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Discrete Discrete and Combinatorial Mathematics: An Applied Introduction by Grimaldi

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  1. Feb 5, 2013 #1

    micromass

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    Table of Contents:
    Code (Text):

    [LIST]
    [*] Fundamentals of Discrete Mathematics
    [LIST]
    [*] Fundamental Principles of Counting
    [LIST]
    [*] The Rules of Sum and Product
    [*] Permutations
    [*] Combinations: The Binomial Theorem
    [*] Combinations with Repetition
    [*] The Catalan Numbers (Optional)
    [*] Summary and Historical Review
    [/LIST]
    [*] Fundamentals of Logic
    [LIST]
    [*] 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
    [*] Summary and Historical Review
    [/LIST]
    [*] Set Theory
    [LIST]
    [*] Sets and Subsets
    [*] Set Operations and the Laws of Set Theory
    [*] Counting and Venn Diagrams
    [*] A First Word on Probability
    [*] The Axioms of Probability (Optional)
    [*] Conditional Probability: Independence (Optional)
    [*] Discrete Random Variables (Optional)
    [*] Summary and Historical Review
    [/LIST]
    [*] Properties of the Integers: Mathematical Induction
    [LIST]
    [*] 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
    [*] Summary and Historical Review
    [/LIST]
    [*] Relations and Functions
    [LIST]
    [*] 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
    [*] Summary and Historical Review
    [/LIST]
    [*] Languages: Finite State Machines
    [LIST]
    [*] Language: The Set Theory of Strings
    [*] Finite State Machines: A Frst Encounter
    [*] Finite State Machines: A Second Encounter
    [*] Summary and Historical Review
    [/LIST]
    [*] Relations: The Second Time Around
    [LIST]
    [*] Relations Revisited: Proper ies of Relations
    [*] Computer Recognition: Zero- One Matrices and Directed Graphs
    [*] Partial Orders: Hasse Diagrams
    [*] Equivalence Relations and Partitions
    [*] Finite State Machines: The Minimization Process
    [*] Summary and Historical Review
    [/LIST]
    [/LIST]
    [*] Further Topics in Enumeration
    [LIST]
    [*] The Principle of Inclusion and Exclusion
    [LIST]
    [*] The Principle of Inclusion aid Exclusion
    [*] Generalizations of the Principle
    [*] Derangements: Nothing Is in Its Right Place
    [*] Rook Polynomials
    [*] Arrangements with Forbidden Positions
    [*] Summary and Historical Review
    [/LIST]
    [*] Generating Functions
    [LIST]
    [*] Introductory Examples
    [*] Definition and Examples: Calculational Techniques
    [*] Partitions of Integers
    [*] The Exponential Generating Function
    [*] The Summation Operator
    [*] Summary and Historical Review
    [/LIST]
    [*] Recurrence Relations
    [LIST]
    [*] The First-Order Linear Recurrence Relation
    [*] The Second-Order Linear Homogeneous 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 Algorithm (Optional)
    [*] Summary and Historical Review
    [/LIST]
    [/LIST]
    [*] Graph Theory and Applications
    [LIST]
    [*] An Introduction to Graph Theory
    [LIST]
    [*] 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
    [*] Summary and Historical Review
    [/LIST]
    [*] Trees
    [LIST]
    [*] Definitions, Properties, and Examples
    [*] Rooted Trees
    [*] Trees and Sorting
    [*] Weighted Trees and Prefix Codes
    [*] Biconnected Components and Articulation Points
    [*] Summary and Historical Review
    [/LIST]
    [*] Optimization and Matching
    [LIST]
    [*] Dijkstra's Shortest-Path Algorithm
    [*] Minimal Spanning Trees: The Algorithms of Kruskal and Prim
    [*] Transport Networks: The Max-Flow Min-Cut Theorem
    [*] Matching Theory
    [*] Summary and Historical Review
    [/LIST]
    [/LIST]
    [*] Modern Applied Algebra
    [LIST]
    [*] Rings and Modular Arithmetic
    [LIST]
    [*] The Ring Structure: Definition and Examples
    [*] Ring Properties and Substructures
    [*] The Integers Modulo n
    [*] Ring Homomorphisms and Isomorphisms
    [*] Summary and Historical Review
    [/LIST]
    [*] Boolean Algebra and Switching Functions
    [LIST]
    [*] 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)
    [*] Summary and Historical Review
    [/LIST]
    [*] Groups, Coding Theory, and Polya's Method of Enumeration
    [LIST]
    [*] Definition, Examples, and Elementary Properties
    [*] Homomorphisms, Isomorphisms, and Cyclic Groups
    [*] Cosets and Lagrange's Theorem
    [*] The RSA Cryptosystem (Optional)
    [*] Elements of Coding Theory
    [*] The Hamming Metric
    [*] The Parity-Check and Generator Matrices
    [*] 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
    [*] Summary and Historical Review
    [/LIST]
    [*] Finite Fields and Combinatorial Designs
    [LIST]
    [*] Polynomial Rings
    [*] Irreducible Polynomials: Finite Fields
    [*] Latin Squares
    [*] Finite Geometries and Affine Planes
    [*] Block Designs and Projective Planes
    [*] Summary and Historical Review
    [/LIST]
    [/LIST]
    [*] Appendix: Exponential and Logarithmic Functions
    [*] Appendix: Matrices, Matrix Operations, and Determinants
    [*] Appendix: Countable and Uncountable Sets
    [*] Contents
    [*] Solutions
    [*] Index
    [/LIST]
     
     
    Last edited by a moderator: May 6, 2017
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