Set Theory For Computing
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Set Theory For Computing
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Author : Domenico Cantone
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Set Theory For Computing written by Domenico Cantone and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Computers categories.
An up-to-date and comprehensive account of set-oriented symbolic manipulation and automated reasoning methods. This book is of interest to graduates and researchers in theoretical computer science and computational logic and automated reasoning.
Set Theory And Its Applications In Physics And Computing
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Author : Yair Shapira
language : en
Publisher: World Scientific
Release Date : 2022-06-24
Set Theory And Its Applications In Physics And Computing written by Yair Shapira and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-24 with Science categories.
Why learn set theory? This book provides the answer — it is interesting, and also useful! Taking a new approach and looking from a fresh perspective, the discussion flows in a friendly and transparent way, supplemented with a lot of examples and figures. This makes the theory easily comprehensible: the proofs get vivid and visual, enveloped with interesting applications for students in (applied) math, physics, and engineering. Given the theory and the applications, the book could serve as a textbook in four (undergraduate) math courses: Introduction to set theory and its application; Chaos theory and stability — a geometrical point of view; Functional analysis — Han-Banach theory; and Cryptography with quantum computing. It teaches set theory from the basics, including the axiom of choice, the well ordering theorem, and Zorn's lemma. Furthermore, it uses Cantor's set to introduce chaos theory from a geometrical point of view. Moreover, it introduces the binomial formula (and other related formulas), and uses them in quantum statistical mechanics. And finally, it uses Zorn's lemma in functional analysis, general relativity, and quantum mechanics. There are also practical applications in cryptography, error correction, quantum computing and programming.
Foundations Of Computing
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Author : Thierry Scheurer
language : en
Publisher: Addison-Wesley Longman
Release Date : 1994
Foundations Of Computing written by Thierry Scheurer and has been published by Addison-Wesley Longman this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Computers categories.
Written for professionals learning the field of discrete mathematics, this book provides the necessary foundations of computer science without requiring excessive mathematical prerequisites. Using a balanced approach of theory and examples, software engineers will find it a refreshing treatment of applications in programming.
Sets Logic And Maths For Computing
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Author : David Makinson
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-02-27
Sets Logic And Maths For Computing written by David Makinson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-02-27 with Computers categories.
This easy-to-follow textbook introduces the mathematical language, knowledge and problem-solving skills that undergraduates need to study computing. The language is in part qualitative, with concepts such as set, relation, function and recursion/induction; but it is also partly quantitative, with principles of counting and finite probability. Entwined with both are the fundamental notions of logic and their use for representation and proof. Features: teaches finite math as a language for thinking, as much as knowledge and skills to be acquired; uses an intuitive approach with a focus on examples for all general concepts; brings out the interplay between the qualitative and the quantitative in all areas covered, particularly in the treatment of recursion and induction; balances carefully the abstract and concrete, principles and proofs, specific facts and general perspectives; includes highlight boxes that raise common queries and clear confusions; provides numerous exercises, with selected solutions.
Topics In Rough Set Theory
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Author : Seiki Akama
language : en
Publisher: Springer Nature
Release Date : 2019-09-10
Topics In Rough Set Theory written by Seiki Akama and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-10 with Technology & Engineering categories.
This book discusses current topics in rough set theory. Since Pawlak’s rough set theory was first proposed to offer a basis for imprecise and uncertain data and reasoning from data, many workers have investigated its foundations and applications. Examining various topical issues, including object-oriented rough set models, recommendation systems, decision tables, and granular computing, the book is a valuable resource for students and researchers in the field.
Computational Logic And Set Theory
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Author : Jacob T. Schwartz
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-07-16
Computational Logic And Set Theory written by Jacob T. Schwartz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-16 with Computers categories.
This must-read text presents the pioneering work of the late Professor Jacob (Jack) T. Schwartz on computational logic and set theory and its application to proof verification techniques, culminating in the ÆtnaNova system, a prototype computer program designed to verify the correctness of mathematical proofs presented in the language of set theory. Topics and features: describes in depth how a specific first-order theory can be exploited to model and carry out reasoning in branches of computer science and mathematics; presents an unique system for automated proof verification in large-scale software systems; integrates important proof-engineering issues, reflecting the goals of large-scale verifiers; includes an appendix showing formalized proofs of ordinals, of various properties of the transitive closure operation, of finite and transfinite induction principles, and of Zorn’s lemma.
Foundations Of Set Theory
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Author : A.A. Fraenkel
language : en
Publisher: Elsevier
Release Date : 1973-12-01
Foundations Of Set Theory written by A.A. Fraenkel and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973-12-01 with Computers categories.
Foundations of Set Theory discusses the reconstruction undergone by set theory in the hands of Brouwer, Russell, and Zermelo. Only in the axiomatic foundations, however, have there been such extensive, almost revolutionary, developments. This book tries to avoid a detailed discussion of those topics which would have required heavy technical machinery, while describing the major results obtained in their treatment if these results could be stated in relatively non-technical terms. This book comprises five chapters and begins with a discussion of the antinomies that led to the reconstruction of set theory as it was known before. It then moves to the axiomatic foundations of set theory, including a discussion of the basic notions of equality and extensionality and axioms of comprehension and infinity. The next chapters discuss type-theoretical approaches, including the ideal calculus, the theory of types, and Quine's mathematical logic and new foundations; intuitionistic conceptions of mathematics and its constructive character; and metamathematical and semantical approaches, such as the Hilbert program. This book will be of interest to mathematicians, logicians, and statisticians.
Notes On Set Theory
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Author : Yiannis N. Moschovakis
language : en
Publisher: Springer
Release Date : 1994
Notes On Set Theory written by Yiannis N. Moschovakis and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
"The axiomatic theory of sets is a vibrant part of pure mathematics, with its own basic notions, fundamental results, and deep open problems. At the same time, it is often viewed as a foundation of mathematics so that in the most prevalent, current mathematical practice "to make a notion precise" simply means "to define it in set theory." This book tries to do justice to both aspects of the subject: it gives a solid introduction to "pure set theory" through transfinite recursion and the construction of the cumulative hierarchy of sets (including the basic results that have applications to computer science), but it also attempts to explain precisely how mathematical objects can be faithfully modeled within the universe of sets." "Topics covered include the naive theory of equinumerosity; paradoxes and axioms; modeling mathematical notions by sets; cardinal numbers; natural numbers; fixed points (continuous least-fixed-point theorem); well-ordered sets (transfinite induction and recursion, Hartogs' theorem, comparability of well-ordered sets, least-fixed-point theorem); the Axiom of Choice and its consequences; Baire space (Cantor-Bendixson theorem, analytic pointsets, perfect set theorem); Replacement and other axioms; ordinal numbers. There is an Appendix on the real numbers and another on natural models, including the antifounded universe." "The book is aimed at advanced undergraduate or beginning graduate mathematics students and at mathematically minded graduate students of computer science and philosophy."--BOOK JACKET.
The Joy Of Sets
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Author : Keith Devlin
language : en
Publisher: Springer Science & Business Media
Release Date : 1994-06-24
The Joy Of Sets written by Keith Devlin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-06-24 with Mathematics categories.
This text covers the parts of contemporary set theory relevant to other areas of pure mathematics. After a review of "naïve" set theory, it develops the Zermelo-Fraenkel axioms of the theory before discussing the ordinal and cardinal numbers. It then delves into contemporary set theory, covering such topics as the Borel hierarchy and Lebesgue measure. A final chapter presents an alternative conception of set theory useful in computer science.
Soft Sets
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Author : Sunil Jacob John
language : en
Publisher: Springer Nature
Release Date : 2020-10-01
Soft Sets written by Sunil Jacob John and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-01 with Technology & Engineering categories.
This book offers a self-contained guide to the theory and main applications of soft sets. It introduces readers to the basic concepts, the algebraic and topological structures, as well as hybrid structures, such as fuzzy soft sets and intuitionistic fuzzy sets. The last part of the book explores a range of interesting applications in the fields of decision-making, pattern recognition, and data science. All in all, the book provides graduate students and researchers in mathematics and various applied science fields with a comprehensive and timely reference guide to soft sets.