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Essentials of Discrete Mathematics, Second Edition is the ideal text for a one-term discrete mathematics course to serve computer science majors as well as students from a wide range of other disciplines. It introduces students to the mathematical way of thinking, and also to many important modern applications. The material is organized around five types of thinking: logical, relational, recursive, quantitative, and analytical. This presentation results in a coherent outline that steadily builds upon mathematical sophistication. Graphs are introduced early and referred to throughout the text, providing a richer context for examples and applications. Students will encounter algorithms near the end of the text, after they have acquired the skills and experience needed to analyze them. The final chapter contains in-depth case studies from a variety of fields, including biology, sociology, linguistics, economics, and music. Clear and concise, Essentials of Discrete Mathematics presents a unified and complete picture of discrete mathematics that instructors can cover in a single semester.

1. Cover Page
2. Title Page
5. Preface
6. How to Use This Book
7. Chapter 1 Logical Thinking
1. 1.1 Formal Logic
2. Exercises 1.1
3. 1.2 Propositional Logic
4. Exercises 1.2
5. 1.3 Predicate Logic
6. Exercises 1.3
7. 1.4 Logic in Mathematics
8. Exercises 1.4
9. 1.5 Methods of Proof
10. Exercises 1.5
8. Chapter 2 Relational Thinking
1. 2.1 Graphs
2. Exercises 2.1
3. 2.2 Sets
4. Exercises 2.2
5. 2.3 Functions
6. Exercises 2.3
7. 2.4 Relations and Equivalences
8. Exercises 2.4
9. 2.5 Partial Orderings
10. Exercises 2.5
11. 2.6 Graph Theory
12. Exercises 2.6
9. Chapter 3 Recursive Thinking
1. 3.1 Recurrence Relations
2. Exercises 3.1
3. 3.2 Closed-Form Solutions and Induction
4. Exercises 3.2
5. 3.3 Recursive Definitions
6. Exercises 3.3
7. 3.4 Proof by Induction
8. Exercises 3.4
9. 3.5 Recursive Data Structures
10. Exercises 3.5
10. Chapter 4 Quantitative Thinking
1. 4.1 Basic Counting Techniques
2. Exercises 4.1
3. 4.2 Selections and Arrangements
4. Exercises 4.2
5. 4.3 Counting with Functions
6. Exercises 4.3
7. 4.4 Discrete Probability
8. Exercises 4.4
9. 4.5 Counting Operations in Algorithms
10. Exercises 4.5
11. 4.6 Estimation
12. Exercises 4.6
11. Chapter 5 Analytical Thinking
1. 5.1 Algorithms
2. Exercises 5.1
3. 5.2 Three Common Types of Algorithms
4. Exercises 5.2
5. 5.3 Algorithm Complexity
6. Exercises 5.3
7. Exercises 5.4
8. 5.5 Program Verification
9. Exercises 5.5
10. 5.6 Loop Invariants
11. Exercises 5.6
12. Chapter 6 Thinking Through Applications
1. 6.1 Patterns in DNA
2. Exercises 6.1
3. 6.2 Social Networks
4. Exercises 6.2
5. 6.3 Structure of Languages
6. Exercises 6.3
7. 6.4 Discrete-Time Population Models
8. Exercises 6.4
9. 6.5 Twelve-Tone Music
10. Exercises 6.5
13. Hints, Answers, and Solutions to Selected Exercises
14. Selected References
15. Index
16. Index of Symbols