Discrete Structure

Definition of sets countable and uncountable sets Venn Diagrams proofs of some general identities on sets Relation: Definition types of relation composition of relations Pictorial representation of relation Equivalence relation Partial ordering relation Job-Scheduling problem Function: Definition type of functions one to one into and onto function inverse function composition of functions recursively defined functions pigeonhole principle Theorem proving Techniques: Mathematical induction Proof by contradiction

Rings and Fields: definition and standard results Algebraic Structures: Definition Properties types: Semi Groups Monoid Groups Abelian group properties of groups Subgroup cyclic groups Cosets factor group Permutation groups Normal subgroup Homomorphism and isomorphism of Groups example and standard results

Propositional Logic: Proposition First order logic Basic logical operation truth tables tautologies Contradictions Algebra of Proposition logical implications logical equivalence predicates Normal Forms Universal and existential quantifiers Introduction to finite state machine Finite state machines as models of physical system equivalence machines Finite state machines as language recognizers

Isomorphism and Homomorphism of graphs Graph Theory: Introduction and basic terminology of graphs Planer graphs Multigraphs and weighted graphs Isomorphic graphs Paths Cycles and connectivity Shortest path in weighted graph Introduction to Eulerian paths and circuits Hamiltonian paths and circuits Graph coloring chromatic number

Posets Hasse Diagram and Lattices: Introduction ordered set Hasse diagram of partially ordered set isomorphic ordered set well ordered set properties of Lattices bounded and complemented lattices Combinatorics: Introduction Permutation and combination Binomial Theorem Multimonial Coefficients Recurrence Relation and Generating Function: Introduction to Recurrence Relation and Recursive algorithms Linear recurrence relations with constant coefficients Homogeneous solutions Particular solutions Total solutions Generating functions Solution by method of generating functions