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Author: Shawn Hedman
Publisher: Oxford University Press on Demand
ISBN: 9780198529811
Category : Mathematics
Languages : en
Pages : 431
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Book Description
"The ability to reason and think in a logical manner forms the basis of learning for most mathematics, computer science, philosophy and logic students. Based on the author's teaching notes at the University of Maryland and aimed at a broad audience, thistext covers the fundamental topics in classical logic in a clear, thorough and accurate style that is accessible to all the above. Covering propositional logic, first-order logic, and second-order logic, as well as proof theory, computability theory, andmodel theory, the text also contains numerous carefully graded exercises and is ideal for a first or refresher course."--BOOK JACKET.
Author: Shawn Hedman
Publisher: Oxford University Press on Demand
ISBN: 9780198529811
Category : Mathematics
Languages : en
Pages : 431
Get Book Here
Book Description
"The ability to reason and think in a logical manner forms the basis of learning for most mathematics, computer science, philosophy and logic students. Based on the author's teaching notes at the University of Maryland and aimed at a broad audience, thistext covers the fundamental topics in classical logic in a clear, thorough and accurate style that is accessible to all the above. Covering propositional logic, first-order logic, and second-order logic, as well as proof theory, computability theory, andmodel theory, the text also contains numerous carefully graded exercises and is ideal for a first or refresher course."--BOOK JACKET.
Author: Mark Verus Lawson
Publisher: CRC Press
ISBN: 135117536X
Category : Mathematics
Languages : en
Pages : 238
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Book Description
A First Course in Logic is an introduction to first-order logic suitable for first and second year mathematicians and computer scientists. There are three components to this course: propositional logic; Boolean algebras; and predicate/first-order, logic. Logic is the basis of proofs in mathematics — how do we know what we say is true? — and also of computer science — how do I know this program will do what I think it will? Surprisingly little mathematics is needed to learn and understand logic (this course doesn't involve any calculus). The real mathematical prerequisite is an ability to manipulate symbols: in other words, basic algebra. Anyone who can write programs should have this ability.
Author: K. Codell Carter
Publisher: Addison-Wesley Longman
ISBN: 9780321277329
Category : Logic
Languages : en
Pages : 0
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Book Description
Providing students with a more understandable introduction to logic without sacrificing rigor, A First Course in Logic presents topics and methods in a highly accessible and integrated manner. By integrating and comparing topics throughout and using the same examples in different chapters, the author shows the utility and limitations of each method of logic. Consistent pedagogical structure helps students learn and study better; the introduction now emphasizes strategies and tactics for applying memorization rules. One-of-a-kind LSAT-type exercises apply logic to pre-professional exams. This Gold Edition of the text now uses more standard notation and has been thoroughly class-tested and revised for absolute accuracy of information.
Author: Michael L. O'Leary
Publisher: John Wiley & Sons
ISBN: 1118548019
Category : Mathematics
Languages : en
Pages : 464
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Book Description
A mathematical introduction to the theory and applications of logic and set theory with an emphasis on writing proofs Highlighting the applications and notations of basic mathematical concepts within the framework of logic and set theory, A First Course in Mathematical Logic and Set Theory introduces how logic is used to prepare and structure proofs and solve more complex problems. The book begins with propositional logic, including two-column proofs and truth table applications, followed by first-order logic, which provides the structure for writing mathematical proofs. Set theory is then introduced and serves as the basis for defining relations, functions, numbers, mathematical induction, ordinals, and cardinals. The book concludes with a primer on basic model theory with applications to abstract algebra. A First Course in Mathematical Logic and Set Theory also includes: Section exercises designed to show the interactions between topics and reinforce the presented ideas and concepts Numerous examples that illustrate theorems and employ basic concepts such as Euclid’s lemma, the Fibonacci sequence, and unique factorization Coverage of important theorems including the well-ordering theorem, completeness theorem, compactness theorem, as well as the theorems of Löwenheim–Skolem, Burali-Forti, Hartogs, Cantor–Schröder–Bernstein, and König An excellent textbook for students studying the foundations of mathematics and mathematical proofs, A First Course in Mathematical Logic and Set Theory is also appropriate for readers preparing for careers in mathematics education or computer science. In addition, the book is ideal for introductory courses on mathematical logic and/or set theory and appropriate for upper-undergraduate transition courses with rigorous mathematical reasoning involving algebra, number theory, or analysis.
Author: Patrick Suppes
Publisher: Courier Corporation
ISBN: 0486150941
Category : Mathematics
Languages : en
Pages : 308
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Book Description
Rigorous introduction is simple enough in presentation and context for wide range of students. Symbolizing sentences; logical inference; truth and validity; truth tables; terms, predicates, universal quantifiers; universal specification and laws of identity; more.
Author: Hung T. Nguyen
Publisher: CRC Press
ISBN: 1420057103
Category : Computers
Languages : en
Pages : 436
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Book Description
A First Course in Fuzzy Logic, Third Edition continues to provide the ideal introduction to the theory and applications of fuzzy logic. This best-selling text provides a firm mathematical basis for the calculus of fuzzy concepts necessary for designing intelligent systems and a solid background for readers to pursue further studies and real-world a
Author: Bruno Poizat
Publisher: Springer Science & Business Media
ISBN: 1441986227
Category : Mathematics
Languages : en
Pages : 472
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Book Description
Translated from the French, this book is an introduction to first-order model theory. Starting from scratch, it quickly reaches the essentials, namely, the back-and-forth method and compactness, which are illustrated with examples taken from algebra. It also introduces logic via the study of the models of arithmetic, and it gives complete but accessible exposition of stability theory.
Author: Shashi Mohan Srivastava
Publisher: Springer Science & Business Media
ISBN: 1461457467
Category : Mathematics
Languages : en
Pages : 207
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Book Description
This is a short, modern, and motivated introduction to mathematical logic for upper undergraduate and beginning graduate students in mathematics and computer science. Any mathematician who is interested in getting acquainted with logic and would like to learn Gödel’s incompleteness theorems should find this book particularly useful. The treatment is thoroughly mathematical and prepares students to branch out in several areas of mathematics related to foundations and computability, such as logic, axiomatic set theory, model theory, recursion theory, and computability. In this new edition, many small and large changes have been made throughout the text. The main purpose of this new edition is to provide a healthy first introduction to model theory, which is a very important branch of logic. Topics in the new chapter include ultraproduct of models, elimination of quantifiers, types, applications of types to model theory, and applications to algebra, number theory and geometry. Some proofs, such as the proof of the very important completeness theorem, have been completely rewritten in a more clear and concise manner. The new edition also introduces new topics, such as the notion of elementary class of structures, elementary diagrams, partial elementary maps, homogeneous structures, definability, and many more.
Author: Nelson P. Lande
Publisher: Hackett Publishing
ISBN: 1624660444
Category : Philosophy
Languages : en
Pages : 500
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Book Description
Many students ask, 'What is the point of learning formal logic?' This book gives them the answer. Using the methods of deductive logic, Nelson Lande introduces each new element in exquisite detail, as he takes students through example after example, proof after proof, explaining the thinking behind each concept. Shaded areas and appendices throughout the book provide explanations and justifications that go beyond the main text, challenging those students who wish to delve deeper, and giving instructors the option of confining their course to the basics, or expanding it, when they wish, to more rigorous levels. Lande encourages students to think for themselves, while at the same time providing them with the level of explanation they need to succeed. It is a rigorous approach presented in a style that is informal, engaging, and accessible. Students will come away with a solid understanding of formal logic and why it is not only important, but also interesting and sometimes even fun. It is a text that brings the human element back into the teaching of logic. --Hans Halvorson, Princeton University
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.
