Discrete Mathematics and Its Applications, 7/e
Kenneth H. Rosen
ISBN: 0073383090
Copyright year: 2012
CHAPTER 1 The Foundations: Logic and Proofs
1.1 Propositional Logic
1.2 Applications of Propositional Logic
1.3 Propositional Equivalences
1.4 Predicates and Quantifiers
1.5 Nested Quantifiers
1.6 Rules of Inference
1.7 Introduction to Proofs
1.8 Proof Methods and Strategy
CHAPTER 2 Basic Structures: Sets, Functions, Sequences, Sums, and Matrices
2.1 Sets
2.2 Set Operations
2.3 Functions
2.4 Sequences and Summations
2.5 Cardinality of Sets
2.6 Matrices
CHAPTER 3 Algorithms
3.1 Algorithms
3.2 The Growth of Functions
3.3 Complexity of Algorithms
CHAPTER 4 Number Theory and Cryptography
4.1 Divisibility and Modular Arithmetic
4.2 Integer Representations and Algorithms
4.3 Primes and Greatest Common Divisors
4.4 Solving Congruences
4.5 Applications of Congruences
4.6 Cryptography
CHAPTER 5 Induction and Recursion
5.1 Mathematical Induction
5.2 Strong Induction and Well-Ordering
5.3 Recursive Definitions and Structural Induction
5.4 Recursive Algorithms
5.5 Program Correctness
CHAPTER 6 Counting
6.1 The Basics of Counting
6.2 The Pigeonhole Principle
6.3 Permutations and Combinations
6.4 Binomial Coefficients and Identities
6.5 Generalized Permutations and Combinations
6.6 Generating Permutations and Combinations
CHAPTER 7 Discrete Probability
7.1 An Introduction to Discrete Probability
7.2 Probability Theory
7.3 Bayes' Theorem
7.4 Expected Value and Variance
CHAPTER 8 Advanced Counting Techniques
8.1 Applications of Recurrence Relations
8.2 Solving Linear Recurrence Relations
8.3 Divide-and-Conquer Algorithms and Recurrence Relations
8.4 Generating Functions
8.5 Inclusion-Exclusion
8.6 Applications of Inclusion-Exclusion
CHAPTER 9 Relations
9.1 Relations and Their Properties
9.2 n-ary Relations and Their Applications
9.3 Representing Relations
9.4 Closures of Relations
9.5 Equivalence Relations
9.6 Partial Orderings
CHAPTER 10 Graphs
10.1 Graphs and Graph Models
10.2 Graph Terminology and Special Types of Graphs
10.3 Representing Graphs and Graph Isomorphism
10.4 Connectivity
10.5 Euler and Hamilton Paths
10.6 Shortest-Path Problems
10.7 Planar Graphs
10.8 Graph Coloring
CHAPTER 11 Trees
11.1 Introduction to Trees
11.2 Applications of Trees
11.3 Tree Traversal
11.4 Spanning Trees
11.5 Minimum Spanning Trees
CHAPTER 12 Boolean Algebra
12.1 Boolean Functions
12.2 Representing Boolean Functions
12.3 Logic Gates
12.4 Minimization of Circuits
CHAPTER 13 Modeling Computation
13.1 Languages and Grammars
13.2 finite-State Machines with Output
13.3 finite-State Machines with No Output
13.4 Language Recognition
13.5 Turing Machines
APPENDIXES
A1 Axioms for the Real Numbers and the Positive Integers
A2 Exponential and Logarithmic Functions
A3 Pseudocode