DS (B-TECH Information Technology 4th)

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]

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

Isomorphism and Homomorphism. Applications.