Discrete Mathematics and its Applications, Sixth Edition, is intended for one- or two-term introductory discrete mathematics courses taken by students from a wide variety of majors, including computer science, mathematics, and engineering. This renowned best-selling text, which has been used at over 500 institutions around the world, gives a focused introduction to the primary themes in a discrete mathematics course and demonstrates the relevance and practicality of discrete mathematics to a wide a wide variety of real-world applications¿from computer science to data networking, to psychology, to chemistry, to engineering, to linguistics, to biology, to business, and to many other important fields.

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Preface

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To the Student 1 The Foundations: Logic and Proofs

1.1 Propositional Logic

1.2 Propositional Equivalences

1.3 Predicates and Quantifiers

1.4 Nested Quantifiers

1.5 Rules of Inference

1.6 Introduction to Proofs

1.7 Proof Methods and Strategy

End-of-Chapter Material 2 Basic Structures: Sets, Functions, Sequences and Sums

2.1 Sets

2.2 Set Operations

2.3 Functions

2.4 Sequences and Summations

End-of-Chapter Material 3 The Fundamentals: Algorithms, the Integers, and Matrices

3.1 Algorithms

3.2 The Growth of Functions

3.3 Complexity of Algorithms

3.4 The Integers and Division

3.5 Primes and Greatest Common Divisors

3.6 Integers and Algorithms

3.7 Applications of Number Theory

3.8 Matrices

End-of-Chapter Material 4 Induction and Recursion

4.1 Mathematical Induction

4.2 Strong Induction and Well-Ordering

4.3 Recursive Definitions and Structural Induction

4.4 Recursive Algorithms

4.5 Program Correctness

End-of-Chapter Material 5 Counting

5.1 The Basics of Counting

5.2 The Pigeonhole Principle

5.3 Permutations and Combinations

5.4 Binomial Coefficients

5.5 Generalized Permutations and Combinations

5.6 Generating Permutations and Combinations

End-of-Chapter Material 6 Discrete Probability

6.1 An Introduction to Discrete Probability

6.2 Probability Theory

6.3 Bayes¿ Theorem

6.4 Expected Value and Variance

End-of-Chapter Material 7 Advanced Counting Techniques

7.1 Recurrence Relations

7.2 Solving Linear Recurrence Relations

7.3 Divide-and-Conquer Algorithms and Recurrence elations

7.4 Generating Functions

7.5 Inclusion-Exclusion

7.6 Applications of Inclusion-Exclusion

End-of-Chapter Material 8 Relations

8.1 Relations and Their Properties

8.2 n-ary Relations and Their Applications

8.3 Representing Relations

8.4 Closures of Relations

8.5 Equivalence Relations

8.6 Partial Orderings

End-of-Chapter Material 9 Graphs

9.1 Graphs and Graph Models

9.2 Graph Terminology and Special Types of Graphs

9.3 Representing Graphs and Graph Isomorphism

9.4 Connectivity

9.5 Euler and Hamilton Paths

9.6 Shortest-Path Problems

9.7 Planar Graphs

9.8 Graph Coloring

End-of-Chapter Material 10 Trees

10.1 Introduction to Trees

10.2 Applications of Trees

10.3 Tree Traversal

10.4 Spanning Trees

10.5 Minimum Spanning Trees

End-of-Chapter Material 11 Boolean Algebra

11.1 Boolean Functions

11.2 Representing Boolean Functions

11.3 Logic Gates

11.4 Minimization of Circuits

End-of-Chapter Material 12 Modeling Computation

12.1 Languages and Grammars

12.2 Finite-State Machines with Output

12.3 Finite-State Machines with No Output

12.4 Language Recognition

12.5 Turing Machines

End-of-Chapter Material Appendixes

A.1 Axioms for the Real Numbers and the Positive Integers

A.2 Exponential and Logarithmic Functions

A.3 Pseudocode Suggested Readings Answers to Odd-Numbered Exercises Photo Credits Index of Biographies Index