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.

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.

A Profile of Mathematical Logic

Author: Howard DeLong

Publisher: Courier Corporation

ISBN: 0486139158

Category: Mathematics

Page: 320

View: 9524

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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

View: 1553

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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.

Popular Lectures on Mathematical Logic

Author: Hao Wang

Publisher: Courier Corporation

ISBN: 0486171043

Category: Mathematics

Page: 292

View: 7615

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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.

An Introduction to Mathematical Logic

Author: Richard E. Hodel

Publisher: Courier Corporation

ISBN: 0486497852

Category: Mathematics

Page: 491

View: 9859

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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.

First Order Mathematical Logic

Author: Angelo Margaris

Publisher: Courier Corporation

ISBN: 9780486662695

Category: Mathematics

Page: 211

View: 4061

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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

Introduction to Elementary Mathematical Logic

Author: Abram Aronovich Stolyar

Publisher: Courier Corporation

ISBN: 0486645614

Category: Mathematics

Page: 209

View: 5057

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This lucid, non-intimidating presentation by a Russian scholar explores propositional logic, propositional calculus, and predicate logic. Topics include computer science and systems analysis, linguistics, and problems in the foundations of mathematics. Accessible to high school students, it also constitutes a valuable review of fundamentals for professionals. 1970 edition.

A Beginner's Guide to Mathematical Logic

Author: Raymond M. Smullyan

Publisher: Courier Corporation

ISBN: 0486492370

Category: Mathematics

Page: 288

View: 1981

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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 B. Curry

Publisher: Courier Corporation

ISBN: 0486153053

Category: Mathematics

Page: 416

View: 6129

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Comprehensive graduate-level account of constructive theory of first-order predicate calculus covers formal methods: algorithms and epitheory, brief treatment of Markov's approach to algorithms, elementary facts about lattices, logical connectives, and more. 1963 edition.

Mathematics and Logic

Author: Mark Kac,Stanislaw M. Ulam

Publisher: Courier Corporation

ISBN: 0486670856

Category: Philosophy

Page: 170

View: 5926

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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."

Mathematical Logic

Author: Stephen Cole Kleene

Publisher: Courier Corporation

ISBN: 0486317072

Category: Mathematics

Page: 416

View: 2230

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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.

My Best Mathematical and Logic Puzzles

Author: Martin Gardner

Publisher: Courier Corporation

ISBN: 0486320324

Category: Games & Activities

Page: 96

View: 9970

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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.

Mathematical Puzzles

Author: Samuel Loyd,Martin Gardner

Publisher: Courier Corporation

ISBN: 9780486204987

Category: Games

Page: 167

View: 909

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Choice puzzles by one of America's most ingenious creators of mathematical entertainments, ranging from simple exercises in arithmetic to complex calculus problems

Entertaining Mathematical Puzzles

Author: Martin Gardner

Publisher: Courier Corporation

ISBN: 9780486252117

Category: Juvenile Nonfiction

Page: 112

View: 4881

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Playing with mathematical riddles can be an intriguing and fun-filled pastime — as popular science writer Martin Gardner proves in this entertaining collection. Puzzlists need only an elementary knowledge of math and a will to resist looking up the answer before trying to solve a problem. Written in a light and witty style, Entertaining Mathematical Puzzles is a mixture of old and new riddles, grouped into sections that cover a variety of mathematical topics: money, speed, plane and solid geometry, probability, topology, tricky puzzles, and more. The probability section, for example, points out that everything we do, everything that happens around us, obeys the laws of probability; geometry puzzles test our ability to think pictorially and often, in more than one dimension; while topology, among the "youngest and rowdiest branches of modern geometry," offers a glimpse into a strange dimension where properties remain unchanged, no matter how a figure is twisted, stretched, or compressed. Clear and concise comments at the beginning of each section explain the nature and importance of the math needed to solve each puzzle. A carefully explained solution follows each problem. In many cases, all that is needed to solve a puzzle is the ability to think logically and clearly, to be "on the alert for surprising, off-beat angles...that strange hidden factor that everyone else had overlooked." Fully illustrated, this engaging collection will appeal to parents and children, amateur mathematicians, scientists, and students alike, and may, as the author writes, make the reader "want to study the subject in earnest" and explains "some of the inviting paths that wind away from the problems into lusher areas of the mathematical jungle." 65 black-and-white illustrations.

Kurt Gödel

Jahrhundertmathematiker und großer Entdecker

Author: Rebecca Goldstein

Publisher: N.A

ISBN: 9783492249607

Category:

Page: 312

View: 8814

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Symbolic Logic and the Game of Logic

Author: Lewis Carroll

Publisher: Courier Corporation

ISBN: 0486204928

Category: Games & Activities

Page: 295

View: 9045

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Lewis Carroll explains the theory and applications of symbolic logic in a collection of entertaining problems

Puzzles in Math and Logic

100 New Recreations

Author: Aaron J. Friedland

Publisher: Courier Corporation

ISBN: 9780486222561

Category: Games

Page: 66

View: 8063

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Selected brain teasers requiring geometric, algebraic, and logical solutions