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DISCRETE MATHEMATICS
ISBN: 9780023607219 | 0023607211
Edition: 3rdPublisher: Prentice Hall Professional Technical Reference
Pub. Date: 1/1/1993
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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.
| Preface | |
| Logic and Proofs | |
| Propositions | |
| Conditional Propositions and Logical Equivalence | |
| Quantifiers | |
| Proofs | |
| Resolution Proofs | |
| Mathematical Induction | |
| Strong Form of Induction and well ordering Property | |
| The Language of Mathematics | |
| Sets | |
| Functions | ... MORE |
| Sequences and Strings | |
| Relations | |
| Relations | |
| Relations | |
| Equivalence Relations | |
| Matrices of Relations | |
| Relational Databases | |
| Algorithms | |
| Introduction | |
| Correctness of Algorithms | |
| Analysis of Algorithms | |
| Recursive Algorithms | |
| Introduction to Number Theory | |
| Divisors | |
| Representation of Integers and Integer Algorithims | |
| The Euclidean Algorithm | |
| The RSA Public-Key Cryptosystem | |
| 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 | |
| Recurrence Relations | |
| Introduction | |
| Solving Recurrence Relations | |
| Applications to the Analysis of Algorithms | |
| Graph Theory | |
| Introduction | |
| Paths and Cycles | |
| 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 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 | |
| Matching | |
| Boolean Algebras and Combinatorial Circuits | |
| Combinatorial Circuits | |
| Properties of Combinatorial Circuits | |
| 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 | |
| Appendices | |
| Matrices | |
| Algebra Review | |
| References | |
| Hints and Solutions to Selected Exercises | |
| Index | |
| Table of Contents provided by Publisher. All Rights Reserved. |
