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Essays on the Complexity of Continuous Problems by Erich Novak,Henryk Woźniakowski Pdf
This book contains five essays on the complexity of continuous problems, written for a wider audience. The first four essays are based on talks presented in 2008 when Henryk Wozniakowski received an honorary doctoral degree from the Friedrich Schiller University of Jena. The focus is on the introduction and history of the complexity of continuous problems, as well as on recent progress concerning the complexity of high-dimensional numerical problems. The last essay provides a brief and informal introduction to the basic notions and concepts of information-based complexity addressed to a general readership.
The Human Face of Computing by Cristian S Calude Pdf
Computation is ubiquitous: modern life would be inconceivable without it. Written as a series of conversations with influential computer scientists, mathematicians and physicists, this book provides access to the inner thinking of those who have made essential contributions to the development of computing and its applications. You will learn about the interviewees' education, career path, influences, methods of work, how they cope with failure and success, how they relax, how they see the future, and much more. The conversations are presented in jargon-free language suitable for a general audience, but with enough technical detail for more specialized readers. The aim of the book is not only to inform and entertain, but also to motivate and stimulate. Contents:Computing Science: Formal Methods (Dines Bjørner) Computer System and Network Performance Analysis (Erol Gelenbe)From Theoretical Computer Science to Behavioural Programming, Biology and Smell (David Harel) Computational Complexity (Juris Hartmanis)From Theory to Library of Efficient Data Types and Algorithms (LEDA) and Algorithm Engineering (Kurt Mehlhorn) Theoretical Computer Science (Arto Salomaa) Concurrent Systems Specification and Verification (Joseph Sifakis) Information-Based Complexity (Joseph F Traub)A Stroll Through the Gardens of Computer Science (Ian H Witten)Computing in Biology, Mathematics and Physics: Experimental Mathematics (Jon Borwein) Constructive Mathematics (Douglas Bridges)Mathematics, Physics, Biology and Philosophy (Gregory Chaitin) Qualitative Computing (Françoise Chatelin) Computability, Complexity Theory, Reverse Mathematics and Algorithmic Information Theory (Rod Downey) Informatics, Physics and Mathematics (Jozef Gruska) Computations and Natural Sciences (Giuseppe Longo) My Life Is Not a Conveyor Belt (Yuri Manin) Mathematical Analysis, Languages and Fractals (Solomon Marcus) Information, Quantum Mechanics and Probabilities (Mioara Mugur-Schachter) Natural Computing (Grzegorz Rozenberg) Social Aspects of Computing: Internet (Brian E Carpenter) Systems, Art and CONICYT (Eric Goles) Mathematics, Computer Science and Life (Yuri Gurevich)Computing and Thinking about the Future (Hermann Maurer) From Theory and Practice in Computing to Research Ethics and the Surveillance State (Moshe Y Vardi) Compiler Construction and Dagstuhl (Reinhard Wilhelm) Readership: Readers and specialists with a background in computer science interested in the lives and motivations of eminent computer scientists. Key Features:Unique format and treatmentFeatures eminent scientistsIncludes stimulating conversations with renowned scientistsKeywords:Computing;ConversationsReviews: "Cristian Calude has assembled a remarkable collection of fascinating essays by distinguished computer scientists concerning the myriad ways in which computers impact our lives at this time and how they will do so in the future." Martin Davis author of The Universal Computer "Let us thank Cristian Calude for having produced this accurate and inspiring book on the human aspects of computer science." Maurice Nivat French Academy of Sciences
Tractability of Multivariate Problems: Standard information for functionals by Erich Novak,H. Woźniakowski Pdf
This is the second volume of a three-volume set comprising a comprehensive study of the tractability of multivariate problems. The second volume deals with algorithms using standard information consisting of function values for the approximation of linear and selected nonlinear functionals. An important example is numerical multivariate integration. The proof techniques used in volumes I and II are quite different. It is especially hard to establish meaningful lower error bounds for the approximation of functionals by using finitely many function values. Here, the concept of decomposable reproducing kernels is helpful, allowing it to find matching lower and upper error bounds for some linear functionals. It is then possible to conclude tractability results from such error bounds. Tractability results, even for linear functionals, are very rich in variety. There are infinite-dimensional Hilbert spaces for which the approximation with an arbitrarily small error of all linear functionals requires only one function value. There are Hilbert spaces for which all nontrivial linear functionals suffer from the curse of dimensionality. This holds for unweighted spaces, where the role of all variables and groups of variables is the same. For weighted spaces one can monitor the role of all variables and groups of variables. Necessary and sufficient conditions on the decay of the weights are given to obtain various notions of tractability. The text contains extensive chapters on discrepancy and integration, decomposable kernels and lower bounds, the Smolyak/sparse grid algorithms, lattice rules and the CBC (component-by-component) algorithms. This is done in various settings. Path integration and quantum computation are also discussed. This volume is of interest to researchers working in computational mathematics, especially in approximation of high-dimensional problems. It is also well suited for graduate courses and seminars. There are 61 open problems listed to stimulate future research in tractability.
Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan by Josef Dick,Frances Y. Kuo,Henryk Woźniakowski Pdf
This book is a tribute to Professor Ian Hugh Sloan on the occasion of his 80th birthday. It consists of nearly 60 articles written by international leaders in a diverse range of areas in contemporary computational mathematics. These papers highlight the impact and many achievements of Professor Sloan in his distinguished academic career. The book also presents state of the art knowledge in many computational fields such as quasi-Monte Carlo and Monte Carlo methods for multivariate integration, multi-level methods, finite element methods, uncertainty quantification, spherical designs and integration on the sphere, approximation and interpolation of multivariate functions, oscillatory integrals, and in general in information-based complexity and tractability, as well as in a range of other topics. The book also tells the life story of the renowned mathematician, family man, colleague and friend, who has been an inspiration to many of us. The reader may especially enjoy the story from the perspective of his family, his wife, his daughter and son, as well as grandchildren, who share their views of Ian. The clear message of the book is that Ian H. Sloan has been a role model in science and life.
Lattice Rules by Josef Dick,Peter Kritzer,Friedrich Pillichshammer Pdf
Lattice rules are a powerful and popular form of quasi-Monte Carlo rules based on multidimensional integration lattices. This book provides a comprehensive treatment of the subject with detailed explanations of the basic concepts and the current methods used in research. This comprises, for example, error analysis in reproducing kernel Hilbert spaces, fast component-by-component constructions, the curse of dimensionality and tractability, weighted integration and approximation problems, and applications of lattice rules.
Bases in Function Spaces, Sampling, Discrepancy, Numerical Integration by Hans Triebel Pdf
The first chapters of this book deal with Haar bases, Faber bases and some spline bases for function spaces in Euclidean $n$-space and $n$-cubes. These are used in the subsequent chapters to study sampling and numerical integration preferably in spaces with dominating mixed smoothness. The subject of the last chapter is the symbiotic relationship between numerical integration and discrepancy, measuring the deviation of sets of points from uniformity. This book is addressed to graduate students and mathematicians who have a working knowledge of basic elements of function spaces and approximation theory and who are interested in the subtle interplay between function spaces, complexity theory and number theory (discrepancy).
The Best Writing on Mathematics 2010 by Mircea Pitici Pdf
The year’s most memorable writing on mathematics This anthology brings together the year's finest writing on mathematics from around the world. Featuring promising new voices alongside some of the foremost names in mathematics, The Best Writing on Mathematics 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 readers will discover why Freeman Dyson thinks some mathematicians are birds while others are frogs; why Keith Devlin believes there's more to mathematics than proof; what Nick Paumgarten has to say about the timing patterns of New York City's traffic lights (and why jaywalking is the most mathematically efficient way to cross Sixty-sixth Street); what Samuel Arbesman can tell us about the epidemiology of the undead in zombie flicks; and much, much more. In addition to presenting the year's most memorable writing on mathematics, this must-have anthology also includes a foreword by esteemed mathematician William Thurston and an informative introduction by Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us—and where it's headed.
Revised and updated, this second edition of Walter Gautschi's successful Numerical Analysis explores computational methods for problems arising in the areas of classical analysis, approximation theory, and ordinary differential equations, among others. Topics included in the book are presented with a view toward stressing basic principles and maintaining simplicity and teachability as far as possible, while subjects requiring a higher level of technicality are referenced in detailed bibliographic notes at the end of each chapter. Readers are thus given the guidance and opportunity to pursue advanced modern topics in more depth. Along with updated references, new biographical notes, and enhanced notational clarity, this second edition includes the expansion of an already large collection of exercises and assignments, both the kind that deal with theoretical and practical aspects of the subject and those requiring machine computation and the use of mathematical software. Perhaps most notably, the edition also comes with a complete solutions manual, carefully developed and polished by the author, which will serve as an exceptionally valuable resource for instructors.
The Challenge of Complexity by Amy Heath-Carpentier Pdf
The Challenge of Complexity gathers in one volume over 32 essays by the esteemed French philosopher and sociologist, Edgar Morin, probably France's greatest living public intellectual. The essays span six decades of his career, addressing topics such as complexity, sociology, ecology, education, film, biology, and politics. At his centenary (July 2021), Morin holds honorary doctorates from over 20 universities in Europe and Latin America, and recently the Centre d'Etudes Transdisciplinaires, Sociologie, Anthropologie, Histoire, at the Centre National de la Recherche Scientifique (CNRS), the prestigious French National Research Center, was renamed the Centre Edgar-Morin. He is also the UNESCO Chair of Complex Thought. Several university centres and institutes have been dedicated to advancing his work in Europe and Latin America. He is the author of more than 80 books, translated into 28 languages, and the 1960 documentary Chronicle of a Summer, which he co-directed with Jean Rouch, has become a classic and the first example of cinema verite. Morin's work on complexity is distinct from the mathematically driven science of complexity. He argues for an epistemological revolution and focuses on the need to develop complex thought to address the lived complexity of an interconnected, interdependent, uncertain world. Morin's contribution in such a wide range of disciplines has been influential because of his ability to bring complex thought to bear on seemingly diverse topics, reflecting on the limitations of how they are approached and articulating a transdisciplinary way that doesnt sacrifice complexity in an effort to find an oversimplified clarity. Morin illuminates the complexity and creativity of the world and of our lived experience, and invites us to participate in the creative process that is existence itself. A substantive overview of Morin's philosophical journey by Alfonso Montuori introduces the reader to Morin's remarkable work and life. And the work is completed by a substantive Letter from Edgar Morin, putting his life's work in the context of recent advances in Science and the Humanities.
Essays in the Economics of Uncertainty by Jean-Jacques Laffont Pdf
These three elegant essays develop principles central to the understanding of the diverse ways in which imperfect information affects the distribution of resources, incentives, and the evaluation of economic policy. The first concerns the special role that information plays in the allocation process when it is possible to improve accuracy through private investment. The common practice of hiring "experts" whose information is presumably much better than their clients' is analyzed. Issues of cooperative behavior when potential group members possess diverse pieces of information are addressed. Emphasis is placed on the adaptation of the "core" concept from game theory to the resource allocation model with differential information. The second essay deals with the extent to which agents can influence the random events they face. This is known as moral hazard, and in its presence there is a potential inefficiency in the economic system. Two special models are studied: the role of moral hazard in a monetary economy, and the role of an outside adjudicatory agency that has the power to enforce fines and compensation. The final essay discusses the problem of certainty equivalence in economic policy. Conditions under which a full stochastic optimization can be calculated by solving a related, much simpler "certainty equivalence" problem are developed. The reduction in the complexity of calculation involved is very great compared with the potential loss of efficiency.
Computable, Constructive & Behavioural Economic Dynamics by Stefano Zambelli Pdf
The book contains thirty original articles dealing with important aspects of theoretical as well as applied economic theory. While the principal focus is on: the computational and algorithmic nature of economic dynamics; individual as well as collective decision process and rational behavior, some contributions emphasize also the importance of classical recursion theory and constructive mathematics for dynamical systems, business cycles theories, growth theories, and others are in the area of history of thought, methodology and behavioural economics. The contributors range from Nobel Laureates to the promising new generation of innovative thinkers. This volume is also a Festschrift in honour of Professor Kumaraswamy Vela Velupillai, the founder of Computable Economics, a growing field of research where important results stemming from classical recursion theory and constructive mathematics are applied to economic theory. The aim and hope is to provide new tools for economic modelling. This book will be of particular appeal to postgraduate students and scholars in one or more of the following fields: computable economics, business cycles, macroeconomics, growth theories, methodology, behavioural economics, financial economics, experimental and agent based economics. It might be also of importance to those interested on the general theme of algorithmic foundations for social sciences.
Computable, Constructive & Behavioural Economic Dynamics by Stefano Zambelli Pdf
The book contains thirty original articles dealing with important aspects of theoretical as well as applied economic theory. While the principal focus is on: the computational and algorithmic nature of economic dynamics; individual as well as collective decision process and rational behavior, some contributions emphasize also the importance of classical recursion theory and constructive mathematics for dynamical systems, business cycles theories, growth theories, and others are in the area of history of thought, methodology and behavioural economics. The contributors range from Nobel Laureates to the promising new generation of innovative thinkers. This volume is also a Festschrift in honour of Professor Kumaraswamy Vela Velupillai, the founder of Computable Economics, a growing field of research where important results stemming from classical recursion theory and constructive mathematics are applied to economic theory. The aim and hope is to provide new tools for economic modelling. This book will be of particular appeal to postgraduate students and scholars in one or more of the following fields: computable economics, business cycles, macroeconomics, growth theories, methodology, behavioural economics, financial economics, experimental and agent based economics. It might be also of importance to those interested on the general theme of algorithmic foundations for social sciences.
People, Problems, and Proofs by Richard J. Lipton,Kenneth W. Regan Pdf
People, problems, and proofs are the lifeblood of theoretical computer science. Behind the computing devices and applications that have transformed our lives are clever algorithms, and for every worthwhile algorithm there is a problem that it solves and a proof that it works. Before this proof there was an open problem: can one create an efficient algorithm to solve the computational problem? And, finally, behind these questions are the people who are excited about these fundamental issues in our computational world. In this book the authors draw on their outstanding research and teaching experience to showcase some key people and ideas in the domain of theoretical computer science, particularly in computational complexity and algorithms, and related mathematical topics. They show evidence of the considerable scholarship that supports this young field, and they balance an impressive breadth of topics with the depth necessary to reveal the power and the relevance of the work described. Beyond this, the authors discuss the sustained effort of their community, revealing much about the culture of their field. A career in theoretical computer science at the top level is a vocation: the work is hard, and in addition to the obvious requirements such as intellect and training, the vignettes in this book demonstrate the importance of human factors such as personality, instinct, creativity, ambition, tenacity, and luck. The authors' style is characterize d by personal observations, enthusiasm, and humor, and this book will be a source of inspiration and guidance for graduate students and researchers engaged with or planning careers in theoretical computer science.
