Structure of Proof With Logic and Set Theory

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
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: 1.738
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
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