Discrete Mathematics, 8th edition
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Overview
Hallmark features of this title
 Problem Solving Corners help students attack and solve problems, and show them how to do proofs.
 Strong emphasis on reading and writing proofs illustrates most proofs of theorems with annotated figures to provide additional explanation and insight into the proofs.
 Extensive discussion of algorithms, recursive algorithms, and the analysis of algorithms: Algorithms are written in a flexible form of pseudocode resembling languages such as C, C++ and Java.
 Figures and tables illustrate concepts, show how algorithms work, elucidate proofs, and motivate the material.
 Short URLs give easy access to corresponding web pages, especially with a mobile device.
Published by Pearson (June 1st 2023)  Copyright © 2023
ISBN13: 9780137848577
Subject: Advanced Math
Category: Discrete Math
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
Appendices
 A. Matrices
 B. Algebra Review
 C. Pseudocode
References
Hints and Solutions to Selected Exercises
Index
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