The Structure of Proof

The Structure of Proof : With Logic and Set Theory

4 (4 ratings by Goodreads)
By (author) 

List price: US$111.00

Currently unavailable

Add to wishlist

AbeBooks may have this title (opens in new window).

Try AbeBooks

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.show more

Product details

  • Hardback | 418 pages
  • 181.4 x 239.8 x 20.6mm | 798.34g
  • Pearson Education (US)
  • Pearson
  • United States
  • English
  • 0130190772
  • 9780130190772

Table of contents

Preface. I. LOGICAL FOUNDATIONS. 1. Propositional Logic. Propositions. Propositional Forms. Rules of Inference. Rules of Replacement.2. Predicates and Proofs. Predicates and Sets. Quantification. Negating Quantifiers. Proofs with Quantifiers. Direct and Indirect Proof. More Methods.II. MAIN TOPICS. 3. Set Theory. Set Basics. Subsets. Equality of Sets. Families of Sets. Generalized Union and Intersection. Chapter Exercises.4. Mathematical Induction. The First Principle. Combinatorics. The Second Principle. The Well-Ordering Principle. Chapter Exercises.5. Number Theory. Axioms. Divisibility. Primes. Congruences. Chapter Exercises.6. Relations and Functions. Relations. Equivalence Relations. Functions. Function Operations. One-to-one and Onto. Images and Inverse Images. Cardinality. Chapter Exercises.III. COMING ATTRACTIONS. 7. Ring Theory. Types of Rings. Subrings and Ideals. Factor Rings. Homomorphisms. Polynomials. Chapter Exercises8. Topology. Spaces. Open Sets. Closed Sets. Isometries. Limits. Chapter Exercises.IV. APPENDICES. Appendix A: Logic Summary. Appendix B: Summation Notation. Appendix C: Greek Alphabet. Bibliography. Selected Solutions. Index.show more

Rating details

4 ratings
4 out of 5 stars
5 25% (1)
4 50% (2)
3 25% (1)
2 0% (0)
1 0% (0)
Book ratings by Goodreads
Goodreads is the world's largest site for readers with over 50 million reviews. We're featuring millions of their reader ratings on our book pages to help you find your new favourite book. Close X