Discrete Mathematics / Edition 3

Discrete Mathematics / Edition 3

3.0 2
by Richard Johnsonbaugh
     
 

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ISBN-10: 0023607211

ISBN-13: 9780023607219

Pub. Date: 02/28/1993

Publisher: Prentice Hall Professional Technical Reference

This best-selling book provides an accessible introduction to discrete mathematics through an algorithmic approach that focuses on problem- solving techniques. This edition has the techniques of proofs woven into the text as a running theme and each chapter has the problem-solving corner. The text provides complete coverage of: Logic and Proofs; Algorithms;

Overview

This best-selling book provides an accessible introduction to discrete mathematics through an algorithmic approach that focuses on problem- solving techniques. This edition has the techniques of proofs woven into the text as a running theme and each chapter has the problem-solving corner. The text provides complete coverage of: Logic and Proofs; Algorithms; Counting Methods and the Pigeonhole Principle; Recurrence Relations; Graph Theory; Trees; Network Models; Boolean Algebra and Combinatorial Circuits; Automata, Grammars, and Languages; Computational Geometry. For individuals interested in mastering introductory discrete mathematics.

Product Details

ISBN-13:
9780023607219
Publisher:
Prentice Hall Professional Technical Reference
Publication date:
02/28/1993
Edition description:
Older Edition
Pages:
816

Table of Contents

(NOTE: Each chapter concludes with Notes, Chapter Review, Chapter Self-Test, and Computer Exercises.)
1. Logic and Proofs.

Propositions. Conditional Propositions and Logical Equivalence. Quantifiers. Proofs. Resolutions Proofs. Mathematical Induction.

2. The Language of Mathematics.
Sets. Sequences and Strings. Number Systems. Relations. Equivalence Relations. Matrices of Relations. Relational Databases. Functions.

3. Algorithms.
Introduction. Notation for Algorithms. The Euclidean Algorithm. Recursive Algorithms. Complexity of Algorithms. Analysis of the Ruclidean Algorithm. The RSA Public-Key Cryptosystem.

4. Counting Methods and the Pigeonhole Principle.
Basic Principles. Permutations and Combinations. Algorithms for Generating Permutations and Combinations. Introduction to Discrete Probability. Discrete Probability Theory. Generalized Permutations and Combinations. Binomial Coefficients and Combinatorial Identities. The Pigeonhole Principle.

5. Recurrence Relations.
Introduction. Solving Recurrence Relations. Applications to the Analysis of Algorithms.

6. Graph Theory.
Introduction. Paths and Cycles. Hamiltonian Cycles and the Traveling Salesperson Problem. A Shortest-Path Algorithm. Representation of Graphs. Isomorphisms of Graphs. Planar Graphs. Instant Insanity.

7. Trees.
Introduction. Terminology and Characterizations of Trees. Spanning Trees. Minimal Spanning Trees. Binary Trees. Tree Traversals. Decision Trees and the Minimum Time for Sorting. Isomorphisms of Trees. Game Trees.

8. Network Models.
Introduction. A Maximal Flow Algorithm. The Max Flow, Min Cut Theorem. Matching.

9. Boolean Algebra and Combinatorial Circuits.
Combinatorial Circuits. Properties of Combinatorial Circuits. Boolean Algebras. Boolean Functions and Synthesis of Circuits. Applications.

10. Automata, Grammars, and Languages.
Sequential Circuits and Finite-State Machines. Finite-State Automata. Languages and Grammars. Nondeterministic Finite-State Automata. Relationships between Languages and Automata.

11. Computational Geometry.
The Closest-Pair Problem. A Lower Bound for the Closest-Pair Problem. An Algorithm to Compute the Convex Hull.

Appendix A: Matrices.
Appendix B: Algebra Review.
References.
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.