Discrete Mathematics, 8th edition
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Overview
Discrete Mathematics, 8th Edition is an accessible introduction that helps to develop your mathematical maturity. Ample opportunities to practice, apply and demonstrate conceptual understanding are provided. Exercise sets feature a large number of applications, especially to computer science. Worked examples provide ready reference as you work. The text models various problem-solving techniques in detail, then encourages you to practice these techniques; it also emphasizes how to read and write proofs. Many proofs are illustrated with annotated figures and/or motivated by special Discussion sections. URLs throughout direct you to relevant applications, extensions, and computer programs.
Published by Pearson (June 1st 2023) - Copyright © 2023
ISBN-13: 9780137848577
Subject: Advanced Math
Category: Discrete Math
Overview
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
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
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
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
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
6. Counting Methods and the Pigeonhole Principle
- 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
7. Recurrence Relations
- 7.1 Introduction
- 7.2 Solving Recurrence Relations
- Problem-Solving Corner: Recurrence Relations
- 7.3 Applications to the Analysis of Algorithms
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
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 Trees
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
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
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
13. Computational Geometry
- 13.1 The Closest-Pair 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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