Discrete Mathematics / Edition 7

Discrete Mathematics / Edition 7

by Richard Johnsonbaugh
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Discrete Mathematics / Edition 7

For a one- or two-term introductory course in discrete mathematics.

Focused on helping students understand and construct proofs and expanding their mathematical maturity, this best-selling text is an accessible introduction to discrete mathematics. Johnsonbaugh’s algorithmic approach emphasizes problem-solving techniques. The Seventh Edition reflects user and reviewer feedback on both content and organization.

Product Details

ISBN-13: 9780131593183
Publisher: Pearson
Publication date: 01/12/2008
Series: Featured Titles for Discrete Mathematics Series
Edition description: Older Edition
Pages: 792
Product dimensions: 8.10(w) x 10.10(h) x 1.30(d)

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

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 Notes Chapter Review Chapter Self-Test 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

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


A Matrices

B Algebra Review

C Pseudocode


Hints and Solutions to Selected Exercises Index

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Discrete Mathematics 3 out of 5 based on 0 ratings. 2 reviews.
TheStudent101101 More than 1 year ago
I agree with the others that this book needs to be burned. I have taken Discrete Mathematics one using this textbook and I also tried looking at the authors earlier edition, but it was a worthless attempt. I have to resort to using other resources such as the internet, other text, and individuals who have a firm undersatnding of the subject. The same individuals who are Computer Science or Math majors all agree that this book is trash. The author is probably a very intelligent individual but he does not explain much of anything in great detail. That is something that a novice needs to grasp a full understanding of the concepts. Without concepts the foundation is weak and clarity is non-existent. To whom it may concern choose another text book.
Guest More than 1 year ago
I am a Comp Sci student from WCU in Pa., this is a required reading for a 100 level math course (MAT151 to be exact). I found this book to be extremely informative and helpful, especially chapter 5 on Recurrence Relations. Perhaps the people who didn't do so well were either not ready for the course material or not devoted to their studying. Either way, good or bad, go to the B.N. store and read some of the book before you buy to see if you like it or not.