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How Geometric Algebra can naturally serve for constructing solutions for pattern recognition, machine learning, data compression, games, robotics, quantum computing, data encoding, to cite a few. Moreover, there is ample evidence that further research on GA and related areas can significantly expand the number of real-world applications in a wide variety of areas. A mathematical system that is very easy to handle, highly robust and superior performance for engineering applications. Good thematic introduction for engineers and researchers new to the subject. Extensive illustrations and code examples. Thematically well structured with many hands on examples. Learning about GA and how to use it for daily tasks in engineering research and development.

The original goal of writing this book was to introduce the reader to the tools of combinatorics from an applied point of view. This third edition of Applied Combinatorics was substantially rewritten. There are many new examples and exercises. References throughout the book to modern literature and real applications, a key feature of the book, have been updated and expanded. The exposition continues to be updated with each new edition, as the first edition was published 40 years ago.The emphasis on applications from computer science, genetics, experimental design, chemistry, scheduling, voting, and other topics remains a central feature of the book. Unique to the literature is that entire sections focus on applications such as switching functions, the use of enzymes to uncover unknown RNA chains, searching and sorting problems of information retrieval, construction of error-correcting codes, counting of chemical compounds, calculation of power in voting situations, and uses of Fibonacci numbers. There are entire sections on applications of recurrences involving convolutions, applications of eulerian chains, and applications of generating functions.The book continues to be based on the authors'philosophy that the best way to learn mathematics is through problem solving. Combinatorics can be a wonderful mechanism for introducing students to proofs. However, the book is not designed for an introduction to proofs course. The authors treat proofs as rather informal, and many of the harder proofs in the book are optional.Applied Combinatorics, Third Edition is divided into four parts. The first part introduces the basic tools of combinatorics and their applications. The remaining three parts are organized around the three basic problems of combinatorics: the counting problem, the existence problem, and the optimization problem.Most of the book is written for a first course on the topic at the undergraduate level. On the other hand, at a fast pace, there is more than enough material for a challenging graduate course. This book first appeared when courses on combinatorics were rare. We are pleased to think that, through its use, the book has helped to establish a key course in many colleges and universities throughout the world. We hope that this new edition will remain a valuable tool for instructors and students alike

Samson Abramsky's wide-ranging contributions to logical and structural aspects of Computer Science have had a major influence on the field. This book is a rich collection of papers, inspired by and extending Abramsky's work. It contains both survey material and new results, organised around six major themes: domains and duality, game semantics, contextuality and quantum computation, comonads and descriptive complexity, categorical and logical semantics, and probabilistic computation. These relate to different stages and aspects of Abramsky's work, reflecting its exceptionally broad scope and his ability to illuminate and unify diverse topics.Chapters in the volume include a review of his entire body of work, spanning from philosophical aspects to logic, programming language theory, quantum theory, economics and psychology, and relating it to a theory of unification of sciences using dual adjunctions. The section on game semantics shows how Abramsky's work hasled to a powerful new paradigm for the semantics of computation. The work on contextuality and categorical quantum mechanics has been highly influential, and provides the foundation for increasingly widely used methods in quantum computing. The work on comonads and descriptive complexity is building bridges between currently disjoint research areas in computer science, relating Structure to Power.The volume also includes a scientific autobiography, and an overview of the contributions. The outstanding set of contributors to this volume, including both senior and early career academics, serve as testament to Samson Abramsky's enduring influence. It will provide an invaluable and unique resource for both students and established researchers.

Dieses Handbuch gibt einen aktuellen Überblick über Forschungsgebiete der Mathematikdidaktik. In 26 Kapiteln stellen führende Vertreterinnen und Vertreter der Disziplin Diskussionsstände zu Mathematik als Bildungsgegenstand, als Lehr- und Lerninhalt, als Denkprozess sowie zu Mathematik im Unterrichtsprozess und zur Mathematikdidaktik als Forschungsdisziplin dar. Seit der 1. Auflage des Handbuchs im Jahr 2015 hat sich die Forschung auf allen dargestellten Gebieten so weiterentwickelt, dass eine gründliche Überarbeitung und Erweiterung erforderlich wurde. An der 2. Auflage haben zahlreiche neue Autorinnen und Autoren mitgewirkt, einzelne Kapitel wurden ergänzt, Themengebiete der Primarstufe finden nun eine größere Beachtung und es wurde stärker auf historische bzw. fachliche und fachdidaktische Entwicklungen aus einer Metaperspektive eingegangen. Das Handbuch wurde geschriebenfür im Studium fortgeschrittene Studierende als eine grundlegende und einführende Lektüre für ein Referat, eine Hausarbeit oder eine Abschlussarbeit in der Mathematikdidaktik;für Masterstudierende und angehende Promovierende zu Beginn einer eigenen Forschungsarbeit in der Mathematikdidaktik;für Lehrerinnen und Lehrer zum Kennenlernen forschungsbasierter Fragestellungen in der Mathematikdidaktik sowie als Grundlage für theoriegeleitete Reflexionen über eigenen oder fremden Unterricht;für Mathematikdidaktikerinnen und -didaktiker, die sich einen Überblick über zentrale Themen und derzeit aktuelle Forschungsfragen in verschiedenen Teilbereichen ihrer Disziplin verschaffen möchten.

This era of science and engineering has attracted researchers tasked with evaluating performance and optimization of problems in the field of operations research. The book covers mathematical analysis, methods and applications involving processes such as system performance, optimization, inventory theory, reliability theory, and queueing theory. Operations Research: Methods, Techniques, and Advancements explores recent and innovative methods and advancements associated with the mathematical theory of operations research. It offers a detailed overview of mathematical modelling for general industrial systems and emphasizes the latest ideas for the benefit of society and the research community. Intended for a broad range of readers, this book is useful to academicians, industrialists, researchers, students, academia and specialists from various disciplines and those working in the industry.

Through the previous three editions, Handbook of Differential Equations has proven an invaluable reference for anyone working within the field of mathematics, including academics, students, scientists, and professional engineers.The book is a compilation of methods for solving and approximating differential equations. These include the most widely applicable methods for solving and approximating differential equations, as well as numerous methods. Topics include methods for ordinary differential equations, partial differential equations, stochastic differential equations, and systems of such equations. Included for nearly every method are: The types of equations to which the method is applicable The idea behind the method The procedure for carrying out the method At least one simple example of the method Any cautions that should be exercised Notes for more advanced users The fourth edition includes corrections, many supplied by readers, as well as many new methods and techniques. These new and corrected entries make necessary improvements in this edition.

Dies ist der Tagungsband zur 5. Fachtagung der Gemeinsamen Kommission Lehrerbildung;Der Band enthält Beiträge zu Enkulturation, Brücken von der Hochschulmathematik zurück zur Schulmathematik, Fachwissenbedarf von Lehrern, Studienverlauf und -erfolg von Lehramtsstudierenden, ausgewählten Lehramtskomponenten in der universitären Lehrerausbildung, Identifikation der Lehramtsstudierenden mit ihrem Fach.Kapitel-Nr. 15 ist unter den Bedingungen der Creative Commons Attribution 4.0 International License über SpringerLink (link.springer.com) frei zugänglich.

Landscape of 21st Century Mathematics offers a detailed cross section of contemporary mathematics. Important results of the 21st century are motivated and formulated, providing an overview of recent progress in the discipline.The theorems presented in this book have been selected among recent achievements whose statements can be fully appreciated without extensive background. Grouped by subject, the selected theorems represent all major areas of mathematics: number theory, combinatorics, analysis, algebra, geometry and topology, probability and statistics, algorithms and complexity, and logic and set theory. The presentation is self-contained with context, background and necessary definitions provided for each theorem, all without sacrificing mathematical rigour. Where feasible, brief indications of the main ideas of a proof are given.Rigorous yet accessible, this book presents an array of breathtaking recent advances in mathematics. It is written for everyone with a background in mathematics, from inquisitive university students to mathematicians curious about recent achievements in areas beyond their own.

The book provides an introduction to deterministic (and some stochastic) modeling of spatiotemporal phenomena in ecology, epidemiology, and neural systems. A survey of the classical models in the fields with up to date applications is given. The book begins with detailed description of how spatial dynamics/diffusive processes influence the dynamics of biological populations. These processes play a key role in understanding the outbreak and spread of pandemics which help us in designing the control strategies from the public health perspective. A brief discussion on the functional mechanism of the brain (single neuron models and network level) with classical models of neuronal dynamics in space and time is given. Relevant phenomena and existing modeling approaches in ecology, epidemiology and neuroscience are introduced, which provide examples of pattern formation in these models. The analysis of patterns enables us to study the dynamics of macroscopic and microscopic behaviour of underlying systems and travelling wave type patterns observed in dispersive systems. Moving on to virus dynamics, authors present a detailed analysis of different types models of infectious diseases including two models for influenza, five models for Ebola virus and seven models for Zika virus with diffusion and time delay. A Chapter is devoted for the study of Brain Dynamics (Neural systems in space and time).Significant advances made in modeling the reaction-diffusion systems are presented and spatiotemporal patterning in the systems is reviewed. Development of appropriate mathematical models and detailed analysis (such as linear stability, weakly nonlinear analysis, bifurcation analysis, control theory, numerical simulation) are presented.Key Features Covers the fundamental concepts and mathematical skills required to analyse reaction-diffusion models for biological populations. Concepts are introduced in such a way that readers with a basic knowledge of differential equations and numerical methods can understand the analysis. The results are also illustrated with figures. Focuses on mathematical modeling and numerical simulations using basic conceptual and classic models of population dynamics, Virus and Brain dynamics. Covers wide range of models using spatial and non-spatial approaches. Covers single, two and multispecies reaction-diffusion models from ecology and models from bio-chemistry. Models are analysed for stability of equilibrium points, Turing instability, Hopf bifurcation and pattern formations. Uses Mathematica for problem solving and MATLAB for pattern formations. Contains solved Examples and Problems in Exercises. The Book is suitable for advanced undergraduate, graduate and research students. For those who are working in the above areas, it provides information from most of the recent works. The text presents all the fundamental concepts and mathematical skills needed to build models and perform analyses.

50 Years of Combinatorics, Graph Theory, and Computing advances research in discrete mathematics by providing current research surveys, each written by experts in their subjects. The book also celebrates outstanding mathematics from 50 years at the Southeastern International Conference on Combinatorics, Graph Theory & Computing (SEICCGTC). The conference is noted for the dissemination and stimulation of research, while fostering collaborations among mathematical scientists at all stages of their careers. The authors of the chapters highlight open questions. The sections of the book include: Combinatorics; Graph Theory; Combinatorial Matrix Theory; Designs, Geometry, Packing and Covering. Readers will discover the breadth and depth of the presentations at the SEICCGTC, as well as current research in combinatorics, graph theory and computer science.Features: Commemorates 50 years of the Southeastern International Conference on Combinatorics, Graph Theory & Computing with research surveys Surveys highlight open questions to inspire further research Chapters are written by experts in their fields Extensive bibliographies are provided at the end of each chapter

Sturm-Liouville problems arise naturally in solving technical problems in engineering, physics, and more recently in biology and the social sciences. These problems lead to eigenvalue problems for ordinary and partial differential equations. Sturm-Liouville Problems: Theory and Numerical Implementation addresses, in a unified way, the key issues that must be faced in science and engineering applications when separation of variables, variational methods, or other considerations lead to Sturm-Liouville eigenvalue problems and boundary value problems.

Nonlinear Systems and Their Remarkable Mathematical Structures, Volume 2 is written in a careful pedagogical manner by experts from the field of nonlinear differential equations and nonlinear dynamical systems (both continuous and discrete). This book aims to clearly illustrate the mathematical theories of nonlinear systems and its progress to both non-experts and active researchers in this area. Just like the first volume, this book is suitable for graduate students in mathematics, applied mathematics and engineering sciences, as well as for researchers in the subject of differential equations and dynamical systems. Features Collects contributions on recent advances in the subject of nonlinear systems Aims to make the advanced mathematical methods accessible to the non-experts Suitable for a broad readership including researchers and graduate students in mathematics and applied mathematics

Dieses Werk ist eine Einführung in philosophische Probleme und Hintergründe des mathematischen Denkens, Lehrens und Lernens. Es beinhaltet mathematische und philosophische Probleme und Fragen, einen umfangreichen Abriss der Geschichte bis hin zu aktuellen Strömungen, sowie Kapitel über Mengenlehre, Logik, Axiomatik, fundamentale Ergebnisse, ungelöste und unlösbare Probleme.

The year's finest mathematical writing from around the worldThis annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2018 makes available to a wide audience many pieces not easily found anywhere else—and you don't need to be a mathematician to enjoy them. These essays delve into the history, philosophy, teaching, and everyday aspects of math, offering surprising insights into its nature, meaning, and practice—and taking readers behind the scenes of today's hottest mathematical debates.James Grime shows how to build subtly mischievous dice for playing slightly unfair games and Michael Barany traces how our appreciation of the societal importance of mathematics has developed since World War II. In other essays, Francis Su extolls the inherent values of learning, doing, and sharing mathematics, and Margaret Wertheim takes us on a mathematical exploration of the mind and the world—with glimpses at science, philosophy, music, art, and even crocheting. And there's much, much more.In addition to presenting the year's most memorable math writing, this must-have anthology includes an introduction by the editor and a bibliography of other notable pieces on mathematics.This is a must-read for anyone interested in where math has taken us—and where it is headed.

The Enhancing Diversity in Graduate Education (EDGE) Program began twenty years ago to provide support for women entering doctoral programs in the mathematical sciences. With a steadfast commitment to diversity among participants, faculty, and staff, EDGE initially alternated between Bryn Mawr and Spelman Colleges. In later years, EDGE has been hosted on campuses around the nation and expanded to offer support for women throughout their graduate school and professional careers. The refereed papers in A Celebration of the EDGE Program's Impact on the Mathematics Community and Beyond range from short memoirs, to pedagogical studies, to current mathematics research. All papers are written by former EDGE participants, mentors, instructors, directors, and others connected to EDGE. Together, these papers offer compelling testimony that EDGE has produced a diverse new generation of leaders in the mathematics community. This volume contains technical and non-technical works, and it is intended for a far-reaching audience, including mathematicians, mathematics teachers, diversity officers, university administrators, government employees writing educational or science policy, and mathematics students at the high school, college, and graduate levels. By highlighting the scope of the work done by those supported by EDGE, the volume offers strong evidence of the American Mathematical Society's recognition that EDGE is'a program that makes a difference.”This volume offers unique testimony that a 20-year old summer program has expanded its reach beyond the summer experience to produce a diverse new generation of women leaders, nearly half of whom are underrepresented women. While some books with a women-in-math theme focus only on one topic such as research or work-life balance, this book's broad scope includes papers on mathematics research, teaching, outreach, and career paths.

A First Course in Fuzzy Logic, Fourth Edition is an expanded version of the successful third edition. It provides a comprehensive introduction to the theory and applications of fuzzy logic.This popular text offers a firm mathematical basis for the calculus of fuzzy concepts necessary for designing intelligent systems and a solid background for readers to pursue further studies and real-world applications.New in the Fourth Edition: Features new results on fuzzy sets of type-2 Provides more information on copulas for modeling dependence structures Includes quantum probability for uncertainty modeling in social sciences, especially in economics With its comprehensive updates, this new edition presents all the background necessary for students, instructors and professionals to begin using fuzzy logic in its many—applications in computer science, mathematics, statistics, and engineering. About the Authors:Hung T. Nguyen is a Professor Emeritus at the Department of Mathematical Sciences, New Mexico State University. He is also an Adjunct Professor of Economics at Chiang Mai University, Thailand.Carol L. Walker is also a Professor Emeritus at the Department of Mathematical Sciences, New Mexico State University.Elbert A. Walker is a Professor Emeritus, Department of Mathematical Sciences, New Mexico State University.

'Points, questions, stories, and occasional rants introduce the 24 chapters of this engaging volume. With a focus on mathematics and peppered with a scattering of computer science settings, the entries range from lightly humorous to curiously thought-provoking. Each chapter includes sections and sub-sections that illustrate and supplement the point at hand. Most topics are self-contained within each chapter, and a solid high school mathematics background is all that is needed to enjoy the discussions. There certainly is much to enjoy here.'CHOICEEver notice how people sometimes use math words inaccurately? Or how sometimes you instinctively know a math statement is false (or not known)?Each chapter of this book makes a point like those above and then illustrates the point by doing some real mathematics through step-by-step mathematical techniques.This book gives readers valuable information about how mathematics and theoretical computer science work, while teaching them some actual mathematics and computer science through examples and exercises. Much of the mathematics could be understood by a bright high school student. The points made can be understood by anyone with an interest in math, from the bright high school student to a Field's medal winner.

An effort has been made to present the various topics in the theory of graphs in a logical order, to indicate the historical background, and to clarify the exposition by including figures to illustrate concepts and results. In addition, there are three appendices which provide diagrams of graphs, directed graphs, and trees. The emphasis throughout is on theorems rather than algorithms or applications, which however are occaisionally mentioned.

The Handbook of Ordinary Differential Equations: Exact Solutions, Methods, and Problems, is an exceptional and complete reference for scientists and engineers as it contains over 7,000 ordinary differential equations with solutions. This book contains more equations and methods used in the field than any other book currently available.Included in the handbook are exact, asymptotic, approximate analytical, numerical symbolic and qualitative methods that are used for solving and analyzing linear and nonlinear equations. The authors also present formulas for effective construction of solutions and many different equations arising in various applications like heat transfer, elasticity, hydrodynamics and more. This extensive handbook is the perfect resource for engineers and scientists searching for an exhaustive reservoir of information on ordinary differential equations.

The Handbook of Geometric Constraint Systems Principles is an entry point to the currently used principal mathematical and computational tools and techniques of the geometric constraint system (GCS). It functions as a single source containing the core principles and results, accessible to both beginners and experts. The handbook provides a guide for students learning basic concepts, as well as experts looking to pinpoint specific results or approaches in the broad landscape. As such, the editors created this handbook to serve as a useful tool for navigating the varied concepts, approaches and results found in GCS research. Key Features: A comprehensive reference handbook authored by top researchers Includes fundamentals and techniques from multiple perspectives that span several research communities Provides recent results and a graded program of open problems and conjectures Can be used for senior undergraduate or graduate topics course introduction to the area Detailed list of figures and tables About the Editors: Meera Sitharam is currently an Associate Professor at the University of Florida's Department of Computer & Information Science and Engineering. She received her Ph.D. at the University of Wisconsin, Madison. Audrey St. John is an Associate Professor of Computer Science at Mount Holyoke College, who received her Ph. D. from UMass Amherst.Jessica Sidman is a Professor of Mathematics on the John S. Kennedy Foundation at Mount Holyoke College. She received her Ph.D. from the University of Michigan.

Methods of solution for partial differential equations (PDEs) used in mathematics, science, and engineering are clarified in this self-contained source. The reader will learn how to use PDEs to predict system behaviour from an initial state of the system and from external influences, and enhance the success of endeavours involving reasonably smooth, predictable changes of measurable quantities. This text enables the reader to not only find solutions of many PDEs, but also to interpret and use these solutions. It offers 6000 exercises ranging from routine to challenging. The palatable, motivated proofs enhance understanding and retention of the material. Topics not usually found in books at this level include but examined in this text:the application of linear and nonlinear first-order PDEs to the evolution of population densities and to traffic shocks convergence of numerical solutions of PDEs and implementation on a computer convergence of Laplace series on spheres quantum mechanics of the hydrogen atom solving PDEs on manifoldsThe text requires some knowledge of calculus but none on differential equations or linear algebra.

This book is inspired by Roger E. Howe's contributions to the international communities of mathematics and mathematics education. Renowned for his research contributions in the fields of representation theory, automorphic forms, harmonic analysis, and invariant theory, Dr. Howe has also fundamentally deepened our understanding of the mathematics taught in the early school grades and has challenged and stimulated mathematicians and mathematics educators to work together to examine this part of the mathematical universe more critically and in imaginative new ways. This volume will help summarize and highlight Howe's contributions to several topic areas in mathematics education, demonstrating the possibility and importance of engaging mathematicians in high-impact research in mathematics education, and showcasing the importance of cross-disciplinary collaboration and exchange.

Elementary Differential Equations, Second Edition is written with the knowledge that there has been a dramatic change in the past century in how solutions to differential equations are calculated. However, the way the topic has been taught in introductory courses has barely changed to reflect these advances, which leaves students at a disadvantage. This second edition has been created to address these changes and help instructors facilitate new teaching methods and the latest tools, which includes computers. The text is designed to help instructors who want to use computers in their classrooms. It accomplishes this by emphasizing and integrating computers in teaching elementary or ordinary differential equations. Many examples and exercises included in the text require the use of computer software to solve problems. It should be noted that since instructors use their own preferred software, this book has been written to be independent of any specific software package. Features: Focuses on numerical methods and computing to generate solutions Features extensive coverage of nonlinear differential equations and nonlinear systems Includes software programs to solve problems in the text which are located on the author's website Contains a wider variety of non-mathematical models than any competing textbook This second edition is a valuable, up-to-date tool for instructors teaching courses about differential equations. It serves as an excellent introductory textbook for undergraduate students majoring in applied mathematics, computer science, various engineering disciplines and other sciences. They also will find that the textbook will aide them greatly in their professional careers because of its instructions on how to use computers to solve equations.

Richard Stanley's work in combinatorics revolutionized and reshaped the subject. Many of his hallmark ideas and techniques imported from other areas of mathematics have become mainstays in the framework of modern combinatorics. In addition to collecting several of Stanley's most influential papers, this volume also includes his own short reminiscences on his early years, and on his celebrated proof of The Upper Bound Theorem.

The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields.The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in fields as diverse as operations research, molecular biology and robotics.Discrete geometry has contributed significantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young field of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook.A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.

Modelling with Ordinary Differential Equations integrates standard material from an elementary course on ordinary differential equations with the skills of mathematical modeling in a number of diverse real-world situations. Each situation highlights a different aspect of the theory or modeling. Carefully selected exercises and projects present excellent opportunities for tutorial sessions and self-study.This text/reference addresses common types of first order ordinary differential equations and the basic theory of linear second order equations with constant coefficients. It also explores the elementary theory of systems of differential equations, Laplace transforms, and numerical solutions. Theorems on the existence and uniqueness of solutions are a central feature. Topics such as curve fitting, time-delay equations, and phase plane diagrams are introduced. The book includes algorithms for computer programs as an integral part of the answer-finding process. Professionals and students in the social and biological sciences, as well as those in physics and mathematics will find this text/reference indispensable for self-study.

The year's finest writing on mathematics from around the worldThis annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2015 makes available to a wide audience many articles not easily found anywhere else—and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates.Here David Hand explains why we should actually expect unlikely coincidences to happen; Arthur Benjamin and Ethan Brown unveil techniques for improvising custom-made magic number squares; Dana Mackenzie describes how mathematicians are making essential contributions to the development of synthetic biology; Steven Strogatz tells us why it's worth writing about math for people who are alienated from it; Lisa Rougetet traces the earliest written descriptions of Nim, a popular game of mathematical strategy; Scott Aaronson looks at the unexpected implications of testing numbers for randomness; and much, much more.In addition to presenting the year's most memorable writings on mathematics, this must-have anthology includes a bibliography of other notable writings and an introduction by the editor, Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us—and where it is headed.

High temperature, high oil pressure, oil and gas well completion testing have always been a technical challenge and basic theoretical research is one of the key factors needed to ensure a successful completion test. The completion test basic theory includes: a stress analysis of the completion string, completion string buckling behavior, and temperature and pressure distribution prediction. The completion string is the main bearing and power transmission component for oil and gas well operations and production, and it is required to take on a combination of loads, which result in completion string deformation. Because of these complex relationships, completion string stress analysis has become increasingly more complicated.This book discusses the characters of tubular strings in HTHP (High Temperature - High Pressure) oil and gas wells. These characters include the mechanical behavior of tubular strings and the temperature and pressure variation of tubular strings in different conditions. Mathematical models are established for different conditions and solution existence and uniqueness of some models is discussed, providing algorithms corresponding to the different models. Numerical experiments are presented to verify the validity of models and the feasibility of algorithms, and the impact of the parameters of models for oil and gas wells is also discussed.This book is written for production and testing engineers to provide them with the tools to deal more effectively with the numerical decisions they have to take and for researchers and technicians in petroleum and gas testing and production engineering. Finally, it is also intended to serve as a reference book for mathematicians, college teachers and students.

Das Handbuch gibt einen einzigartigen Überblick über die Didaktik der Mathematik, seine Lehr- und Lerninhalte, Denk- und Unterrichtsprozesse wie auch seine Forschungsthemen und -methoden. In 24 Kapitel leiten führende Vertreter der Mathematikdidaktik den Leser durch die vielfältigen Themen Ihres Fachgebietes. Ergänzt wird es durch drei Kapitel zu „Mathematik als Bildungsgegenstand“. Das Handbuch vermittelt dem Leser tiefe Einblicke in das aktuelle Wissen der Mathematikdidaktik und bietet deshalb Studierenden wie Lehrern unverzichtbare Informationen.

Doing Mathematics discusses some ways mathematicians and mathematical physicists do their work and the subject matters they uncover and fashion. The conventions they adopt, the subject areas they delimit, what they can prove and calculate about the physical world, and the analogies they discover and employ, all depend on the mathematics — what will work out and what won't. The cases studied include the central limit theorem of statistics, the sound of the shape of a drum, the connections between algebra and topology, and the series of rigorous proofs of the stability of matter. The many and varied solutions to the two-dimensional Ising model of ferromagnetism make sense as a whole when they are seen in an analogy developed by Richard Dedekind in the 1880s to algebraicize Riemann's function theory; by Robert Langlands'program in number theory and representation theory; and, by the analogy between one-dimensional quantum mechanics and two-dimensional classical statistical mechanics. In effect, we begin to see'an identity in a manifold presentation of profiles,'as the phenomenologists would say.This second edition deepens the particular examples; it describe the practical role of mathematical rigor; it suggests what might be a mathematician's philosophy of mathematics; and, it shows how an'ugly'first proof or derivation embodies essential features, only to be appreciated after many subsequent proofs. Natural scientists and mathematicians trade physical models and abstract objects, remaking them to suit their needs, discovering new roles for them as in the recent case of the Painlevé transcendents, the Tracy-Widom distribution, and Toeplitz determinants. And mathematics has provided the models and analogies, the ordinary language, for describing the everyday world, the structure of cities, or God's infinitude.

The identity of computing has been fiercely debated throughout its short history. Why is it still so hard to define computing as an academic discipline? Is computing a scientific, mathematical, or engineering discipline? By describing the mathematical, engineering, and scientific traditions of computing, The Science of Computing: Shaping a Discipli

This is the eBook of the printed book and may not include any media, website access codes, or print supplements that may come packaged with the bound book. This is the best seller in this market. It provides a comprehensive introduction to complex variable theory and its applications to current engineering problems. It is designed to make the fundamentals of the subject more easily accessible to students who have little inclination to wade through the rigors of the axiomatic approach. Modeled after standard calculus books–both in level of exposition and layout–it incorporates physical applications throughout the presentation, so that the mathematical methodology appears less sterile to engineering students.

Suchmaschinen und Qualitätsmanagement, Versicherungen und Erdbebenvorhersagen, Verkehrsflüsse, Geheimcodes und medizinische Prognosen – die sogenannte Bayes'sche Regel ist geradezu allgegenwärtig und dennoch nur wenigen vertraut. Dabei ist sie in ihrer grundlegenden Aussage bestechend einfach: Man beginnt mit einer Vermutung und revidiert diese anhand neuer, objektiver Informationen – und gelangt so zu einer verbesserten Annahme. Für seine Anhänger ist das Bayes-Theorem eine elegante Formulierung dafür, dass man aus Erfahrung klug wird, und ein mathematisches Instrument, das einer klaren Linie folgt. Für seine Gegner ist es ein Amoklauf der Subjektivität.Sharon Bertsch McGrayne schildert in ihrem spannenden Sachbuch die erstaunliche Geschichte dieser Regel und berichtet von der Besessenheit ihrer Anhänger und Gegner. Sie beschreibt die Entdeckung des Theorems durch den britischen Geistlichen und Amateurmathematiker Thomas Bayes in den 1740er-Jahren und seine Weiterentwicklung in eine moderne Form, die fast der heutigen entspricht, durch den französischen Wissenschaftler Pierre Simon Laplace. Sie deckt auf, warum angesehene Statistiker das Theorem 150 Jahre lang mit einem Tabu belegten, während in der gleichen Zeit Praktiker darauf zurückgriffen, um Probleme zu lösen, die mit großen Unsicherheiten und einem Mangel an Informationen einhergingen. Eine wichtige Rolle spielte dabei Alan Turing, als er im Zweiten Weltkrieg den deutschen Enigma-Code knackte. Die Autorin erklärt schließlich, wie mit dem Aufkommen der immer preiswerter und für alle verfügbaren Computertechnologie in den 1980er-Jahren ein ganz neues Zeitalter für das Bayes-Theorem anbrach. Heute spielt es in Wissenschaft, Technik und Gesellschaft fast überall eine Rolle – ob es nun um die Entschlüsselung der DNA, das Börsengeschehen oder die Terrorabwehr geht.

This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe­ matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by'Soviet Encyclopaedia Publishing House'in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi­ sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en­ gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.

ie ältesten uns bekannten mathematischen Schriftta­ D feln stammen aus der Zeit um 2400 v. ehr. ; aber wir dürfen davon ausgehen, daß das Bedürfnis, Mathematik zu schaffen, ein Ausdruck der menschlichen Zivilisation an sich ist. In vier bis fünf Jahrtausenden hat sich ein gewalti­ ges System von Praktiken und Begriffen - die Mathematik­ herangebildet, die in vielfältiger Weise mit unserem Alltag verknüpft ist. Was ist Mathematik? Was bedeutet sie? Wo­ mit befaßt sie sich? Was sind ihre Methoden? Wie wird sie geschaffen und benützt? Wo ist ihr Platz in der Vielgestalt der menschlichen Erfahrung? Welchen Nutzen bringt sie? Was für Schaden richtet sie an? Welches Gewicht kommt ihr zu? Diese schwierigen Fragen werden noch zusätzlich kompliziert durch die Fülle des Materials und die weitver­ zweigten Querverbindungen, die es dem einzelnen verun­ möglichen, alles zu begreifen, geschweige denn, es in seiner Gesamtheit zu erfassen und zwischen den Deckeln eines normalen Buches unterzubringen. Um von dieser Material­ fülle nicht erdrückt zu werden, haben sich die Autoren für eine andere Betrachtungsweise entschieden. Die Mathema­ tik ist seit Tausenden von Jahren ein Feld menschlicher Ak­ tivität. In begrenztem Rahmen ist jeder von uns ein Mathe­ matiker und betreibt bewußt Mathematik, wenn er zum Beispiel auf dem Markt einkauft, Tapeten ausmißt oder ei­ nen Keramiktopf mit einem regelmäßigen Muster verziert. In bescheidenem Ausmaß versucht sich auch jeder von uns als mathematischer Denker. Schon mit dem Ausruf «Aber Zahlen lügen nicht!» befinden wir uns in der Gesellschaft von Plato oder Lakatos.

Der. vorliegende Band enthält eine Reihe von einführenden Vorlesungen, die von verschiedenen Autoren im Rahmen von zwei DMV-Seminaren zum Thema'Algebraische Transjormationsgruppen und Invariantentheorie'gehalten wur­ den. Entsprechend der allgemeinen Zielsetzung der DMV-Seminare sollten sowohl grundlegende Techniken und Resultate vorgestellt als auch Einblicke in aktuelle Entwickl~ngen gegeben werden. Was die Grundlagen anbetrifft, so haben wir sie hier nicht in vollem Umfang widergegeben. Im Bedarfsfall mag der Leser unsere Bücher'Geometrische Methoden in der Invariantentheorie'l und'Invariant Theory'2 zu Rate ziehen, auf die sich die einführenden Vorträge stützten. Leider konnten auch nicht alle aktuellen Entwicklungen berücksichtigt werden, über die im Seminar berichtet wurde. Die Ziele der hier vorliegenden Beiträge, auf deren Inhalt wir in der Einführung ausführlicher eingehen werden, sind entsprechend unterschiedlicher Natur. Einige liefern Darstellungen bereits publizierter Theorien, wobei sie allerdings ein größeres Gewicht auf Motivation und die Ausführung von Beispie­ len legen, als dies in den Originalarbeiten möglich war. Andere leiten grundle­ gende Resultate auf neue'reise her oder stellen sie aus anderer Sicht dar. Schließlich werden auch noch einzelne Einblicke in aktuelle Forschungsrichtun­ gen gegeben. Wir hoffen, daß durch diesen Band zahlreiche Resultate der Theorie der algebraischen Transformationsgruppen leichter zugänglich geworden sind, und daß der Leser mit ihm eine nützliche Basis für die Lektüre aktueller Forschungsarbeiten erhält.

Zum Anlass des 100. Geburtstages der Deutschen Mathematiker-Vereinigung erscheint diese Festschrift, bestehend aus neunzehn Beiträgen, in denen anerkannte Fachwissenschaftler die Entwicklung ihres jeweiligen mathematischen Fachgebietes beschreiben und dabei auch kritische Rückschau auf die Geschichte der Deutschen Mathematiker-Vereinigung seit ihrer Gründung 1890 halten. Insbesondere der erste Beitrag setzt sich intensiv mit der Historie der Mathematik und der Mathematiker im Dritten Reich auseinander.'Mit diesem Band wird ein wichtiger Beitrag zur bisher wenig entwickelten Geschichtsschreibung der neueren Mathematik geleistet. (R. Siegmund-Schultze in'Deutsche Literatur-Zeitung'1,2/1992, Bd. 113)

In this book Lee Rudolph brings together international contributors who combine psychological and mathematical perspectives to analyse how qualitative mathematics can be used to create models of social and psychological processes. Bridging the gap between the fields with an imaginative and stimulating collection of contributed chapters, the volume updates the current research on the subject, which until now has been rather limited, focussing largely on the use of statistics. Qualitative Mathematics for the Social Sciences contains a variety of useful illustrative figures, introducing readers from the social sciences to the rich contribution that modern mathematics has made to our knowledge of logic, structures, and dynamic systems. A beguiling array of conceptual systems, topological models and fractals are discussed which transcend the application of statistics, and bring a fresh perspective to the study of social representations.The wide selection of qualitative mathematical methodologies discussed in this volume will be hugely valuable to higher-level undergraduate and postgraduate students of psychology, sociology and mathematics. It will also be useful for researchers, academics and professionals from the social sciences who want a firmer grasp on the use of qualitative mathematics.

Der Band behandelt Grundfragen und zentrale Themen der Informatikgeschichte in Beiträgen von herausragenden Pionieren, von in Theoriefragen engagierten Informatikern und namhaften Technikhistoriern. Der Band kreist um Leitideen und Paradigmen der Informatik, wobei die Visionen einer'Universalmaschine', einer'Universalsprache', eines'Universalmediums'und einer'Universalwissenschaft'sich letimotivisch durch die Beiträge ziehen. Der Band löst sich von der engen Computergeschichte und arbeitet so bisher unterbewertete Innovationsleistungen der deutschen und europäischen Informatik- und Computer-Community heraus. Er gibt der Zuse-Forschung neue Anstöße und bietet neue Einblicke in die Geschichte der Rechnerarchitektur, der Programmierung und Programmiersprachen und der Mensch-Computer-Beziehung. Der Band ist reichhaltig mit instruktiven Abbildungen illustriert und zeigt sich als Extrakt eines über viele Jahre gehenden Generationen- und Disziplinen-übergreifenden Geschichts- und Theorie-Diskurses.

This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe­ matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by'Soviet Encyclopaedia Publishing House'in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi­ sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en­ gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.

This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe­ matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by'Soviet Encyclopaedia Publishing House'in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fme subdivi­ sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en­ gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.