Discrete and combinatorial mathematics - Info and Reading Options

"Discrete and combinatorial mathematics" Table Of Contents:

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

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