People, Problems, and Proofs, Richard J. Lipton; Kenneth W. Regan

Автор: Stillwell John
Название: Reverse Mathematics: Proofs from the Inside Out
ISBN: 0691177171 ISBN-13(EAN): 9780691177175
Издательство: Wiley
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Цена: 23230.00 T
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Описание:

This book presents reverse mathematics to a general mathematical audience for the first time. Reverse mathematics is a new field that answers some old questions. In the two thousand years that mathematicians have been deriving theorems from axioms, it has often been asked: which axioms are needed to prove a given theorem? Only in the last two hundred years have some of these questions been answered, and only in the last forty years has a systematic approach been developed. In Reverse Mathematics, John Stillwell gives a representative view of this field, emphasizing basic analysis--finding the "right axioms" to prove fundamental theorems--and giving a novel approach to logic.

Stillwell introduces reverse mathematics historically, describing the two developments that made reverse mathematics possible, both involving the idea of arithmetization. The first was the nineteenth-century project of arithmetizing analysis, which aimed to define all concepts of analysis in terms of natural numbers and sets of natural numbers. The second was the twentieth-century arithmetization of logic and computation. Thus arithmetic in some sense underlies analysis, logic, and computation. Reverse mathematics exploits this insight by viewing analysis as arithmetic extended by axioms about the existence of infinite sets. Remarkably, only a small number of axioms are needed for reverse mathematics, and, for each basic theorem of analysis, Stillwell finds the "right axiom" to prove it.

By using a minimum of mathematical logic in a well-motivated way, Reverse Mathematics will engage advanced undergraduates and all mathematicians interested in the foundations of mathematics.

Автор: Richard J. Lipton; Kenneth W. Regan
Название: People, Problems, and Proofs
ISBN: 3662523019 ISBN-13(EAN): 9783662523018
Издательство: Springer
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Цена: 41920.00 T
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Описание: This book offers insights into theoretical computer science and mathematics, distilling complex topics into manageable essays that summarize and explain key developments, historical context, and future directions of complexity, computability and algorithms.

Автор: Gilles Dowek
Название: Proofs and Algorithms: Introduction to Logic and Computability Theory
ISBN: 0857291203 ISBN-13(EAN): 9780857291202
Издательство: Springer
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Цена: 32560.00 T
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Описание: Logic is a branch of philosophy, mathematics and computer science. It studies the required methods to determine whether a statement is true, such as reasoning and computation.Proofs and Algorithms: Introduction to Logic and Computability is an introduction to the fundamental concepts of contemporary logic - those of a proof, a computable function, a model and a set. It presents a series of results, both positive and negative, - Church's undecidability theorem, G?del’s incompleteness theorem, the theorem asserting the semi-decidability of provability - that have profoundly changed our vision of reasoning, computation, and finally truth itself.Designed for undergraduate students, this book presents all that philosophers, mathematicians and computer scientists should know about logic.

Автор: Mauricio Ayala Rincon
Название: Applied logic for computer scientists. Computational Deduction and formal Proofs
ISBN: 3319516515 ISBN-13(EAN): 9783319516516
Издательство: Springer
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Цена: 41920.00 T
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Описание: A strong mathematical foundation of the logical engines available in modern proof assistants, such as the PVS verification system, is essential for computer scientists, mathematicians and engineers to increment their capabilities to provide formal proofs of theorems and to certify the robustness of software and hardware systems.

Автор: Margus Veanes; Luca Vigano
Название: Tests and Proofs
ISBN: 3642389155 ISBN-13(EAN): 9783642389153
Издательство: Springer
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Цена: 42860.00 T
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Описание: This book constitutes the refereed proceedings of the 7th International Conference on Test and Proofs, TAP 2013, held in Budapest, Hungary, in June 2013, as part of the STAF 2013 Federated Conferences.

Автор: Chris Hawblitzel; Dale Miller
Название: Certified Programs and Proofs
ISBN: 364235307X ISBN-13(EAN): 9783642353079
Издательство: Springer
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Цена: 46570.00 T
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Описание: This book constitutes the refereed proceedings of the Second International Conference on Certified Programs and Proofs, CPP 2012, held in Kyoto, Japan, in December 2012. They deal with those topics in computer science and mathematics in which certification via formal techniques is crucial.

Автор: Georges Gonthier; Michael Norrish
Название: Certified Programs and Proofs
ISBN: 3319035444 ISBN-13(EAN): 9783319035444
Издательство: Springer
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Цена: 46570.00 T
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Описание: This book constitutes the refereed proceedings of the Third International Conference on Certified Programs and Proofs, CPP 2013, colocated with APLAS 2013 held in Melbourne, Australia, in December 2013. The papers are organized in topical sections on code verification, elegant proofs, proof libraries, certified transformations and security.

Автор: Oded Goldreich
Название: Modern Cryptography, Probabilistic Proofs and Pseudorandomness
ISBN: 364208432X ISBN-13(EAN): 9783642084324
Издательство: Springer
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Цена: 121110.00 T
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Описание: Cryptography is one of the most active areas in current mathematics research and applications. This book focuses on cryptography along with two related areas: the study of probabilistic proof systems, and the theory of computational pseudorandomness.

Автор: Jean-Christophe Filliatre; Christine Paulin-Mohrin
Название: Types for Proofs and Programs
ISBN: 3540314288 ISBN-13(EAN): 9783540314288
Издательство: Springer
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Цена: 65210.00 T
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Описание: The 17 revised full papers presented here cover all current issues of formal reasoning and computer programming based on type theory are addressed; in particular languages and computerised tools for reasoning, and applications in several domains such as analysis of programming languages, certified software, formalisation of mathematics and mathematics education.

Автор: Stefano Berardi; Ferruccio Damiani; Ugo de Liguoro
Название: Types for Proofs and Programs
ISBN: 3642024432 ISBN-13(EAN): 9783642024436
Издательство: Springer
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Цена: 65210.00 T
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Описание: These proceedings contain a selection of refereed papers presented at or - lated to the Annual Workshop of the TYPES project (EU coordination action 510996), which was held during March 26-29, 2008 in Turin, Italy.

Автор: Fernando Ferreira; Benedikt L?we; Elvira Mayordomo
Название: Programs, Proofs, Processes
ISBN: 3642139612 ISBN-13(EAN): 9783642139611
Издательство: Springer
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Цена: 83850.00 T
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Описание: Constitutes the refereed proceedings of the 6th Conference on Computability in Europe, CiE 2010, held in Ponta Delgada, Azores, Portugal, in June/July 2010.

Автор: Gordon Fraser; Angelo Gargantini
Название: Tests and Proofs
ISBN: 3642139760 ISBN-13(EAN): 9783642139765
Издательство: Springer
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Цена: 65210.00 T
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Описание: Today, m- ern test systems rely on techniques deeply rooted in formal proof techniques, and testing techniques make it possible to apply proof techniques where there was no possibility previously.