Discrete Mathematics and Its Applications with MathZone by Kenneth H. Rosen

Preface
The MathZone Companion Website
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 Recurrenceelations
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
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11 Boolean Algebra
11.1 Boolean Functions
11.2 Representing Boolean Functions
11.3 Logic Gates
11.4 Minimization of Circuits
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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