Discrete and Combinatorial Mathematics: An Applied Introduction, 4/e (精裝)
Ralph Grimaldi
- 出版商: Addison Wesley
- 售價: $1,078
- 語言: 英文
- 頁數: 896
- 裝訂: Hardcover
- ISBN: 0201199122
- ISBN-13: 9780201199123
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Description
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. 
Features
- 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.
I. FUNDAMENTALS OF DISCRETE MATHEMATICS.
1. Fundamental Principles of Counting.
2. Fundamentals of Logic.
3. Set Theory.
4. Properties of the Integers: Mathematical Induction.
5. Relations and Functions.
6. Languages: Finite State Machines.
7. Relations: The Second Time Around.
The Rules of Sum and Product.
Permutations.
Combinations: The Binomial Theorem.
Combinations with Repetition.
An Application in the Physical Sciences (Optional).
The Catalan Numbers (Optional).
Permutations.
Combinations: The Binomial Theorem.
Combinations with Repetition.
An Application in the Physical Sciences (Optional).
The Catalan Numbers (Optional).
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.
Logical Equivalence: The Laws of Logic.
Logical Implication: Rules of Inference.
The Use of Quantifiers.
Quantifiers, Definitions, and the Proofs of Theorems.
3. Set Theory.
Sets and Subsets.
Set Operations and the Laws of Set Theory.
Counting and Venn Diagrams.
A Word on Probability.
Set Operations and the Laws of Set Theory.
Counting and Venn Diagrams.
A Word on Probability.
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.
Recursive Definitions.
The Division Algorithm: Prime Numbers.
The Greatest Common Divisor: The Euclidean Algorithm.
The Fundamental Theorem of Arithmetic.
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.
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.
6. Languages: Finite State Machines.
Language: The Set Theory of Strings.
Finite State Machines: A First Encounter.
Finite State Machines: A Second Encounter.
Finite State Machines: A First Encounter.
Finite State Machines: A Second Encounter.
7. Relations: The Second Time Around.
Relations Revisited: Properties of Relations.
Computer Recognition: Zero-One Matrices and Directed Graphs.
Partial Orders: Hasse Diagrams.
Equivalence Relations and Partitions.
Finite State Machines: The Minimization Process.
Computer Recognition: Zero-One Matrices and Directed Graphs.
Partial Orders: Hasse Diagrams.
Equivalence Relations and Partitions.
Finite State Machines: The Minimization Process.
II. FURTHER TOPICS IN ENUMERATION.
8. The Principle of Inclusion and Exclusion.
9. Generating Functions.
10. Recurrence Relations.
The Principle of Inclusion and Exclusion.
Generalizations of the Principle (Optional).
Derangements: Nothing Is in Its Right Place.
Rook Polynomials.
Arrangements with Forbidden Positions.
Generalizations of the Principle (Optional).
Derangements: Nothing Is in Its Right Place.
Rook Polynomials.
Arrangements with Forbidden Positions.
9. Generating Functions.
Introductory Examples.
Definition and Examples: Calculational Techniques.
Partitions of Integers.
The Exponential Generating Functions.
The Summation Operator.
Definition and Examples: Calculational Techniques.
Partitions of Integers.
The Exponential Generating Functions.
The Summation Operator.
10. 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).
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).
III. GRAPH THEORY AND APPLICATIONS.
11. An Introduction to Graph Theory.
12. Trees.
13. Optimization and Matching.
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.
Subgraphs, Complements, and Graph Isomorphism.
Vertex Degree: Euler Trails and Circuits.
Planar Graphs.
Hamilton Paths and Cycles.
Graph Coloring and Chromatic Polynomials.
12. Trees.
Definitions, Properties, and Examples.
Rooted Trees.
Trees and Sorting.
Weighted Trees and Prefix Codes.
Biconnected Components and Articulation Points.
Rooted Trees.
Trees and Sorting.
Weighted Trees and Prefix Codes.
Biconnected Components and Articulation Points.
13. Optimization and Matching.
Dijkstra's Shortest Path Algorithm.
Minimal Spanning Trees: The Algorithms of Kruskal and Prim.
Transport Networks: The Max-Flow Min-Cut Theorem.
Matching Theory.
Minimal Spanning Trees: The Algorithms of Kruskal and Prim.
Transport Networks: The Max-Flow Min-Cut Theorem.
Matching Theory.
IV. MODERN APPLIED ALGEBRA.
14. Rings and Modular Arithmetic.
15. Boolean Algebra and Switching Functions.
16. Groups, Coding Theory, and Polya's Method of Enumeration.
17. Finite Fields and Combinatorial Designs.
Appendices.
Solutions.
Index.
The Ring Structure: Definition and Examples.
Ring Properties and Substructures.
The Integers Modulo n.
Ring Homomorphisms and Isomorphisms.
Ring Properties and Substructures.
The Integers Modulo n.
Ring Homomorphisms and Isomorphisms.
15. 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).
Gating Networks: Minimal Sums of Products: Karnaugh Maps.
Further Applications: Don't Care Conditions.
The Structure of a Boolean Algebra (Optional).
16. 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.
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.
17. Finite Fields and Combinatorial Designs.
Polynomial Rings.
Irreducible Polynomials: Finite Fields.
Latin Squares.
Finite Geometries and Affine Planes.
Block Designs and Projective Planes.
Irreducible Polynomials: Finite Fields.
Latin Squares.
Finite Geometries and Affine Planes.
Block Designs and Projective Planes.
Appendices.
Exponential and Logarithmic Functions.
Matrices, Matrix Operations, and Determinants.
Countable and Uncountable Sets.
Matrices, Matrix Operations, and Determinants.
Countable and Uncountable Sets.
Solutions.
Index.
Supplements
Instructor Supplements
For more information about any of the supplements listed below, use our Rep. Locator to contact your Addison Wesley representative.
- Instructor's Solutions Manual / 0-201-43448-2
