Problems and Theorems in Classical Set Theory, Komj?th
Автор: Kechris Название: Classical Descriptive Set Theory ISBN: 0387943749 ISBN-13(EAN): 9780387943749 Издательство: Springer Рейтинг: Цена: 8903 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Descriptive set theory has been one of the main areas of research in set theory for almost a century. This text attempts to present a largely balanced approach, which combines many elements of the different traditions of the subject. It includes a wide variety of examples, exercises (over 400), and applications, in order to illustrate the general concepts and results of the theory. This text provides a first basic course in classical descriptive set theory and covers material with which mathematicians interested in the subject for its own sake or those that wish to use it in their field should be familiar. Over the years, researchers in diverse areas of mathematics, such as logic and set theory, analysis, topology, probability theory, etc., have brought to the subject of descriptive set theory their own intuitions, concepts, terminology and notation.
Описание: Problems in Set Theory, Mathematical Logic and the Theory of Algorithms by I. Lavrov & L. Maksimova is an English translation of the fourth edition of the most popular student problem book in mathematical logic in Russian. It covers major classical topics in proof theory and the semantics of propositional and predicate logic as well as set theory and computation theory. Each chapter begins with 1-2 pages of terminology and definitions that make the book self-contained. Solutions are provided. The book is likely to become an essential part of curricula in logic.
Автор: P. Odifreddi Название: Classical Recursion Theory, ISBN: 0444894837 ISBN-13(EAN): 9780444894830 Издательство: Elsevier Science Рейтинг: Цена: 11130 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Includes a number of applications to logic (in particular Godel`s theorems) and to computer science, for which Recursion Theory provides the theoretical foundation. This book presents a comprehensive reference for the subject starting from first principles.
Описание: This book presents a clear, systematic treatment of convergence theorems of set-valued random variables (random sets) and fuzzy set-valued random variables (random fuzzy sets). Topics such as strong laws of large numbers and central limit theorems, including new results in connection with the theory of empirical processes are covered. The author's own recent developments on martingale convergence theorems and their applications to data processing are also included. The mathematical foundations along with a clear explanation such as HГ¶lmander's embedding theorem, notions of various convergence of sets and fuzzy sets, Aumann integrals, conditional expectations, selection theorems, measurability and integrability arguments for both set-valued and fuzzy set-valued random variables and newly obtained optimizations techniques based on invariant properties are also given.
Автор: Peter Smith Название: An Introduction to G?del`s Theorems ISBN: 0521674530 ISBN-13(EAN): 9780521674539 Издательство: Cambridge Academ Рейтинг: Цена: 3071 р. Наличие на складе: Поставка под заказ.
Описание: In 1931, the young Kurt G?del published his First Incompleteness Theorem, which tells us that, for any sufficiently rich theory of arithmetic, there are some arithmetical truths the theory cannot prove. This remarkable result is among the most intriguing (and most misunderstood) in logic. G?del also outlined an equally significant Second Incompleteness Theorem. How are these Theorems established, and why do they matter? Peter Smith answers these questions by presenting an unusual variety of proofs for the First Theorem, showing how to prove the Second Theorem, and exploring a family of related results (including some not easily available elsewhere). The formal explanations are interwoven with discussions of the wider significance of the two Theorems. This book will be accessible to philosophy students with a limited formal background. It is equally suitable for mathematics students taking a first course in mathematical logic.
Описание: Eigenvectors of graph Laplacians have not, to date, been the subject of expository articles and thus they may seem a surprising topic for a book. The authors propose two motivations for this new LNM volume: (1) There are fascinating subtle differences between the properties of solutions of SchrГ¶dinger equations on manifolds on the one hand, and their discrete analogs on graphs. (2) вЂњGeometricвЂќ properties of (cost) functions defined on the vertex sets of graphs are of practical interest for heuristic optimization algorithms. The observation that the cost functions of quite a few of the well-studied combinatorial optimization problems are eigenvectors of associated graph Laplacians has prompted the investigation of such eigenvectors.The volume investigates the structure of eigenvectors and looks at the number of their sign graphs (вЂњnodal domainsвЂќ), Perron components, graphs with extremal properties with respect to eigenvectors. The Rayleigh quotient and rearrangement of graphs form the main methodology.
Автор: Smith Название: An Introduction to G?del`s Theorems ISBN: 1107022843 ISBN-13(EAN): 9781107022843 Издательство: Cambridge Academ Рейтинг: Цена: 12110 р. Наличие на складе: Поставка под заказ.
Описание: In 1931, the young Kurt G?del published his First Incompleteness Theorem, which tells us that, for any sufficiently rich theory of arithmetic, there are some arithmetical truths the theory cannot prove. This remarkable result is among the most intriguing (and most misunderstood) in logic. G?del also outlined an equally significant Second Incompleteness Theorem. How are these Theorems established, and why do they matter? Peter Smith answers these questions by presenting an unusual variety of proofs for the First Theorem, showing how to prove the Second Theorem, and exploring a family of related results (including some not easily available elsewhere). The formal explanations are interwoven with discussions of the wider significance of the two Theorems. This book – extensively rewritten for its second edition – will be accessible to philosophy students with a limited formal background. It is equally suitable for mathematics students taking a first course in mathematical logic.
Описание: Addressing the frustration many students experience as they make the transition from computational mathematics to advanced calculus and algebraic structures, this work equips students with the tools needed to succeed while providing a firm foundation in the axiomatic structure of modern mathematics.
Автор: Marcja Annalisa, Toffalori Carlo Название: A Guide to Classical and Modern Model Theory ISBN: 1402013310 ISBN-13(EAN): 9781402013317 Издательство: Springer Рейтинг: Цена: 15591 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Since its birth, Model Theory has been developing a number of methods and concepts that have their intrinsic relevance, but also provide fruitful and notable applications in various fields of Mathematics. It is a lively and fertile research area which deserves the attention of the mathematical world.This volume: -is easily accessible to young people and mathematicians unfamiliar with logic; -gives a terse historical picture of Model Theory; -introduces the latest developments in the area; -provides 'hands-on' proofs of elimination of quantifiers, elimination of imaginaries and other relevant matters.A Guide to Classical and Modern Model Theory is for trainees and professional model theorists, mathematicians working in Algebra and Geometry and young people with a basic knowledge of logic.
Автор: Andreescu Название: 104 Number Theory Problems ISBN: 0817645276 ISBN-13(EAN): 9780817645274 Издательство: Springer Рейтинг: Цена: 7424 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This challenging problem book is written by renowned US Olympiad coaches, mathematics teachers, and researchers. It develops a multitude of problem-solving skills needed to excel in mathematical contests and in mathematical research in number theory.
Автор: Tedre Название: The Science of Computing ISBN: 1482217694 ISBN-13(EAN): 9781482217698 Издательство: Taylor&Francis Рейтинг: Цена: 7803 р. Наличие на складе: Невозможна поставка.
Описание: The identity of computing has been fiercely debated throughout its short history. Why is it still so hard to define computing as an academic discipline? Is computing a scientific, mathematical, or engineering discipline? By describing the mathematical, engineering, and scientific traditions of computing, The Science of Computing: Shaping a Discipline presents a rich picture of computing from the viewpoints of the field’s champions. The book helps readers understand the debates about computing as a discipline. It explains the context of computing’s central debates and portrays a broad perspective of the discipline. The book first looks at computing as a formal, theoretical discipline that is in many ways similar to mathematics, yet different in crucial ways. It traces a number of discussions about the theoretical nature of computing from the field’s intellectual origins in mathematical logic to modern views of the role of theory in computing. The book then explores the debates about computing as an engineering discipline, from the central technical innovations to the birth of the modern technical paradigm of computing to computing’s arrival as a new technical profession to software engineering gradually becoming an academic discipline. It presents arguments for and against the view of computing as engineering within the context of software production and analyzes the clash between the theoretical and practical mindsets. The book concludes with the view of computing as a science in its own right—not just as a tool for other sciences. It covers the early identity debates of computing, various views of computing as a science, and some famous characterizations of the discipline. It also addresses the experimental computer science debate, the view of computing as a natural science, and the algorithmization of sciences.
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