Math A Logic

Author : Dianne Draze
Publisher : Routledge
Page : 84 pages
File Size : 47,8 Mb
Release : 2021-09-03
Category : Education
ISBN : 9781000494549

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Math-a-Logic by Dianne Draze Pdf

If you thought math was all numbers, you're in for a surprise. The ability to reason logically is both a prerequisite for learning mathematics and a desired outcome of mathematics instruction. Mathematics provides an excellent context in which to make students aware of the logical structures they need to function successfully in any setting. Math-A-Logic is an award-winning text that successfully merges logical thinking with mathematical concepts and calculations. Eight areas of logic are introduced: patterns and sequences, analogies, deduction, inference, sets and Venn diagram, propositions and logical notation, syllogisms, and logical problem solving. Attractive, reproducible worksheets lead students through each topic, providing explanations, examples, and exercises to test their understanding. With mathematics as the vehicle for presenting and practicing the logical concept, students get practice in mathematical concepts and computations while building thinking skills. The end result is clearer thinking and enhanced problem-solving abilities. This unique approach is sure to be a favorite supplement to your regular math program. The attractive illustrations, clear instructions, solid content, and ease of use make this book a winner. This book is the winner of Learning Magazine's Teacher Choice award. Grades 4-8

Author : Dianne Draze
Publisher : Unknown
Page : 84 pages
File Size : 41,9 Mb
Release : 2005-01-01
Category : Education
ISBN : 1593631073

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Math-a-Logic by Dianne Draze Pdf

If you thought math was all numbers, you're in for a surprise. The ability to reason logically is both a prerequisite for learning mathematics and a desired outcome of mathematics instruction. Mathematics provides an excellent context in which to make students aware of the logical structures they need to function successfully in any setting. Math-A-Logic is an award-winning text that successfully merges logical thinking with mathematical concepts and calculations. Eight areas of logic are introduced, including: patterns and sequences, analogies, deduction, inference, sets and Venn diagrams, propositions and logical notation, syllogisms, and logical problem solving. Attractive, reproducible worksheets lead students through each topic, providing explanations, examples, and exercises to test their understanding. With mathematics as the vehicle for presenting and practicing the logical concept, students get practice in mathematical concepts and computations while building thinking skills. The end result is clearer thinking and enhanced problem-solving abilities. This unique approach is sure to be a favorite supplement to your regular math program. The attractive illustrations, clear instructions, solid content, and ease of use make this book a winner. This book is the winner of Learning Magazine's Teacher Choice award.

Author : Elliot Mendelsohn
Publisher : Springer Science & Business Media
Page : 351 pages
File Size : 46,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461572886

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Introduction to Mathematical Logic by Elliot Mendelsohn Pdf

This is a compact mtroduction to some of the pnncipal tOpICS of mathematical logic . In the belief that beginners should be exposed to the most natural and easiest proofs, I have used free-swinging set-theoretic methods. The significance of a demand for constructive proofs can be evaluated only after a certain amount of experience with mathematical logic has been obtained. If we are to be expelled from "Cantor's paradise" (as nonconstructive set theory was called by Hilbert), at least we should know what we are missing. The major changes in this new edition are the following. (1) In Chapter 5, Effective Computability, Turing-computabIlity IS now the central notion, and diagrams (flow-charts) are used to construct Turing machines. There are also treatments of Markov algorithms, Herbrand-Godel-computability, register machines, and random access machines. Recursion theory is gone into a little more deeply, including the s-m-n theorem, the recursion theorem, and Rice's Theorem. (2) The proofs of the Incompleteness Theorems are now based upon the Diagonalization Lemma. Lob's Theorem and its connection with Godel's Second Theorem are also studied. (3) In Chapter 2, Quantification Theory, Henkin's proof of the completeness theorem has been postponed until the reader has gained more experience in proof techniques. The exposition of the proof itself has been improved by breaking it down into smaller pieces and using the notion of a scapegoat theory. There is also an entirely new section on semantic trees.

Author : Stefan Bilaniuk
Publisher : Orange Groove Books
Page : 166 pages
File Size : 40,9 Mb
Release : 2009-09-01
Category : Mathematics
ISBN : 1616100060

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A Problem Course in Mathematical Logic by Stefan Bilaniuk Pdf

Author : H.-D. Ebbinghaus,J. Flum,Wolfgang Thomas
Publisher : Springer Science & Business Media
Page : 290 pages
File Size : 44,7 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781475723557

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Mathematical Logic by H.-D. Ebbinghaus,J. Flum,Wolfgang Thomas Pdf

This introduction to first-order logic clearly works out the role of first-order logic in the foundations of mathematics, particularly the two basic questions of the range of the axiomatic method and of theorem-proving by machines. It covers several advanced topics not commonly treated in introductory texts, such as Fraïssé's characterization of elementary equivalence, Lindström's theorem on the maximality of first-order logic, and the fundamentals of logic programming.

Author : Wolfgang Rautenberg
Publisher : Springer
Page : 337 pages
File Size : 50,8 Mb
Release : 2010-07-01
Category : Mathematics
ISBN : 9781441912213

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A Concise Introduction to Mathematical Logic by Wolfgang Rautenberg Pdf

Mathematical logic developed into a broad discipline with many applications in mathematics, informatics, linguistics and philosophy. This text introduces the fundamentals of this field, and this new edition has been thoroughly expanded and revised.

Author : Patrick Suppes,Shirley Hill
Publisher : Courier Corporation
Page : 308 pages
File Size : 40,8 Mb
Release : 2012-04-30
Category : Mathematics
ISBN : 9780486150949

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First Course in Mathematical Logic by Patrick Suppes,Shirley Hill Pdf

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.

Author : Zofia Adamowicz,Pawel Zbierski
Publisher : John Wiley & Sons
Page : 276 pages
File Size : 50,9 Mb
Release : 2011-09-26
Category : Mathematics
ISBN : 9781118030790

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Logic of Mathematics by Zofia Adamowicz,Pawel Zbierski Pdf

A thorough, accessible, and rigorous presentation of the central theorems of mathematical logic . . . ideal for advanced students of mathematics, computer science, and logic Logic of Mathematics combines a full-scale introductory course in mathematical logic and model theory with a range of specially selected, more advanced theorems. Using a strict mathematical approach, this is the only book available that contains complete and precise proofs of all of these important theorems: * Gödel's theorems of completeness and incompleteness * The independence of Goodstein's theorem from Peano arithmetic * Tarski's theorem on real closed fields * Matiyasevich's theorem on diophantine formulas Logic of Mathematics also features: * Full coverage of model theoretical topics such as definability, compactness, ultraproducts, realization, and omission of types * Clear, concise explanations of all key concepts, from Boolean algebras to Skolem-Löwenheim constructions and other topics * Carefully chosen exercises for each chapter, plus helpful solution hints At last, here is a refreshingly clear, concise, and mathematically rigorous presentation of the basic concepts of mathematical logic-requiring only a standard familiarity with abstract algebra. Employing a strict mathematical approach that emphasizes relational structures over logical language, this carefully organized text is divided into two parts, which explain the essentials of the subject in specific and straightforward terms. Part I contains a thorough introduction to mathematical logic and model theory-including a full discussion of terms, formulas, and other fundamentals, plus detailed coverage of relational structures and Boolean algebras, Gödel's completeness theorem, models of Peano arithmetic, and much more. Part II focuses on a number of advanced theorems that are central to the field, such as Gödel's first and second theorems of incompleteness, the independence proof of Goodstein's theorem from Peano arithmetic, Tarski's theorem on real closed fields, and others. No other text contains complete and precise proofs of all of these theorems. With a solid and comprehensive program of exercises and selected solution hints, Logic of Mathematics is ideal for classroom use-the perfect textbook for advanced students of mathematics, computer science, and logic.

Author : Herbert B. Enderton
Publisher : Elsevier
Page : 330 pages
File Size : 44,7 Mb
Release : 2001-01-23
Category : Computers
ISBN : 9780080496467

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A Mathematical Introduction to Logic by Herbert B. Enderton Pdf

A Mathematical Introduction to Logic

Author : Richard E. Hodel
Publisher : Courier Corporation
Page : 514 pages
File Size : 40,5 Mb
Release : 2013-01-01
Category : Mathematics
ISBN : 9780486497853

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An Introduction to Mathematical Logic by Richard E. Hodel Pdf

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.

Author : Michael L. O'Leary
Publisher : John Wiley & Sons
Page : 464 pages
File Size : 54,8 Mb
Release : 2015-09-14
Category : Mathematics
ISBN : 9781118548011

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A First Course in Mathematical Logic and Set Theory by Michael L. O'Leary Pdf

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.

Author : Stephen Cole Kleene
Publisher : Courier Corporation
Page : 416 pages
File Size : 51,7 Mb
Release : 2013-04-22
Category : Mathematics
ISBN : 9780486317076

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Mathematical Logic by Stephen Cole Kleene Pdf

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.

Author : Mark Kac,Stanislaw M. Ulam
Publisher : Courier Corporation
Page : 189 pages
File Size : 47,7 Mb
Release : 1992-01-01
Category : Philosophy
ISBN : 9780486670850

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Mathematics and Logic by Mark Kac,Stanislaw M. Ulam Pdf

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."

Author : Howard DeLong
Publisher : Courier Corporation
Page : 322 pages
File Size : 43,5 Mb
Release : 2012-09-26
Category : Mathematics
ISBN : 9780486139159

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A Profile of Mathematical Logic by Howard DeLong Pdf

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.

Author : Robert S. Wolf
Publisher : American Mathematical Soc.
Page : 397 pages
File Size : 52,6 Mb
Release : 2005-12-31
Category : Algebra, Abstract
ISBN : 9781614440284

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A Tour Through Mathematical Logic by Robert S. Wolf Pdf

A Tour Through Mathematical Logic provides a tour through the main branches of the foundations of mathematics. It contains chapters covering elementary logic, basic set theory, recursion theory, Gödel's (and others') incompleteness theorems, model theory, independence results in set theory, nonstandard analysis, and constructive mathematics. In addition, this monograph discusses several topics not normally found in books of this type, such as fuzzy logic, nonmonotonic logic, and complexity theory.