Discrete and combinatorial mathematics
Subtitle: an applied introduction
By: by Ralph P. Grimaldi.
Edition: 2nd ed.
Publisher: Addison-Wesley
Published: 1989
Place of publication: Reading, Mass
Language: eng
Subjects: Mathematics; Computer science -- Mathematics; Algebra
Notes: Includes index.
Table of contents: label: Chapter 1
title: Fundamental Principles of Counting; label: 1.1
title: The Rules of Sum and Product
pagenum: 1; label: 1.2
title: Permutations
pagenum: 4; label: 1.3
title: Combinations: The Binomial Theorem
pagenum: 14; label: 1.4
title: Combinations with Repetition: Distributions
pagenum: 23; label: 1.5
title: An Application in the Physical Sciences (Optional)
pagenum: 32; label: 1.6
title: Summary and Historical Review
pagenum: 32; label: Chapter 2
title: Fundamentals of Logic; label: 2.1
title: Basic Connectives and Truth Tables
pagenum: 41; label: 2.2
title: Logical Equivalence: The Laws of Logic
pagenum: 49; label: 2.3
title: Logical Implication: Methods of Proof
pagenum: 60; label: 2.4
title: The Use of Quantifiers
pagenum: 77; label: 2.5
title: Summary and Historical Review
pagenum: 91; label: Chapter 3
title: Set Theory; label: 3.1
title: Sets and Subsets
pagenum: 97; label: 3.2
title: Set Operations and the Laws of Set Theory
pagenum: 106; label: 3.3
title: Counting and Venn Diagrams
pagenum: 117; label: 3.4
title: A Word on Probability
pagenum: 120; label: 3.5
title: Summary and Historical Review
pagenum: 123; label: Chapter 4
title: Properties of the Integers: Mathematical Induction; label: 4.1
title: The Well-Ordering Principle: Mathematical Induction
pagenum: 129; label: 4.2
title: The Division Algorithm: Prime Numbers
pagenum: 145; label: 4.3
title: The Greatest Common Divisor: The Euclidean Algorithm
pagenum: 153; label: 4.4
title: The Fundamental Theorem of Arithmetic
pagenum: 159; label: 4.5
title: Summary and Historical Review
pagenum: 161; label: Chapter 5
title: Relations and Functions; label: 5.1
title: Cartesian Products and Relations
pagenum: 166; label: 5.2
title: Functions: Plain and One-to-One
pagenum: 170; label: 5.3
title: Onto Functions: Stirling Numbers of the Second Kind
pagenum: 175; label: 5.4
title: Special Functions
pagenum: 180; label: 5.5
title: The Pigeonhole Principle
pagenum: 186; label: 5.6
title: Function Composition and Inverse Functions
pagenum: 190; label: 5.7
title: Computational Complexity
pagenum: 199; label: 5.8
title: Analysis of Algorithms
pagenum: 204; label: 5.9
title: Summary and Historical Review
pagenum: 212; label: Chapter 6
title: Languages: Finite State Machines; label: 6.1
title: Language: The Set Theory of Strings
pagenum: 220; label: 6.2
title: Finite State Machines: A First Encounter
pagenum: 228; label: 6.3
title: Finite State Machines: A Second Encounter
pagenum: 236; label: 6.4
title: Summary and Historical Review
pagenum: 243; label: Chapter 7
title: Relations: The Second Time Around; label: 7.1
title: Relations Revisited: Properties of Relations
pagenum: 249; label: 7.2
title: Computer Recognition: Zero-One Matrices and Directed Graphs
pagenum: 255; label: 7.3
title: Partial Orders: Hasse Diagrams
pagenum: 266; label: 7.4
title: Equivalence Relations and Partitions
pagenum: 276; label: 7.5
title: Finite State Machines: The Minimization Process
pagenum: 281; label: 7.6
title: Summary and Historical Review
pagenum: 287; label: Chapter 8
title: The Principle of Inclusion and Exclusion; label: 8.1
title: The Principle of Inclusion and Exclusion
pagenum: 295; label: 8.2
title: Generalizations of the Principle
pagenum: 305; label: 8.3
title: Derangements: Nothing Is in Its Right Place
pagenum: 309; label: 8.4
title: Rook Polynomials
pagenum: 311; label: 8.5
title: Arrangements with Forbidden Positions
pagenum: 315; label: 8.6
title: Summary and Historical Review
pagenum: 319; label: Chapter 9
title: Generating Functions; label: 9.1
title: Introductory Examples
pagenum: 323; label: 9.2
title: Definition and Examples: Calculational Techniques
pagenum: 327; label: 9.3
title: Partitions of Integers
pagenum: 336; label: 9.4
title: The Exponential Generating Function
pagenum: 339; label: 9.5
title: The Summation Operator
pagenum: 344; label: 9.6
title: Summary and Historical Review
pagenum: 345; label: Chapter 10
title: Recurrence Relations; label: 10.1
title: The First-Order Linear Recurrence Relation
pagenum: 351; label: 10.2
title: The Second-Order Linear Homogeneous Recurrence Relation with Constant Coefficients
pagenum: 361; label: 10.3
title: The Nonhomogeneous Recurrence Relation
pagenum: 371; label: 10.4
title: The Method of Generating Functions
pagenum: 377; label: 10.5
title: A Special Kind of Nonlinear Recurrence Relation (Optional)
pagenum: 382; label: 10.6
title: Divide-and-Conquer Algorithms (Optional)
pagenum: 388; label: 10.7
title: Summary and Historical Review
pagenum: 399; label: Chapter 11
title: An Introduction to Graph Theory; label: 11.1
title: Definitions and Examples
pagenum: 405; label: 11.2
title: Subgraphs, Complements, and Graph Isomorphism
pagenum: 413; label: 11.3
title: Vertex Degree: Euler Trails and Circuits
pagenum: 424; label: 11.4
title: Planar Graphs
pagenum: 433; label: 11.5
title: Hamilton Paths and Cycles
pagenum: 448; label: 11.6
title: Graph Coloring and Chromatic Polynomials
pagenum: 457; label: 11.7
title: Summary and Historical Review
pagenum: 466; label: Chapter 12
title: Trees; label: 12.1
title: Definitions, Properties and Examples
pagenum: 475; label: 12.2
title: Rooted Trees
pagenum: 482; label: 12.3
title: Trees and Sorting Algorithms
pagenum: 501; label: 12.4
title: Weighted Trees and Prefix Codes
pagenum: 506; label: 12.5
title: Biconnected Components and Articulation Points
pagenum: 511; label: 12.6
title: Summary and Historical Review
pagenum: 517; label: Chapter 13
title: Optimization and Matching; label: 13.1
title: Dijkstra's Shortest-Path Algorithm
pagenum: 523; label: 13.2
title: Minimal Spanning Trees: The Algorithms of Kruskal and Prim
pagenum: 531; label: 13.3
title: Transport Networks: The Max-Flow Min-Cut Theorem
pagenum: 538; label: 13.4
title: Matching Theory
pagenum: 549; label: 13.5
title: Summary and Historical Review
pagenum: 558; label: Chapter 14
title: Rings and Modular Arithmetic; label: 14.1
title: The Ring Structure: Definition and Examples
pagenum: 563; label: 14.2
title: Ring Properties and Substructures
pagenum: 568; label: 14.3
title: The Integers Modulo n
pagenum: 575; label: 14.4
title: Ring Homomorphisms and Isomorphisms
pagenum: 580; label: 14.5
title: Summary and Historical Review
pagenum: 587; label: Chapter 15
title: Boolean Algebra and Switching Functions; label: 15.1
title: Switching Functions: Disjunctive and Conjunctive Normal Forms
pagenum: 591; label: 15.2
title: Gating Networks: Minimal Sums of Products: Karnaugh Maps
pagenum: 600; label: 15.3
title: Further Applications: Don't-Care Conditions
pagenum: 609; label: 15.4
title: The Structure of a Boolean Algebra (Optional)
pagenum: 615; label: 15.5
title: Summary and Historical Review
pagenum: 624; label: Chapter 16
title: Groups, Coding Theory, and Polya's Method of Enumeration; label: 16.1
title: Definition, Examples, and Elementary Properties
pagenum: 629; label: 16.2
title: Homomorphisms, Isomorphisms, and Cyclic Groups
pagenum: 635; label: 16.3
title: Cosets and Lagrange's Theorem
pagenum: 639; label: 16.4
title: Elements of Coding Theory
pagenum: 642; label: 16.5
title: The Hamming Metric
pagenum: 647; label: 16.6
title: The Parity-Check and Generator Matrices
pagenum: 649; label: 16.7
title: Group Codes: Decoding with Coset Leaders
pagenum: 654; label: 16.8
title: Hamming Matrices
pagenum: 658; label: 16.9
title: Counting and Equivalence: Burnside's Theorem
pagenum: 661; label: 16.10
title: The Cycle Index
pagenum: 669; label: 16.11
title: The Pattern Inventory: Polya's Method of Enumeration
pagenum: 673; label: 16.12
title: Summary and Historical Review
pagenum: 679; label: Chapter 17
title: Finite Fields and Combinatorial Designs; label: 17.1
title: Polynomial Rings
pagenum: 685; label: 17.2
title: Irreducible Polynomials: Finite Fields
pagenum: 693; label: 17.3
title: Latin Squares
pagenum: 700; label: 17.4
title: Finite Geometries and Affine Planes
pagenum: 707; label: 17.5
title: Block Designs and Projective Planes
pagenum: 713; label: 17.6
title: Summary and Historical Review
pagenum: 718; title: Answers
pagenum: A-1; title: Index
pagenum: I-1