Preface XI
1 Sets and Logic
1.1 Sets
1.2 Propositions
1.3 Conditional Propositions and Logical Equivalence
1.4 Arguments and Rules of Inference
1.5 Quantifiers
1.6 Nested Quantifiers
Problem-Solving Corner: Quantifiers
Notes
Chapter Review
Chapter Self-Test
Computer Exercises
2 Proofs
2.1 Mathematical Systems, Direct Proofs, and Counterexamples
2.2 More Methods of Proof
Problem-Solving Corner: Proving Some Properties of Real Numbers
2.3 Resolution Proofst
2.4 Mathematical Induction
Problem-Solving Corner: Mathematical Induction
2.5 Strong Form of Induction and the Well-Ordering Property
Notes
Chapter Review
Chapter Self-Test
Computer Exercises
3 Functions,Sequences,and Relations
3.1 Functions
Problem-Solving Corner: Functions
3.2 Sequences and Strings
3.3 Relations
3.4 Equivalence Relations
Problem-Solving Corner: Equivalence Relations
3.5 Matrices of Relations
3.6 Relational Databases
Notes
Chapter Review
Chapter Self-Test
Computer Exercises
4 Algorithms
4.1 Introduction
4.2 Examples of Algorithms
4.3 Analysis of Algorithms
Problem-Solving Corner: Design and Analysis of an Algorithm
4.4 Recursive Algorithms
Notes
Chapter Review
Chapter Self-Test
Computer Exercises
5 Introduction to Number Theory
5.1 Divisors
5.2 Representations of Integers and Integer Algorithms
5.3 The Euclidean Algorithm
Problem-Solving Corner: Making Postage
5.4 The RSA Public-Key Cryptosystem
Notes
Chapter Review
Chapter Self-Test
Computer Exercises
6 Counting Methods and the Pigeonhole Principle
6.1 Basic Principles
Problem-Solving Corner: Counting
6.2 Permutations and Combinations
Problem-Solving Comer:. Combinations
6.3 Generalized Permutations and Combinations
6.4 Algorithms for Generating Permutations and Combinations
6.5 Introduction to Discrete Probabilityt
6.6 Discrete Probability Theoryt
6.7 Binomial Coefficients and Combinatorial Identities
6.8 The Pigeonhole Principle
Notes
Chapter Review
Chapter Self-Test
Computer Exercises
7 Recurrence Relations
7.1 Introduction
7.2 Solving Recurrence Relations
Problem-Solving Corner: Recurrence Relations
7.3 Applications to the Analysis of Algorithms ..
Notes
Chapter Review
Chapter Self-Test
Computer Exercises
8 Graph Theory
8.1 Introduction
8.2 Paths and Cycles
Problem-Solving Corner: Graphs
8.3 Hamiltonian Cycles and the Traveling Salesperson Problem
8.4 A Shortest-Path Algorithm
8.5 Representations of Graphs
8.6 Isomorphisms of Graphs
8.7 Planar Graphs
8.8 Instant Insanityt
Notes
Chapter Review
Chapter Self-Test
Computer Exercises
9 Trees
9.1 Introduction
9.2 Terminology and Characterizations of Trees
Problem-Solving Corner: Trees
9.3 Spanning Trees
9.4 Minimal Spanning Trees
9.5 Binary Trees
9.6 Tree Traversals
9.7 Decision Trees and the Minimum Time for Sorting
9.8 Isomorphisms of Trees
9.9 Game Treest
Notes
Chapter Review
Chapter Self-Test
Computer Exercises
10 Network Models
10.1 Introduction
10.2 A Maximal Flow Algorithm
10.3 The Max Flow, Min Cut Theorem
10.4 Matching
Problem-Solving Corner: Matching
Notes
Chapter Review
Chapter Self-Test
Computer Exercises
11 Boolean Algebras and Combinatorial Circuits
11.1 Combinatorial Circuits
11.2 Properties of Combinatorial Circuits
11.3 Boolean Algebras
Problem-Solving Corner: Boolean Algebras
11.4 Boolean Functions and Synthesis of Circuits
11.5 Applications
Notes
Chapter Review
Chapter Self-Test
Computer Exercises
12 Automata,Grammars,and Languages
12.1 Sequential Circuits and Finite-State Machines
12.2 Finite-State Automata
12.3 Languages and Grammars
12.4 Nondeterministic Finite-State Automata
12.5 Relationships Between Languages and Automata
Notes
Chapter Review
Chapter Self-Test
Computer Exercises
13 Computational Geometry
13.1 The Closest-Pair Problem
13.2 An Algorithm to Compute the Convex Hull
Notes
Chapter Review
Chapter Self-Test
Computer Exercises
Appendix
A Matrices
B Algebra Review
C Pseudocode
References
Hints and Solutions to Selected Exercises
Index
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