Essentials of discrete mathematics / by David J. Hunter.

Includes bibliographical references and index.

Table of contents Cover
Title Page
Copyright Page
Contents
Preface
Introduction
What's New in the Fourth Edition
How to Use this Book
About the Cover
Supplements
Acknowledgments
Chapter 1 Logical Thinking
1.1 Formal Logic
1.1.1 Preview Questions
1.1.2 Connectives and Propositions
1.1.3 Truth Tables
1.1.4 Activities
1.1.5 Logical Equivalences
Exercises 1.1
1.2 Propositional Logic
1.2.1 Tautologies and Contradictions
1.2.2 Derivation Rules
1.2.3 Proof Sequences
1.2.4 Forward-Backward
Exercises 1.2
1.3 Predicate Logic
1.3.1 Predicates 1.3.2 Quantifiers
1.3.3 Translation
1.3.4 Negation
1.3.5 Two Common Constructions
Exercises 1.3
1.4 Logic in Mathematics
1.4.1 The Role of Definitions in Mathematics
1.4.2 Other Types of Mathematical Statements
1.4.3 Counterexamples
1.4.4 Axiomatic Systems
Exercises 1.4
1.5 Methods of Proof
1.5.1 Direct Proofs
1.5.2 Proof by Contraposition
1.5.3 Proof by Contradiction
Exercises 1.5
Chapter 2 Relational Thinking
2.1 Graphs
2.1.1 Edges and Vertices
2.1.2 Terminology
2.1.3 Modeling Relationships with Graphs
Exercises 2.1
2.2 Sets 2.2.1 Membership and Containment
2.2.2 New Sets from Old
2.2.3 Identities
Exercises 2.2
2.3 Functions
2.3.1 Definition and Examples
2.3.2 One-to-One and Onto Functions
2.3.3 New Functions from Old
Exercises 2.3
2.4 Relations and Equivalences
2.4.1 Definition and Examples
2.4.2 Graphs of Relations
2.4.3 Relations vs. Functions
2.4.4 Equivalence Relations
2.4.5 Modular Arithmetic
Exercises 2.4
2.5 Partial Orderings
2.5.1 Definition and Examples
2.5.2 Hasse Diagrams
2.5.3 Topological Sorting
2.5.4 Isomorphisms
2.5.5 Boolean Algebras Exercises 2.5
2.6 Graph Theory
2.6.1 Graphs: Formal Definitions
2.6.2 Isomorphisms of Graphs
2.6.3 Degree Counting
2.6.4 Euler Paths and Circuits
2.6.5 Hamilton Paths and Circuits
2.6.6 Trees
Exercises 2.6
Chapter 3 Recursive Thinking
3.1 Recurrence Relations
3.1.1 Definition and Examples
3.1.2 The Fibonacci Sequence
3.1.3 Modeling with Recurrence Relations
Exercises 3.1
3.2 Closed-Form Solutions and Induction
3.2.1 Guessing a Closed-Form Solution
3.2.2 Polynomial Sequences: Using Differences
3.2.3 Inductively Verifying a Solution Exercises 3.2
3.3 Recursive Definitions
3.3.1 Definition and Examples
3.3.2 Writing Recursive Definitions
3.3.3 Recursive Geometry
3.3.4 Recursive Jokes
Exercises 3.3
3.4 Proof by Induction
3.4.1 The Principle of Induction
3.4.2 Examples
3.4.3 Strong Induction
3.4.4 Structural Induction
Exercises 3.4
3.5 Recursive Data Structures
3.5.1 Lists
3.5.2 Efficiency
3.5.3 Binary Search Trees Revisited
Exercises 3.5
Chapter 4 Quantitative Thinking
4.1 Basic Counting Techniques
4.1.1 Addition
4.1.2 Multiplication

"Essentials of Discrete Mathematics is designed for the one-semester undergraduat,e discrete math course. This course geared towards math and computer science majors. The textbook is organized around five types of mathematical thinking, with each chapter addressing a different type of thinking: logical, relational, recursive, quantitative, and analytical. The final chapter, "Thinking Through Applications" looks at different ways that discrete math thinking can be applied. Applications are included throughout the textbook and are sourced from a variety of disciplines, including biology, economics, music, and more"--

Computer Science & Engineering Computer Science & Engineering

Muktadir Rahman