Discrete Mathematics
ISBN: 9780131593183 | 0131593188
Edition: 7thFormat: Hardcover
Publisher: Pearson
Pub. Date: 12/29/2007
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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.
Focused on helping readers understand and construct proofs and, generally, expanding their mathematical mat... MORE
Focused on helping readers understand and construct proofs and, generally, expanding their mathematical mat... MORE
| Sets and Logic | |
| Sets | |
| Propositions | |
| Conditional Propositions and Logical Equivalence | |
| Arguments and Rules of Inference | |
| Quantifiers | |
| Nested QuantifiersProblem-Solving Corner: Quantifiers | |
| Proofs | |
| Mathematical Systems, Direct Proofs, and Counterexamples | |
| More Methods of ProofProblem-Solving Corner: Proving Som... MORE | |
| Resolution Proofs | |
| Mathematical InductionProblem-Solving Corner: Mathematical Induction | |
| Strong Form of Induction and the Well-Ordering Property Notes Chapter Review Chapter Self-Test Computer Exercises | |
| Functions, Sequences, and Relations | |
| FunctionsProblem-Solving Corner: Functions | |
| Sequences and Strings | |
| Relations | |
| Equivalence RelationsProblem-Solving Corner: Equivalence Relations | |
| Matrices of Relations | |
| Relational Databases | |
| Algorithms | |
| Introduction | |
| Examples of Algorithms | |
| Analysis of AlgorithmsProblem-Solving Corner: Design and Analysis of an Algorithm | |
| Recursive Algorithms | |
| Introduction to Number Theory | |
| Divisors | |
| Representations of Integers and Integer Algorithms | |
| The Euclidean AlgorithmProblem-Solving Corner: Making Postage | |
| The RSA Public-Key Cryptosystem | |
| Counting Methods and the Pigeonhole Principle | |
| Basic PrinciplesProblem-Solving Corner: Counting | |
| Permutations and CombinationsProblem-Solving Corner: Combinations | |
| Generalized Permutations and Combinations | |
| Algorithms for Generating Permutations and Combinations | |
| Introduction to Discrete Probability | |
| Discrete Probability Theory | |
| Binomial Coefficients and Combinatorial Identities | |
| The Pigeonhole Principle | |
| Recurrence Relations | |
| Introduction | |
| Solving Recurrence RelationsProblem-Solving Corner: Recurrence Relations | |
| Applications to the Analysis of Algorithms | |
| Graph Theory | |
| Introduction | |
| Paths and CyclesProblem-Solving Corner: Graphs | |
| Hamiltonian Cycles and the Traveling Salesperson Problem | |
| A Shortest-Path Algorithm | |
| Representations of Graphs | |
| Isomorphisms of Graphs | |
| Planar Graphs | |
| Instant Insanity | |
| Trees | |
| Introduction | |
| Terminology and Characterizations of TreesProblem-Solving Corner: Trees | |
| Spanning Trees | |
| Minimal Spanning Trees | |
| Binary Trees | |
| Tree Traversals | |
| Decision Trees and the Minimum Time for Sorting | |
| Isomorphisms of Trees | |
| Game Trees | |
| Network Models | |
| Introduction | |
| A Maximal Flow Algorithm | |
| The Max Flow, Min Cut Theorem | |
| MatchingProblem-Solving Corner: Matching | |
| Boolean Algebras and Combinatorial Circuits | |
| Combinatorial Circuits | |
| Properties of Combinatorial Circuits | |
| Boolean AlgebrasProblem-Solving Corner: Boolean Algebras | |
| Boolean Functions and Synthesis of Circuits | |
| Applications | |
| 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 | |
| Computational Geometry | |
| The Closest-Pair Problem | |
| An Algorithm to Compute the Convex Hull | |
| Appendix | |
| Matrices | |
| Algebra Review | |
| Pseudocode | |
| References | |
| Hints and Solutions to Selected Exercises | |
| Index | |
| Table of Contents provided by Publisher. All Rights Reserved. |
Richard Johnsonbaugh is Professor Emeritus of Computer Science, Telecommunications and Information Systems, DePaul University, Chicago. Prior to his 20-year service at DePaul University, he was a member and sometime chair of the mathematics departments at Morehouse College and Chicago State University. He has a B.A. degree in mathematics from Yale University, M.A. and Ph.D. degrees in mathematics from the University of Oregon, and an M.S. degree in computer science from the University of Illinois, Chicago. His most recent research interests are in pattern recognition, programming languages, algorithms, and discrete mathematics. He is the author or co-author of numerous books and articles in these areas. Several of his books have been translated into various languages. He is a member of the Mathematical Association of America.
