by Bob A. Dumas and John E. McCarthy
List price: $197.75
Chapter 0. Introduction
0.1. Why this book is
0.2. What this book is
0.3. What this book is not
0.4. Advice to the Student
0.5. Advice to the Instructor
0.6. Acknowledgements
Chapter 1. Preliminaries
1.1. ''And'' ''Or''
1.2. Sets
1.3. Functions
1.4. Injections, Surjections, Bijections
1.5. Images and Inverses
1.6. Sequences
1.7. Russell's Paradox
1.8. Exercises
1.9. Hints to Get Started on Some Exercises
Chapter 2. Relations
2.1. Definitions
2.2. Orderings
2.3. Equivalence Relations
2.4. Constructing Bijections
2.5. Modular Arithmetic
2.6. Exercises
Chapter 3. Proofs
3.1. Mathematics and Proofs
3.2. Propositional Logic
3.3. Formulas
3.4. Quantifiers
3.5. Proof Strategies
3.6. Exercises
Chapter 4. Principle of Induction
4.1. Well-Orderings
4.2. Principle of Induction
4.3. Polynomials
4.4. Arithmetic-Geometric Inequality
4.5. Exercises
Chapter 5. Limits
5.1. Limits
5.2. Continuity
5.3. Sequences of Functions
5.4. Exercises
Chapter 6. Cardinality
6.1. Cardinality
6.2. Infinite Sets
6.3. Uncountable Sets
6.4. Countable Sets
6.5. Functions and Computability
6.6. Exercises
Chapter 7. Divisibility
7.1. Fundamental Theorem of Arithmetic
7.2. The Division Algorithm
7.3. Euclidean Algorithm
7.4. Fermat's Little Theorem
7.5. Divisibility and Polynomials
7.6. Exercises
Chapter 8. The Real Numbers
8.1. The Natural Numbers
8.2. The Integers
8.3. The Rational Numbers
8.4. The Real Numbers
8.5. The Least Upper Bound Principle
8.6. Real Sequences
8.7. Ratio Test
8.8. Real Functions
8.9. Cardinality of the Real Numbers
8.10. Order-Completeness
8.11. Exercises
Chapter 9. Complex Numbers
9.1. Cubics
9.2. Complex Numbers
9.3. Tartaglia-Cardano Revisited
9.4. Fundamental Theorem of Algebra
9.5. Application to Real Polynomials
9.6. Further Remarks
9.7. Exercises
Appendix A. The Greek Alphabet
Appendix B. Axioms of Zermelo-Fraenkel with the Axiom of Choice
Bibliography
Index
Bob A. Dumas and John E. McCarthy
ISBN13: 978-0073533537Table of Contents
Chapter 0. Introduction
0.1. Why this book is
0.2. What this book is
0.3. What this book is not
0.4. Advice to the Student
0.5. Advice to the Instructor
0.6. Acknowledgements
Chapter 1. Preliminaries
1.1. ''And'' ''Or''
1.2. Sets
1.3. Functions
1.4. Injections, Surjections, Bijections
1.5. Images and Inverses
1.6. Sequences
1.7. Russell's Paradox
1.8. Exercises
1.9. Hints to Get Started on Some Exercises
Chapter 2. Relations
2.1. Definitions
2.2. Orderings
2.3. Equivalence Relations
2.4. Constructing Bijections
2.5. Modular Arithmetic
2.6. Exercises
Chapter 3. Proofs
3.1. Mathematics and Proofs
3.2. Propositional Logic
3.3. Formulas
3.4. Quantifiers
3.5. Proof Strategies
3.6. Exercises
Chapter 4. Principle of Induction
4.1. Well-Orderings
4.2. Principle of Induction
4.3. Polynomials
4.4. Arithmetic-Geometric Inequality
4.5. Exercises
Chapter 5. Limits
5.1. Limits
5.2. Continuity
5.3. Sequences of Functions
5.4. Exercises
Chapter 6. Cardinality
6.1. Cardinality
6.2. Infinite Sets
6.3. Uncountable Sets
6.4. Countable Sets
6.5. Functions and Computability
6.6. Exercises
Chapter 7. Divisibility
7.1. Fundamental Theorem of Arithmetic
7.2. The Division Algorithm
7.3. Euclidean Algorithm
7.4. Fermat's Little Theorem
7.5. Divisibility and Polynomials
7.6. Exercises
Chapter 8. The Real Numbers
8.1. The Natural Numbers
8.2. The Integers
8.3. The Rational Numbers
8.4. The Real Numbers
8.5. The Least Upper Bound Principle
8.6. Real Sequences
8.7. Ratio Test
8.8. Real Functions
8.9. Cardinality of the Real Numbers
8.10. Order-Completeness
8.11. Exercises
Chapter 9. Complex Numbers
9.1. Cubics
9.2. Complex Numbers
9.3. Tartaglia-Cardano Revisited
9.4. Fundamental Theorem of Algebra
9.5. Application to Real Polynomials
9.6. Further Remarks
9.7. Exercises
Appendix A. The Greek Alphabet
Appendix B. Axioms of Zermelo-Fraenkel with the Axiom of Choice
Bibliography
Index