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Discrete and Combinatorial Mathematics: An Applied Introduction

Discrete and Combinatorial Mathematics: An Applied Introduction - 4th edition

Discrete and Combinatorial Mathematics: An Applied Introduction - 4th edition

ISBN13: 9780201199123

ISBN10: 0201199122

Discrete and Combinatorial Mathematics: An Applied Introduction by Ralph P. Grimaldi - ISBN 9780201199123
Edition: 4TH 99
Copyright: 1999
Publisher: Addison-Wesley Longman, Inc.
International: No
Discrete and Combinatorial Mathematics: An Applied Introduction by Ralph P. Grimaldi - ISBN 9780201199123

ISBN13: 9780201199123

ISBN10: 0201199122

Edition: 4TH 99

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This fourth edition continues to improve on the features that have made it the market leader. The text offers a flexible organization, enabling instructors to adapt the book to their particular courses: discrete mathematics, graph theory, modern algebra, and/or combinatorics. More elementary problems were added, creating a greater variety of level in problem sets, which allows students to perfect skills as they practice. This new edition continues to feature numerous computer science applications--making this the ideal text for preparing students for advanced study.


  • This text has an enhanced mathematical approach, with carefully thought out examples, including many examples with computer sciences applications.
  • Historical reviews and biographies bring a human element to their assignments.
  • Chapter summaries allow students to review what they have learned.

Author Bio

Grimaldi, Ralph P. : Rose-Hulman Institute of Technology

Table of Contents

Table of Contents

Chapter 1: Fundamentals of Discrete Mathematics

Fundamental Principles of Counting
The Rules of Sum and Product
The Binomial Theorem
Combinations with Repetition: Distributions
An Application in the Physical Sciences (Optional)
Catalan Numbers

Chapter 2: Fundamentals of Logic

Basic Connectives and Truth Tables
Logical Equivalence: The Laws of Logic
Logical Implication: Rules of Inference
The Use of Quantifiers
Quantifiers, Definitions, and the Proofs of Theorems

Chapter 3: Set Theory

Sets and Subsets
Set Operations and the Laws of Set Theory
Counting and Venn Diagrams
A Word on Probability

Chapter 4: Properties of the Integers: Mathematical Induction

The Well-Ordering Principle: Mathematical Induction
Recursive Definitions
The Division Algorithm: Prime Numbers
The Greatest Common Divisor: The Euclidean Algorithm
The Fundamental Theorem of Arithmetic

Chapter 5: Relations and Functions

Cartesian Products and Relations
Functions: Plain and One-to-One
Onto Functions: Stirling Numbers of the Second Kind
Special Functions
The Pigeonhole Principle
Function Composition and Inverse Functions
Computational Complexity
Analysis of Algorithms

Chapter 6: Languages: Finite State Machines

Language: The Set Theory of Strings
Finite State Machines: A First Encounter
Finite State Machines: A Second Encounter
Relations: The Second Time Around
Relations Revisited: Properties of Relations
Computer Recognition: Zero­One Matrices and Directed Graphs
Partial Orders: Hasse Diagrams
Equivalence Relations and Partitions
Finite State Machines: The Minimization Process

Chapter 7: Further Topics in Enumeration

The Principle of Inclusion and Exclusion
Generalizations of the Principle (Optional)
Derangements: Nothing Is in Its Right Place
Rook Polynomials
Arrangements with Forbidden Positions

Chapter 8: Generating Functions

Introductory Examples
Definition and Examples: Calculational Techniques
Partitions of Integers
Exponential Generating Functions
The Summation Operator

Chapter 9: Recurrence Relations

The First-Order Linear Recurrence Relation
The Second-Order Linear Recurrence Relation with Constant Coefficients
The Nonhomogeneous Recurrence Relation
The Method of Generating Functions
A Special Kind of Nonlinear Recurrence Relation (Optional)
Divide and Conquer Algorithms (Optional)

Chapter 10: Graph Theory and Applications

An Introduction to Graph Theory
Definitions and Examples
Subgraphs, Complements, and Graph Isomorphism
Vertex Degree: Euler Trails and Circuits
Planar Graphs
Hamilton Paths and Cycles
Graph Coloring and Chromatic Polynomials

Chapter 11: Trees

Definitions, Properties, and Examples
Rooted Trees
Trees and Sorting Algorithms
Weighted Trees and Prefix Codes
Biconnected Components and Articulation Points

Chapter 12: Optimization and Matching

Dijkstra's Shortest Path Algorithm
Minimal Spanning Trees
Transport Networks: The Max-Flow Min-Cut Theorem
Matching Theory

Chapter 13: Modern Applied Algebra

Rings and Modular Arithmetic
The Ring Structure: Definition and Examples
Ring Properties and Substructures
The Integers Modulo n
Ring Homomorphisms and Isomorphisms

Chapter 14: Boolean Algebra and Switching Functions

Switching Functions: Disjunctive and Conjunctive Normal Forms
Gating Networks: Minimal Sums of Products: Karnaugh Maps
Further Applications: Don't Care Conditions
The Structure of a Boolean Algebra (Optional)

Chapter 15: Groups, Coding Theory, and Polya's Method of Enumeration

Definition, Examples, and Elementary Properties
Homomorphisms, Isomorphisms, and Cyclic Groups
Cosets and Lagrange's Theorem
Elements of Coding Theory
The Hamming Metric
The Parity-Check and Generator trices
Group Codes: Decoding with Coset Leaders
Hamming Matrices Counting and Equivalence: Burnside's Theorem
The Cycle Index
The Pattern Inventory: Polya's Method of Enumeration

Chapter 16: Finite Fields and Combinatorial Designs

Polynomial Rings
Irreducible Polynomials: Finite Fields
Latin Squares
Finite Geometries and Affine Planes
Block Designs and Projective Planes

Exponential and Logarithmic Functions
Matrices, Matrix Operations, and Determinants
Countable and Uncountable Sets

Other Editions of Discrete and Combinatorial Mathematics: An Applied Introduction

Discrete and Combinatorial Mathematics by Ralph Grimaldi - ISBN 9780201726343