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Computability In Analysis And Physics
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Book Synopsis Computability in Analysis and Physics by : Marian B. Pour-El
Download or read book Computability in Analysis and Physics written by Marian B. Pour-El and published by Cambridge University Press. This book was released on 2017-03-02 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first graduate-level treatment of computable analysis within the tradition of classical mathematical reasoning.
Book Synopsis Computability in Analysis and Physics by : Marian B. Pour-El
Download or read book Computability in Analysis and Physics written by Marian B. Pour-El and published by Cambridge University Press. This book was released on 2017-03-02 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the first publication in the Perspectives in Logic series, Pour-El and Richards present the first graduate-level treatment of computable analysis within the tradition of classical mathematical reasoning. The book focuses on the computability or noncomputability of standard processes in analysis and physics. Topics include classical analysis, Hilbert and Banach spaces, bounded and unbounded linear operators, eigenvalues, eigenvectors, and equations of mathematical physics. The work is self-contained, and although it is intended primarily for logicians and analysts, it should also be of interest to researchers and graduate students in physics and computer science.
Book Synopsis Computability in Analysis and Physics by : Marian Boykan Pour-El
Download or read book Computability in Analysis and Physics written by Marian Boykan Pour-El and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the first publication in the Perspectives in Logic series, Pour-El and Richards present the first graduate-level treatment of computable analysis within the tradition of classical mathematical reasoning. The book focuses on the computability or noncomputability of standard processes in analysis and physics. Topics include classical analysis, Hilbert and Banach spaces, bounded and unbounded linear operators, eigenvalues, eigenvectors, and equations of mathematical physics. The work is self-contained, and although it is intended primarily for logicians and analysts, it should also be of interest to researchers and graduate students in physics and computer science.
Book Synopsis Computability in Analysis and Physics by : Marian Boykan Pour-El
Download or read book Computability in Analysis and Physics written by Marian Boykan Pour-El and published by . This book was released on 1989 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Computable Analysis by : Klaus Weihrauch
Download or read book Computable Analysis written by Klaus Weihrauch and published by Springer Science & Business Media. This book was released on 2000-09-14 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Merging fundamental concepts of analysis and recursion theory to a new exciting theory, this book provides a solid fundament for studying various aspects of computability and complexity in analysis. It is the result of an introductory course given for several years and is written in a style suitable for graduate-level and senior students in computer science and mathematics. Many examples illustrate the new concepts while numerous exercises of varying difficulty extend the material and stimulate readers to work actively on the text.
Book Synopsis New Computational Paradigms by : S.B. Cooper
Download or read book New Computational Paradigms written by S.B. Cooper and published by Springer Science & Business Media. This book was released on 2007-11-28 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: This superb exposition of a complex subject examines new developments in the theory and practice of computation from a mathematical perspective, with topics ranging from classical computability to complexity, from biocomputing to quantum computing. This book is suitable for researchers and graduate students in mathematics, philosophy, and computer science with a special interest in logic and foundational issues. Most useful to graduate students are the survey papers on computable analysis and biological computing. Logicians and theoretical physicists will also benefit from this book.
Book Synopsis Models of Computation by : Maribel Fernandez
Download or read book Models of Computation written by Maribel Fernandez and published by Springer Science & Business Media. This book was released on 2009-04-14 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Concise Introduction to Computation Models and Computability Theory provides an introduction to the essential concepts in computability, using several models of computation, from the standard Turing Machines and Recursive Functions, to the modern computation models inspired by quantum physics. An in-depth analysis of the basic concepts underlying each model of computation is provided. Divided into two parts, the first highlights the traditional computation models used in the first studies on computability: - Automata and Turing Machines; - Recursive functions and the Lambda-Calculus; - Logic-based computation models. and the second part covers object-oriented and interaction-based models. There is also a chapter on concurrency, and a final chapter on emergent computation models inspired by quantum mechanics. At the end of each chapter there is a discussion on the use of computation models in the design of programming languages.
Book Synopsis Computability and Complexity Theory by : Steven Homer
Download or read book Computability and Complexity Theory written by Steven Homer and published by Springer Science & Business Media. This book was released on 2011-12-09 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: This revised and extensively expanded edition of Computability and Complexity Theory comprises essential materials that are core knowledge in the theory of computation. The book is self-contained, with a preliminary chapter describing key mathematical concepts and notations. Subsequent chapters move from the qualitative aspects of classical computability theory to the quantitative aspects of complexity theory. Dedicated chapters on undecidability, NP-completeness, and relative computability focus on the limitations of computability and the distinctions between feasible and intractable. Substantial new content in this edition includes: a chapter on nonuniformity studying Boolean circuits, advice classes and the important result of Karp─Lipton. a chapter studying properties of the fundamental probabilistic complexity classes a study of the alternating Turing machine and uniform circuit classes. an introduction of counting classes, proving the famous results of Valiant and Vazirani and of Toda a thorough treatment of the proof that IP is identical to PSPACE With its accessibility and well-devised organization, this text/reference is an excellent resource and guide for those looking to develop a solid grounding in the theory of computing. Beginning graduates, advanced undergraduates, and professionals involved in theoretical computer science, complexity theory, and computability will find the book an essential and practical learning tool. Topics and features: Concise, focused materials cover the most fundamental concepts and results in the field of modern complexity theory, including the theory of NP-completeness, NP-hardness, the polynomial hierarchy, and complete problems for other complexity classes Contains information that otherwise exists only in research literature and presents it in a unified, simplified manner Provides key mathematical background information, including sections on logic and number theory and algebra Supported by numerous exercises and supplementary problems for reinforcement and self-study purposes
Book Synopsis Handbook of Computability and Complexity in Analysis by : Vasco Brattka
Download or read book Handbook of Computability and Complexity in Analysis written by Vasco Brattka and published by Springer. This book was released on 2022-06-06 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computable analysis is the modern theory of computability and complexity in analysis that arose out of Turing's seminal work in the 1930s. This was motivated by questions such as: which real numbers and real number functions are computable, and which mathematical tasks in analysis can be solved by algorithmic means? Nowadays this theory has many different facets that embrace topics from computability theory, algorithmic randomness, computational complexity, dynamical systems, fractals, and analog computers, up to logic, descriptive set theory, constructivism, and reverse mathematics. In recent decades computable analysis has invaded many branches of analysis, and researchers have studied computability and complexity questions arising from real and complex analysis, functional analysis, and the theory of differential equations, up to (geometric) measure theory and topology. This handbook represents the first coherent cross-section through most active research topics on the more theoretical side of the field. It contains 11 chapters grouped into parts on computability in analysis; complexity, dynamics, and randomness; and constructivity, logic, and descriptive complexity. All chapters are written by leading experts working at the cutting edge of the respective topic. Researchers and graduate students in the areas of theoretical computer science and mathematical logic will find systematic introductions into many branches of computable analysis, and a wealth of information and references that will help them to navigate the modern research literature in this field.
Book Synopsis Turing Computability by : Robert I. Soare
Download or read book Turing Computability written by Robert I. Soare and published by Springer. This book was released on 2016-06-20 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: Turing's famous 1936 paper introduced a formal definition of a computing machine, a Turing machine. This model led to both the development of actual computers and to computability theory, the study of what machines can and cannot compute. This book presents classical computability theory from Turing and Post to current results and methods, and their use in studying the information content of algebraic structures, models, and their relation to Peano arithmetic. The author presents the subject as an art to be practiced, and an art in the aesthetic sense of inherent beauty which all mathematicians recognize in their subject. Part I gives a thorough development of the foundations of computability, from the definition of Turing machines up to finite injury priority arguments. Key topics include relative computability, and computably enumerable sets, those which can be effectively listed but not necessarily effectively decided, such as the theorems of Peano arithmetic. Part II includes the study of computably open and closed sets of reals and basis and nonbasis theorems for effectively closed sets. Part III covers minimal Turing degrees. Part IV is an introduction to games and their use in proving theorems. Finally, Part V offers a short history of computability theory. The author has honed the content over decades according to feedback from students, lecturers, and researchers around the world. Most chapters include exercises, and the material is carefully structured according to importance and difficulty. The book is suitable for advanced undergraduate and graduate students in computer science and mathematics and researchers engaged with computability and mathematical logic.
Book Synopsis Recursively Enumerable Sets and Degrees by : Robert I. Soare
Download or read book Recursively Enumerable Sets and Degrees written by Robert I. Soare and published by Springer Science & Business Media. This book was released on 1999-11-01 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: ..."The book, written by one of the main researchers on the field, gives a complete account of the theory of r.e. degrees. .... The definitions, results and proofs are always clearly motivated and explained before the formal presentation; the proofs are described with remarkable clarity and conciseness. The book is highly recommended to everyone interested in logic. It also provides a useful background to computer scientists, in particular to theoretical computer scientists." Acta Scientiarum Mathematicarum, Ungarn 1988 ..."The main purpose of this book is to introduce the reader to the main results and to the intricacies of the current theory for the recurseively enumerable sets and degrees. The author has managed to give a coherent exposition of a rather complex and messy area of logic, and with this book degree-theory is far more accessible to students and logicians in other fields than it used to be." Zentralblatt für Mathematik, 623.1988
Book Synopsis Slicing the Truth by : Denis R Hirschfeldt
Download or read book Slicing the Truth written by Denis R Hirschfeldt and published by World Scientific. This book was released on 2014-07-18 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a brief and focused introduction to the reverse mathematics and computability theory of combinatorial principles, an area of research which has seen a particular surge of activity in the last few years. It provides an overview of some fundamental ideas and techniques, and enough context to make it possible for students with at least a basic knowledge of computability theory and proof theory to appreciate the exciting advances currently happening in the area, and perhaps make contributions of their own. It adopts a case-study approach, using the study of versions of Ramsey's Theorem (for colorings of tuples of natural numbers) and related principles as illustrations of various aspects of computability theoretic and reverse mathematical analysis. This book contains many exercises and open questions. Contents:Setting Off: An IntroductionGathering Our Tools: Basic Concepts and NotationFinding Our Path: König's Lemma and ComputabilityGauging Our Strength: Reverse MathematicsIn Defense of DisarrayAchieving Consensus: Ramsey's TheoremPreserving Our Power: ConservativityDrawing a Map: Five DiagramsExploring Our Surroundings: The World Below RT22Charging Ahead: Further TopicsLagniappe: A Proof of Liu's Theorem Readership: Graduates and researchers in mathematical logic. Key Features:This book assumes minimal background in mathematical logic and takes the reader all the way to current research in a highly active areaIt is the first detailed introduction to this particular approach to this area of researchThe combination of fully worked out arguments and exercises make this book well suited to self-study by graduate students and other researchers unfamiliar with the areaKeywords:Reverse Mathematics;Computability Theory;Computable Mathematics;Computable Combinatorics
Book Synopsis Connecting with Computability by : Liesbeth De Mol
Download or read book Connecting with Computability written by Liesbeth De Mol and published by Springer. This book was released on 2021-07-02 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 17th Conference on Computability in Europe, CiE 2021, organized by the University of Ghent in July 2021. Due to COVID-19 pandemic the conference was held virtually. The 48 full papers presented in this volume were carefully reviewed and selected from 50 submissions. CiE promotes the development of computability-related science, ranging over mathematics, computer science and applications in various natural and engineering sciences, such as physics and biology, as well as related fields, such as philosophy and history of computing. CiE 2021 had as its motto Connecting with Computability, a clear acknowledgement of the connecting and interdisciplinary nature of the conference series which is all the more important in a time where people are more than ever disconnected from one another due to the COVID-19 pandemic.
Book Synopsis Computer Science by : National Research Council
Download or read book Computer Science written by National Research Council and published by National Academies Press. This book was released on 2004-10-06 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computer Science: Reflections on the Field, Reflections from the Field provides a concise characterization of key ideas that lie at the core of computer science (CS) research. The book offers a description of CS research recognizing the richness and diversity of the field. It brings together two dozen essays on diverse aspects of CS research, their motivation and results. By describing in accessible form computer science's intellectual character, and by conveying a sense of its vibrancy through a set of examples, the book aims to prepare readers for what the future might hold and help to inspire CS researchers in its creation.
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
Download or read book Computability written by B. Jack Copeland and published by MIT Press. This book was released on 2015-01-30 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computer scientists, mathematicians, and philosophers discuss the conceptual foundations of the notion of computability as well as recent theoretical developments. In the 1930s a series of seminal works published by Alan Turing, Kurt Gödel, Alonzo Church, and others established the theoretical basis for computability. This work, advancing precise characterizations of effective, algorithmic computability, was the culmination of intensive investigations into the foundations of mathematics. In the decades since, the theory of computability has moved to the center of discussions in philosophy, computer science, and cognitive science. In this volume, distinguished computer scientists, mathematicians, logicians, and philosophers consider the conceptual foundations of computability in light of our modern understanding. Some chapters focus on the pioneering work by Turing, Gödel, and Church, including the Church-Turing thesis and Gödel's response to Church's and Turing's proposals. Other chapters cover more recent technical developments, including computability over the reals, Gödel's influence on mathematical logic and on recursion theory and the impact of work by Turing and Emil Post on our theoretical understanding of online and interactive computing; and others relate computability and complexity to issues in the philosophy of mind, the philosophy of science, and the philosophy of mathematics. Contributors Scott Aaronson, Dorit Aharonov, B. Jack Copeland, Martin Davis, Solomon Feferman, Saul Kripke, Carl J. Posy, Hilary Putnam, Oron Shagrir, Stewart Shapiro, Wilfried Sieg, Robert I. Soare, Umesh V. Vazirani
Book Synopsis Computability and Complexity in Analysis by : Jens Blanck
Download or read book Computability and Complexity in Analysis written by Jens Blanck and published by Springer Science & Business Media. This book was released on 2001-05-23 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-proceedings of the 4th International Workshop on Computability and Complexity in Analysis, CCA 2000, held in Swansea, UK, in September 2000. The 23 revised full papers presented together with a report on a competition of exact real arithmetic systems were carefully selected from 28 papers accepted for presentation during the workshop. The book presents a cross-section on current research on computability and complexity in analysis.
