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ISBNSpecification
  SPECIFICATION
LOGIC, SETS, AND RECURSION 2e(pb)2010
Author: CAUSEY
ISBN: 9789380108087
Year: 2010
Publisher: VIVA BOOKS PRIVATE LIMITED
Category: NUMERICAL METHODS / DISCREATE MATHEMATICS
Edition: 2
Format: Paperback
Language: English
Pages: 512
 ABOUT THE TITLE
Logic Sets, and Recursion, Second Edition provides a comprehensive introduction to logic, the basic ideas of set theory, and mathematical induction at the undergraduate level. This text paves the way for students preparing to enter more advanced math courses, furnishing them with the experience to
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 TABLE OF CONTENTS
Introduction
1.Sentential Calculus
1.1Syntax of the Sentential Calculus
1.2Correspondence to Natural Languages
1.3Semantics of the Sentential Calculus
1.4Some Metatheoretical Concepts
1.5Principles for Sentential Calculus Derivations
1.6Adequacy and Use of Sentential Calculus Derivation Rules
1.6 1Soundness and Completeness
1.6 2Strategies for Constructing Proofs
1.6 3Sentential Calculus Derivation Examples
1.7 Conjunctive Normal Form and Resolution Proofs
2. Basic Set Theory
2.1 Sets
2.1 1Extensionality, Predicates, and Abstraction
2.1 2Some Special Sets and Set Operations
2.2 Relations
2.2 1General Features
2.2 2Special Kinds of Relations
2.3 Functions
2.3 1Basic Ideas
2.3 2Compositions and Inverses
2.4 Relational Systems
3. Recursion and mathematical Induction
3.1 The Natural Number System
3.1 1Introduction
3.1 2Peano's Axioms and the Induction Principle
3.1 3Definition by Recursion
3.2 Basic Arithmetic
3.2 1Some Simple Functions
3.2 2Additional Arithmetical Definitions
3.3 Extensions of Recursive Definition and Induction
3.3 1Some Additional Applications of the Recursion Theorem
3.3 2The Well-Ordering of the Natural Numbers
3.3 3Course of Values Induction
3.3 4Two Arithmetical Algorithms
3.3 5Pitfalls of Recursion
3.4 Non-Numerical Data
3.4 1Strings
3.4 2A Simple Treatment of Lists
3.4 3Sentential Calculus Expressions
3.4 4Stacks and Queues
4.Predicate Calculus
4.1 Syntax of the Predicate Calculus
4.2 Semantical Aspects of the Predicate Calculus
4.2 1Interpretations and Truth
4.2 2Tautologous Sentences in Predicate Calculus
4.2 3Tautological Consequences in Predicate Calculus
4.3 Predicate Calculus Derivations
4.3 1Derivation Rules
4.3 2Proof Strategies and Examples
4.3 3Adequacy of the Predicate Calculus Rules
4.4 Application Example
4.5 Identity and Function Symbols
4.5 1Extension of the Syntax
4.5 2Semantics of Predicate Calculus with Identity and Function Symbols
4.5 3Derivation Rules for Predicate Calculus with Identity and Function Symbols
4.5 4Use of Identity in Representing Information
4.6 Formalized Theories
References
Answers to Selected Exercises
The Greek Alphabet
Glossary of Symbols
Index
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