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Discrete Mathematics, 5/E
Richard Johnsonbaugh, DePaul University

ISBN-10: 0130890081
ISBN-13: 9780130890085

Publisher: Pearson
Copyright: 2001
Format: Cloth; 621 pp
Published: 08/23/2000

For one or two term introductory courses in discrete mathematics.

This best-selling book provides an accessible introduction to discrete mathematics through an algorithmic approach that focuses on problem- solving techniques. This edition has woven techniques of proofs into the text as a running theme. Each chapter has a problem-solving corner that shows students how to attack and solve problems.

NEW - Expanded emphasis on reading and doing proofs.
- Helps students develop problem-solving skills. Ex.___

NEW - Enhanced logic sections.
- Provides students with new motivational examples. Ex.___

NEW - More exercises and examples—3500 exercises in all, 1/3 with answers and over 500 worked examples.
- Helps students practice solving problems. Ex.___

NEW - New icons and examples referencing World Wide Web links and Web help.
- Provides students with easy access to supplemental references. Ex.___

NEW - Logic Game.
- Offers students an alternative way to determine whether a quantified propositional function is true or false. Ex.___

NEW - Arrow diagrams and graphs of functions added.
- Offers students a pictorial view of functions. Ex.___

NEW - Sections on discrete probability.

NEW - Appendix on basic algebra review.
- Provides students with easy-access to review important mathematical functions. Ex.___

NEW - Computer examples and exercises.
- Helps students connect theory to use of computer. Ex.___

NEW - Section Reviews.
- Provides students with a review of key concepts, definitions and techniques. Ex.___

NEW - 650 figures and tables.
- Improves students understanding by illustrating concepts and showing how algorithms work. Ex.___

Hallmark Features.

Thorough discussion of algorithms, recursive algorithms, and the analysis of algorithms.
- Written in pseudocode, algorithms aid comprehension and help to enliven the material and motivate students. Ex.___

Significant number of applications, especially applications related to computer science.
- Helps students to see concepts' practicality. Ex.___

Notes sections with suggestions for further reading and reference section.
- Provides students with up-to-date readings so they can conduct further investigation. Ex.___

Problem-solving corners.
- Helps students solve problems and shows how to do proofs. Ex.___

Expanded emphasis on reading and doing proofs.
- Helps students develop problem-solving skills. Ex.___

Enhanced logic sections.
- Provides students with new motivational examples. Ex.___

More exercises and examples—3500 exercises in all, 1/3 with answers and over 500 worked examples.
- Helps students practice solving problems. Ex.___

New icons and examples referencing World Wide Web links and Web help.
- Provides students with easy access to supplemental references. Ex.___

Logic Game.
- Offers students an alternative way to determine whether a quantified propositional function is true or false. Ex.___

Arrow diagrams and graphs of functions added.
- Offers students a pictorial view of functions. Ex.___

Sections on discrete probability.

Appendix on basic algebra review.
- Provides students with easy-access to review important mathematical functions. Ex.___

Computer examples and exercises.
- Helps students connect theory to use of computer. Ex.___

Section Reviews.
- Provides students with a review of key concepts, definitions and techniques. Ex.___

650 figures and tables.
- Improves students understanding by illustrating concepts and showing how algorithms work. Ex.___

(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.

Discrete Math (Mathematics)

Discrete Mathematics, 7/E
Johnsonbaugh
©2009 | Pearson | Cloth; 792 pp | Instock
ISBN-10: 0131593188 | ISBN-13: 9780131593183
Net price: $96.00 (What's this?)Brief Description

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.

Author Bios

Richard Johnsonbaugh has a Ph.D. from the University of Oregon. He is professor of Computer Science and Information Systems, at DePaul University. He has 25 years of experience in teaching and research, including programming in general and in the C language. Dr. Johnsonbaugh specializes in programming languages, compilers, data structures, and pattern recognition. He is the author of two very successful books on Discrete Mathematics.

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