Logic, Sets, and Recursion

ISBN-10: 0763716952
ISBN-13: 9780763716950
Edition: 2001 (Revised)
Authors: Robert L. Causey
List price: $116.95
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Description: Logic, Sets, and Recursion - Revised Edition introduces logic with an orientation towards mathematics and computing theory. The goal of this text is to teach students how to construct and write informal, but rigorous, mathematical proofs using basic  More...

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Book details

List price: $116.95
Copyright year: 2001
Publisher: Jones & Bartlett Learning, LLC
Publication date: 11/15/2000
Binding: Hardcover
Pages: 416
Size: 6.00" wide x 9.00" long x 1.00" tall
Weight: 1.232
Language: English

Logic, Sets, and Recursion - Revised Edition introduces logic with an orientation towards mathematics and computing theory. The goal of this text is to teach students how to construct and write informal, but rigorous, mathematical proofs using basic set theory, recursive definitions, and mathematical induction. This book provides the undergraduate students with a systematic introduction to the principles of logic and the basic ideas of set theory and mathematical induction. The Revised Edition includes a special supplement for students that presents additional examples and exercises in core topics from the main text. A primary goal of this text is to teach students how to construct and write informal, but rigorous, mathematical proofs using basic set theory, recursive definitions, and mathematical induction. Recursion and induction are introduced with the natural numbers but are also applied to non-numerical data types. The semantics of formalized languages are emphasized along with formal derivations and elementary metatheory. Relations between formal and informal proofs are discussed, as are heuristic strategies for constructing proofs.

Preface
Introduction
The Subject Matter
Goals and Organization
Assumed Background Knowledge
The Presentation
Sentential Calculus
Syntax of the Sentential Calculus
Correspondence to Natural Languages
Semantics of the Sentential Calculus
Some Metatheoretical Concepts
Principles for Sentential Calculus Derivations
Adequacy and Use of Sentential Calculus Derivation Rules
Soundness and Completeness
Strategies for Constructing Proofs
Sentential Calculus Derivation Examples
Conjunctive Normal Form and Resolution Proofs
Basic Set Theory
Sets
Extensionality, Predicates, and Abstraction
Some Special Sets and Set Operations
Relations
General Features
Special Kinds of Relations
Functions
Basic Ideas
Compositions and Inverses
Relational Systems
Recursion and Mathematical Induction
The Natural Number System
Introduction
Peano's Axioms and the Induction Principle
Definition by Recursion
Basic Arithmetic
Some Simple Functions
Additional Arithmetical Definitions
Extensions of Recursive Definition and Induction
Some Additional Applications of the Recursion Theorem
The Well-Ordering of the Natural Numbers
Course of Values Induction
Two Arithmetical Algorithms
Pitfalls of Recursion
Non-Numerical Data
Strings
A Simple Treatment of Lists
Sentential Calculus Expressions
Stacks and Queues
Predicate Calculus
Syntax of the Predicate Calculus
Semantical Aspects of the Predicate Calculus
Interpretations and Truth
Tautologous Sentences in Predicate Calculus
Tautological Consequences in Predicate Calculus
Predicate Calculus Derivations
Derivation Rules
Proof Strategies and Examples
Adequacy of the Predicate Calculus Rules
Application Example
Identity and Function Symbols
Extension of the Syntax
Semantics of Predicate Calculus with Identity and Function Symbols
Derivation Rules for Predicate Calculus with Identity and Function Symbols
Use of Identity in Representing Information
Formalized Theories
References
Answers to Selected Exercises
The Greek Alphabet
Glossary of Symbols
Index

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