Algorithms And Complexity In Mathematics Epistemology And Science

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Algorithms and Complexity in Mathematics, Epistemology, and Science

Nicolas Fillion,Robert M. Corless,Ilias S. Kotsireas
Algorithms and Complexity in Mathematics Epistemology and Science Book PDF

Author : Nicolas Fillion,Robert M. Corless,Ilias S. Kotsireas
Publisher : Springer
Page : 294 pages
File Size : 51,9 Mb
Release : 2019-02-07
Category : Mathematics
ISBN : 9781493990511

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Algorithms and Complexity in Mathematics, Epistemology, and Science by Nicolas Fillion,Robert M. Corless,Ilias S. Kotsireas Pdf

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

Gerard Meurant
Algorithms and Complexity Book PDF

Author : Gerard Meurant
Publisher : Elsevier
Page : 1003 pages
File Size : 53,8 Mb
Release : 2014-06-28
Category : Mathematics
ISBN : 9780080933917

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Algorithms and Complexity by Gerard Meurant Pdf

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.

Mathematics and Computation

Avi Wigderson
Mathematics and Computation Book PDF

Author : Avi Wigderson
Publisher : Princeton University Press
Page : 434 pages
File Size : 50,8 Mb
Release : 2019-10-29
Category : Computers
ISBN : 9780691189130

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Mathematics and Computation by Avi Wigderson Pdf

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

Information, Randomness & Incompleteness

Gregory J. Chaitin
Information Randomness Incompleteness Book PDF

Author : Gregory J. Chaitin
Publisher : World Scientific
Page : 332 pages
File Size : 42,8 Mb
Release : 1990-01-01
Category : Mathematics
ISBN : 9810201710

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Information, Randomness & Incompleteness by Gregory J. Chaitin Pdf

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 G”del 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.

Structures and Algorithms

Jens Erik Fenstad
Structures and Algorithms Book PDF

Author : Jens Erik Fenstad
Publisher : Springer
Page : 134 pages
File Size : 54,8 Mb
Release : 2018-03-10
Category : Philosophy
ISBN : 9783319729749

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Structures and Algorithms by Jens Erik Fenstad Pdf

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.

Induction, Algorithmic Learning Theory, and Philosophy

Michèle Friend,Norma B. Goethe,Valentina S. Harizanov
Induction Algorithmic Learning Theory and Philosophy Book PDF

Author : Michèle Friend,Norma B. Goethe,Valentina S. Harizanov
Publisher : Springer Science & Business Media
Page : 290 pages
File Size : 40,8 Mb
Release : 2007-08-21
Category : Philosophy
ISBN : 9781402061271

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Induction, Algorithmic Learning Theory, and Philosophy by Michèle Friend,Norma B. Goethe,Valentina S. Harizanov Pdf

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.

The Justificatory Force of Experiences

Philipp Berghofer
The Justificatory Force of Experiences Book PDF

Author : Philipp Berghofer
Publisher : Springer Nature
Page : 382 pages
File Size : 54,6 Mb
Release : 2022-03-24
Category : Science
ISBN : 9783030961138

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The Justificatory Force of Experiences by Philipp Berghofer Pdf

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.

Advances in Algorithms, Languages, and Complexity

Ding-Zhu Du,Ker-I Ko
Advances in Algorithms Languages and Complexity Book PDF

Author : Ding-Zhu Du,Ker-I Ko
Publisher : Springer Science & Business Media
Page : 419 pages
File Size : 45,8 Mb
Release : 2013-12-01
Category : Computers
ISBN : 9781461333944

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Advances in Algorithms, Languages, and Complexity by Ding-Zhu Du,Ker-I Ko Pdf

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.

An Introduction to Kolmogorov Complexity and Its Applications

Ming Li,Paul Vitanyi
An Introduction to Kolmogorov Complexity and Its Applications Book PDF

Author : Ming Li,Paul Vitanyi
Publisher : Springer Science & Business Media
Page : 550 pages
File Size : 50,7 Mb
Release : 2013-04-18
Category : Computers
ISBN : 9781475738605

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An Introduction to Kolmogorov Complexity and Its Applications by Ming Li,Paul Vitanyi Pdf

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

Justin Clarke-Doane
Morality and Mathematics Book PDF

Author : Justin Clarke-Doane
Publisher : Oxford University Press
Page : 208 pages
File Size : 41,8 Mb
Release : 2020-03-12
Category : Philosophy
ISBN : 9780192556806

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Morality and Mathematics by Justin Clarke-Doane Pdf

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.

Imitation of Rigor

Mark Wilson
Imitation of Rigor Book PDF

Author : Mark Wilson
Publisher : Oxford University Press
Page : 229 pages
File Size : 51,9 Mb
Release : 2022-01-27
Category : Philosophy
ISBN : 9780192896469

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Imitation of Rigor by Mark Wilson Pdf

"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'"--

Causation with a Human Face

James Woodward
Causation with a Human Face Book PDF

Author : James Woodward
Publisher : Oxford University Press
Page : 128 pages
File Size : 53,7 Mb
Release : 2021-09-27
Category : Science
ISBN : 9780197585436

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Causation with a Human Face by James Woodward Pdf

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.

Algorithmic Randomness and Complexity

Rodney G. Downey,Denis R. Hirschfeldt
Algorithmic Randomness and Complexity Book PDF

Author : Rodney G. Downey,Denis R. Hirschfeldt
Publisher : Springer Science & Business Media
Page : 855 pages
File Size : 41,6 Mb
Release : 2010-10-29
Category : Computers
ISBN : 9780387684413

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Algorithmic Randomness and Complexity by Rodney G. Downey,Denis R. Hirschfeldt Pdf

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.

Complexity and Real Computation

Lenore Blum,Felipe Cucker,Michael Shub,Steve Smale
Complexity and Real Computation Book PDF

Author : Lenore Blum,Felipe Cucker,Michael Shub,Steve Smale
Publisher : Springer Science & Business Media
Page : 456 pages
File Size : 46,8 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9781461207016

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Complexity and Real Computation by Lenore Blum,Felipe Cucker,Michael Shub,Steve Smale Pdf

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.

Complexity Theory

Ingo Wegener
Complexity Theory Book PDF

Author : Ingo Wegener
Publisher : Springer Science & Business Media
Page : 307 pages
File Size : 54,6 Mb
Release : 2005-07-05
Category : Computers
ISBN : 9783540274773

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Complexity Theory by Ingo Wegener Pdf

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