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, Karnaughmap)

[8]

3. Combinatorial Mathematics: Basic counting principles Permutations and combinations

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

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.