A Beginner s Guide to Mathematical Logic

A Beginner s Guide to Mathematical Logic

Written by a creative master of mathematical logic, this introductory text combines stories of great philosophers, quotations, and riddles with the fundamentals of mathematical logic.

Author: Raymond M. Smullyan

Publisher: Courier Corporation

ISBN: 9780486492377

Category: Mathematics

Page: 288

View: 996

Written by a creative master of mathematical logic, this introductory text combines stories of great philosophers, quotations, and riddles with the fundamentals of mathematical logic. Author Raymond Smullyan offers clear, incremental presentations of difficult logic concepts. He highlights each subject with inventive explanations and unique problems. Smullyan's accessible narrative provides memorable examples of concepts related to proofs, propositional logic and first-order logic, incompleteness theorems, and incompleteness proofs. Additional topics include undecidability, combinatoric logic, and recursion theory. Suitable for undergraduate and graduate courses, this book will also amuse and enlighten mathematically minded readers. Dover (2014) original publication. See every Dover book in print at www.doverpublications.com
Categories: Mathematics

The Foundations of Computability Theory

The Foundations of Computability Theory

Dover Publications (1995) 239. Smullyan, R.M.: A Beginner's Guide to Mathematical Logic. Dover Books on Mathematics. Dover Publications (2014) 240. Smullyan, R.M., Fitting, M.: Set Theory and the Continuum Hypothesis. Dover Books on ...

Author: Borut Robič

Publisher: Springer Nature

ISBN: 9783662624210

Category: Computers

Page: 422

View: 129

This book offers an original and informative view of the development of fundamental concepts of computability theory. The treatment is put into historical context, emphasizing the motivation for ideas as well as their logical and formal development. In Part I the author introduces computability theory, with chapters on the foundational crisis of mathematics in the early twentieth century, and formalism. In Part II he explains classical computability theory, with chapters on the quest for formalization, the Turing Machine, and early successes such as defining incomputable problems, c.e. (computably enumerable) sets, and developing methods for proving incomputability. In Part III he explains relative computability, with chapters on computation with external help, degrees of unsolvability, the Turing hierarchy of unsolvability, the class of degrees of unsolvability, c.e. degrees and the priority method, and the arithmetical hierarchy. Finally, in the new Part IV the author revisits the computability (Church-Turing) thesis in greater detail. He offers a systematic and detailed account of its origins, evolution, and meaning, he describes more powerful, modern versions of the thesis, and he discusses recent speculative proposals for new computing paradigms such as hypercomputing. This is a gentle introduction from the origins of computability theory up to current research, and it will be of value as a textbook and guide for advanced undergraduate and graduate students and researchers in the domains of computability theory and theoretical computer science. This new edition is completely revised, with almost one hundred pages of new material. In particular the author applied more up-to-date, more consistent terminology, and he addressed some notational redundancies and minor errors. He developed a glossary relating to computability theory, expanded the bibliographic references with new entries, and added the new part described above and other new sections.
Categories: Computers

Logic as a Tool

Logic as a Tool

Smullyan, R. 2014. A Beginner's Guide to Mathematical Logic. Dover Publications, USA, Books on Mathematics. Solow, D. 1990. How to Read and Do Proofs: An Introduction to Mathematical Thought Processes. John Wiley & Sons, New York.

Author: Valentin Goranko

Publisher: John Wiley & Sons

ISBN: 9781118880050

Category: Mathematics

Page: 384

View: 822

Written in a clear, precise and user-friendly style, Logic as a Tool: A Guide to Formal Logical Reasoning is intended for undergraduates in both mathematics and computer science, and will guide them to learn, understand and master the use of classical logic as a tool for doing correct reasoning. It offers a systematic and precise exposition of classical logic with many examples and exercises, and only the necessary minimum of theory. The book explains the grammar, semantics and use of classical logical languages and teaches the reader how grasp the meaning and translate them to and from natural language. It illustrates with extensive examples the use of the most popular deductive systems -- axiomatic systems, semantic tableaux, natural deduction, and resolution -- for formalising and automating logical reasoning both on propositional and on first-order level, and provides the reader with technical skills needed for practical derivations in them. Systematic guidelines are offered on how to perform logically correct and well-structured reasoning using these deductive systems and the reasoning techniques that they employ. •Concise and systematic exposition, with semi-formal but rigorous treatment of the minimum necessary theory, amply illustrated with examples •Emphasis both on conceptual understanding and on developing practical skills •Solid and balanced coverage of syntactic, semantic, and deductive aspects of logic •Includes extensive sets of exercises, many of them provided with solutions or answers •Supplemented by a website including detailed slides, additional exercises and solutions For more information browse the book's website at: https://logicasatool.wordpress.com
Categories: Mathematics

Optimization in Function Spaces

Optimization in Function Spaces

(0-486-47187-X) A BEGINNER'S GUIDE TO MATHEMATICAL LOGIC, Raymond M. Smullyan. (0-486-49237-0) A BOOK OF ABSTRACT ALGEBRA: SECOND EDITION, Charles C. Pinter. (0-486-47417-8) CALCULUS: AN INTUITIVE AND PHYSICAL APPROACH (SECOND EDITION), ...

Author: Amol Sasane

Publisher: Courier Dover Publications

ISBN: 9780486789453

Category: Mathematics

Page: 256

View: 349

Classroom-tested at the London School of Economics, this original, highly readable text offers numerous examples and exercises as well as detailed solutions. Prerequisites are multivariable calculus and basic linear algebra. 2015 edition.
Categories: Mathematics

A First Course in Logic

A First Course in Logic

SmullyanRM. Logical labyrinths. Peters, Ltd: A. K; 2009. R. M. Smullyan, A beginner's guide to mathematical logic, Dover, 2014. A. Sokal, J. Bricmont, Intellectual impostures, Profile Books, 1998. StollRR. Set theory and logic.

Author: Mark Verus Lawson

Publisher: CRC Press

ISBN: 9781351175364

Category: Mathematics

Page: 234

View: 413

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.
Categories: Mathematics

The Theory and Practice of Conformal Geometry

The Theory and Practice of Conformal Geometry

(0-486-47187-X) A beGinner's Guide to MAtheMAticAl loGic, Raymond M. Smullyan. (0-486-49237-0) A book of AbstrAct AlGebrA: second edition, Charles C. Pinter. (0-486-47417-8) cAlculus: An intuitive And physicAl ApproAch (second edition), ...

Author: Steven G. Krantz

Publisher: Courier Dover Publications

ISBN: 9780486810324

Category: Mathematics

Page: 304

View: 956

In this original text, prolific mathematics author Steven G. Krantz addresses conformal geometry, a subject that has occupied him for four decades and for which he helped to develop some of the modern theory. This book takes readers with a basic grounding in complex variable theory to the forefront of some of the current approaches to the topic. "Along the way," the author notes in his Preface, "the reader will be exposed to some beautiful function theory and also some of the rudiments of geometry and analysis that make this subject so vibrant and lively." More up-to-date and accessible to advanced undergraduates than most of the other books available in this specific field, the treatment discusses the history of this active and popular branch of mathematics as well as recent developments. Topics include the Riemann mapping theorem, invariant metrics, normal families, automorphism groups, the Schwarz lemma, harmonic measure, extremal length, analytic capacity, and invariant geometry. A helpful Bibliography and Index complete the text.
Categories: Mathematics

Raymond Smullyan on Self Reference

Raymond Smullyan on Self Reference

Recursion theory for metamathematics. Oxford University Press. Smullyan, R. M. (1994a). Diagonalization and self-reference. Oxford University Press. Smullyan, R. M. (2014a). A beginner's guide to mathematical logic. Dover.

Author: Melvin Fitting

Publisher: Springer

ISBN: 9783319687322

Category: Philosophy

Page: 195

View: 594

This book collects, for the first time in one volume, contributions honoring Professor Raymond Smullyan’s work on self-reference. It serves not only as a tribute to one of the great thinkers in logic, but also as a celebration of self-reference in general, to be enjoyed by all lovers of this field. Raymond Smullyan, mathematician, philosopher, musician and inventor of logic puzzles, made a lasting impact on the study of mathematical logic; accordingly, this book spans the many personalities through which Professor Smullyan operated, offering extensions and re-evaluations of his academic work on self-reference, applying self-referential logic to art and nature, and lastly, offering new puzzles designed to communicate otherwise esoteric concepts in mathematical logic, in the manner for which Professor Smullyan was so well known. This book is suitable for students, scholars and logicians who are interested in learning more about Raymond Smullyan's work and life.
Categories: Philosophy

Elementary Point Set Topology

Elementary Point Set Topology

DOVER BOOKS ON MATHEM ATICS APPLICATIONS OF GREEN's FUNCTIONS IN SCIENCE AND ENGINEERING, Michael D. Greenberg. (O-486-79796-1) APPLIED MATHEMATICS FOR ... (0-486-47187-X) A BEGINNER's GUIDE TO MATHEMATICAL LOGIC, Raymond M. Smullyan.

Author: Andre L. Yandl

Publisher: Courier Dover Publications

ISBN: 9780486803494

Category: Mathematics

Page: 256

View: 847

This versatile, original approach, which focuses on learning to read and write proofs, serves as both an introductory treatment and a bridge between elementary calculus and more advanced courses. 2016 edition.
Categories: Mathematics

Principles of Abstract Interpretation

Principles of Abstract Interpretation

The Two Variable Per Inequality Abstract Domain ” Higher - Order and Symbolic Computation . 23.1 ( 2010 ) , pp . ... A Beginner's Guide to Mathematical Logic . Dover Books on Mathematics , 2014 ( p . 9 ) . pour le problème RCPSP .

Author: Patrick Cousot

Publisher: MIT Press

ISBN: 9780262044905

Category: Computers

Page: 832

View: 920

Introduction to abstract interpretation, with examples of applications to the semantics, specification, verification, and static analysis of computer programs. Formal methods are mathematically rigorous techniques for the specification, development, manipulation, and verification of safe, robust, and secure software and hardware systems. Abstract interpretation is a unifying theory of formal methods that proposes a general methodology for proving the correctness of computing systems, based on their semantics. The concepts of abstract interpretation underlie such software tools as compilers, type systems, and security protocol analyzers. This book provides an introduction to the theory and practice of abstract interpretation, offering examples of applications to semantics, specification, verification, and static analysis of programming languages with emphasis on calculational design. The book covers all necessary computer science and mathematical concepts--including most of the logic, order, linear, fixpoint, and discrete mathematics frequently used in computer science--in separate chapters before they are used in the text. Each chapter offers exercises and selected solutions. Chapter topics include syntax, parsing, trace semantics, properties and their abstraction, fixpoints and their abstractions, reachability semantics, abstract domain and abstract interpreter, specification and verification, effective fixpoint approximation, relational static analysis, and symbolic static analysis. The main applications covered include program semantics, program specification and verification, program dynamic and static analysis of numerical properties and of such symbolic properties as dataflow analysis, software model checking, pointer analysis, dependency, and typing (both for forward and backward analysis), and their combinations. Principles of Abstract Interpretation is suitable for classroom use at the graduate level and as a reference for researchers and practitioners.
Categories: Computers