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Structure of Proof With Logic and Set Theory

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ISBN-10: 0130190772

ISBN-13: 9780130190772

Edition: 2002

Authors: Michael L. O'Leary

List price: $111.00
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Description:

For a one-semester freshman or sophomore level course on the fundamentals of proof writing or transition to advanced mathematics course. Rather than teach mathematics and the structure of proofs simultaneously, this text first introduces logic as the foundation of proofs and then demonstrates how logic applies to mathematical topics. This method ensures that the students gain a firm understanding of how logic interacts with mathematics and empowers them to solve more complex problems in future math courses.
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Book details

List price: $111.00
Copyright year: 2002
Publisher: Prentice Hall PTR
Publication date: 7/23/2001
Binding: Hardcover
Pages: 418
Size: 7.00" wide x 9.25" long x 0.75" tall
Weight: 2.002
Language: English

Preface
Logical Foundations
Propositional Logic
Propositions
Propositional Forms
Rules of Inference
Rules of Replacement
Predicates and Proofs
Predicates and Sets
Quantification
Negating Quantifiers
Proofs with Quantifiers
Direct and Indirect Proof
More Methods
Main Topics
Set Theory
Set Basics
Subsets
Equality of Sets
Families of Sets
Generalized Union and Intersection
Chapter Exercises
Mathematical Induction
The First Principle
Combinatorics
The Second Principle
The Well-Ordering Principle
Chapter Exercises
Number Theory
Axioms
Divisibility
Primes
Congruences
Chapter Exercises
Relations and Functions
Relations
Equivalence Relations
Functions
Function Operations
One-to-one and Onto
Images and Inverse Images
Cardinality
Chapter Exercises
Coming Attractions
Ring Theory
Types of Rings
Subrings and Ideals
Factor Rings
Homomorphisms
Polynomials
Chapter Exercises
Topology
Spaces
Open Sets
Closed Sets
Isometries
Limits
Chapter Exercises
Appendices
Logic Summary
Summation Notation
Greek Alphabet
Bibliography
Selected Solutions
Index