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: Поставка под заказ.
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: Kirtland Joseph Название: Proofs 101: An Introduction to Formal Mathematics ISBN: 0367536935 ISBN-13(EAN): 9780367536930 Издательство: Taylor&Francis Рейтинг: Цена: 22202.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book serves as an introduction to proofs for mathematics majors who have completed the calculus sequence (at least Calculus I and II) and Linear Algebra. It prepares students for the proofs they will need to analyse and write, the axiomatic nature of mathematics, and the rigors of upper-level mathematics courses.
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: Jean-Christophe Filliatre; Christine Paulin-Mohrin Название: Types for Proofs and Programs ISBN: 3540314288 ISBN-13(EAN): 9783540314288 Издательство: Springer Рейтинг: Цена: 9781.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
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: 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.
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