Metamathematics, Machines and Gödel's Proof PDF Download
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Author: N. Shankar
Publisher: Cambridge University Press
ISBN: 9780521585330
Category : Computers
Languages : en
Pages : 224
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Book Description
Describes the use of computer programs to check several proofs in the foundations of mathematics.
Author: N. Shankar
Publisher: Cambridge University Press
ISBN: 9780521585330
Category : Computers
Languages : en
Pages : 224
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Book Description
Describes the use of computer programs to check several proofs in the foundations of mathematics.
Author: Rebecca Goldstein
Publisher: W. W. Norton & Company
ISBN: 0393327604
Category : Biography & Autobiography
Languages : en
Pages : 299
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Book Description
"An introduction to the life and thought of Kurt Gödel, who transformed our conception of math forever"--Provided by publisher.
Author: Ernest Nagel
Publisher: Routledge
ISBN: 1134953992
Category : Philosophy
Languages : en
Pages : 109
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Book Description
The first book to present a readable explanation of Godel's theorem to both scholars and non-specialists, this is a gripping combination of science and accessibility, offering those with a taste for logic and philosophy the chance to satisfy their intellectual curiosity.
Author: Norman Megill
Publisher: Lulu.com
ISBN: 0359702236
Category : Computers
Languages : en
Pages : 250
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Book Description
Metamath is a computer language and an associated computer program for archiving, verifying, and studying mathematical proofs. The Metamath language is simple and robust, with an almost total absence of hard-wired syntax, and we believe that it provides about the simplest possible framework that allows essentially all of mathematics to be expressed with absolute rigor. While simple, it is also powerful; the Metamath Proof Explorer (MPE) database has over 23,000 proven theorems and is one of the top systems in the "Formalizing 100 Theorems" challenge. This book explains the Metamath language and program, with specific emphasis on the fundamentals of the MPE database.
Author: Donald MacKenzie
Publisher: MIT Press
ISBN: 9780262632959
Category : Social Science
Languages : en
Pages : 448
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Book Description
Most aspects of our private and social lives—our safety, the integrity of the financial system, the functioning of utilities and other services, and national security—now depend on computing. But how can we know that this computing is trustworthy? In Mechanizing Proof, Donald MacKenzie addresses this key issue by investigating the interrelations of computing, risk, and mathematical proof over the last half century from the perspectives of history and sociology. His discussion draws on the technical literature of computer science and artificial intelligence and on extensive interviews with participants. MacKenzie argues that our culture now contains two ideals of proof: proof as traditionally conducted by human mathematicians, and formal, mechanized proof. He describes the systems constructed by those committed to the latter ideal and the many questions those systems raise about the nature of proof. He looks at the primary social influence on the development of automated proof—the need to predict the behavior of the computer systems upon which human life and security depend—and explores the involvement of powerful organizations such as the National Security Agency. He concludes that in mechanizing proof, and in pursuing dependable computer systems, we do not obviate the need for trust in our collective human judgment.
Author: Petr Hájek
Publisher: Cambridge University Press
ISBN: 1107168414
Category : Mathematics
Languages : en
Pages : 475
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Book Description
A much-needed monograph on the metamathematics of first-order arithmetic, paying particular attention to fragments of Peano arithmetic.
Author: Stefano Zambelli
Publisher: John Wiley & Sons
ISBN: 1118300432
Category : Business & Economics
Languages : en
Pages : 352
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Book Description
Nonlinearity, Complexity and Randomness in Economics presents a variety of papers by leading economists, scientists, and philosophers who focus on different aspects of nonlinearity, complexity and randomness, and their implications for economics. A theme of the book is that economics should be based on algorithmic, computable mathematical foundations. Features an interdisciplinary collection of papers by economists, scientists, and philosophers Presents new approaches to macroeconomic modelling, agent-based modelling, financial markets, and emergent complexity Reveals how economics today must be based on algorithmic, computable mathematical foundations
Author: Dines Bjørner
Publisher: Springer Science & Business Media
ISBN: 3540312889
Category : Computers
Languages : en
Pages : 736
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Book Description
The art, craft, discipline, logic, practice, and science of developing large-scale software products needs a believable, professional base. The textbooks in this three-volume set combine informal, engineeringly sound practice with the rigour of formal, mathematics-based approaches. Volume 1 covers the basic principles and techniques of formal methods abstraction and modelling. First this book provides a sound, but simple basis of insight into discrete mathematics: numbers, sets, Cartesians, types, functions, the Lambda Calculus, algebras, and mathematical logic. Then it trains its readers in basic property- and model-oriented specification principles and techniques. The model-oriented concepts that are common to such specification languages as B, VDM-SL, and Z are explained here using the RAISE specification language (RSL). This book then covers the basic principles of applicative (functional), imperative, and concurrent (parallel) specification programming. Finally, the volume contains a comprehensive glossary of software engineering, and extensive indexes and references. These volumes are suitable for self-study by practicing software engineers and for use in university undergraduate and graduate courses on software engineering. Lecturers will be supported with a comprehensive guide to designing modules based on the textbooks, with solutions to many of the exercises presented, and with a complete set of lecture slides.
Author: Osvaldo Gervasi
Publisher: Springer Nature
ISBN: 3031371054
Category : Computers
Languages : en
Pages : 781
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Book Description
This nine-volume set LNCS 14104 – 14112 constitutes the refereed workshop proceedings of the 23rd International Conference on Computational Science and Its Applications, ICCSA 2023, held at Athens, Greece, during July 3–6, 2023. The 350 full papers and 29 short papers and 2 PHD showcase papers included in this volume were carefully reviewed and selected from a total of 876 submissions. These nine-volumes includes the proceedings of the following workshops: Advances in Artificial Intelligence Learning Technologies: Blended Learning, STEM, Computational Thinking and Coding (AAILT 2023); Advanced Processes of Mathematics and Computing Models in Complex Computational Systems (ACMC 2023); Artificial Intelligence supported Medical data examination (AIM 2023); Advanced and Innovative web Apps (AIWA 2023); Assessing Urban Sustainability (ASUS 2023); Advanced Data Science Techniques with applications in Industry and Environmental Sustainability (ATELIERS 2023); Advances in Web Based Learning (AWBL 2023); Blockchain and Distributed Ledgers: Technologies and Applications (BDLTA 2023); Bio and Neuro inspired Computing and Applications (BIONCA 2023); Choices and Actions for Human Scale Cities: Decision Support Systems (CAHSC-DSS 2023); and Computational and Applied Mathematics (CAM 2023).
Author: Hugh G. Gauch
Publisher: Cambridge University Press
ISBN: 9780521017084
Category : Science
Languages : en
Pages : 458
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Book Description
As the gateway to scientific thinking, an understanding of the scientific method is essential for success and productivity in science. This book is the first synthesis of the practice and the philosophy of the scientific method. It will enable scientists to be better scientists by offering them a deeper understanding of the underpinnings of the scientific method, thereby leading to more productive research and experimentation. It will also give scientists a more accurate perspective on the rationality of the scientific approach and its role in society. Beginning with a discussion of today's 'science wars' and science's presuppositions, the book then explores deductive and inductive logic, probability, statistics, and parsimony, and concludes with an examination of science's powers and limits, and a look at science education. Topics relevant to a variety of disciplines are treated, and clarifying figures, case studies, and chapter summaries enhance the pedagogy. This adeptly executed, comprehensive, yet pragmatic work yields a new synergy suitable for scientists and instructors, and graduate students and advanced undergraduates.
