Discrete Mathematics, 8th edition

Richard Johnsonbaugh

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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.

ISBN-13: 9780137848577

Subject: Advanced Math

Category: Discrete Math

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