Discrete and Combinatorial Mathematics: An Applied Introduction, Global Edition

Name: Discrete and Combinatorial Mathematics: An Applied Introduction, Global Edition
Price: 4390 ISK
Availability: InStock
Author: Ralph P. Grimaldi
ISBN: 9781292753577

Höfundur: Ralph P. Grimaldi (Útgáfa: 5)

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This 5th 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. The book is both complete and careful, and it continues to maintain its emphasis on algorithms and applications. Excellent exercise sets allow 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.

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Útgefandi: Pearson International Content

ISBN: 9781292753577

Print ISBN: 9781292485768

Format: ePub

Útgáfa: 5

Höfundar: Ralph P. Grimaldi

Tungumál: English

Útgefið: 2025-07-15

Prent takmörkun á líftíma: 100

Prent takmörkun: 2

Afritunar takmörkun: 2

Kaflar

Cover
Cover
Front Matter
Title Page
Copyright Page
Dedication
Preface
Acknowledgments
Contents
Part 1 Fundamentals of Discrete Mathematics
Part 1 Fundamentals of Discrete Mathematics
Chapter 1 Fundamental Principles of Counting
Chapter 1 Fundamental Principles of Counting
1.1 The Rules of Sum and Product
1.2 Permutations
1.1 and 1.2 Exercises
1.3 Combinations: The Binomial Theorem
1.3 Exercises
1.4 Combinations with Repetition
1.4 Exercises
1.5 The Catalan Numbers (Optional)
1.5 Exercises
1.6 Summary and Historical Review
Chapter 1 References
Chapter 1 Test Your Understanding
Chapter 1 Supplementary Exercises
Chapter 2 Fundamentals of Logic
Chapter 2 Fundamentals of Logic
2.1 Basic Connectives and Truth Tables
2.1 Exercises
2.2 Logical Equivalence: The Laws of Logic
2.2 Exercises
2.3 Logical Implication: Rules of Inference
2.3 Exercises
2.4 The Use of Quantifiers
2.4 Exercises
2.5 Quantifiers, Definitions, and the Proofs of Theorems
2.5 Exercises
2.6 Summary and Historical Review
Chapter 2 References
Chapter 2 Test Your Understanding
Chapter 2 Supplementary Exercises
Chapter 3 Set Theory
Chapter 3 Set Theory
3.1 Sets and Subsets
3.1 Exercises
3.2 Set Operations and the Laws of Set Theory
3.2 Exercises
3.3 Counting and Venn Diagrams
3.3 Exercises
3.4 A First Word on Probability
3.4 Exercises
3.5 The Axioms of Probability (Optional)
3.5 Exercises
3.6 Conditional Probability: Independence (Optional)
3.6 Exercises
3.7 Discrete Random Variables (Optional)
3.7 Exercises
3.8 Summary and Historical Review
Chapter 3 References
Chapter 3 Test Your Understanding
Chapter 3 Supplementary Exercises
Chapter 4 Properties of the Integers: Mathematical Induction
Chapter 4 Properties of the Integers: Mathematical Induction
4.1 The Well-Ordering Principle: Mathematical Induction
4.1 Exercises
4.2 Recursive Definitions
4.2 Exercises
4.3 The Division Algorithm: Prime Numbers
4.3 Exercises
4.4 The Greatest Common Divisor: The Euclidean Algorithm
4.4 Exercises
4.5 The Fundamental Theorem of Arithmetic
4.5 Exercises
4.6 Summary and Historical Review
Chapter 4 References
Chapter 4 Test Your Understanding
Chapter 4 Supplementary Exercises
Chapter 5 Relations and Functions
Chapter 5 Relations and Functions
5.1 Cartesian Products and Relations
5.1 Exercises
5.2 Functions: Plain and One-to-One
5.2 Exercises
5.3 Onto Functions: Stirling Numbers of the Second Kind
5.3 Exercises
5.4 Special Functions
5.4 Exercises
5.5 The Pigeonhole Principle
5.5 Exercises
5.6 Function Composition and Inverse Functions
5.6 Exercises
5.7 Computational Complexity
5.7 Exercises
5.8 Analysis of Algorithms
5.8 Exercises
5.9 Summary and Historical Review
Chapter 5 References
Chapter 5 Test Your Understanding
Chapter 5 Supplementary Exercises
Chapter 6 Languages: Finite State Machines
Chapter 6 Languages: Finite State Machines
6.1 Language: The Set Theory of Strings
6.1 Exercises
6.2 Finite State Machines: A First Encounter
6.2 Exercises
6.3 Finite State Machines: A Second Encounter
6.3 Exercises
6.4 Summary and Historical Review
Chapter 6 References
Chapter 6 Test Your Understanding
Chapter 6 Supplementary Exercises
Chapter 7 Relations: The Second Time Around
Chapter 7 Relations: The Second Time Around
7.1 Relations Revisited: Properties of Relations
7.1 Exercises
7.2 Computer Recognition: Zero-One Matrices and Directed Graphs
7.2 Exercises
7.3 Partial Orders: Hasse Diagrams
7.3 Exercises
7.4 Equivalence Relations and Partitions
7.4 Exercises
7.5 Finite State Machines: The Minimization Process
7.5 Exercises
7.6 Summary and Historical Review
Chapter 7 References
Chapter 7 Test Your Understanding
Chapter 7 Supplementary Exercises
Part 2 Further Topics in Enumeration
Part 2 Further Topics in Enumeration
Chapter 8 The Principle of Inclusion and Exclusion
Chapter 8 The Principle of Inclusion and Exclusion
8.1 The Principle of Inclusion and Exclusion
8.1 Exercises
8.2 Generalizations of the Principle
8.2 Exercises
8.3 Derangements: Nothing Is in Its Right Place
8.3 Exercises
8.4 Rook Polynomials
8.5 Arrangements with Forbidden Positions
8.4 and 8.5 Exercises
8.6 Summary and Historical Review
Chapter 8 References
Chapter 8 Test Your Understanding
Chapter 8 Supplementary Exercises
Chapter 9 Generating Functions
Chapter 9 Generating Functions
9.1 Introductory Examples
9.1 Exercises
9.2 Definition and Examples: Calculational Techniques
9.2 Exercises
9.3 Partitions of Integers
9.3 Exercises
9.4 The Exponential Generating Function
9.4 Exercises
9.5 The Summation Operator
9.5 Exercises
9.6 Summary and Historical Review
Chapter 9 References
Chapter 9 Test Your Understanding
Chapter 9 Supplementary Exercises
Chapter 10 Recurrence Relations
Chapter 10 Recurrence Relations
10.1 The First-Order Linear Recurrence Relation
10.1 Exercises
10.2 The Second-Order Linear Homogeneous Recurrence Relation with Constant Coefficients
10.2 Exercises
10.3 The Nonhomogeneous Recurrence Relation
10.3 Exercises
10.4 The Method of Generating Functions
10.4 Exercises
10.5 A Special Kind of Nonlinear Recurrence Relation (Optional)
10.5 Exercises
10.6 Divide-and-Conquer Algorithms (Optional)
10.6 Exercises
10.7 Summary and Historical Review
Chapter 10 References
Chapter 10 Test Your Understanding
Chapter 10 Supplementary Exercises
Part 3 Graph Theory and Applications
Part 3 Graph Theory and Applications
Chapter 11 An Introduction to Graph Theory
Chapter 11 An Introduction to Graph Theory
11.1 Definitions and Examples
11.1 Exercises
11.2 Subgraphs, Complements, and Graph Isomorphism
11.2 Exercises
11.3 Vertex Degree: Euler Trails and Circuits
11.3 Exercises
11.4 Planar Graphs
11.4 Exercises
11.5 Hamilton Paths and Cycles
11.5 Exercises
11.6 Graph Coloring and Chromatic Polynomials
11.6 Exercises
11.7 Summary and Historical Review
Chapter 11 References
Chapter 11 Test Your Understanding
Chapter 11 Supplementary Exercises
Chapter 12 Trees
Chapter 12 Trees
12.1 Definitions, Properties, and Examples
12.1 Exercises
12.2 Rooted Trees
12.2 Exercises
12.3 Trees and Sorting
12.3 Exercises
12.4 Weighted Trees and Prefix Codes
12.4 Exercises
12.5 Biconnected Components and Articulation Points
12.5 Exercises
12.6 Summary and Historical Review
Chapter 12 References
Chapter 12 Test Your Understanding
Chapter 12 Supplementary Exercises
Chapter 13 Optimization and Matching
Chapter 13 Optimization and Matching
13.1 Dijkstra's Shortest-Path Algorithm
13.1 Exercises
13.2 Minimal Spanning Trees: The Algorithms of Kruskal and Prim
13.2 Exercises
13.3 Transport Networks: The Max-Flow Min-Cut Theorem
13.3 Exercises
13.4 Matching Theory
13.4 Exercises
13.5 Summary and Historical Review
Chapter 13 References
Chapter 13 Test Your Understanding
Chapter 13 Supplementary Exercises
Part 4 Modern Applied Algebra
Part 4 Modern Applied Algebra
Chapter 14 Rings and Modular Arithmetic
Chapter 14 Rings and Modular Arithmetic
14.1 The Ring Structure: Definition and Examples
14.1 Exercises
14.2 Ring Properties and Substructures
14.2 Exercises
14.3 The Integers Modulo n
14.3 Exercises
14.4 Ring Homomorphisms and Isomorphisms
14.4 Exercises
14.5 Summary and Historical Review
Chapter 14 References
Chapter 14 Test Your Understanding
Chapter 14 Supplementary Exercises
Chapter 15 Boolean Algebra and Switching Functions
Chapter 15 Boolean Algebra and Switching Functions
15.1 Switching Functions: Disjunctive and Conjunctive Normal Forms
15.1 Exercises
15.2 Gating Networks: Minimal Sums of Products: Karnaugh Maps
15.2 Exercises
15.3 Further Applications: Donâ€™t-Care Conditions
15.3 Exercises
15.4 The Structure of a Boolean Algebra (Optional)
15.4 Exercises
15.5 Summary and Historical Review
Chapter 15 References
Chapter 15 Test Your Understanding
Chapter 15 Supplementary Exercises
Chapter 16 Groups, Coding Theory, and Polya's Method of Enumeration
Chapter 16 Groups, Coding Theory, and Polya's Method of Enumeration
16.1 Definition, Examples, and Elementary Properties
16.1 Exercises
16.2 Homomorphisms, Isomorphisms, and Cyclic Groups
16.2 Exercises
16.3 Cosets and Lagrange's Theorem
16.3 Exercises
16.4 The RSA Cryptosystem (Optional)
16.4 Exercises
16.5 Elements of Coding Theory
16.5 Exercises
16.6 The Hamming Metric
16.7 The Parity-Check and Generator Matrices
16.6 and 16.7 Exercises
16.8 Group Codes: Decoding with Coset Leaders
16.9 Hamming Matrices
16.8 and 16.9 Exercises
16.10 Counting and Equivalence: Burnside's Theorem
16.10 Exercises
16.11 The Cycle Index
16.11 Exercises
16.12 The Pattern Inventory: Polya's Method of Enumeration
16.12 Exercises
16.13 Summary and Historical Review
Chapter 16 References
Chapter 16 Test Your Understanding
Chapter 16 Supplementary Exercises
Chapter 17 Finite Fields and Combinatorial Designs
Chapter 17 Finite Fields and Combinatorial Designs
17.1 Polynomial Rings
17.1 Exercises
17.2 Irreducible Polynomials: Finite Fields
17.2 Exercises
17.3 Latin Squares
17.3 Exercises
17.4 Finite Geometries and Affine Planes
17.4 Exercises
17.5 Block Designs and Projective Planes
17.5 Exercises
17.6 Summary and Historical Review
Chapter 17 References
Chapter 17 Test Your Understanding
Chapter 17 Supplementary Exercises
Appendix 1 Exponential and Logarithmic Functions
Appendix 1 Exponential and Logarithmic Functions
Exercise A.1
Appendix 2 Matrices, Matrix Operations, and Determinants
Appendix 2 Matrices, Matrix Operations, and Determinants
References
Exercise A.2
Appendix 3 Countable and Uncountable Sets
Appendix 3 Countable and Uncountable Sets
References
Exercises A.3
Solutions
Solutions: Chapter 1
Solutions: Chapter 2
Solutions: Chapter 3
Solutions: Chapter 4
Solutions: Chapter 5
Solutions: Chapter 6
Solutions: Chapter 7
Solutions: Chapter 8
Solutions: Chapter 9
Solutions: Chapter 10
Solutions: Chapter 11
Solutions: Chapter 12
Solutions: Chapter 13
Solutions: Chapter 14
Solutions: Chapter 15
Solutions: Chapter 16
Solutions: Chapter 17
Solutions: Appendix 1
Solutions: Appendix 2
Solutions: Appendix 3
Index
Index
Glossary