Bücher veröffentlicht von Birkhauser Verlag AG

Accounting for approximately 10 % of the land mass of Planet Earth, the Antarctic is a Global Commons we collectively neglect. Far from being a pristine natural landscape, the continent is a contested territory which conceals resources that might prove irresistible in a world with ever increasing population growth. The 26 quadrillion tons of ice accumulated on its bedrock, equivalent to around 70 % of the fresh water on our planet, represent at once the most significant repository of scientific data available, providing crucial information for future environmental policies, and the greatest menace to global coastal settlements threatened by the rise in sea levels induced by anthropogenic global warming. ΓÇ£Antarctic ResolutionΓÇ¥ advocates the rejection of the pixelated view of Antarctica offered to us by Big Data companies and urges the construction of a high-resolution image focusing on the continentΓÇÖs unique geography, unparalleled scientific potential, contemporary geopolitical significance, experimental governance system, and extreme inhabitation model. Only the concerted determination of a transnational network of multidisciplinary polar experts ΓÇô represented here in the form of authored texts, photographic essays, and data-based visual portfolios ΓÇô could construct such an image and reveal the intricate web of growing economic and strategic interests, tensions, and international rivalries, which are enveloped in darkness, as is the continent for six months of the year.

Was it necessary for a 17th century painter to know principles of optics to hide a skull in one of his masterpieces? Is it possible the violent deaths of Roman emperors obey a statistical law? Are there connections between market trends and geometry? How did Islamic artists draw almost perfectly regular nine-sided polygons, when these cannot be traced with the use of compasses? Dirk Huylebrouk asks these and other exciting questions in this collection of essays, originally written for the science magazine EOS, a Dutch equivalent of Scientific American, distributed in Belgium and in The Netherlands. Every chapter can be read independently, as some subjects are repeated, and not strictly interconnected. Such is the case for instance of the golden section, an often-recurring topic in general mathematics. The reader will appreciate the original point of view expressed through each chapter, which makes this book stand out against the general information one can find by browsing the general media. The subtly provocative character of some parts is meant to stimulate the reader for further exploration. The book's title itself may already generate surprise. Sure, to many, mathematics seems to come from hell, but the darkness in the title in fact refers to the lugubrious stories about math and skulls, murders or World War II. There is also a more down-to-earth part is about math and maps, money, Facebook, folding paper, shapes in ice and the most earthly yet unsolved math problems. ¿Bright mathematics¿ alludes to Vedic, Islam, New Age, a meta-divine section, and is concluded by an interview with a top mathematician who also wrote about the existence of God.

This volume, originally published in China and translated into four other languages, presents a fascinating and unique account of the history of mathematics, divided into eight chronologically organized chapters. Tracing the development of mathematics across disparate regions and peoples, with particular emphasis on the relationship between mathematics and civilization, it examines mathematical sources and inspirations leading from Egypt, Babylon and ancient Greece and expanding to include Chinese, Indian and Arabic mathematics, the European Renaissance and the French revolution up through the Nineteenth and Twentieth Centuries. Each chapter explores connections among mathematics and cultural elements of the time and place treated, accompanying the reader in a varied and exciting journey through human civilizations. The book contemplates the intersections of mathematics with other disciplines, including the relationship between modern mathematics and modern art, and the resulting applications, with the aid of images and photographs, often taken by the author, which further enhance the enjoyment for the reader. Written for a general audience, this book will be of interest to anyone who's studied mathematics in university or even high school, while also benefiting researchers in mathematics and the humanities.

This textbook offers a uniquely accessible introduction to flows on compact surfaces, filling a gap in the existing literature. The book can be used for a single semester course and/or for independent study. It demonstrates that covering spaces provide a suitable and modern setting for studying the structure of flows on compact surfaces. The thoughtful treatment of flows on surfaces uses topology (especially covering spaces), the classification of compact surfaces, and Euclidean and hyperbolic rigid motions to establish structural theorems that describe flows on surfaces generally. Several of the topics from dynamical systems that appear in this book (e.g., fixed points, invariant sets, orbits, almost periodic points) also appear in the many subareas of dynamical systems. The book successfully presents the reader with a self-contained introduction to dynamical systems or an expansion of one's existing knowledge of the field. Prerequisites include completion of a graduate-level topology course; a background in dynamical systems is not assumed.

Logicians have developed beautiful algorithmic techniques for the construction of computably enumerable sets. This textbook presents these techniques in a unified way that should appeal to computer scientists.Specifically, the book explains, organizes, and compares various algorithmic techniques used in computability theory (which was formerly called "classical recursion theory"). This area of study has produced some of the most beautiful and subtle algorithms ever developed for any problems. These algorithms are little-known outside of a niche within the mathematical logic community. By presenting them in a style familiar to computer scientists, the intent is to greatly broaden their influence and appeal.Topics and features:· All other books in this field focus on the mathematical results, rather than on the algorithms.· There are many exercises here, most of which relate to details of the algorithms.· The proofs involving priority trees are written here in greater detail, and with more intuition, than can be found elsewhere in the literature.· The algorithms are presented in a pseudocode very similar to that used in textbooks (such as that by Cormen, Leiserson, Rivest, and Stein) on concrete algorithms.· In addition to their aesthetic value, the algorithmic ideas developed for these abstract problems might find applications in more practical areas.Graduate students in computer science or in mathematical logic constitute the primary audience. Furthermore, when the author taught a one-semester graduate course based on this material, a number of advanced undergraduates, majoring in computer science or mathematics or both, took the course and flourished in it.Kenneth J. Supowit is an Associate Professor Emeritus, Department of Computer Science & Engineering, Ohio State University, Columbus, Ohio, US.

This textbook provides a thorough introduction to spectrahedra, which are the solution sets to linear matrix inequalities, emerging in convex and polynomial optimization, analysis, combinatorics, and algebraic geometry. Including a wealth of examples and exercises, this textbook guides the reader in helping to determine the convex sets that can be represented and approximated as spectrahedra and their shadows (projections). Several general results obtained in the last 15 years by a variety of different methods are presented in the book, along with the necessary background from algebra and geometry.

This textbook focuses on the study of different kinds of elementary functions ubiquitous both in high school Algebra and Calculus. To analyze the functions ranging from polynomial to trigonometric ones, it uses rudimentary techniques available to high school students, and at the same time follows the mathematical rigor appropriate for university level courses.Contrary to other books of Pre-Calculus, this textbook emphasizes the study of elementary functions with rigor appropriate for university level courses in mathematics, although the exposition is confined to the pre-limit topics and techniques. This makes the book useful, on the one hand, as an introduction to mathematical reasoning and methods of proofs in mathematical analysis, and on the other hand, as a preparatory course on the properties of different kinds of elementary functions.The textbook is aimed at university freshmen and high-school students interested in learning strict mathematical reasoning and in preparing a solid base for subsequent study of elementary functions at advanced level of Calculus and Analysis. The required prerequisites correspond to the level of the high school Algebra. All the preliminary concepts and results related to the elementary functions are covered in the initial part of the text. This makes the textbook suitable for both classroom use and self-study.

This monograph provides an exhaustive treatment of several classes of Noetherian rings and morphisms of Noetherian local rings. Chapters carefully examine some of the most important topics in the area, including Nagata, F-finite and excellent rings, Bertini¿s Theorem, and Cohen factorizations. Of particular interest is the presentation of Popescüs Theorem on Neron Desingularization and the structure of regular morphisms, with a complete proof. Classes of Good Noetherian Rings will be an invaluable resource for researchers in commutative algebra, algebraic and arithmetic geometry, and number theory.

This book presents the notes from the seminar on wave phenomena given in 2019 at the Mathematical Research Center in Oberwolfach.The research on wave-type problems is a fascinating and emerging field in mathematical research with many challenging applications in sciences and engineering. Profound investigations on waves require a strong interaction of several mathematical disciplines including functional analysis, partial differential equations, mathematical modeling, mathematical physics, numerical analysis, and scientific computing.The goal of this book is to present a comprehensive introduction to the research on wave phenomena. Starting with basic models for acoustic, elastic, and electro-magnetic waves, topics such as the existence of solutions for linear and some nonlinear material laws, efficient discretizations and solution methods in space and time, and the application to inverse parameter identification problems are covered. The aim of this book is to intertwine analysis and numerical mathematics for wave-type problems promoting thus cooperative research projects in this field.

This innovative textbook presents material for a course on modern statistics that incorporates Python as a pedagogical and practical resource. Drawing on many years of teaching and conducting research in various applied and industrial settings, the authors have carefully tailored the text to provide an ideal balance of theory and practical applications. Numerous examples and case studies are incorporated throughout, and comprehensive Python applications are illustrated in detail. A custom Python package is available for download, allowing students to reproduce these examples and explore others.The first chapters of the text focus on analyzing variability, probability models, and distribution functions. Next, the authors introduce statistical inference and bootstrapping, and variability in several dimensions and regression models. The text then goes on to cover sampling for estimation of finite population quantities and time series analysis and prediction, concluding with two chapters on modern data analytic methods. Each chapter includes exercises, data sets, and applications to supplement learning.Modern Statistics: A Computer-Based Approach with Python is intended for a one- or two-semester advanced undergraduate or graduate course. Because of the foundational nature of the text, it can be combined with any program requiring data analysis in its curriculum, such as courses on data science, industrial statistics, physical and social sciences, and engineering. Researchers, practitioners, and data scientists will also find it to be a useful resource with the numerous applications and case studies that are included. A second, closely related textbook is titled Industrial Statistics: A Computer-Based Approach with Python. It covers topics such as statistical process control, including multivariate methods, the design of experiments, including computerexperiments and reliability methods, including Bayesian reliability. These texts can be used independently or for consecutive courses.The mistat Python package can be accessed at https://gedeck.github.io/mistat-code-solutions/ModernStatistics/"In this book on Modern Statistics, the last two chapters on modern analytic methods contain what is very popular at the moment, especially in Machine Learning, such as classifiers, clustering methods and text analytics. But I also appreciate the previous chapters since I believe that people using machine learning methods should be aware that they rely heavily on statistical ones. I very much appreciate the many worked out cases, based on the longstanding experience of the authors. They are very useful to better understand, and then apply, the methods presented in the book. The use of Python corresponds to the best programming experience nowadays. For all these reasons, I thinkthe book has also a brilliant and impactful future and I commend the authors for that."Professor Fabrizio RuggeriResearch Director at the National Research Council, ItalyPresident of the International Society for Business and Industrial Statistics (ISBIS)Editor-in-Chief of Applied Stochastic Models in Business and Industry (ASMBI)

Introduction.- Metric Based Mesh Representation.- Interpolation Error Estimates for Two Dimensions.- Interpolation Error Estimates for Three Dimensions.- Anisotropic Mesh Adaptation, h-Variant.- Anisotropic Mesh Adaptation Method, hp-Variant.- Framework of the Goal-Oriented Error Estimates.- Goal-Oriented Anisotropic Mesh Adaptation.- Implementation Aspects.- Applications.

These include integral inequalities, differential inequalities and difference inequalities, which play a crucial role in establishing (uniform) bounds, global existence, large-time behavior, decay rates and blow-up of solutions to various classes of evolutionary differential equations.

This new and expanded monograph improves upon Mohan's earlier book, Residue Number Systems (Springer, 2002) with a state of the art treatment of the subject.

This book examines the design of two care pathways to establish how key principles associated with systems thinking, quality improvement, and supply chain management can improve the design of these services.

Fraenkel was a world-renowned mathematician in pre-Second World War Germany, whose work on set theory was fundamental to the development of modern mathematics.

This is a comprehensive survey on the research on the parabolic Anderson model - the heat equation with random potential or the random walk in random potential - of the years 1990 - 2015.

In addition some advanced methods and extensions, including path integrals, jump diffusion and others are presented.The book consists of four parts: Analysis, Geometry, Perturbations and Applications.

An introduction to the basic tools of the theory of (partially) ordered sets such as visualization via diagrams, subsets, homomorphisms, important order-theoretical constructions and classes of ordered sets.

Each chapter that follows provides a detailed case study of alternative proofs for particular theorems, including the Pythagorean Theorem, the Fundamental Theorem of Arithmetic, Desargues' Theorem, the Prime Number Theorem, and the proof of the irreducibility of cyclotomic polynomials.Why Prove It Again?

Louis I. Kahn (1901ΓÇô1974) was one of the most significant architects of the twentieth century and his influence is present today in ways both profound and subtle. Unlike previous publications on Kahn, which have focused on his built work and which considered the drawings foremost as illustrations of these, this is the first in-depth study of drawings as primary sources of insight into KahnΓÇÖs architecture and creative imagination.By offering a spectrum of close readings of drawings by Kahn and his associates in a series of incisive and richly illustrated essays, this book is at once an intimate artistic portrait of this important architect and a provocative and timely contribution to the current discourse on representation in architecture. For architects and students of architecture, KahnΓÇÖs lasting significance is not only in the buildings he built, but in how he designed them.Based on unprecedented archival research, engagingly presented by a group of eminent scholars and architects, and lavishly illustrated with over 600 highest quality reproductions, The Importance of a Drawing is destined to become a standard work in the literature on Louis Kahn.

This first of three volumes starts with a short introduction to historical metrology as a scientific discipline and goes on with an anthology of acient and modern measurement systems of all kind, scientific measures, units of time, weights, currencies etc.