Discrete and Combinatorial Mathematics - Info and Reading Options

"Discrete and Combinatorial Mathematics" Table Of Contents:

• 1- Fundamental Principles of Counting
• 2- The Rules of Sum and Product
• 3- Permutations
• 4- Combinations: The Binomial Theorem
• 5- Combinations with Repetition: Distributions
• 6- An Application in the Physical Sciences (Optional)
• 7- Summary and Historical Review
• 8- Fundamentals of Logic
• 9- Basic Connectives and Truth Tables
• 10- Logical Equivalence: The Laws of Logic
• 11- Logical Implication: Methods of Proof
• 12- The Use of Quantifiers
• 13- Summary and Historical Review
• 14- Set Theory
• 15- Sets and Subsets
• 16- Set Operations and the Laws of Set Theory
• 17- Counting and Venn Diagrams
• 18- A Word on Probability
• 19- Summary and Historical Review
• 20- Properties of the Integers: Mathematical Induction
• 21- The Well-Ordering Principle: Mathematical Induction
• 22- The Division Algorithm: Prime Numbers
• 23- The Greatest Common Divisor: The Euclidean Algorithm
• 24- The Fundamental Theorem of Arithmetic
• 25- Summary and Historical Review
• 26- Relations and Functions
• 27- Cartesian Products and Relations
• 28- Functions: Plain and One-to-One
• 29- Onto Functions: Stirling Numbers of the Second Kind
• 30- Special Functions
• 31- The Pigeonhole Principle
• 32- Function Composition and Inverse Functions
• 33- Computational Complexity
• 34- Analysis of Algorithms
• 35- Summary and Historical Review
• 36- Languages: Finite State Machines
• 37- Language: The Set Theory of Strings
• 38- Finite State Machines: A First Encounter
• 39- Finite State Machines: A Second Encounter
• 40- Summary and Historical Review
• 41- Relations: The Second Time Around
• 42- Relations Revisited: Properties of Relations
• 43- Computer Recognition: Zero-One Matrices and Directed Graphs
• 44- Partial Orders: Hasse Diagrams
• 45- Equivalence Relations and Partitions
• 46- Finite State Machines: The Minimization Process
• 47- Summary and Historical Review
• 48- The Principle of Inclusion and Exclusion
• 49- The Principle of Inclusion and Exclusion
• 50- Generalizations of the Principle
• 51- Derangements: Nothing Is in Its Right Place
• 52- Rook Polynomials
• 53- Arrangements with Forbidden Positions
• 54- Summary and Historical Review
• 55- Generating Functions
• 56- Introductory Examples
• 57- Definition and Examples: Calculational Techniques
• 58- Partitions of Integers
• 59- The Exponential Generating Function
• 60- The Summation Operator
• 61- Summary and Historical Review
• 62- Recurrence Relations
• 63- The First-Order Linear Recurrence Relation
• 64- The Second-Order Linear Homogeneous Recurrence Relation with Constant Coefficients
• 65- The Nonhomogeneous Recurrence Relation
• 66- The Method of Generating Functions
• 67- A Special Kind of Nonlinear Recurrence Relation (Optional)
• 68- Divide-and-Conquer Algorithms (Optional)
• 69- Summary and Historical Review
• 70- An Introduction to Graph Theory
• 71- Definitions and Examples
• 72- Subgraphs, Complements, and Graph Isomorphism
• 73- Vertex Degree: Euler Trails and Circuits
• 74- Planar Graphs
• 75- Hamilton Paths and Cycles
• 76- Graph Coloring and Chromatic Polynomials
• 77- Summary and Historical Review
• 78- Trees
• 79- Definitions, Properties and Examples
• 80- Rooted Trees
• 81- Trees and Sorting Algorithms
• 82- Weighted Trees and Prefix Codes
• 83- Biconnected Components and Articulation Points
• 84- Summary and Historical Review
• 85- Optimization and Matching
• 86- Dijkstra's Shortest-Path Algorithm
• 87- Minimal Spanning Trees: The Algorithms of Kruskal and Prim
• 88- Transport Networks: The Max-Flow Min-Cut Theorem
• 89- Matching Theory
• 90- Summary and Historical Review
• 91- Rings and Modular Arithmetic
• 92- The Ring Structure: Definition and Examples
• 93- Ring Properties and Substructures
• 94- The Integers Modulo n
• 95- Ring Homomorphisms and Isomorphisms
• 96- Summary and Historical Review
• 97- Boolean Algebra and Switching Functions
• 98- Switching Functions: Disjunctive and Conjunctive Normal Forms
• 99- Gating Networks: Minimal Sums of Products: Karnaugh Maps
• 100- Further Applications: Don't-Care Conditions
• 101- The Structure of a Boolean Algebra (Optional)
• 102- Summary and Historical Review
• 103- Groups, Coding Theory, and Polya's Method of Enumeration
• 104- Definition, Examples, and Elementary Properties
• 105- Homomorphisms, Isomorphisms, and Cyclic Groups
• 106- Cosets and Lagrange's Theorem
• 107- Elements of Coding Theory
• 108- The Hamming Metric
• 109- The Parity-Check and Generator Matrices
• 110- Group Codes: Decoding with Coset Leaders
• 111- Hamming Matrices
• 112- Counting and Equivalence: Burnside's Theorem
• 113- The Cycle Index
• 114- The Pattern Inventory: Polya's Method of Enumeration
• 115- Summary and Historical Review
• 116- Finite Fields and Combinatorial Designs
• 117- Polynomial Rings
• 118- Irreducible Polynomials: Finite Fields
• 119- Latin Squares
• 120- Finite Geometries and Affine Planes
• 121- Block Designs and Projective Planes
• 122- Summary and Historical Review
• 123- Answers
• 124- Index

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