Discrete Mathematics, 8th edition
Published by Pearson (March 6th 2017)  Copyright © 2018
8th edition

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Overview
For one or twoterm introductory courses in discrete mathematics.
An accessible introduction to the topics of discrete math, this bestselling text also works to expand students’ mathematical maturity.
With nearly 4,500 exercises, Discrete Mathematics provides ample opportunities for students to practice, apply, and demonstrate conceptual understanding. Exercise sets features a large number of applications, especially applications to computer science. The almost 650 worked examples provide ready reference for students as they work. A strong emphasis on the interplay among the various topics serves to reinforce understanding. The text models various problemsolving techniques in detail, then provides opportunity to practice these techniques. The text also builds mathematical maturity by emphasizing how to read and write proofs. Many proofs are illustrated with annotated figures and/or motivated by special Discussion sections. The side margins of the text now include “tiny URLs” that direct students to relevant applications, extensions, and computer programs on the textbook website.
Table of contents
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
ProblemSolving Corner: Quantifiers
2. Proofs
2.1 Mathematical Systems, Direct Proofs, and Counterexamples
2.2 More Methods of Proof
ProblemSolving Corner: Proving Some Properties of Real Numbers
2.3 Resolution Proofs
2.4 Mathematical Induction
ProblemSolving Corner: Mathematical Induction
2.5 Strong Form of Induction and the WellOrdering Property
3. Functions, Sequences, and Relations
3.1 Functions
ProblemSolving Corner: Functions
3.2 Sequences and Strings
3.3 Relations
3.4 Equivalence Relations
ProblemSolving Corner: Equivalence Relations
3.5 Matrices of Relations
3.6 Relational Databases
4. Algorithms
4.1 Introduction
4.2 Examples of Algorithms
4.3 Analysis of Algorithms
ProblemSolving Corner: Design and Analysis of an Algorithm
4.4 Recursive Algorithms
5. Introduction to Number Theory
5.1 Divisors
5.2 Representations of Integers and Integer Algorithms
5.3 The Euclidean Algorithm
ProblemSolving Corner: Making Postage
5.4 The RSA PublicKey Cryptosystem
6. Counting Methods and the Pigeonhole Principle
6.1 Basic Principles
ProblemSolving Corner: Counting
6.2 Permutations and Combinations
ProblemSolving Corner: Combinations
6.3 Generalized Permutations and Combinations
6.4 Algorithms for Generating Permutations and Combinations
6.5 Introduction to Discrete Probability
6.6 Discrete Probability Theory
6.7 Binomial Coefficients and Combinatorial Identities
6.8 The Pigeonhole Principle
7. Recurrence Relations
7.1 Introduction
7.2 Solving Recurrence Relations
ProblemSolving Corner: Recurrence Relations
7.3 Applications to the Analysis of Algorithms
8. Graph Theory
8.1 Introduction
8.2 Paths and Cycles
ProblemSolving Corner: Graphs
8.3 Hamiltonian Cycles and the Traveling Salesperson Problem
8.4 A ShortestPath Algorithm
8.5 Representations of Graphs
8.6 Isomorphisms of Graphs
8.7 Planar Graphs
8.8 Instant Insanity
9. Trees
9.1 Introduction
9.2 Terminology and Characterizations of Trees
ProblemSolving 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 Trees
10. Network Models
10.1 Introduction
10.2 A Maximal Flow Algorithm
10.3 The Max Flow, Min Cut Theorem
10.4 Matching
ProblemSolving Corner: Matching
11. Boolean Algebras and Combinatorial Circuits
11.1 Combinatorial Circuits
11.2 Properties of Combinatorial Circuits
11.3 Boolean Algebras
ProblemSolving Corner: Boolean Algebras
11.4 Boolean Functions and Synthesis of Circuits
11.5 Applications
12. Automata, Grammars, and Languages
12.1 Sequential Circuits and FiniteState Machines
12.2 FiniteState Automata
12.3 Languages and Grammars
12.4 Nondeterministic FiniteState Automata
12.5 Relationships Between Languages and Automata
13. Computational Geometry
13.1 The ClosestPair Problem
13.2 An Algorithm to Compute the Convex Hull
Appendix
A. Matrices
B. Algebra Review
C. Pseudocode
References
Hints and Solutions to Selected Exercises
Index
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