Logic for Mathematicians


Author: J. Barkley Rosser
Publisher: Courier Dover Publications
ISBN: 0486468984
Category: Mathematics
Page: 574
View: 1990
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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
View: 3658
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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
View: 6313
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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
View: 1316
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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
View: 4190
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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: 1370
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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: 1832
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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
View: 1094
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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.

Foundations of Mathematical Logic


Author: Haskell Brooks Curry
Publisher: Courier Corporation
ISBN: 9780486634623
Category: Mathematics
Page: 408
View: 2884
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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.

A Beginner's Guide to Mathematical Logic


Author: Raymond M. Smullyan
Publisher: Courier Corporation
ISBN: 0486492370
Category: Mathematics
Page: 288
View: 8814
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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

First Order Mathematical Logic


Author: Angelo Margaris
Publisher: Courier Corporation
ISBN: 9780486662695
Category: Mathematics
Page: 211
View: 6198
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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

Popular Lectures on Mathematical Logic


Author: Hao Wang
Publisher: Courier Corporation
ISBN: 0486171043
Category: Mathematics
Page: 292
View: 6810
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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.

Handbook of Mathematical Logic


Author: J. Barwise
Publisher: Elsevier
ISBN: 9780080933641
Category: Mathematics
Page: 1164
View: 4303
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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
View: 7260
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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.

My Best Mathematical and Logic Puzzles


Author: Martin Gardner
Publisher: Courier Corporation
ISBN: 0486320324
Category: Games & Activities
Page: 96
View: 1384
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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.

Logic and Boolean Algebra


Author: Bradford Henry Arnold
Publisher: Courier Corporation
ISBN: 0486483851
Category: Mathematics
Page: 144
View: 4639
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Orignally published: Englewood Cliffs, N.J.: Prentice-Hall, 1962.

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: 6059
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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: 3025
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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: 5413
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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.

The Stanford Mathematics Problem Book

With Hints and Solutions
Author: George Polya,Jeremy Kilpatrick
Publisher: Courier Corporation
ISBN: 048631832X
Category: Mathematics
Page: 80
View: 724
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Based on Stanford University's well-known competitive exam, this excellent mathematics workbook offers students at both high school and college levels a complete set of problems, hints, and solutions. 1974 edition.