Taking the "Oof! " Out of Proofs, Draganov, Alexandr
Автор: Lakatos Название: Proofs and Refutations ISBN: 1107534054 ISBN-13(EAN): 9781107534056 Издательство: Cambridge Academ Рейтинг: Цена: 3326.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Imre Lakatos`s influential and enduring work on the nature of mathematic discovery and development continues to be relevant to philosophers of mathematics. Including a specially commissioned preface written by Paolo Mancosu, and presented in a fresh twenty-first-century series livery, it is now available for a new generation of readers.
Автор: Mancosu, Paolo (uc Berkeley) Galvan, Sergio (catholic University Of Milan) Zach, Richard (university Of Calgary) Название: Introduction to proof theory ISBN: 019289594X ISBN-13(EAN): 9780192895943 Издательство: Oxford Academ Рейтинг: Цена: 3960.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: An Introduction to Proof Theory provides an accessible introduction to the theory of proofs, with details of proofs worked out and examples and exercises to aid the reader`s understanding.
Автор: Stillwell John Название: Reverse Mathematics: Proofs from the Inside Out ISBN: 0691196419 ISBN-13(EAN): 9780691196411 Издательство: Wiley Рейтинг: Цена: 2850.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
The first book surveying the history and ideas behind reverse mathematics
Reverse mathematics is a new field that seeks to find the axioms needed to prove given theorems. In Reverse Mathematics, John Stillwell offers a historical and representative view, emphasizing basic analysis and giving a novel approach to logic. 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: Stillwell John Название: Reverse Mathematics: Proofs from the Inside Out ISBN: 0691177171 ISBN-13(EAN): 9780691177175 Издательство: Wiley Рейтинг: Цена: 3485.00 р. Наличие на складе: Поставка под заказ.
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: Kuznets Roman, Studer Thomas Название: Logics of Proofs and Justifications ISBN: 1848901682 ISBN-13(EAN): 9781848901681 Издательство: Неизвестно Рейтинг: Цена: 4230.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
Justification logics are closely related to modal logics and can be viewed as a refinement of the latter with machinery for justification manipulation. Justifications are represented directly in the language by terms, which can be interpreted as formal proofs in a deductive system, evidence for knowledge, winning strategy in a game, etc. This more expressive language proved beneficial in both proof theory and epistemology and helped investigate problems ranging from a classical provability semantics for intuitionistic logic to the logical omniscience problem.
Justification logic is a new and fast evolving field that offers unexpected new approaches and insights into old problems. Its position at the junction of mathematics, philosophy, and computer science makes it of interest to a wide audience.
This book provides a rigorous introduction to justification logic. It covers the basic constructions of justification logic as well as epistemic models and provability semantics. Further it includes chapters on decidability and complexity of justification logics as well as a chapter on self-referentiality. It also contains detailed historic remarks on the subject.
Автор: K. Kunen Название: Set Theory An Introduction To Independence Proofs, ISBN: 0444868399 ISBN-13(EAN): 9780444868398 Издательство: Elsevier Science Рейтинг: Цена: 8420.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Studies in Logic and the Foundations of Mathematics, Volume 102: Set Theory: An Introduction to Independence Proofs offers an introduction to relative consistency proofs in axiomatic set theory, including combinatorics, sets, trees, and forcing. The book first tackles the foundations of set theory and infinitary combinatorics. Discussions focus on the Suslin problem, Martin's axiom, almost disjoint and quasi-disjoint sets, trees, extensionality and comprehension, relations, functions, and well-ordering, ordinals, cardinals, and real numbers. The manuscript then ponders on well-founded sets and easy consistency proofs, including relativization, absoluteness, reflection theorems, properties of well-founded sets, and induction and recursion on well-founded relations. The publication examines constructible sets, forcing, and iterated forcing. Topics include Easton forcing, general iterated forcing, Cohen model, forcing with partial functions of larger cardinality, forcing with finite partial functions, and general extensions. The manuscript is a dependable source of information for mathematicians and researchers interested in set theory.
Описание: This text makes a great supplement and provides a systematic approach for teaching undergraduate and graduate students how to read, understand, think about, and do proofs.
Автор: Cooper S. Barry, Truss John K., Hitchin N. J. Название: Sets and Proofs ISBN: 0521635497 ISBN-13(EAN): 9780521635493 Издательство: Cambridge Academ Рейтинг: Цена: 8710.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book and its sister volume, Models and Computability, provide readers with a comprehensive guide to the mathematical logic. All the authors are leaders in their fields and are drawn from invited speakers at `Logic Colloquium `97` (the major international meeting of the Association of Symbolic Logic).
Автор: Sylvie, Boldo Название: Computer arithmetic and Formal Proofs ISBN: 1785481126 ISBN-13(EAN): 9781785481123 Издательство: Elsevier Science Рейтинг: Цена: 22570.00 р. Наличие на складе: Нет в наличии.
Описание:
Floating-point arithmetic is ubiquitous in modern computing, as it is the tool of choice to approximate real numbers. Due to its limited range and precision, its use can become quite involved and potentially lead to numerous failures. One way to greatly increase confidence in floating-point software is by computer-assisted verification of its correctness proofs.
This book provides a comprehensive view of how to formally specify and verify tricky floating-point algorithms with the Coq proof assistant. It describes the Flocq formalization of floating-point arithmetic and some methods to automate theorem proofs. It then presents the specification and verification of various algorithms, from error-free transformations to a numerical scheme for a partial differential equation. The examples cover not only mathematical algorithms but also C programs as well as issues related to compilation.
Автор: Stewart David & Oliveira Suely Название: Building Proofs: A Practical Guide ISBN: 9814641308 ISBN-13(EAN): 9789814641302 Издательство: World Scientific Publishing Рейтинг: Цена: 3168.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
This book introduces students to the art and craft of writing proofs, beginning with the basics of writing proofs and logic, and continuing on with more in-depth issues and examples of creating proofs in different parts of mathematics, as well as introducing proofs-of-correctness for algorithms. The creation of proofs is covered for theorems in both discrete and continuous mathematics, and in difficulty ranging from elementary to beginning graduate level.
Just beyond the standard introductory courses on calculus, theorems and proofs become central to mathematics. Students often find this emphasis difficult and new. This book is a guide to understanding and creating proofs. It explains the standard "moves" in mathematical proofs: direct computation, expanding definitions, proof by contradiction, proof by induction, as well as choosing notation and strategies.
Автор: Stewart David & Oliveira Suely Название: Building Proofs: A Practical Guide ISBN: 9814641294 ISBN-13(EAN): 9789814641296 Издательство: World Scientific Publishing Рейтинг: Цена: 7603.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
This book introduces students to the art and craft of writing proofs, beginning with the basics of writing proofs and logic, and continuing on with more in-depth issues and examples of creating proofs in different parts of mathematics, as well as introducing proofs-of-correctness for algorithms. The creation of proofs is covered for theorems in both discrete and continuous mathematics, and in difficulty ranging from elementary to beginning graduate level.
Just beyond the standard introductory courses on calculus, theorems and proofs become central to mathematics. Students often find this emphasis difficult and new. This book is a guide to understanding and creating proofs. It explains the standard "moves" in mathematical proofs: direct computation, expanding definitions, proof by contradiction, proof by induction, as well as choosing notation and strategies.
Автор: Roberts Название: Introduction to Mathematical Proofs, Second Edition ISBN: 1482246872 ISBN-13(EAN): 9781482246872 Издательство: Taylor&Francis Рейтинг: Цена: 15312.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
Introduction to Mathematical Proofs helps students develop the necessary skills to write clear, correct, and concise proofs.
Unlike similar textbooks, this one begins with logic since it is the underlying language of mathematics and the basis of reasoned arguments. The text then discusses deductive mathematical systems and the systems of natural numbers, integers, rational numbers, and real numbers.
It also covers elementary topics in set theory, explores various properties of relations and functions, and proves several theorems using induction. The final chapters introduce the concept of cardinalities of sets and the concepts and proofs of real analysis and group theory. In the appendix, the author includes some basic guidelines to follow when writing proofs.
This new edition includes more than 125 new exercises in sections titled More Challenging Exercises. Also, numerous examples illustrate in detail how to write proofs and show how to solve problems. These examples can serve as models for students to emulate when solving exercises.
Several biographical sketches and historical comments have been included to enrich and enliven the text. Written in a conversational style, yet maintaining the proper level of mathematical rigor, this accessible book teaches students to reason logically, read proofs critically, and write valid mathematical proofs. It prepares them to succeed in more advanced mathematics courses, such as abstract algebra and analysis.
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