Titre :	Discrete and combinatorial mathematics : An applied introduction
Type de document :	texte imprimé
Auteurs :	Ralph P. Grimaldi, Auteur
Mention d'édition :	2e éd.
Editeur :	Reading, Mass. : Addison-Wesley
Année de publication :	1989
Importance :	1vol. (722, [149] p.)
Présentation :	ill.
Format :	24 cm
ISBN/ISSN/EAN :	978-0-201-11954-1
Langues :	Anglais (eng)
Catégories :	Mathématique
Mots-clés :	Informatique : Mathématiques Analyse combinatoire
Index. décimale :	510 Mathématique
Résumé :	Le texte offre une organisation flexible, permettant aux enseignants d'adapter le livre à leurs cours particuliers: mathématiques discrètes, théorie des graphes, algèbre moderne et / ou combinatoire. Des problèmes plus élémentaires ont été ajoutés, créant une plus grande variété de niveaux dans les ensembles de problèmes, ce qui permet aux étudiants de perfectionner leurs compétences pendant leur pratique. Cette nouvelle édition continue de présenter de nombreuses applications informatiques, ce qui en fait le texte idéal pour préparer les étudiants à des études avancées.
Note de contenu :	Sommaire Contents 1 Fundamental Principles of Counting 1.1 The Rules of Sum and Product 1.2 Permutations 1.3 Combinations: The Binomial Theorem 1.4 Combinations with Repetition: Distributions 1.5 An Application in the Physical Sciences (Optional) 1.6 Summary and Historical Review 2 Fundamentals of Logic 2.1 Basic Connectives and Truth Tables 2.2 Logical Equivalence: The Laws of Logic 2.3 Logical Implication: Rules of Inference 2.4 The Use of Quantifiers 2.5 Quantifiers, Definitions, and the Proofs of Theorems 2.6 Summary and Historical Review 3 Set Theory 3.1 Sets and Subsets 3.2 Set Operations and the Laws of Set Theory 3.3 Counting and Venn Diagrams 3.4 A Word of Probability 3.5 Summary and Historical Review 4 Properties of the Integers: Mathematical Induction 4.1 The Well-Ordering Principle: Mathematical Induction 4.2 The Division Algorithm: Prime Numbers 4.3 The Greatest Common Divisor: The Euclidean Algorithm 4.4 The Fundamental Theorem of Arithmetic 4.5 Summary and Historical Review 5 Relations and Functions 5.1 Cartesian Products and Relations 5.2 Functions: Piain and One-To-One 5.3 Onto Functions: Stirling Numbers of the Second Kind 5.4 Special Functions 5.5 The Pigeonhole Principle 5.6 Function Composition and Inverse Functions 5.7 Computational Complexity 5.8 Analysis of Algorithms 5.9 Summary and Historical Review 6 Languages: Finite State Machines 6.1 Language: The Set Theory of Strings 6.2 Finite State Machines: A First Encounter 3 6.3 Finite State Machines: A Second Encounter 6.4 Summary and Historical Review 7 Relations: The Second Time Around 7.1 Relations Revisited: Properties of Relations 7.2 Computer Recognition: Zero-One Matrices and Directed Graphs 7.3 Partial Orders: Hasse Diagrams 7.4 Equivalence Relations and Partitions 7.5 Finite State Machines: The Minimization Process 7.6 Summary and Historical Review 8 The Principle of Inclusion and Exclusion 8.1 The Principle of Inclusion and Exclusion 8.2 Generalizations of the Principle 8.3 Derangements: Nothing Is in Its Right Place 8.4 Rook Polynomials 8.5 Arrangements with Forbidden Positions 8.6 Summary and Historical Review 9 Generating Functions 9.1 Introductory Examples 9.2 Definition and Examples: Calculational Techniques 9.3 Partitions of Integers 9.4 The Exponential Generating Function 9.5 The Summation Operator 9.6 Summary and Historical Review 10 Recurrence Relations 10.1 The First-Order Linear Recurrence Relation 10.2 The Second-Order Linear Homogeneous Recurrence Relation with Constant Coefficients 10.3 The Nonhomogeneous Recurrence Relation 10.4 The Method of Generating Functions 10.5 A Special Kind of Nonlinear Recurrence Relation (Optional) 10.6 Divide-and-Conquer Algorithms (Optional) 10.7 Summary and Historical Review 11 An Introduction to Graph Theory 11.1 Definitions and Examples 11.2 Subgraphs, Complements, and Graph Isomorphism 11.3 Vertex Degree: Euler Trails and Circuits 11.4 Planar Graphs 11.5 Hamilton Paths and Cycles 11.6 Graph Coloring and Chromatic Polynomials 11.7 Summary and Historical Review 12 Trees 12.1 Definitions, Properties, and Examples 12.2 Rooted Trees 12.3 Trees and Sorting 12.4 Weighted Trees and Prefix Codes 12.5 Biconnected Components and Articulation Points 12.6 Summary and Historical Review 13 Optimization and Matching 13.1 Dijkstra's Shortest-Path Algorithm 13.2 Minimal Spanning Trees: The Algorithms of Kruskal and Prim 13.3 Transport Networks: The Max-Flow Min-Cut Theorem 13.4 Matching Theory 13.5 Summary and Historical Review 14 Rings and Modular Arithmetic 14.1 The Ring Structure: Definition and Examples 14.2 Ring Properties and Substructures xvi Contents 14.3 The Integers Modulo n 14.4 Ring Homomorphisms and Isomorphisms 14.5 Summary and Historical Review 15 Boolean Algebra and Switching Functions 15.1 Switching Functions: Disjunctive and Conjunctive Normal Forms 15.2 Gating Networks: Minimal Sums of Products: Karnaugh Maps 15.3 Further Applications: Don't-Care Conditions 15.4 The Structure of a Boolean Algebra (Optional) 15.5 Summary and Historical Review 16 Groups, Coding Theory, and Polya's Method of Enumeration 16.1 Definition, Examples, and Elementary Properties 16.2 Homomorphisms, Isomorphisms, and Cyclic Groups 16.3 Cosets and Lagrange's Theorem 16.4 Elements of Coding Theory 16.5 The Hamming Metrie 798 16.6 The Parity-Check and Generator Matrices 16.7 Group Codes: Decoding with Coset Leaders 16.8 Hamming Matrices 16.9 Counting and Equivalence: Burnside's Theorem 16.10 The Cycle Index 16.11 The Pattern Inventory: Polya's Method of Enumeration 16.12 Summary and Historical Review 17 Finite Fields and Combinatorial Designs 17.1 Polynomial Rings 17.2 Irreducible Polynomials: Finite Fields 17.3 Latin Squares 17.4 Finite Geometries and Affine Planes 17.5 Block Designs and Projective Planes 17.6 Summary and Historical Review
Côte titre :	Fs/14313

Discrete and combinatorial mathematics : An applied introduction [texte imprimé] / Ralph P. Grimaldi, Auteur  . -  2e éd. . - Reading, Mass. : Addison-Wesley, 1989 . - 1vol. (722, [149] p.) : ill. ; 24 cm.
ISBN : 978-0-201-11954-1
Langues : Anglais (eng)

Catégories :	Mathématique
Mots-clés :	Informatique : Mathématiques Analyse combinatoire
Index. décimale :	510 Mathématique
Résumé :	Le texte offre une organisation flexible, permettant aux enseignants d'adapter le livre à leurs cours particuliers: mathématiques discrètes, théorie des graphes, algèbre moderne et / ou combinatoire. Des problèmes plus élémentaires ont été ajoutés, créant une plus grande variété de niveaux dans les ensembles de problèmes, ce qui permet aux étudiants de perfectionner leurs compétences pendant leur pratique. Cette nouvelle édition continue de présenter de nombreuses applications informatiques, ce qui en fait le texte idéal pour préparer les étudiants à des études avancées.
Note de contenu :	Sommaire Contents 1 Fundamental Principles of Counting 1.1 The Rules of Sum and Product 1.2 Permutations 1.3 Combinations: The Binomial Theorem 1.4 Combinations with Repetition: Distributions 1.5 An Application in the Physical Sciences (Optional) 1.6 Summary and Historical Review 2 Fundamentals of Logic 2.1 Basic Connectives and Truth Tables 2.2 Logical Equivalence: The Laws of Logic 2.3 Logical Implication: Rules of Inference 2.4 The Use of Quantifiers 2.5 Quantifiers, Definitions, and the Proofs of Theorems 2.6 Summary and Historical Review 3 Set Theory 3.1 Sets and Subsets 3.2 Set Operations and the Laws of Set Theory 3.3 Counting and Venn Diagrams 3.4 A Word of Probability 3.5 Summary and Historical Review 4 Properties of the Integers: Mathematical Induction 4.1 The Well-Ordering Principle: Mathematical Induction 4.2 The Division Algorithm: Prime Numbers 4.3 The Greatest Common Divisor: The Euclidean Algorithm 4.4 The Fundamental Theorem of Arithmetic 4.5 Summary and Historical Review 5 Relations and Functions 5.1 Cartesian Products and Relations 5.2 Functions: Piain and One-To-One 5.3 Onto Functions: Stirling Numbers of the Second Kind 5.4 Special Functions 5.5 The Pigeonhole Principle 5.6 Function Composition and Inverse Functions 5.7 Computational Complexity 5.8 Analysis of Algorithms 5.9 Summary and Historical Review 6 Languages: Finite State Machines 6.1 Language: The Set Theory of Strings 6.2 Finite State Machines: A First Encounter 3 6.3 Finite State Machines: A Second Encounter 6.4 Summary and Historical Review 7 Relations: The Second Time Around 7.1 Relations Revisited: Properties of Relations 7.2 Computer Recognition: Zero-One Matrices and Directed Graphs 7.3 Partial Orders: Hasse Diagrams 7.4 Equivalence Relations and Partitions 7.5 Finite State Machines: The Minimization Process 7.6 Summary and Historical Review 8 The Principle of Inclusion and Exclusion 8.1 The Principle of Inclusion and Exclusion 8.2 Generalizations of the Principle 8.3 Derangements: Nothing Is in Its Right Place 8.4 Rook Polynomials 8.5 Arrangements with Forbidden Positions 8.6 Summary and Historical Review 9 Generating Functions 9.1 Introductory Examples 9.2 Definition and Examples: Calculational Techniques 9.3 Partitions of Integers 9.4 The Exponential Generating Function 9.5 The Summation Operator 9.6 Summary and Historical Review 10 Recurrence Relations 10.1 The First-Order Linear Recurrence Relation 10.2 The Second-Order Linear Homogeneous Recurrence Relation with Constant Coefficients 10.3 The Nonhomogeneous Recurrence Relation 10.4 The Method of Generating Functions 10.5 A Special Kind of Nonlinear Recurrence Relation (Optional) 10.6 Divide-and-Conquer Algorithms (Optional) 10.7 Summary and Historical Review 11 An Introduction to Graph Theory 11.1 Definitions and Examples 11.2 Subgraphs, Complements, and Graph Isomorphism 11.3 Vertex Degree: Euler Trails and Circuits 11.4 Planar Graphs 11.5 Hamilton Paths and Cycles 11.6 Graph Coloring and Chromatic Polynomials 11.7 Summary and Historical Review 12 Trees 12.1 Definitions, Properties, and Examples 12.2 Rooted Trees 12.3 Trees and Sorting 12.4 Weighted Trees and Prefix Codes 12.5 Biconnected Components and Articulation Points 12.6 Summary and Historical Review 13 Optimization and Matching 13.1 Dijkstra's Shortest-Path Algorithm 13.2 Minimal Spanning Trees: The Algorithms of Kruskal and Prim 13.3 Transport Networks: The Max-Flow Min-Cut Theorem 13.4 Matching Theory 13.5 Summary and Historical Review 14 Rings and Modular Arithmetic 14.1 The Ring Structure: Definition and Examples 14.2 Ring Properties and Substructures xvi Contents 14.3 The Integers Modulo n 14.4 Ring Homomorphisms and Isomorphisms 14.5 Summary and Historical Review 15 Boolean Algebra and Switching Functions 15.1 Switching Functions: Disjunctive and Conjunctive Normal Forms 15.2 Gating Networks: Minimal Sums of Products: Karnaugh Maps 15.3 Further Applications: Don't-Care Conditions 15.4 The Structure of a Boolean Algebra (Optional) 15.5 Summary and Historical Review 16 Groups, Coding Theory, and Polya's Method of Enumeration 16.1 Definition, Examples, and Elementary Properties 16.2 Homomorphisms, Isomorphisms, and Cyclic Groups 16.3 Cosets and Lagrange's Theorem 16.4 Elements of Coding Theory 16.5 The Hamming Metrie 798 16.6 The Parity-Check and Generator Matrices 16.7 Group Codes: Decoding with Coset Leaders 16.8 Hamming Matrices 16.9 Counting and Equivalence: Burnside's Theorem 16.10 The Cycle Index 16.11 The Pattern Inventory: Polya's Method of Enumeration 16.12 Summary and Historical Review 17 Finite Fields and Combinatorial Designs 17.1 Polynomial Rings 17.2 Irreducible Polynomials: Finite Fields 17.3 Latin Squares 17.4 Finite Geometries and Affine Planes 17.5 Block Designs and Projective Planes 17.6 Summary and Historical Review
Côte titre :	Fs/14313