ISBN-10:
0321079124
ISBN-13:
9780321079121
Pub. Date:
10/10/2001
Publisher:
Pearson Education
Discrete Mathematics / Edition 4

Discrete Mathematics / Edition 4

by John A. Dossey
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Overview

The strong algorithmic emphasis of Discrete Mathematics is independent of a specific programming language, allowing students to concentrate on foundational problem-solving and analytical skills. Instructors get the topical breadth and organizational flexibility to tailor the course to the level and interests of their students.

Algorithms are presented in English, eliminating the need for knowledge of a particular programming language. Computational and algorithmic exercise sets follow each chapter section and supplementary exercises and computer projects are included in the end-of-chapter material. This Fifth Edition features a new Chapter 3 covering matrix codes, error correcting codes, congruence, Euclidean algorithm and Diophantine equations, and the RSA algorithm.

MARKET: Intended for use in a one-semester introductory course in discrete mathematics.

Product Details

ISBN-13: 9780321079121
Publisher: Pearson Education
Publication date: 10/10/2001
Edition description: Older Edition
Pages: 600
Product dimensions: 7.20(w) x 9.00(h) x 1.40(d)

Table of Contents

(Each Chapter, excluding Chapter 7, concludes with "Historical Notes," "Supplement Exercises," "Computer Projects," and "Suggested Readings.").
1. An Introduction to Combinatorial Problems and Techniques.
The Time to Complete a Project.
A Matching Problem.
A Knapsack Problem.
Algorithms and Their Efficiency.

2. Sets, Relations, and Functions.
Set Operations.
Equivalence Relations.
Congruence.
Partial Ordering Relations.
Functions.
Mathematical Induction.
Applications.

3. Graphs.
Graphs and Their Representations.
Paths and Circuits.
Shortest Paths and Distance.
Coloring a Graph.
Directed Graphs and Multi Graphs.

4. Trees.
Properties of Trees.
Spanning Trees.
Depth-First Search.
Rooted Trees.
Binary Trees and Traversals.
Optimal Binary Trees and Binary Search Trees.

5. Matching.
Systems of Distinct Representatives.
Matching in Graphs.
A Matching Algorithm.
Applications of the Algorithm.
The Hungarian Method.

6. Network Flows.
Flows and Cuts.
A Flow Augmentation Algorithm.
The Max-Flow Min-Cut Theorem.
Flows and Matchings.

7. Counting Techniques.
Pascal's Triangle and the Binomial Theorem.
Three Fundamental Principles.
Permutations and Combinations.
Arrangements and Selections with Repetitions.
Probability.
*The Principle of Inclusion-Exclusion.
*Generating Permutations and r-Combinations.

8. Recurrence Relations and Generating Functions.
Recurrence Relations.
The Method of Iteration.
Linear Difference Equations with Constant Coefficients.
*Analyzing the Efficiency of Algorithms with RecurrenceRelations.
Counting with Generating Functions.
The Algebra of Generating Functions.

9. Combinatorial Circuits and Finite State Machines.
Logical Gates.
Creating Combinatorial Circuits.
Karnaugh Maps.
Finite State Machines.

Appendix A: An Introduction to Logic and Proof.
Statements and Connectives.
Logical Equivalence.
Methods of Proof.

Appendix B: Matrices.
Appendix C: The Algorithms in this Book.
Bibliography.
Answers to Odd-Numbered Exercises.
Index.
*Optional Sections.

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