Discrete Mathematics

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Module- I

  • Propositional logic
  •  Propositional Equivalence
  •  Predicates and Quantifiers
  •  Nested Quantifiers
  •  Rules of Inference
  •  Proof methods and Strategies
  •  Sequences and Summations
  •  Mathematical Induction
  •  Recursive definition and structural induction
  •  Program Correction
  • Recurrence relation
  •  Solution to recurrence relation
  •  Generating functions
  •  Inclusion and exclusion
  •  Application of Inclusion and Exclusion Principle
  •  Relation and their properties
  •  Closure of relations
  •  Equivalence relations
  •  Partial orderings

Module-II

  • Introduction to graph theory
  •  Graph terminology
  •  Representation of graphs
  •  Isomorphism
  •  Connectivity
  •  Euler and Hamiltonian paths
  •  Shortest path problems
  •  Planar graph
  •  Graph coloring
  •  Introduction to trees
  •  Application of trees
  •  Tree Traversal
  •  Minimum Spanning tree

Module-III

  • Semi groups
  •  Monoids
  •  Groups
  •  Subgrorups
  •  Cosets
  •  Lagrange theorem
  •  Permuation groups
  •  Group codes
  •  isomorphism
  •  Homomorphisms
  •  Normal subgroups
  •  Rings
  •  Integral Domain and Fields
  • Algebraic systems
  •  Lattices
  •  Distributive and Complemented Lattices
  •  Boolean Lattices and Boolean Algrebra
  •  Boolean Functions and Boolean Expressions

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