Algorithms And Complexity In Mathematics Epistemology And Science

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Algorithms and Complexity in Mathematics, Epistemology, and Science

Author : Nicolas Fillion
Publisher : Springer
ISBN 13 : 1493990519
Total Pages : 294 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Algorithms and Complexity in Mathematics, Epistemology, and Science by : Nicolas Fillion

Download or read book Algorithms and Complexity in Mathematics, Epistemology, and Science written by Nicolas Fillion and published by Springer. This book was released on 2019-02-07 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: ACMES (Algorithms and Complexity in Mathematics, Epistemology, and Science) is a multidisciplinary conference series that focuses on epistemological and mathematical issues relating to computation in modern science. This volume includes a selection of papers presented at the 2015 and 2016 conferences held at Western University that provide an interdisciplinary outlook on modern applied mathematics that draws from theory and practice, and situates it in proper context. These papers come from leading mathematicians, computational scientists, and philosophers of science, and cover a broad collection of mathematical and philosophical topics, including numerical analysis and its underlying philosophy, computer algebra, reliability and uncertainty quantification, computation and complexity theory, combinatorics, error analysis, perturbation theory, experimental mathematics, scientific epistemology, and foundations of mathematics. By bringing together contributions from researchers who approach the mathematical sciences from different perspectives, the volume will further readers' understanding of the multifaceted role of mathematics in modern science, informed by the state of the art in mathematics, scientific computing, and current modeling techniques.

Algorithms and Complexity

Author : Gerard Meurant
Publisher : Elsevier
ISBN 13 : 0080933912
Total Pages : 1003 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis Algorithms and Complexity by : Gerard Meurant

Download or read book Algorithms and Complexity written by Gerard Meurant and published by Elsevier. This book was released on 2014-06-28 with total page 1003 pages. Available in PDF, EPUB and Kindle. Book excerpt: This first part presents chapters on models of computation, complexity theory, data structures, and efficient computation in many recognized sub-disciplines of Theoretical Computer Science.

Information, Randomness & Incompleteness

Author : Gregory J. Chaitin
Publisher : World Scientific
ISBN 13 : 9789810201715
Total Pages : 332 pages
Book Rating : 4.2/5 (17 download)

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Book Synopsis Information, Randomness & Incompleteness by : Gregory J. Chaitin

Download or read book Information, Randomness & Incompleteness written by Gregory J. Chaitin and published by World Scientific. This book was released on 1990-01-01 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains in easily accessible form all the main ideas of the creator and principal architect of algorithmic information theory. This expanded second edition has added thirteen abstracts, a 1988 Scientific American Article, a transcript of a EUROPALIA 89 lecture, an essay on biology, and an extensive bibliography. Its new larger format makes it easier to read. Chaitin's ideas are a fundamental extension of those of Gdel and Turning and have exploded some basic assumptions of mathematics and thrown new light on the scientific method, epistemology, probability theory, and of course computer science and information theory.

Mathematics and Computation

Author : Avi Wigderson
Publisher : Princeton University Press
ISBN 13 : 0691189137
Total Pages : 434 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Mathematics and Computation by : Avi Wigderson

Download or read book Mathematics and Computation written by Avi Wigderson and published by Princeton University Press. This book was released on 2019-10-29 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography

Induction, Algorithmic Learning Theory, and Philosophy

Author : Michèle Friend
Publisher : Springer Science & Business Media
ISBN 13 : 1402061277
Total Pages : 290 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Induction, Algorithmic Learning Theory, and Philosophy by : Michèle Friend

Download or read book Induction, Algorithmic Learning Theory, and Philosophy written by Michèle Friend and published by Springer Science & Business Media. This book was released on 2007-08-21 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to collect essays from philosophers, mathematicians and computer scientists working at the exciting interface of algorithmic learning theory and the epistemology of science and inductive inference. Readable, introductory essays provide engaging surveys of different, complementary, and mutually inspiring approaches to the topic, both from a philosophical and a mathematical viewpoint.

Structures and Algorithms

Author : Jens Erik Fenstad
Publisher : Springer
ISBN 13 : 3319729748
Total Pages : 134 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Structures and Algorithms by : Jens Erik Fenstad

Download or read book Structures and Algorithms written by Jens Erik Fenstad and published by Springer. This book was released on 2018-03-10 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explains exactly what human knowledge is. The key concepts in this book are structures and algorithms, i.e., what the readers “see” and how they make use of what they see. Thus in comparison with some other books on the philosophy (or methodology) of science, which employ a syntactic approach, the author’s approach is model theoretic or structural. Properly understood, it extends the current art and science of mathematical modeling to all fields of knowledge. The link between structure and algorithms is mathematics. But viewing “mathematics” as such a link is not exactly what readers most likely learned in school; thus, the task of this book is to explain what “mathematics” should actually mean. Chapter 1, an introductory essay, presents a general analysis of structures, algorithms and how they are to be linked. Several examples from the natural and social sciences, and from the history of knowledge, are provided in Chapters 2–6. In turn, Chapters 7 and 8 extend the analysis to include language and the mind. Structures are what the readers see. And, as abstract cultural objects, they can almost always be seen in many different ways. But certain structures, such as natural numbers and the basic theory of grammar, seem to have an absolute character. Any theory of knowledge grounded in human culture must explain how this is possible. The author’s analysis of this cultural invariance, combining insights from evolutionary theory and neuroscience, is presented in the book’s closing chapter. The book will be of interest to researchers, students and those outside academia who seek a deeper understanding of knowledge in our present-day society.

The Justificatory Force of Experiences

Author : Philipp Berghofer
Publisher : Springer Nature
ISBN 13 : 3030961133
Total Pages : 382 pages
Book Rating : 4.0/5 (39 download)

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Book Synopsis The Justificatory Force of Experiences by : Philipp Berghofer

Download or read book The Justificatory Force of Experiences written by Philipp Berghofer and published by Springer Nature. This book was released on 2022-03-24 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a phenomenological conception of experiential justification that seeks to clarify why certain experiences are a source of immediate justification and what role experiences play in gaining (scientific) knowledge. Based on the author's account of experiential justification, this book exemplifies how a phenomenological experience-first epistemology can epistemically ground the individual sciences. More precisely, it delivers a comprehensive picture of how we get from epistemology to the foundations of mathematics and physics. The book is unique as it utilizes methods and insights from the phenomenological tradition in order to make progress in current analytic epistemology. It serves as a starting point for re-evaluating the relevance of Husserlian phenomenology to current analytic epistemology and making an important step towards paving the way for future mutually beneficial discussions. This is achieved by exemplifying how current debates can benefit from ideas, insights, and methods we find in the phenomenological tradition.

An Introduction to Kolmogorov Complexity and Its Applications

Author : Ming Li
Publisher : Springer Science & Business Media
ISBN 13 : 1475738609
Total Pages : 550 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis An Introduction to Kolmogorov Complexity and Its Applications by : Ming Li

Download or read book An Introduction to Kolmogorov Complexity and Its Applications written by Ming Li and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: With this book, the authors are trying to present in a unified treatment an introduction to the central ideas and their applications of the Kolmogorov Complexity, the theory dealing with the quantity of information in individual objects. This book is appropriate for either a one- or two-semester introductory course in departments of computer science, mathematics, physics, probability theory and statistics, artificial intelligence, and philosophy. Although the mathematical theory of Kolmogorov complexity contains sophisticated mathematics, the amount of math one needs to know to apply the notions in widely divergent areas, is very little. The authors' purpose is to develop the theory in detail and outline a wide range of illustrative applications. This book is an attempt to grasp the mass of fragmented knowledge of this fascinating theory. Chapter 1 is a compilation of material on the diverse notations and disciplines we draw upon in order to make the book self-contained. The mathematical theory of Kolmogorov complexity is treated in chapters 2-4; the applications are treated in chapters 4-8.

Morality and Mathematics

Author : Justin Clarke-Doane
Publisher : Oxford University Press
ISBN 13 : 0192556800
Total Pages : 208 pages
Book Rating : 4.1/5 (925 download)

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Book Synopsis Morality and Mathematics by : Justin Clarke-Doane

Download or read book Morality and Mathematics written by Justin Clarke-Doane and published by Oxford University Press. This book was released on 2020-03-12 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: To what extent are the subjects of our thoughts and talk real? This is the question of realism. In this book, Justin Clarke-Doane explores arguments for and against moral realism and mathematical realism, how they interact, and what they can tell us about areas of philosophical interest more generally. He argues that, contrary to widespread belief, our mathematical beliefs have no better claim to being self-evident or provable than our moral beliefs. Nor do our mathematical beliefs have better claim to being empirically justified than our moral beliefs. It is also incorrect that reflection on the genealogy of our moral beliefs establishes a lack of parity between the cases. In general, if one is a moral antirealist on the basis of epistemological considerations, then one ought to be a mathematical antirealist as well. And, yet, Clarke-Doane shows that moral realism and mathematical realism do not stand or fall together — and for a surprising reason. Moral questions, insofar as they are practical, are objective in a sense that mathematical questions are not, and the sense in which they are objective can only be explained by assuming practical anti-realism. One upshot of the discussion is that the concepts of realism and objectivity, which are widely identified, are actually in tension. Another is that the objective questions in the neighborhood of factual areas like logic, modality, grounding, and nature are practical questions too. Practical philosophy should, therefore, take center stage.

Advances in Algorithms, Languages, and Complexity

Author : Ding-Zhu Du
Publisher : Springer Science & Business Media
ISBN 13 : 1461333946
Total Pages : 419 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Advances in Algorithms, Languages, and Complexity by : Ding-Zhu Du

Download or read book Advances in Algorithms, Languages, and Complexity written by Ding-Zhu Du and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a collection of survey papers in the areas of algorithms, lan guages and complexity, the three areas in which Professor Ronald V. Book has made significant contributions. As a fonner student and a co-author who have been influenced by him directly, we would like to dedicate this book to Professor Ronald V. Book to honor and celebrate his sixtieth birthday. Professor Book initiated his brilliant academic career in 1958, graduating from Grinnell College with a Bachelor of Arts degree. He obtained a Master of Arts in Teaching degree in 1960 and a Master of Arts degree in 1964 both from Wesleyan University, and a Doctor of Philosophy degree from Harvard University in 1969, under the guidance of Professor Sheila A. Greibach. Professor Book's research in discrete mathematics and theoretical com puter science is reflected in more than 150 scientific publications. These works have made a strong impact on the development of several areas of theoretical computer science. A more detailed summary of his scientific research appears in this volume separately.

Imitation of Rigor

Author : Mark Wilson
Publisher : Oxford University Press
ISBN 13 : 0192896466
Total Pages : 229 pages
Book Rating : 4.1/5 (928 download)

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Book Synopsis Imitation of Rigor by : Mark Wilson

Download or read book Imitation of Rigor written by Mark Wilson and published by Oxford University Press. This book was released on 2022-01-27 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Mark Wilson aims to reconnect analytic philosophy with the evolving practicalities within science from which many of its grander concerns originally sprang. He offers an alternative history of how the subject might have developed had the insights of its philosopher/scientist forebears not been cast aside in the vain pursuit of 'ersatz rigor'"--

Algorithmic Randomness and Complexity

Author : Rodney G. Downey
Publisher : Springer Science & Business Media
ISBN 13 : 0387684417
Total Pages : 855 pages
Book Rating : 4.3/5 (876 download)

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Book Synopsis Algorithmic Randomness and Complexity by : Rodney G. Downey

Download or read book Algorithmic Randomness and Complexity written by Rodney G. Downey and published by Springer Science & Business Media. This book was released on 2010-10-29 with total page 855 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computability and complexity theory are two central areas of research in theoretical computer science. This book provides a systematic, technical development of "algorithmic randomness" and complexity for scientists from diverse fields.

Causation with a Human Face

Author : James Woodward
Publisher : Oxford University Press
ISBN 13 : 0197585434
Total Pages : pages
Book Rating : 4.1/5 (975 download)

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Book Synopsis Causation with a Human Face by : James Woodward

Download or read book Causation with a Human Face written by James Woodward and published by Oxford University Press. This book was released on 2021-09-27 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The past few decades have seen an explosion of research on causal reasoning in philosophy, computer science, and statistics, as well as descriptive work in psychology. In Causation with a Human Face, James Woodward integrates these lines of research and argues for an understanding of how each can inform the other: normative ideas can suggest interesting experiments, while descriptive results can suggest important normative concepts. Woodward's overall framework builds on the interventionist treatment of causation that he developed in Making Things Happen. Normative ideas discussed include proposals about the role of invariant or stable relationships in successful causal reasoning and the notion of proportionality. He argues that these normative ideas are reflected in the causal judgments that people actually make as a descriptive matter. Woodward also discusses the common philosophical practice-particularly salient in philosophical accounts of causation--of appealing to "intuitions" or "judgments about cases" in support of philosophical theses. He explores how, properly understood, such appeals are not different in principle from appeals to results from empirical research, and demonstrates how they may serve as a useful source of information about causal cognition.

Complexity Theory

Author : Ingo Wegener
Publisher : Springer Science & Business Media
ISBN 13 : 3540274774
Total Pages : 307 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis Complexity Theory by : Ingo Wegener

Download or read book Complexity Theory written by Ingo Wegener and published by Springer Science & Business Media. This book was released on 2005-07-05 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reflects recent developments in its emphasis on randomized and approximation algorithms and communication models All topics are considered from an algorithmic point of view stressing the implications for algorithm design

Complexity and Real Computation

Author : Lenore Blum
Publisher : Springer Science & Business Media
ISBN 13 : 1461207010
Total Pages : 456 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Complexity and Real Computation by : Lenore Blum

Download or read book Complexity and Real Computation written by Lenore Blum and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: The classical theory of computation has its origins in the work of Goedel, Turing, Church, and Kleene and has been an extraordinarily successful framework for theoretical computer science. The thesis of this book, however, is that it provides an inadequate foundation for modern scientific computation where most of the algorithms are real number algorithms. The goal of this book is to develop a formal theory of computation which integrates major themes of the classical theory and which is more directly applicable to problems in mathematics, numerical analysis, and scientific computing. Along the way, the authors consider such fundamental problems as: * Is the Mandelbrot set decidable? * For simple quadratic maps, is the Julia set a halting set? * What is the real complexity of Newton's method? * Is there an algorithm for deciding the knapsack problem in a ploynomial number of steps? * Is the Hilbert Nullstellensatz intractable? * Is the problem of locating a real zero of a degree four polynomial intractable? * Is linear programming tractable over the reals? The book is divided into three parts: The first part provides an extensive introduction and then proves the fundamental NP-completeness theorems of Cook-Karp and their extensions to more general number fields as the real and complex numbers. The later parts of the book develop a formal theory of computation which integrates major themes of the classical theory and which is more directly applicable to problems in mathematics, numerical analysis, and scientific computing.

The Nature of Computation

Author : Cristopher Moore
Publisher : Oxford University Press
ISBN 13 : 0199233217
Total Pages : 1004 pages
Book Rating : 4.1/5 (992 download)

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Book Synopsis The Nature of Computation by : Cristopher Moore

Download or read book The Nature of Computation written by Cristopher Moore and published by Oxford University Press. This book was released on 2011-08-11 with total page 1004 pages. Available in PDF, EPUB and Kindle. Book excerpt: The boundary between physics and computer science has become a hotbed of interdisciplinary collaboration. In this book the authors introduce the reader to the fundamental concepts of computational complexity and give in-depth explorations of the major interfaces between computer science and physics.

Complexity and Information

Author : J. F. Traub
Publisher : Cambridge University Press
ISBN 13 : 9780521485067
Total Pages : 152 pages
Book Rating : 4.4/5 (85 download)

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Book Synopsis Complexity and Information by : J. F. Traub

Download or read book Complexity and Information written by J. F. Traub and published by Cambridge University Press. This book was released on 1998-12-10 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: The twin themes of computational complexity and information pervade this 1998 book. It starts with an introduction to the computational complexity of continuous mathematical models, that is, information-based complexity. This is then used to illustrate a variety of topics, including breaking the curse of dimensionality, complexity of path integration, solvability of ill-posed problems, the value of information in computation, assigning values to mathematical hypotheses, and new, improved methods for mathematical finance. The style is informal, and the goals are exposition, insight and motivation. A comprehensive bibliography is provided, to which readers are referred for precise statements of results and their proofs. As the first introductory book on the subject it will be invaluable as a guide to the area for the many students and researchers whose disciplines, ranging from physics to finance, are influenced by the computational complexity of continuous problems.