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.