A Mathematical Introduction to Logic

Author: Herbert Enderton,Herbert B. Enderton

Publisher: Elsevier

ISBN: 0080496466

Category: Mathematics

Page: 317

View: 1911

A Mathematical Introduction to Logic, Second Edition, offers increased flexibility with topic coverage, allowing for choice in how to utilize the textbook in a course. The author has made this edition more accessible to better meet the needs of today's undergraduate mathematics and philosophy students. It is intended for the reader who has not studied logic previously, but who has some experience in mathematical reasoning. Material is presented on computer science issues such as computational complexity and database queries, with additional coverage of introductory material such as sets. * Increased flexibility of the text, allowing instructors more choice in how they use the textbook in courses. * Reduced mathematical rigour to fit the needs of undergraduate students
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A mathematical introduction to logic

Author: Herbert B. Enderton

Publisher: Academic Pr

ISBN: N.A

Category: Mathematics

Page: 295

View: 993

A Mathematical Introduction to Logic, Second Edition, offers increased flexibility with topic coverage, allowing for choice in how to utilize the textbook in a course. The author has made this edition more accessible to better meet the needs of today's undergraduate mathematics and philosophy students. It is intended for the reader who has not studied logic previously, but who has some experience in mathematical reasoning. Material is presented on computer science issues such as computational complexity and database queries, with additional coverage of introductory material such as sets.* Increased flexibility of the text, allowing instructors more choice in how they use the textbook in courses. * Reduced mathematical rigour to fit the needs of undergraduate students
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Principia Mathematica.

Author: Alfred North Whitehead,Bertrand Russell

Publisher: N.A

ISBN: N.A

Category: Logic, Symbolic and mathematical

Page: 167

View: 5487

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Die spezielle Relativitätstheorie

M.I.T. Einführungskurs Physik

Author: Anthony P. French

Publisher: Springer-Verlag

ISBN: 332290122X

Category: Science

Page: 288

View: 5683

Das Education Research Center am M.I. T. (früher: Science Teaching Center) befaßt sich mit Verbesserungen des Lehrplanes, mit dem Lehr- und Lernprozeß sowie mit Unterrichtshilfen, vor allem für die unteren Semester. Das Center wurde im Jahre 1960 vom M.I. T. geschaffen. Sein erster Direktor war der verstorbene Professor Francis L. Friedman. Seit 1961 wurde das Center hauptsächlich von der National Science Foundation unterstützt; großzügige Hilfe wurde auch von den folgenden Fonds gewährt: Kettering Foundation, Shell Companies Foundation, Victoria Foundation, W. T. Grant Foundation und Bing Foundation. Die M.I.T.-Reihe: Einführung ist die Physik (Introductory Physics Series) ist ein direktes Resultat der Arbeit des Centers. Die Reihe wird aus einer Anzahl kurzgefaßter Einführungswerke bestehen, die die wichtigsten Gebiete der Physik behandeln werden. Es soll dabei der wechselseitige Einfluß von Experiment und Intuition bei der Aufstellung physikalischer Theorien betont werden. Die Bücher der Reihe sind als Grundlage für eine Auswahl von Einflihrungskursen gedacht, beginnend mit den Werken, in denen vor allem die klassische Physik behandelt wird, bis zu jenen, dieThemen der Atom- und Quantenphysik behandeln. Die einzelnen Bände sollen in Niveau und Behandlungsweise ihrer Themen zwar ein heitlich sein, sind jedoch nicht als untrennbare Einheit anzusehen; im Gegenteil. Eswurde getrachtet, daß jedes Buch in vernünftigem Maße eine Einheit für sich ist und als individuelle Komponente in den Aufbau eines Kurses einbezogen werden kann .
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Introduction to Mathematical Logic, Fourth Edition

Author: Elliott Mendelson

Publisher: CRC Press

ISBN: 9780412808302

Category: Mathematics

Page: 440

View: 2799

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.
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Naive Mengenlehre

Author: Paul R. Halmos

Publisher: Vandenhoeck & Ruprecht

ISBN: 9783525405277

Category: Arithmetic

Page: 132

View: 9264

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Einführung in die mathematische Logik

Author: Heinz-Dieter Ebbinghaus,Jörg Flum,Wolfgang Thomas

Publisher: Springer Spektrum

ISBN: 9783662580288

Category: Mathematics

Page: 367

View: 4307

Was ist ein mathematischer Beweis? Wie lassen sich Beweise rechtfertigen? Gibt es Grenzen der Beweisbarkeit? Ist die Mathematik widerspruchsfrei? Kann man das Auffinden mathematischer Beweise Computern übertragen? Erst im 20. Jahrhundert ist es der mathematischen Logik gelungen, weitreichende Antworten auf diese Fragen zu geben: Im vorliegenden Werk werden die Ergebnisse systematisch zusammengestellt; im Mittelpunkt steht dabei die Logik erster Stufe. Die Lektüre setzt – außer einer gewissen Vertrautheit mit der mathematischen Denkweise – keine spezifischen Kenntnisse voraus. In der vorliegenden 5. Auflage finden sich erstmals Lösungsskizzen zu den Aufgaben.
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An Introduction to Mathematical Logic

Author: Richard E. Hodel

Publisher: Courier Corporation

ISBN: 0486497852

Category: Mathematics

Page: 491

View: 6327

This comprehensive overview ofmathematical logic is designedprimarily for advanced undergraduatesand graduate studentsof mathematics. The treatmentalso contains much of interest toadvanced students in computerscience and philosophy. Topics include propositional logic;first-order languages and logic; incompleteness, undecidability,and indefinability; recursive functions; computability;and Hilbert’s Tenth Problem.Reprint of the PWS Publishing Company, Boston, 1995edition.
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A Concise Introduction to Mathematical Logic

Author: Wolfgang Rautenberg

Publisher: Springer Science & Business Media

ISBN: 0387342419

Category: Mathematics

Page: 256

View: 1151

While there are already several well known textbooks on mathematical logic this book is unique in treating the material in a concise and streamlined fashion. This allows many important topics to be covered in a one semester course. Although the book is intended for use as a graduate text the first three chapters can be understood by undergraduates interested in mathematical logic. The remaining chapters contain material on logic programming for computer scientists, model theory, recursion theory, Godel’s Incompleteness Theorems, and applications of mathematical logic. Philosophical and foundational problems of mathematics are discussed throughout the text.
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Real and Abstract Analysis

A modern treatment of the theory of functions of a real variable

Author: Edwin Hewitt,Karl Stromberg

Publisher: Springer-Verlag

ISBN: 3662297949

Category: Mathematics

Page: 476

View: 5658

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Einführung in die Mathematische Logik

Ein Lehrbuch

Author: Wolfgang Rautenberg

Publisher: Springer-Verlag

ISBN: 3322915182

Category: Mathematics

Page: 256

View: 7022

Dieses Lehrbuch enthält über den Stoff einer einsemestrigen Einführungsvorlesung hinaus auch Material für eine Vorlesung über Logik für Informatiker (speziell logisches Programmieren), sowie in begrenztem Maße auch Basismaterial für eine Fortsetzung der Einführung in die Spezialrichtungen Modelltheorie, Rekursionstheorie und Beweistheorie. Für eine gekürzte Einführung in die Mathematische Logik kombiniert mit einer Einführung in die Mengenlehre empfiehlt sich für den logischen Teil der Stoff der ersten drei Kapitel. Unabhängig von Vorlesungskonzepten ist das Buch auch zum Selbststudium geeignet. Für einen Großteil der Übungen gibt es Lösungshinweise. Außer einer gewissen Schulung im mathematischen Schließen sind spezielle Vorkenntnisse nicht erforderlich; lediglich für Teile der Modelltheorie wären algebraische Grundkenntnisse wünschenswert. Die Verzeichnisse (Stichwörter, Symbole, Literatur) sind ausführlich und kommen der selbständigen Erarbeitung des Stoffes sehr entgegen. Das Buch ist inhaltsreich und flüssig geschrieben. Aus der Literatur bekannte Beweise wurden oft erheblich vereinfacht. Auch werden viele interessante Details präsentiert, die in der Lehrbuchliteratur nur schwer zu finden sind. Beispiele: Fragmente der 1. Stufe (etwa der Birkhoffsche Vollständigkeitssatz) und die Solovayschen Vollständigkeitssätze über Selbstreferenz. Die Gödelschen Unvollständigkeitssätze und ihr Umfeld werden besonders ausführlich behandelt. Nur gelegentlich werden weiterführende Betrachtungen angestellt, die mit Verweisen auf entsprechende Literaturstellen abschließen.
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An Introduction to Mathematical Logic and Type Theory

Author: Peter B. Andrews

Publisher: Springer Science & Business Media

ISBN: 9781402007637

Category: Computers

Page: 390

View: 3307

In case you are considering to adopt this book for courses with over 50 students, please contact [email protected] for more information. This introduction to mathematical logic starts with propositional calculus and first-order logic. Topics covered include syntax, semantics, soundness, completeness, independence, normal forms, vertical paths through negation normal formulas, compactness, Smullyan's Unifying Principle, natural deduction, cut-elimination, semantic tableaux, Skolemization, Herbrand's Theorem, unification, duality, interpolation, and definability. The last three chapters of the book provide an introduction to type theory (higher-order logic). It is shown how various mathematical concepts can be formalized in this very expressive formal language. This expressive notation facilitates proofs of the classical incompleteness and undecidability theorems which are very elegant and easy to understand. The discussion of semantics makes clear the important distinction between standard and nonstandard models which is so important in understanding puzzling phenomena such as the incompleteness theorems and Skolem's Paradox about countable models of set theory. Some of the numerous exercises require giving formal proofs. A computer program called ETPS which is available from the web facilitates doing and checking such exercises. Audience: This volume will be of interest to mathematicians, computer scientists, and philosophers in universities, as well as to computer scientists in industry who wish to use higher-order logic for hardware and software specification and verification.
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Introduction to Mathematical Logic

Author: Alonzo Church

Publisher: Princeton University Press

ISBN: 9780691029061

Category: Mathematics

Page: 378

View: 5396

Logic is sometimes called the foundation of mathematics: the logician studies the kinds of reasoning used in the individual steps of a proof. Alonzo Church was a pioneer in the field of mathematical logic, whose contributions to number theory and the theories of algorithms and computability laid the theoretical foundations of computer science. His first Princeton book, The Calculi of Lambda-Conversion (1941), established an invaluable tool that computer scientists still use today. Even beyond the accomplishment of that book, however, his second Princeton book, Introduction to Mathematical Logic, defined its subject for a generation. Originally published in Princeton's Annals of Mathematics Studies series, this book was revised in 1956 and reprinted a third time, in 1996, in the Princeton Landmarks in Mathematics series. Although new results in mathematical logic have been developed and other textbooks have been published, it remains, sixty years later, a basic source for understanding formal logic. Church was one of the principal founders of the Association for Symbolic Logic; he founded the Journal of Symbolic Logic in 1936 and remained an editor until 1979 At his death in 1995, Church was still regarded as the greatest mathematical logician in the world.
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Introduction to Mathematical Logic

Author: Elliott Mendelson

Publisher: CRC Press

ISBN: 1482237784

Category: Mathematics

Page: 513

View: 6767

The new edition of this classic textbook, Introduction to Mathematical Logic, Sixth Edition explores the principal topics of mathematical logic. It covers propositional logic, first-order logic, first-order number theory, axiomatic set theory, and the theory of computability. The text also discusses the major results of Gödel, Church, Kleene, Rosser, and Turing. The sixth edition incorporates recent work on Gödel’s second incompleteness theorem as well as restoring an appendix on consistency proofs for first-order arithmetic. This appendix last appeared in the first edition. It is offered in the new edition for historical considerations. The text also offers historical perspectives and many new exercises of varying difficulty, which motivate and lead students to an in-depth, practical understanding of the material.
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An Introduction to Symbolic Logic

Author: Langer

Publisher: Courier Corporation

ISBN: 9780486601649

Category: Mathematics

Page: 384

View: 1671

Famous classic has introduced countless readers to symbolic logic with its thorough and precise exposition. Starts with simple symbols and conventions and concludes with the Boole-Schroeder and Russell-Whitehead systems. No special knowledge of mathematics necessary. "One of the clearest and simplest introductions to a subject which is very much alive." — Mathematics Gazette.
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Fundamentals of Mathematics, An Introduction to Proofs, Logic, Sets, and Numbers

Mathematics, Mathematics

Author: CTI Reviews

Publisher: Cram101 Textbook Reviews

ISBN: 1467211346

Category: Education

Page: 62

View: 7973

Facts101 is your complete guide to Fundamentals of Mathematics, An Introduction to Proofs, Logic, Sets, and Numbers. In this book, you will learn topics such as as those in your book plus much more. With key features such as key terms, people and places, Facts101 gives you all the information you need to prepare for your next exam. Our practice tests are specific to the textbook and we have designed tools to make the most of your limited study time.
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Introduction to Logic and Theory of Knowledge

Lectures 1906/07

Author: Edmund Husserl

Publisher: Springer Science & Business Media

ISBN: 1402067275

Category: Philosophy

Page: 479

View: 9336

Claire Ortiz Hill The publication of all but a small, unfound, part of the complete text of the lecture course on logic and theory of knowledge that Edmund Husserl gave at Göttingen during the winter semester of 1906/07 became a reality in 1984 with the publication of Einleitung in die Logik und Erkenntnistheorie, Vorlesungen 1906/07 edited by 1 Ullrich Melle. Published in that volume were also 27 appendices containing material selected to complement the content of the main text in significant ways. They provide valuable insight into the evolution of Husserl’s thought between the Logical Investigations and Ideas I and, therefore, into the origins of phenomenology. That text and all those appendices but one are translated and published in the present volume. Omitted are only the “Personal Notes” dated September 25, 1906, November 4, 1907, and March 6, 1908, which were translated by Dallas Willard and published in his translation of Husserl’s Early 2 Writings in the Philosophy of Logic and Mathematics. Introduction to Logic and Theory of Knowledge, Lectures 1906/07 provides valuable insight into the development of the ideas fun- mental to phenomenology. Besides shedding considerable light on the genesis of phenomenology, it sheds needed light on many other dimensions of Husserl’s thought that have puzzled and challenged scholars.
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The Nuts and Bolts of Proofs

An Introduction to Mathematical Proofs

Author: Antonella Cupillari

Publisher: Academic Press

ISBN: 0080537901

Category: Mathematics

Page: 192

View: 8705

The Nuts and Bolts of Proof instructs students on the basic logic of mathematical proofs, showing how and why proofs of mathematical statements work. It provides them with techniques they can use to gain an inside view of the subject, reach other results, remember results more easily, or rederive them if the results are forgotten.A flow chart graphically demonstrates the basic steps in the construction of any proof and numerous examples illustrate the method and detail necessary to prove various kinds of theorems. * The "List of Symbols" has been extended. * Set Theory section has been strengthened with more examples and exercises. * Addition of "A Collection of Proofs"
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Introduction to Mathematical Philosophy

Author: Bertrand Russell

Publisher: Spokesman Books

ISBN: 0851247385

Category: Mathematics

Page: 208

View: 6645

Bertrand Russell is probably the most important philosopher of mathematics in the 20th century. He brought together his formidable knowledge of the subject and skills as a gifted communicator to provide a classic introduction to the philosophy of mathematics.
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