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 and partial ordering relation. Function Definition, type of functions, one toone, into and onto function, inverse function, composition of functions, recursively defined functions, Theorem proving Techniques, mathematical induction, pigeonhole principle, prove by contradiction.

Definition, Properties, SemiGroups, 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, Rings and Fields.

Posets, Hasse Diagram and Lattices, ordered set, Hasse diagram ofpartially, ordered set, isomorphic ordered set, well ordered set, properties of Lattices, bounded I and complemented lattices, Boolean Algebra, sum of products and product of sums, form in Boolean Algebra, Logic gates and Karnaugh maps. Tree, Rooted tree, properties of trees, binary search tree, tree traversal.

Propositional Logic First order logic, Basic logical operation, truth tables, tautologies, Contradictions, Algebra of Proposition, logical implications, logical equivalence, predicates, Universal and existential quantifiers.

Combinatorics & Graphs, Recurrence Relation, Generating function, Simple graph, multi graph, graph terminology, representation of graphs, Bipartite, Regular, Planar and connected graphs, connected components in a graph, Euler graphs, Hamiltonian path and circuits, Graph coloring, chromatic number, isomorphism and Homomorphism of graphs.