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.