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  • Graph Theory
    • Introduction to Graphs
    • Directed Graph
    • Graph Models
    • Graph Terminology
    • Some Special Simple Graphs
    • Bipartite Graphs
    • Bipartite Graphs and Matchings
    • Applications of Graphs
    • Original and Sub Graphs
    • Representing Graphs
    • Adjacency Matrices
    • Incidence Matrices
    • Isomorphism of Graphs
    • Paths in the Graphs
    • Connectedness in Undirected Graphs
    • Connectivity of Graphs
    • Paths and Isomorphism
    • Euler Paths and Circuits
    • Hamilton Paths and Circuits
    • Shortest-Path Problems
    • A Shortest-Path Algorithm (Dijkstra’s Algorithm.)
    • The Traveling Salesperson Problem
    • Graph Coloring
    • Applications of Graph Colorings
    • Introduction to Trees
    • Rooted Trees
    • Trees as Models
    • Properties of Trees
    • Applications of Trees
    • Decision Trees
    • Prefix Codes
    • Huffman Coding
    • Game Trees
    • Tree Traversal

  • Mathematical Logic
    • Introduction to Logical Operations
    • Logical Operations and Logical Connectivity
    • Logical Implications
    • Normal Forms and Truth Table
    • Normal Form of a well formed formula
    • Principle Disjunctive Normal Form
    • Principal Conjunctive Normal form
    • Predicates and Quantifiers
    • Theory of inference for the Predicate Calculas
    • Mathematical Induction
    • The Computer Representation of Sets
    • Introductio to Planer Graphs
    • Propositional Logic
    • Conditional Statements
    • Truth Tables of Compound Propositions
    • Precedence of Logical Operators and Logic and Bit Operations
    • Applications of Propositional Logic
    • Propositional Satisfiability
    • Nested Quantifiers
    • Translating from Nested Quantifiers into English
    • Inference
    • Rules of Inference for Propositional Logic
    • Using Rules of Inference to Build Arguments
    • Resolution and Fallacies
    • Rules of Inference for Quantified Statements

  • Propositional logic
    • Boolean Algebra
    • Identities of Boolean Algebra
    • Duality
    • The Abstract Definition of a Boolean Algebra
    • Representing Boolean Functions
    • Logic Gates
    • Minimization of Circuits
    • Karnaugh Maps
    • Don’t Care Conditions
    • The Quine–MCCluskey Method
    • Introduction to Lattices
    • The Transitive Closure of a Relation
    • Cartesian Product of Lattices
    • Properties of Lattices
    • Lattices as Algebraic System
    • Partial Order Relations on a Lattice
    • Least Upper Bounds and Latest Lower Bounds in a Lattice
    • Sublattices
    • Lattice Isomorphism
    • Bounded, Complemented and Distributive Lattices
    • Quantifiers

  • Algebraic Structure
    • Introduction to Algebra
    • Rings
    • Properties of rings
    • Subrings
    • Homomorphisms and quotient rings
    • Groups
    • Properties of groups
    • Subgroups
    • Lagrange’s Theorem
    • Homomorphisms and normal subgroups
    • Normal subgroups
    • Symmetric groups

  • Set Theory and Functions
    • Set Theory
    • Decimal number System
    • Binary Number System
    • Octal Number System
    • Hexadecimal Number System
    • Binary Arithmetic
    • Sets and Membership
    • Subsets
    • Logical Equivalance
    • Digramatic Representation of Sets
    • The Algebra of Sets
    • Relations
    • Representation of Relations
    • Introduction to Partial Order Relations
    • Digramatic Representation of Partial Order Relations and Posets
    • Maximal, Minimal Elements and Lattices
    • Recurrence Relation
    • Formulation of Recurrence Relation
    • Method of Solving Recurrence Relation
    • Method for solving linear homogeneous recurrence relations with constant coefficients:
    • Functions

Branch : Computer Science and Engineering | Subject : Discrete Mathematics
Mathematical Logic
  • Introduction to Logical Operations

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  • Logical Operations and Logical Connectivity

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  • Logical Implications

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  • Normal Forms and Truth Table

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  • Normal Form of a well formed formula

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  • Principle Disjunctive Normal Form

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  • Principal Conjunctive Normal form

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  • Predicates and Quantifiers

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  • Theory of inference for the Predicate Calculas

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  • Mathematical Induction

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  • The Computer Representation of Sets

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  • Introductio to Planer Graphs

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  • Propositional Logic

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  • Conditional Statements

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  • Truth Tables of Compound Propositions

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  • Precedence of Logical Operators and Logic and Bit Operations

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  • Applications of Propositional Logic

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  • Propositional Satisfiability

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  • Nested Quantifiers

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  • Translating from Nested Quantifiers into English

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  • Inference

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  • Rules of Inference for Propositional Logic

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  • Using Rules of Inference to Build Arguments

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  • Resolution and Fallacies

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  • Rules of Inference for Quantified Statements

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