Discrete Mathematics, Global Edition, 8th Edition
- Length: 772 pages
- Edition: 8
- Language: English
- Publisher: Pearson
- Publication Date: 2018-09-19
- ISBN-10: 1292233702
- ISBN-13: 9781292233703
- Sales Rank: #253075 (See Top 100 Books)
For one- or two-term introductory courses in discrete mathematics. An accessible introduction to the topics of discrete math, this best-selling 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 problem-solving 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.
Front Cover List of Symbols Title Page Copyright Page Contents Preface 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 Chapter 1 Notes Chapter 1 Review Chapter 1 Self-Test Chapter 1 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 Proofs 2.4 Mathematical Induction Problem-Solving Corner Mathematical Induction 2.5 Strong Form of Induction and the Well-Ordering Property Chapter 2 Notes Chapter 2 Review Chapter 2 Self-Test Chapter 2 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 Chapter 3 Notes Chapter 3 Review Chapter 3 Self-Test Chapter 3 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 Chapter 4 Notes Chapter 4 Review Chapter 4 Self-Test Chapter 4 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 Chapter 5 Notes Chapter 5 Review Chapter 5 Self-Test Chapter 5 Computer Exercises 6 Counting Methods and the PigeonholePrinciple 6.1 Basic Principles Problem-Solving Corner: Counting 6.2 Permutations and Combinations Problem-Solving 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 Chapter 6 Notes Chapter 6 Review Chapter 6 Self-Test Chapter 6 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 7.4 The Closest-Pair Problem Chapter 7 Notes Chapter 7 Review Chapter 7 Self-Test Chapter 7 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 Insanity Chapter 8 Notes Chapter 8 Review Chapter 8 Self-Test Chapter 8 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 Timefor Sorting 9.8 Isomorphisms of Trees 9.9 Game Trees Chapter 9 Notes Chapter 9 Review Chapter 9 Self-Test Chapter 9 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 Chapter 10 Notes Chapter 10 Review Chapter 10 Self-Test Chapter 10 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 Chapter 11 Notes Chapter 11 Review Chapter 11 Self-Test Chapter 11 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 Chapter 12 Notes Chapter 12 Review Chapter 12 Self-Test Chapter 12 Computer Exercises Appendix A Matrices B Algebra Review C Pseudocode References Hints and Solutions to Selected Exercises Index Back Cover
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