Discrete Mathematics

by: Johnsonbaugh, Richard

Discrete Mathematics

by: Johnsonbaugh, Richard

ISBN 13:
9780131176867
ISBN 10:
0131176862
Edition: 6th
Format: Hardcover
Copyright: 01/01/2009
Publisher: Prentice Hall
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Summary

This best-selling book provides an accessible introduction to discrete mathematics through an algorithmic approach that focuses on problem-solving techniques.The book 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
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.

Discrete Mathematics

Discrete Mathematics

9780131176867

0131176862

Summary

Table of Contents

Supplemental Materials

Write a Review

Discrete Mathematics

Discrete Mathematics

9780131176867

0131176862

Summary

Table of Contents

Supplemental Materials

Write a Review

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