A Friendly Introduction To Mathematical Logic
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A Friendly Introduction To Mathematical Logic
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Author : Christopher C. Leary
language : en
Publisher: Lulu.com
Release Date : 2015
A Friendly Introduction To Mathematical Logic written by Christopher C. Leary and has been published by Lulu.com this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Computers categories.
At the intersection of mathematics, computer science, and philosophy, mathematical logic examines the power and limitations of formal mathematical thinking. In this expansion of Leary's user-friendly 1st edition, readers with no previous study in the field are introduced to the basics of model theory, proof theory, and computability theory. The text is designed to be used either in an upper division undergraduate classroom, or for self study. Updating the 1st Edition's treatment of languages, structures, and deductions, leading to rigorous proofs of Gödel's First and Second Incompleteness Theorems, the expanded 2nd Edition includes a new introduction to incompleteness through computability as well as solutions to selected exercises.
Mathematical Logic
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Author : George Tourlakis
language : en
Publisher: John Wiley & Sons
Release Date : 2011-03-01
Mathematical Logic written by George Tourlakis and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-01 with Mathematics categories.
A comprehensive and user-friendly guide to the use of logic in mathematical reasoning Mathematical Logic presents a comprehensive introduction to formal methods of logic and their use as a reliable tool for deductive reasoning. With its user-friendly approach, this book successfully equips readers with the key concepts and methods for formulating valid mathematical arguments that can be used to uncover truths across diverse areas of study such as mathematics, computer science, and philosophy. The book develops the logical tools for writing proofs by guiding readers through both the established "Hilbert" style of proof writing, as well as the "equational" style that is emerging in computer science and engineering applications. Chapters have been organized into the two topical areas of Boolean logic and predicate logic. Techniques situated outside formal logic are applied to illustrate and demonstrate significant facts regarding the power and limitations of logic, such as: Logic can certify truths and only truths. Logic can certify all absolute truths (completeness theorems of Post and Gödel). Logic cannot certify all "conditional" truths, such as those that are specific to the Peano arithmetic. Therefore, logic has some serious limitations, as shown through Gödel's incompleteness theorem. Numerous examples and problem sets are provided throughout the text, further facilitating readers' understanding of the capabilities of logic to discover mathematical truths. In addition, an extensive appendix introduces Tarski semantics and proceeds with detailed proofs of completeness and first incompleteness theorems, while also providing a self-contained introduction to the theory of computability. With its thorough scope of coverage and accessible style, Mathematical Logic is an ideal book for courses in mathematics, computer science, and philosophy at the upper-undergraduate and graduate levels. It is also a valuable reference for researchers and practitioners who wish to learn how to use logic in their everyday work.
A First Course In Mathematical Logic And Set Theory
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Author : Michael L. O'Leary
language : en
Publisher: John Wiley & Sons
Release Date : 2015-10-21
A First Course In Mathematical Logic And Set Theory written by Michael L. O'Leary and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-21 with Mathematics categories.
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.
An Introduction To G Del S Theorems
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Author : Peter Smith
language : en
Publisher: Cambridge University Press
Release Date : 2007-07-26
An Introduction To G Del S Theorems written by Peter Smith and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-26 with Mathematics categories.
Peter Smith examines Gödel's Theorems, how they were established and why they matter.
How To Prove It
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Author : Daniel J. Velleman
language : en
Publisher:
Release Date : 2019-07-24
How To Prove It written by Daniel J. Velleman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-24 with Computers categories.
Helps students transition from problem solving to proving theorems, with a new chapter on number theory and over 150 new exercises.
Hilbert S Tenth Problem An Introduction To Logic Number Theory And Computability
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Author : M. Ram Murty
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-05-09
Hilbert S Tenth Problem An Introduction To Logic Number Theory And Computability written by M. Ram Murty and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-09 with Mathematics categories.
Hilbert's tenth problem is one of 23 problems proposed by David Hilbert in 1900 at the International Congress of Mathematicians in Paris. These problems gave focus for the exponential development of mathematical thought over the following century. The tenth problem asked for a general algorithm to determine if a given Diophantine equation has a solution in integers. It was finally resolved in a series of papers written by Julia Robinson, Martin Davis, Hilary Putnam, and finally Yuri Matiyasevich in 1970. They showed that no such algorithm exists. This book is an exposition of this remarkable achievement. Often, the solution to a famous problem involves formidable background. Surprisingly, the solution of Hilbert's tenth problem does not. What is needed is only some elementary number theory and rudimentary logic. In this book, the authors present the complete proof along with the romantic history that goes with it. Along the way, the reader is introduced to Cantor's transfinite numbers, axiomatic set theory, Turing machines, and Gödel's incompleteness theorems. Copious exercises are included at the end of each chapter to guide the student gently on this ascent. For the advanced student, the final chapter highlights recent developments and suggests future directions. The book is suitable for undergraduates and graduate students. It is essentially self-contained.
Mathematics Applied In Information Systems
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Author : Mangey Ram
language : en
Publisher: Bentham Science Publishers
Release Date : 2018-09-12
Mathematics Applied In Information Systems written by Mangey Ram and has been published by Bentham Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-12 with Computers categories.
Recent developments in information science and technology have been possible due to original and timely research contributions containing new results in various fields of applied mathematics. It is also true that advances in information science create opportunities for developing mathematical models further.
18 Unconventional Essays On The Nature Of Mathematics
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Author : Reuben Hersh
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-01-16
18 Unconventional Essays On The Nature Of Mathematics written by Reuben Hersh 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 2006-01-16 with Mathematics categories.
Collection of the most interesting recent writings on the philosophy of mathematics written by highly respected researchers from philosophy, mathematics, physics, and chemistry Interdisciplinary book that will be useful in several fields—with a cross-disciplinary subject area, and contributions from researchers of various disciplines
Introduction To Mathematical Logic Fourth Edition
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Author : Elliott Mendelson
language : en
Publisher: CRC Press
Release Date : 1997-06-01
Introduction To Mathematical Logic Fourth Edition written by Elliott Mendelson and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-06-01 with Mathematics categories.
The Fourth Edition of this long-established text retains all the key features of the previous editions, covering the basic topics of a solid first course in mathematical logic. This edition includes an extensive appendix on second-order logic, a section on set theory with urlements, and a section on the logic that results when we allow models with empty domains. The text contains numerous exercises and an appendix furnishes answers to many of them. Introduction to Mathematical Logic includes: propositional logic first-order logic first-order number theory and the incompleteness and undecidability theorems of Gödel, Rosser, Church, and Tarski axiomatic set theory theory of computability The study of mathematical logic, axiomatic set theory, and computability theory provides an understanding of the fundamental assumptions and proof techniques that form basis of mathematics. Logic and computability theory have also become indispensable tools in theoretical computer science, including artificial intelligence. Introduction to Mathematical Logic covers these topics in a clear, reader-friendly style that will be valued by anyone working in computer science as well as lecturers and researchers in mathematics, philosophy, and related fields.
Logic As Language
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Author : Aribam Uttam Sharma
language : en
Publisher: Walnut Publication
Release Date : 2024-10-05
Logic As Language written by Aribam Uttam Sharma and has been published by Walnut Publication this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-05 with Philosophy categories.
This book is a compilation of lecture notes that the author has employed in introductory Logic classes. It presents the subject as a language—a medium for representing and communicating about the world. The development of argumentation within the framework of Classical Logic follows an introduction to its vocabulary, syntax, and semantics. The truth-tree method is the chosen proof technique, favored for its visual clarity and versatility. Important meta-theoretical results, such as soundness, consistency, and completeness of the introduced language, are discussed informally. Additionally, the book highlights various extensions of this language, the challenges it encounters, and provides a historical overview of its evolution. Exercises and resources for further self-study are also included.