Discrete Mathematics / Edition 4 available in Hardcover
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.
|Edition description:||Older Edition|
|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.
Partial Ordering Relations.
Graphs and Their Representations.
Paths and Circuits.
Shortest Paths and Distance.
Coloring a Graph.
Directed Graphs and Multi Graphs.
Properties of Trees.
Binary Trees and Traversals.
Optimal Binary Trees and Binary Search Trees.
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.
*The Principle of Inclusion-Exclusion.
*Generating Permutations and r-Combinations.
8. Recurrence Relations and Generating Functions.
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.
Creating Combinatorial Circuits.
Finite State Machines.
Appendix A: An Introduction to Logic and Proof.
Statements and Connectives.
Methods of Proof.
Appendix B: Matrices.
Appendix C: The Algorithms in this Book.
Answers to Odd-Numbered Exercises.