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Author: Mi Lu
Publisher: John Wiley & Sons
ISBN: 0471726214
Category : Computers
Languages : en
Pages : 270
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Book Description
Arithmetic and Logic in Computer Systems provides a useful guide to a fundamental subject of computer science and engineering. Algorithms for performing operations like addition, subtraction, multiplication, and division in digital computer systems are presented, with the goal of explaining the concepts behind the algorithms, rather than addressing any direct applications. Alternative methods are examined, and explanations are supplied of the fundamental materials and reasoning behind theories and examples. No other current books deal with this subject, and the author is a leading authority in the field of computer arithmetic. The text introduces the Conventional Radix Number System and the Signed-Digit Number System, as well as Residue Number System and Logarithmic Number System. This book serves as an essential, up-to-date guide for students of electrical engineering and computer and mathematical sciences, as well as practicing engineers and computer scientists involved in the design, application, and development of computer arithmetic units.
Author: Mi Lu
Publisher: John Wiley & Sons
ISBN: 0471726214
Category : Computers
Languages : en
Pages : 270
Get Book Here
Book Description
Arithmetic and Logic in Computer Systems provides a useful guide to a fundamental subject of computer science and engineering. Algorithms for performing operations like addition, subtraction, multiplication, and division in digital computer systems are presented, with the goal of explaining the concepts behind the algorithms, rather than addressing any direct applications. Alternative methods are examined, and explanations are supplied of the fundamental materials and reasoning behind theories and examples. No other current books deal with this subject, and the author is a leading authority in the field of computer arithmetic. The text introduces the Conventional Radix Number System and the Signed-Digit Number System, as well as Residue Number System and Logarithmic Number System. This book serves as an essential, up-to-date guide for students of electrical engineering and computer and mathematical sciences, as well as practicing engineers and computer scientists involved in the design, application, and development of computer arithmetic units.
Author: Jan Krajicek
Publisher: Cambridge University Press
ISBN: 0521452058
Category : Computers
Languages : en
Pages : 361
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Book Description
Discusses the deep connections between logic and complexity theory, and lists a number of intriguing open problems.
Author: Zofia Adamowicz
Publisher: John Wiley & Sons
ISBN: 1118030796
Category : Mathematics
Languages : en
Pages : 276
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Book Description
A thorough, accessible, and rigorous presentation of the central theorems of mathematical logic . . . ideal for advanced students of mathematics, computer science, and logic Logic of Mathematics combines a full-scale introductory course in mathematical logic and model theory with a range of specially selected, more advanced theorems. Using a strict mathematical approach, this is the only book available that contains complete and precise proofs of all of these important theorems: * Gödel's theorems of completeness and incompleteness * The independence of Goodstein's theorem from Peano arithmetic * Tarski's theorem on real closed fields * Matiyasevich's theorem on diophantine formulas Logic of Mathematics also features: * Full coverage of model theoretical topics such as definability, compactness, ultraproducts, realization, and omission of types * Clear, concise explanations of all key concepts, from Boolean algebras to Skolem-Löwenheim constructions and other topics * Carefully chosen exercises for each chapter, plus helpful solution hints At last, here is a refreshingly clear, concise, and mathematically rigorous presentation of the basic concepts of mathematical logic-requiring only a standard familiarity with abstract algebra. Employing a strict mathematical approach that emphasizes relational structures over logical language, this carefully organized text is divided into two parts, which explain the essentials of the subject in specific and straightforward terms. Part I contains a thorough introduction to mathematical logic and model theory-including a full discussion of terms, formulas, and other fundamentals, plus detailed coverage of relational structures and Boolean algebras, Gödel's completeness theorem, models of Peano arithmetic, and much more. Part II focuses on a number of advanced theorems that are central to the field, such as Gödel's first and second theorems of incompleteness, the independence proof of Goodstein's theorem from Peano arithmetic, Tarski's theorem on real closed fields, and others. No other text contains complete and precise proofs of all of these theorems. With a solid and comprehensive program of exercises and selected solution hints, Logic of Mathematics is ideal for classroom use-the perfect textbook for advanced students of mathematics, computer science, and logic.
Author: H.-D. Ebbinghaus
Publisher: Springer Science & Business Media
ISBN: 1475723555
Category : Mathematics
Languages : en
Pages : 290
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Book Description
This introduction to first-order logic clearly works out the role of first-order logic in the foundations of mathematics, particularly the two basic questions of the range of the axiomatic method and of theorem-proving by machines. It covers several advanced topics not commonly treated in introductory texts, such as Fraïssé's characterization of elementary equivalence, Lindström's theorem on the maximality of first-order logic, and the fundamentals of logic programming.
Author: George Tourlakis
Publisher: Cambridge University Press
ISBN: 9780521168489
Category : Mathematics
Languages : en
Pages : 0
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Book Description
Volume II, on formal (ZFC) set theory, incorporates a self-contained "chapter 0" on proof techniques so that it is based on formal logic, in the style of Bourbaki. The emphasis on basic techniques provides a solid foundation in set theory and a thorough context for the presentation of advanced topics (such as absoluteness, relative consistency results, two expositions of Godel's construstive universe, numerous ways of viewing recursion and Cohen forcing).
Author: Nik Weaver
Publisher: World Scientific
ISBN: 9814566020
Category : Mathematics
Languages : en
Pages : 153
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Book Description
Ever since Paul Cohen's spectacular use of the forcing concept to prove the independence of the continuum hypothesis from the standard axioms of set theory, forcing has been seen by the general mathematical community as a subject of great intrinsic interest but one that is technically so forbidding that it is only accessible to specialists. In the past decade, a series of remarkable solutions to long-standing problems in C*-algebra using set-theoretic methods, many achieved by the author and his collaborators, have generated new interest in this subject. This is the first book aimed at explaining forcing to general mathematicians. It simultaneously makes the subject broadly accessible by explaining it in a clear, simple manner, and surveys advanced applications of set theory to mainstream topics.
Author: Yu. I. Manin
Publisher: Springer Science & Business Media
ISBN: 1441906150
Category : Mathematics
Languages : en
Pages : 389
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Book Description
1. The ?rst edition of this book was published in 1977. The text has been well received and is still used, although it has been out of print for some time. In the intervening three decades, a lot of interesting things have happened to mathematical logic: (i) Model theory has shown that insights acquired in the study of formal languages could be used fruitfully in solving old problems of conventional mathematics. (ii) Mathematics has been and is moving with growing acceleration from the set-theoretic language of structures to the language and intuition of (higher) categories, leaving behind old concerns about in?nities: a new view of foundations is now emerging. (iii) Computer science, a no-nonsense child of the abstract computability theory, has been creatively dealing with old challenges and providing new ones, such as the P/NP problem. Planning additional chapters for this second edition, I have decided to focus onmodeltheory,the conspicuousabsenceofwhichinthe ?rsteditionwasnoted in several reviews, and the theory of computation, including its categorical and quantum aspects. The whole Part IV: Model Theory, is new. I am very grateful to Boris I. Zilber, who kindly agreed to write it. It may be read directly after Chapter II. The contents of the ?rst edition are basically reproduced here as Chapters I–VIII. Section IV.7, on the cardinality of the continuum, is completed by Section IV.7.3, discussing H. Woodin’s discovery.
Author: Stephen Cole Kleene
Publisher: Courier Corporation
ISBN: 0486317072
Category : Mathematics
Languages : en
Pages : 436
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Book Description
Contents include an elementary but thorough overview of mathematical logic of 1st order; formal number theory; surveys of the work by Church, Turing, and others, including Gödel's completeness theorem, Gentzen's theorem, more.
Author: Wolfgang Rautenberg
Publisher: Springer
ISBN: 1441912215
Category : Mathematics
Languages : en
Pages : 337
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Book Description
Mathematical logic developed into a broad discipline with many applications in mathematics, informatics, linguistics and philosophy. This text introduces the fundamentals of this field, and this new edition has been thoroughly expanded and revised.
Author: J. Barkley Rosser
Publisher: Courier Dover Publications
ISBN: 0486468984
Category : Mathematics
Languages : en
Pages : 587
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Book Description
Examination of essential topics and theorems assumes no background in logic. "Undoubtedly a major addition to the literature of mathematical logic." — Bulletin of the American Mathematical Society. 1978 edition.
