovering Advanced Algebra: An Investigative Approach
by Juan Alvarez Jerald Murdock Ellen Kamischke Eric Kamischke Robert Arnow Pamela Hobbs Elizabeth DecarliNIMAC-sourced textbook
Discovering Advanced Algebra: An Investigative Approach (Second Edition)
by Jerald Murdock Ellen Kamischke Eric KamischkeYour journey through Discovering Advanced Algebra will be a meaningful and rewarding experience.
Discovering Algebra: An Investigative Approach
by Jerald Murdock Ellen Kamischke Eric KamischkeNIMAC-sourced textbook
Discovering Algebra: An Investigative Approach (2nd edition)
by Jerald Murdock Ellen Kamischke Eric KamischkeA procedure that you do over and over, each time building on the previous stage, is recursive. You'll see recursion used in many different ways throughout this book. In this lesson you'll draw fractal design using a recursive procedure. After you draw the design, you'll work with fractions to examine its parts.
Discovering Algebra: An Investigative Approach, Lecciones condensadas en español Condensed Lessons in Spanish
NIMAC-sourced textbook
Discovering Computer Science: Interdisciplinary Problems, Principles, and Python Programming (Chapman & Hall/CRC Textbooks in Computing #15)
by Jessen HavillDiscovering Computer Science: Interdisciplinary Problems, Principles, and Python Programming introduces computational problem solving as a vehicle of discovery in a wide variety of disciplines. <P><P>With a principles-oriented introduction to computational thinking, the text provides a broader and deeper introduction to computer science than typical introductory programming books.Organized around interdisciplinary problem domains, rather than programming language features, each chapter guides students through increasingly sophisticated algorithmic and programming techniques. The author uses a spiral approach to introduce Python language features in increasingly complex contexts as the book progresses.<P><P>The text places programming in the context of fundamental computer science principles, such as abstraction, efficiency, and algorithmic techniques, and offers overviews of fundamental topics that are traditionally put off until later courses. <P><P>The book includes thirty well-developed independent projects that encourage students to explore questions across disciplinary boundaries. Each is motivated by a problem that students can investigate by developing algorithms and implementing them as Python programs.The book's accompanying website — http://discoverCS.denison.edu — includes sample code and data files, pointers for further exploration, errata, and links to Python language references. <P><P>Containing over 600 homework exercises and over 300 integrated reflection questions, this textbook is appropriate for a first computer science course for computer science majors, an introductory scientific computing course or, at a slower pace, any introductory computer science course.
Discovering Computer Science: Interdisciplinary Problems, Principles, and Python Programming (Chapman & Hall/CRC Textbooks in Computing #15)
by Jessen Havill"Havill's problem-driven approach introduces algorithmic concepts in context and motivates students with a wide range of interests and backgrounds." -- Janet Davis, Associate Professor and Microsoft Chair of Computer Science, Whitman College "This book looks really great and takes exactly the approach I think should be used for a CS 1 course. I think it really fills a need in the textbook landscape." -- Marie desJardins, Dean of the College of Organizational, Computational, and Information Sciences, Simmons University "Discovering Computer Science is a refreshing departure from introductory programming texts, offering students a much more sincere introduction to the breadth and complexity of this ever-growing field." -- James Deverick, Senior Lecturer, The College of William and Mary "This unique introduction to the science of computing guides students through broad and universal approaches to problem solving in a variety of contexts and their ultimate implementation as computer programs." -- Daniel Kaplan, DeWitt Wallace Professor, Macalester College Discovering Computer Science: Interdisciplinary Problems, Principles, and Python Programming is a problem-oriented introduction to computational problem solving and programming in Python, appropriate for a first course for computer science majors, a more targeted disciplinary computing course or, at a slower pace, any introductory computer science course for a general audience. Realizing that an organization around language features only resonates with a narrow audience, this textbook instead connects programming to students’ prior interests using a range of authentic problems from the natural and social sciences and the digital humanities. The presentation begins with an introduction to the problem-solving process, contextualizing programming as an essential component. Then, as the book progresses, each chapter guides students through solutions to increasingly complex problems, using a spiral approach to introduce Python language features.The text also places programming in the context of fundamental computer science principles, such as abstraction, efficiency, testing, and algorithmic techniques, offering glimpses of topics that are traditionally put off until later courses.This book contains 30 well-developed independent projects that encourage students to explore questions across disciplinary boundaries, over 750 homework exercises, and 300 integrated reflection questions engage students in problem solving and active reading. The accompanying website — https://www.discoveringcs.net — includes more advanced content, solutions to selected exercises, sample code and data files, and pointers for further exploration.