PART-A

1. Sets, relations and functions: Introduction, Combination of Sets, ordered pairs, proofs of general identities

of sets, relations, operations on relations, properties of relations and functions, Hashing Functions,

equivalence relations, compatibility relations, partial order relations. [7]

2. Rings and Boolean algebra: Rings, Subrings, morphism of rings ideals and quotient rings. Euclidean

domains Integral domains and fields Boolean Algebra direct product morphisms Boolean sub-algebra

Boolean Rings Application of Boolean algebra (Logic Implications, Logic Gates, Karnaugh-map) [8]

3. Combinatorial Mathematics: Basic counting principles Permutations and combinations Inclusion and

Exclusion Principle Recurrence relations, Generating Function, Application. [7]

PART-B

4. Monoids and Groups: Groups Semigroups and monoids Cyclic semigraphs and submonoids, Subgroups

and Cosets. Congruence relations on semigroups. Morphisms. Normal subgroups. Dihedral groups. [7]

5. Graph Theory: Graph- Directed and undirected, Eulerian chains and cycles, Hamiltonian chains and cycles

Trees, Chromatic number Connectivity, Graph coloring, Plane and connected graphs, Isomorphism and

Homomorphism. Applications.