Book description
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.
Table of contents
- Cover Page
- Title Page
- Copyright Page
- Table of Contents
- Preface
- How to Use This Book
- Chapter 1 Logical Thinking
- Chapter 2 Relational Thinking
- Chapter 3 Recursive Thinking
- Chapter 4 Quantitative Thinking
- Chapter 5 Analytical Thinking
- Chapter 6 Thinking Through Applications
-
Hints, Answers, and Solutions to Selected Exercises
- 1.1 Formal Logic
- 1.2 Propositional Logic
- 1.3 Predicate Logic
- 1.4 Logic in Mathematics
- 1.5 Methods of Proof
- 2.1 Graphs
- 2.2 Sets
- 2.3 Functions
- 2.4 Relations and Equivalences
- 2.5 Partial Orderings
- 2.6 Graph Theory
- 3.1 Recurrence Relations
- 3.2 Closed-Form Solutions and Induction
- 3.3 Recursive Definitions
- 3.4 Proof by Induction
- 3.5 Recursive Data Structures
- 4.1 Basic Counting Techniques
- 4.2 Selections and Arrangements
- 4.3 Counting with Functions
- 4.4 Discrete Probability
- 4.5 Counting Operations in Algorithms
- 4.6 Estimation
- 5.1 Algorithms
- 5.2 Three Common Types of Algorithms
- 5.3 Algorithm Complexity
- 5.4 Bounds on Complexity
- 5.5 Program Verification
- 5.6 Loop Invariants
- Selected References
- Index
- Index of Symbols
Product information
- Title: Essentials of Discrete Mathematics, 2nd Edition
- Author(s):
- Release date: December 2010
- Publisher(s): Jones & Bartlett Learning
- ISBN: 9781449604448
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