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Proof And Computation Digitization In Mathematics Computer Science And Philosophy
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Book Synopsis Proof And Computation: Digitization In Mathematics, Computer Science And Philosophy by : Klaus Mainzer
Download or read book Proof And Computation: Digitization In Mathematics, Computer Science And Philosophy written by Klaus Mainzer and published by World Scientific. This book was released on 2018-05-30 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is for graduate students and researchers, introducing modern foundational research in mathematics, computer science, and philosophy from an interdisciplinary point of view. Its scope includes Predicative Foundations, Constructive Mathematics and Type Theory, Computation in Higher Types, Extraction of Programs from Proofs, and Algorithmic Aspects in Financial Mathematics. By filling the gap between (under-)graduate level textbooks and advanced research papers, the book gives a scholarly account of recent developments and emerging branches of the aforementioned fields.
Book Synopsis Proof And Computation Ii: From Proof Theory And Univalent Mathematics To Program Extraction And Verification by : Klaus Mainzer
Download or read book Proof And Computation Ii: From Proof Theory And Univalent Mathematics To Program Extraction And Verification written by Klaus Mainzer and published by World Scientific. This book was released on 2021-07-27 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is for graduate students and researchers, introducing modern foundational research in mathematics, computer science, and philosophy from an interdisciplinary point of view. Its scope includes proof theory, constructive mathematics and type theory, univalent mathematics and point-free approaches to topology, extraction of certified programs from proofs, automated proofs in the automotive industry, as well as the philosophical and historical background of proof theory. By filling the gap between (under-)graduate level textbooks and advanced research papers, the book gives a scholarly account of recent developments and emerging branches of the aforementioned fields.
Book Synopsis Temporal Logic: From Philosophy And Proof Theory To Artificial Intelligence And Quantum Computing by : Klaus Mainzer
Download or read book Temporal Logic: From Philosophy And Proof Theory To Artificial Intelligence And Quantum Computing written by Klaus Mainzer and published by World Scientific. This book was released on 2023-05-12 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: Calculi of temporal logic are widely used in modern computer science. The temporal organization of information flows in the different architectures of laptops, the Internet, or supercomputers would not be possible without appropriate temporal calculi. In the age of digitalization and High-Tech applications, people are often not aware that temporal logic is deeply rooted in the philosophy of modalities. A deep understanding of these roots opens avenues to the modern calculi of temporal logic which have emerged by extension of modal logic with temporal operators. Computationally, temporal operators can be introduced in different formalisms with increasing complexity such as Basic Modal Logic (BML), Linear-Time Temporal Logic (LTL), Computation Tree Logic (CTL), and Full Computation Tree Logic (CTL*). Proof-theoretically, these formalisms of temporal logic can be interpreted by the sequent calculus of Gentzen, the tableau-based calculus, automata-based calculus, game-based calculus, and dialogue-based calculus with different advantages for different purposes, especially in computer science.The book culminates in an outlook on trendsetting applications of temporal logics in future technologies such as artificial intelligence and quantum technology. However, it will not be sufficient, as in traditional temporal logic, to start from the everyday understanding of time. Since the 20th century, physics has fundamentally changed the modern understanding of time, which now also determines technology. In temporal logic, we are only just beginning to grasp these differences in proof theory which needs interdisciplinary cooperation of proof theory, computer science, physics, technology, and philosophy.
Book Synopsis Contemporary Natural Philosophy and Philosophies - Part 1 by : Gordana Dodig-Crnkovic
Download or read book Contemporary Natural Philosophy and Philosophies - Part 1 written by Gordana Dodig-Crnkovic and published by MDPI. This book was released on 2019-06-11 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern information communication technology eradicates barriers of geographic distances, making the world globally interdependent, but this spatial globalization has not eliminated cultural fragmentation. The Two Cultures of C.P. Snow (that of science–technology and that of humanities) are drifting apart even faster than before, and they themselves crumble into increasingly specialized domains. Disintegrated knowledge has become subservient to the competition in technological and economic race leading in the direction chosen not by the reason, intellect, and shared value-based judgement, but rather by the whims of autocratic leaders or fashion controlled by marketers for the purposes of political or economic dominance. If we want to restore the authority of our best available knowledge and democratic values in guiding humanity, first we have to reintegrate scattered domains of human knowledge and values and offer an evolving and diverse vision of common reality unified by sound methodology. This collection of articles responds to the call from the journal Philosophies to build a new, networked world of knowledge with domain specialists from different disciplines interacting and connecting with other knowledge-and-values-producing and knowledge-and-values-consuming communities in an inclusive, extended, contemporary natural–philosophic manner. In this process of synthesis, scientific and philosophical investigations enrich each other—with sciences informing philosophies about the best current knowledge of the world, both natural and human-made—while philosophies scrutinize the ontological, epistemological, and methodological foundations of sciences, providing scientists with questions and conceptual analyses. This is all directed at extending and deepening our existing comprehension of the world, including ourselves, both as humans and as societies, and humankind.
Book Synopsis Proofs and Computations by : Helmut Schwichtenberg
Download or read book Proofs and Computations written by Helmut Schwichtenberg and published by Cambridge University Press. This book was released on 2011-12-15 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: Driven by the question, 'What is the computational content of a (formal) proof?', this book studies fundamental interactions between proof theory and computability. It provides a unique self-contained text for advanced students and researchers in mathematical logic and computer science. Part I covers basic proof theory, computability and Gödel's theorems. Part II studies and classifies provable recursion in classical systems, from fragments of Peano arithmetic up to Π11–CA0. Ordinal analysis and the (Schwichtenberg–Wainer) subrecursive hierarchies play a central role and are used in proving the 'modified finite Ramsey' and 'extended Kruskal' independence results for PA and Π11–CA0. Part III develops the theoretical underpinnings of the first author's proof assistant MINLOG. Three chapters cover higher-type computability via information systems, a constructive theory TCF of computable functionals, realizability, Dialectica interpretation, computationally significant quantifiers and connectives and polytime complexity in a two-sorted, higher-type arithmetic with linear logic.
Book Synopsis Limits of Computation by : Edna E. Reiter
Download or read book Limits of Computation written by Edna E. Reiter and published by CRC Press. This book was released on 2012-10-29 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: Limits of Computation: An Introduction to the Undecidable and the Intractable offers a gentle introduction to the theory of computational complexity. It explains the difficulties of computation, addressing problems that have no algorithm at all and problems that cannot be solved efficiently. The book enables readers to understand:What does it mean
Book Synopsis The Universal Computer by : Martin Davis
Download or read book The Universal Computer written by Martin Davis and published by CRC Press. This book was released on 2018-10-08 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: The breathtakingly rapid pace of change in computing makes it easy to overlook the pioneers who began it all. Written by Martin Davis, respected logician and researcher in the theory of computation, The Universal Computer: The Road from Leibniz to Turing explores the fascinating lives, ideas, and discoveries of seven remarkable mathematicians. It tells the stories of the unsung heroes of the computer age – the logicians. The story begins with Leibniz in the 17th century and then focuses on Boole, Frege, Cantor, Hilbert, and Gödel, before turning to Turing. Turing’s analysis of algorithmic processes led to a single, all-purpose machine that could be programmed to carry out such processes—the computer. Davis describes how this incredible group, with lives as extraordinary as their accomplishments, grappled with logical reasoning and its mechanization. By investigating their achievements and failures, he shows how these pioneers paved the way for modern computing. Bringing the material up to date, in this revised edition Davis discusses the success of the IBM Watson on Jeopardy, reorganizes the information on incompleteness, and adds information on Konrad Zuse. A distinguished prize-winning logician, Martin Davis has had a career of more than six decades devoted to the important interface between logic and computer science. His expertise, combined with his genuine love of the subject and excellent storytelling, make him the perfect person to tell this story.
Book Synopsis The Second Machine Age: Work, Progress, and Prosperity in a Time of Brilliant Technologies by : Erik Brynjolfsson
Download or read book The Second Machine Age: Work, Progress, and Prosperity in a Time of Brilliant Technologies written by Erik Brynjolfsson and published by W. W. Norton & Company. This book was released on 2014-01-20 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: The big stories -- The skills of the new machines : technology races ahead -- Moore's law and the second half of the chessboard -- The digitization of just about everything -- Innovation : declining or recombining? -- Artificial and human intelligence in the second machine age -- Computing bounty -- Beyond GDP -- The spread -- The biggest winners : stars and superstars -- Implications of the bounty and the spread -- Learning to race with machines : recommendations for individuals -- Policy recommendations -- Long-term recommendations -- Technology and the future (which is very different from "technology is the future").
Book Synopsis Mathematics of Quantum Computing by : Wolfgang Scherer
Download or read book Mathematics of Quantum Computing written by Wolfgang Scherer and published by Springer Nature. This book was released on 2019-11-13 with total page 773 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook presents the elementary aspects of quantum computing in a mathematical form. It is intended as core or supplementary reading for physicists, mathematicians, and computer scientists taking a first course on quantum computing. It starts by introducing the basic mathematics required for quantum mechanics, and then goes on to present, in detail, the notions of quantum mechanics, entanglement, quantum gates, and quantum algorithms, of which Shor's factorisation and Grover's search algorithm are discussed extensively. In addition, the algorithms for the Abelian Hidden Subgroup and Discrete Logarithm problems are presented and the latter is used to show how the Bitcoin digital signature may be compromised. It also addresses the problem of error correction as well as giving a detailed exposition of adiabatic quantum computing. The book contains around 140 exercises for the student, covering all of the topics treated, together with an appendix of solutions.
Book Synopsis Digital Geometry by : Reinhard Klette
Download or read book Digital Geometry written by Reinhard Klette and published by Morgan Kaufmann. This book was released on 2004-08-06 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first book on digital geometry by the leaders in the field.
Book Synopsis Concepts of Proof in Mathematics, Philosophy, and Computer Science by : Dieter Probst
Download or read book Concepts of Proof in Mathematics, Philosophy, and Computer Science written by Dieter Probst and published by Walter de Gruyter GmbH & Co KG. This book was released on 2016-07-25 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: A proof is a successful demonstration that a conclusion necessarily follows by logical reasoning from axioms which are considered evident for the given context and agreed upon by the community. It is this concept that sets mathematics apart from other disciplines and distinguishes it as the prototype of a deductive science. Proofs thus are utterly relevant for research, teaching and communication in mathematics and of particular interest for the philosophy of mathematics. In computer science, moreover, proofs have proved to be a rich source for already certified algorithms. This book provides the reader with a collection of articles covering relevant current research topics circled around the concept 'proof'. It tries to give due consideration to the depth and breadth of the subject by discussing its philosophical and methodological aspects, addressing foundational issues induced by Hilbert's Programme and the benefits of the arising formal notions of proof, without neglecting reasoning in natural language proofs and applications in computer science such as program extraction.
Book Synopsis Computational Thinking by : Peter J. Denning
Download or read book Computational Thinking written by Peter J. Denning and published by MIT Press. This book was released on 2019-05-14 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This pocket-sized introduction to computational thinking and problem-solving traces its genealogy centuries before the digital computer. A few decades into the digital era, scientists discovered that thinking in terms of computation made possible an entirely new way of organizing scientific investigation. Eventually, every field had a computational branch: computational physics, computational biology, computational sociology. More recently, “computational thinking” has become part of the K–12 curriculum. But what is computational thinking? This volume in the MIT Press Essential Knowledge series offers an accessible overview—tracing a genealogy that begins centuries before digital computers and portraying computational thinking as the pioneers of computing have described it. The authors explain that computational thinking (CT) is not a set of concepts for programming; it is a way of thinking that is honed through practice: the mental skills for designing computations to do jobs for us, and for explaining and interpreting the world as a complex of information processes. Mathematically trained experts (known as “computers”) who performed complex calculations as teams engaged in CT long before electronic computers. In each chapter, the author identify different dimensions of today's highly developed CT: • Computational Methods • Computing Machines • Computing Education • Software Engineering • Computational Science • Design Along the way, they debunk inflated claims for CT and computation while making clear the power of CT in all its complexity and multiplicity.
Book Synopsis Physical Computation by : Gualtiero Piccinini
Download or read book Physical Computation written by Gualtiero Piccinini and published by Oxford University Press, USA. This book was released on 2015 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computation permeates our world, but a satisfactory philosophical theory of what it is has been lacking. Gualtiero Piccinini presents a mechanistic account of what makes a physical system a computing system. He argues that computation does not entail representation or information-processing, although information-processing entails computation.
Book Synopsis The Annotated Turing by : Charles Petzold
Download or read book The Annotated Turing written by Charles Petzold and published by John Wiley & Sons. This book was released on 2008-06-16 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: Programming Legend Charles Petzold unlocks the secrets of the extraordinary and prescient 1936 paper by Alan M. Turing Mathematician Alan Turing invented an imaginary computer known as the Turing Machine; in an age before computers, he explored the concept of what it meant to be computable, creating the field of computability theory in the process, a foundation of present-day computer programming. The book expands Turing’s original 36-page paper with additional background chapters and extensive annotations; the author elaborates on and clarifies many of Turing’s statements, making the original difficult-to-read document accessible to present day programmers, computer science majors, math geeks, and others. Interwoven into the narrative are the highlights of Turing’s own life: his years at Cambridge and Princeton, his secret work in cryptanalysis during World War II, his involvement in seminal computer projects, his speculations about artificial intelligence, his arrest and prosecution for the crime of "gross indecency," and his early death by apparent suicide at the age of 41.
Book Synopsis The Digital Dilemma by : National Research Council
Download or read book The Digital Dilemma written by National Research Council and published by National Academies Press. This book was released on 2000-02-24 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: Imagine sending a magazine article to 10 friends-making photocopies, putting them in envelopes, adding postage, and mailing them. Now consider how much easier it is to send that article to those 10 friends as an attachment to e-mail. Or to post the article on your own site on the World Wide Web. The ease of modifying or copying digitized material and the proliferation of computer networking have raised fundamental questions about copyright and patentâ€"intellectual property protections rooted in the U.S. Constitution. Hailed for quick and convenient access to a world of material, the Internet also poses serious economic issues for those who create and market that material. If people can so easily send music on the Internet for free, for example, who will pay for music? This book presents the multiple facets of digitized intellectual property, defining terms, identifying key issues, and exploring alternatives. It follows the complex threads of law, business, incentives to creators, the American tradition of access to information, the international context, and the nature of human behavior. Technology is explored for its ability to transfer content and its potential to protect intellectual property rights. The book proposes research and policy recommendations as well as principles for policymaking.
Book Synopsis The Mathematical Theory of Communication by : Claude E Shannon
Download or read book The Mathematical Theory of Communication written by Claude E Shannon and published by University of Illinois Press. This book was released on 1998-09-01 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scientific knowledge grows at a phenomenal pace--but few books have had as lasting an impact or played as important a role in our modern world as The Mathematical Theory of Communication, published originally as a paper on communication theory more than fifty years ago. Republished in book form shortly thereafter, it has since gone through four hardcover and sixteen paperback printings. It is a revolutionary work, astounding in its foresight and contemporaneity. The University of Illinois Press is pleased and honored to issue this commemorative reprinting of a classic.
Download or read book Mind Tools written by Rudy Rucker and published by Courier Corporation. This book was released on 2013-11-21 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published: Boston: Houghton Mifflin, 1987.
