The Basic Laws of Arithmetic: Exposition of the System, Frege Gottlob, Furth Montgomery
Автор: Petr Hajek Название: Metamathematics of First-Order Arithmetic ISBN: 1107168414 ISBN-13(EAN): 9781107168411 Издательство: Cambridge Academ Рейтинг: Цена: 16743.00 р. 23918.00-30% Наличие на складе: Есть (1 шт.) Описание: This much-needed monograph on the metamathematics of first-order arithmetic pays particular attention to subsystems (fragments) of Peano arithmetic and gives the reader a deeper understanding of the role of the axiom schema of induction and of the phenomenon of incompleteness.
Автор: Nelson Edward Название: Predicative Arithmetic. (MN-32): ISBN: 0691610290 ISBN-13(EAN): 9780691610290 Издательство: Wiley Рейтинг: Цена: 5544.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book develops arithmetic without the induction principle, working in theories that are interpretable in Raphael Robinson`s theory Q. Certain inductive formulas, the bounded ones, are interpretable in Q. A mathematically strong, but logically very weak, predicative arithmetic is constructed. Originally published in 1986. The Princeton Legacy
Автор: Sticker Henry Название: How to Calculate Quickly: Full Course in Speed Arithmetic ISBN: 1607964201 ISBN-13(EAN): 9781607964209 Издательство: Неизвестно Рейтинг: Цена: 2068.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Автор: Muller Jean-Michel, Brunie Nicolas, De Dinechin Florent Название: Handbook of Floating-Point Arithmetic ISBN: 3030095134 ISBN-13(EAN): 9783030095130 Издательство: Springer Рейтинг: Цена: 20962.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
This handbook is a definitive guide to the effective use of modern floating-point arithmetic, which has considerably evolved, from the frequently inconsistent floating-point number systems of early computing to the recent IEEE 754-2008 standard. Most of computational mathematics depends on floating-point numbers, and understanding their various implementations will allow readers to develop programs specifically tailored for the standard’s technical features. Algorithms for floating-point arithmetic are presented throughout the book and illustrated where possible by example programs which show how these techniques appear in actual coding and design.
The volume itself breaks its core topic into four parts: the basic concepts and history of floating-point arithmetic; methods of analyzing floating-point algorithms and optimizing them; implementations of IEEE 754-2008 in hardware and software; and useful extensions to the standard floating-point system, such as interval arithmetic, double- and triple-word arithmetic, operations on complex numbers, and formal verification of floating-point algorithms. This new edition updates chapters to reflect recent changes to programming languages and compilers and the new prevalence of GPUs in recent years. The revisions also add material on fused multiply-add instruction, and methods of extending the floating-point precision.
As supercomputing becomes more common, more numerical engineers will need to use number representation to account for trade-offs between various parameters, such as speed, accuracy, and energy consumption. The Handbook of Floating-Point Arithmetic is designed for students and researchers in numerical analysis, programmers of numerical algorithms, compiler designers, and designers of arithmetic operators.
Описание: This book is mostly comprised of six sets of notes for lectures Hilbert gave from 1917 to 1933. The notes cover the development of modern mathematical logic, the evolution of proof theory, and the parallel emergence of Hilbert`s finitist standpoint.
Автор: Bimbo Katalin Название: Proof Theory: Sequent Calculi and Related Formalisms ISBN: 1466564660 ISBN-13(EAN): 9781466564664 Издательство: Taylor&Francis Рейтинг: Цена: 16843.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
Although sequent calculi constitute an important category of proof systems, they are not as well known as axiomatic and natural deduction systems. Addressing this deficiency, Proof Theory: Sequent Calculi and Related Formalisms presents a comprehensive treatment of sequent calculi, including a wide range of variations. It focuses on sequent calculi for various non-classical logics, from intuitionistic logic to relevance logic, linear logic, and modal logic.
In the first chapters, the author emphasizes classical logic and a variety of different sequent calculi for classical and intuitionistic logics. She then presents other non-classical logics and meta-logical results, including decidability results obtained specifically using sequent calculus formalizations of logics.
The book is suitable for a wide audience and can be used in advanced undergraduate or graduate courses. Computer scientists will discover intriguing connections between sequent calculi and resolution as well as between sequent calculi and typed systems. Those interested in the constructive approach will find formalizations of intuitionistic logic and two calculi for linear logic. Mathematicians and philosophers will welcome the treatment of a range of variations on calculi for classical logic. Philosophical logicians will be interested in the calculi for relevance logics while linguists will appreciate the detailed presentation of Lambek calculi and their extensions.
Автор: C. Berline; K. McAloon; J.-P. Ressayre Название: Model Theory and Arithmetic ISBN: 354011159X ISBN-13(EAN): 9783540111597 Издательство: Springer Рейтинг: Цена: 5583.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Автор: L. Pacholski; J Wierzejewski; A.J. Wilkie Название: Model Theory of Algebra and Arithmetic ISBN: 3540102698 ISBN-13(EAN): 9783540102694 Издательство: Springer Рейтинг: Цена: 6282.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Автор: Michael D. Fried; Moshe Jarden Название: Field Arithmetic ISBN: 3540772693 ISBN-13(EAN): 9783540772699 Издательство: Springer Рейтинг: Цена: 22354.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Field Arithmetic explores Diophantine fields through their absolute Galois groups. The treatment starts with techniques from algebraic geometry, number theory, and profinite groups. Graduate students can effectively learn generalizations of finite field ideas.
Автор: Frege Gottlob, Furth Montgomery Название: The Basic Laws of Arithmetic: Exposition of the System ISBN: 0520359070 ISBN-13(EAN): 9780520359079 Издательство: Wiley Рейтинг: Цена: 21841.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book explores the concept of `home` in Liverpool over phases of regeneration from the World War Two. Based on qualitative research in the oral history tradition, it examines both the `forward facing` regeneration period up to the 1980s, and the subsequent neo-liberal regeneration projects that have sought to `prioritise the past`.
Автор: Yong Cheng Название: Incompleteness for Higher-Order Arithmetic ISBN: 9811399484 ISBN-13(EAN): 9789811399480 Издательство: Springer Рейтинг: Цена: 6986.00 р. Наличие на складе: Нет в наличии.
Описание:
G?del's true-but-unprovable sentence from the first incompleteness theorem is purely logical in nature, i.e. not mathematically natural or interesting. An interesting problem is to find mathematically natural and interesting statements that are similarly unprovable. A lot of research has since been done in this direction, most notably by Harvey Friedman. A lot of examples of concrete incompleteness with real mathematical content have been found to date. This brief contributes to Harvey Friedman's research program on concrete incompleteness for higher-order arithmetic and gives a specific example of concrete mathematical theorems which is expressible in second-order arithmetic but the minimal system in higher-order arithmetic to prove it is fourth-order arithmetic.
This book first examines the following foundational question: are all theorems in classic mathematics expressible in second-order arithmetic provable in second-order arithmetic? The author gives a counterexample for this question and isolates this counterexample from the Martin-Harrington Theorem in set theory. It shows that the statement “Harrington's principle implies zero sharp' is not provable in second-order arithmetic. This book further examines what is the minimal system in higher-order arithmetic to prove the theorem “Harrington's principle implies zero sharp' and shows that it is neither provable in second-order arithmetic or third-order arithmetic, but provable in fourth-order arithmetic. The book also examines the large cardinal strength of Harrington's principle and its strengthening over second-order arithmetic and third-order arithmetic.
Alhambra G. Deming's entertaining stories fuse fiction with figures, teaching young readers arithmetic while entertaining them with the adventures of Ralph, an entrepreneurial boy who undertakes odd jobs to support his family.
Number Stories was conceived by Deming as a novel way of engaging children with numeracy and basic mathematics. Through the narrative stories in this book, we learn how to add, subtract, multiply and divide, while concepts such as percentages and fractions are also explained. Techniques of mental arithmetic are also explained, with equations demonstrated in clear and understandable ways.
The narration focuses first on Ralph, a boy whose father is injured at work. Lacking a source of income to cover his Dad's health expenses, Ralph sells newspapers and groceries, makes lemonade, and hands in old clothes as a means of generating money. Later he journeys with his uncle to the family farm, where he learns how the farm business is a matter of calculating the size of fields and harvests. All of these adventures are accompanied by sums.
The later portion of Number Stories takes place in Ralph's school, wherein his classmates are asked to raise money as part of a school project. As with the earlier chapters, the various ideas and novelties of the schoolchildren lead to their learning plenty of arithmetic.
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