Logic for Mathematicians

Author: J. Barkley Rosser

Publisher: Courier Dover Publications

ISBN: 0486468984

Category: Mathematics

Page: 574

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Hailed by the Bulletin of the American Mathematical Society as "undoubtedly a major addition to the literature of mathematical logic," this volume examines the essential topics and theorems of mathematical reasoning. No background in logic is assumed, and the examples are chosen from a variety of mathematical fields. Starting with an introduction to symbolic logic, the first eight chapters develop logic through the restricted predicate calculus. Topics include the statement calculus, the use of names, an axiomatic treatment of the statement calculus, descriptions, and equality. Succeeding chapters explore abstract set theory—with examinations of class membership as well as relations and functions—cardinal and ordinal arithmetic, and the axiom of choice. An invaluable reference book for all mathematicians, this text is suitable for advanced undergraduates and graduate students. Numerous exercises make it particularly appropriate for classroom use.

Mathematical Logic

Author: Stephen Cole Kleene

Publisher: Courier Corporation

ISBN: 0486317072

Category: Mathematics

Page: 416

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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.

Mathematics and Logic

Author: Mark Kac,Stanislaw M. Ulam

Publisher: Courier Corporation

ISBN: 0486670856

Category: Philosophy

Page: 170

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Fascinating study of the origin and nature of mathematical thought, including relation of mathematics and science, 20th-century developments, impact of computers, and more.Includes 34 illustrations. 1968 edition."

An Introduction to Mathematical Logic

Author: Richard E. Hodel

Publisher: Courier Corporation

ISBN: 0486497852

Category: Mathematics

Page: 491

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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.

A Profile of Mathematical Logic

Author: Howard DeLong

Publisher: Courier Corporation

ISBN: 0486139158

Category: Mathematics

Page: 320

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This introduction to mathematical logic explores philosophical issues and Gödel's Theorem. Its widespread influence extends to the author of Gödel, Escher, Bach, whose Pulitzer Prize–winning book was inspired by this work.

First Course in Mathematical Logic

Author: Patrick Suppes,Shirley Hill

Publisher: Courier Corporation

ISBN: 0486150941

Category: Mathematics

Page: 288

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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.

Introduction to Logic

and to the Methodology of Deductive Sciences

Author: Alfred Tarski

Publisher: Courier Corporation

ISBN: 0486318893

Category: Mathematics

Page: 272

View: 6700

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This classic undergraduate treatment examines the deductive method in its first part and explores applications of logic and methodology in constructing mathematical theories in its second part. Exercises appear throughout.

Introduction to Logic

Author: Patrick Suppes

Publisher: Courier Corporation

ISBN: 0486138054

Category: Mathematics

Page: 336

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Part I of this coherent, well-organized text deals with formal principles of inference and definition. Part II explores elementary intuitive set theory, with separate chapters on sets, relations, and functions. Ideal for undergraduates.

A Beginner's Guide to Mathematical Logic

Author: Raymond M. Smullyan

Publisher: Courier Corporation

ISBN: 0486492370

Category: Mathematics

Page: 288

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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

Foundations of Mathematical Logic

Author: Haskell Brooks Curry

Publisher: Courier Corporation

ISBN: 9780486634623

Category: Mathematics

Page: 408

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Written by a pioneer of mathematical logic, this comprehensive graduate-level text explores the constructive theory of first-order predicate calculus. It covers formal methods — including algorithms and epitheory — and offers a brief treatment of Markov's approach to algorithms. It also explains elementary facts about lattices and similar algebraic systems. 1963 edition.

Popular Lectures on Mathematical Logic

Author: Hao Wang

Publisher: Courier Corporation

ISBN: 0486171043

Category: Mathematics

Page: 292

View: 3769

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Noted logician discusses both theoretical underpinnings and practical applications, exploring set theory, model theory, recursion theory and constructivism, proof theory, logic's relation to computer science, and other subjects. 1981 edition, reissued by Dover in 1993 with a new Postscript by the author.

Mathematical Fallacies and Paradoxes

Author: Bryan Bunch

Publisher: Courier Corporation

ISBN: 0486137937

Category: Mathematics

Page: 240

View: 9987

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Stimulating, thought-provoking analysis of the most interesting intellectual inconsistencies in mathematics, physics, and language, including being led astray by algebra (De Morgan's paradox). 1982 edition.

First Order Mathematical Logic

Author: Angelo Margaris

Publisher: Courier Corporation

ISBN: 9780486662695

Category: Mathematics

Page: 211

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"Attractive and well-written introduction." — Journal of Symbolic Logic The logic that mathematicians use to prove their theorems is itself a part of mathematics, in the same way that algebra, analysis, and geometry are parts of mathematics. This attractive and well-written introduction to mathematical logic is aimed primarily at undergraduates with some background in college-level mathematics; however, little or no acquaintance with abstract mathematics is needed. Divided into three chapters, the book begins with a brief encounter of naïve set theory and logic for the beginner, and proceeds to set forth in elementary and intuitive form the themes developed formally and in detail later. In Chapter Two, the predicate calculus is developed as a formal axiomatic theory. The statement calculus, presented as a part of the predicate calculus, is treated in detail from the axiom schemes through the deduction theorem to the completeness theorem. Then the full predicate calculus is taken up again, and a smooth-running technique for proving theorem schemes is developed and exploited. Chapter Three is devoted to first-order theories, i.e., mathematical theories for which the predicate calculus serves as a base. Axioms and short developments are given for number theory and a few algebraic theories. Then the metamathematical notions of consistency, completeness, independence, categoricity, and decidability are discussed, The predicate calculus is proved to be complete. The book concludes with an outline of Godel's incompleteness theorem. Ideal for a one-semester course, this concise text offers more detail and mathematically relevant examples than those available in elementary books on logic. Carefully chosen exercises, with selected answers, help students test their grasp of the material. For any student of mathematics, logic, or the interrelationship of the two, this book represents a thought-provoking introduction to the logical underpinnings of mathematical theory. "An excellent text." — Mathematical Reviews

Handbook of Mathematical Logic

Author: J. Barwise

Publisher: Elsevier

ISBN: 9780080933641

Category: Mathematics

Page: 1164

View: 8239

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The handbook is divided into four parts: model theory, set theory, recursion theory and proof theory. Each of the four parts begins with a short guide to the chapters that follow. Each chapter is written for non-specialists in the field in question. Mathematicians will find that this book provides them with a unique opportunity to apprise themselves of developments in areas other than their own.

First-order Logic

Author: Raymond M. Smullyan

Publisher: Courier Corporation

ISBN: 9780486683706

Category: Mathematics

Page: 158

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Considered the best book in the field, this completely self-contained study is both an introduction to quantification theory and an exposition of new results and techniques in "analytic" or "cut free" methods. The focus in on the tableau point of view. Topics include trees, tableau method for propositional logic, Gentzen systems, more. Includes 144 illustrations.

Logic and Boolean Algebra

Author: Bradford Henry Arnold

Publisher: Courier Corporation

ISBN: 0486483851

Category: Mathematics

Page: 144

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Orignally published: Englewood Cliffs, N.J.: Prentice-Hall, 1962.

My Best Mathematical and Logic Puzzles

Author: Martin Gardner

Publisher: Courier Corporation

ISBN: 0486320324

Category: Games & Activities

Page: 96

View: 9914

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The noted expert selects 70 of his favorite "short" puzzles, including such mind-bogglers as The Returning Explorer, The Mutilated Chessboard, Scrambled Box Tops, and dozens more involving logic and basic math. Solutions.

What Is Mathematical Logic?

Author: J. N. Crossley,C.J. Ash,C.J. Brickhill,J.C. Stillwell

Publisher: Courier Corporation

ISBN: 0486151522

Category: Mathematics

Page: 96

View: 7872

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A serious introductory treatment geared toward non-logicians, this survey traces the development of mathematical logic from ancient to modern times and discusses the work of Planck, Einstein, Bohr, Pauli, Heisenberg, Dirac, and others. 1972 edition.

Mathematical Logic and the Foundations of Mathematics

An Introductory Survey

Author: G. T. Kneebone

Publisher: Dover Publications

ISBN: 9780486417127

Category: Mathematics

Page: 435

View: 7445

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Ideal for students intending to specialize in the topic. Part I discusses traditional and symbolic logic. Part II explores the foundations of mathematics. Part III focuses on the philosophy of mathematics.

Paradoxes in Mathematics

Author: Stanley J. Farlow

Publisher: Courier Corporation

ISBN: 048649716X

Category: Mathematics

Page: 192

View: 5488

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Compiled by a prominent educator and author, this volume presents an intriguing mix of mathematical paradoxes — phenomena with surprising outcomes that can be resolved mathematically. Students and puzzle enthusiasts will get plenty of enjoyment mixed with a bit of painless mathematical instruction from 30 conundrums, including The Birthday Paradox, Aristotle's Magic Wheel, and A Greek Tragedy.