Syllabus
Logic: Propositions, negation, disjunction and conjunction, implication and equivalence,truth tables, predicates, quantifiers, rules of inference, methods of proof.
Set theory: definition and simple proofs in set theory, Inductive definition of sets and proof by induction, inclusion and exclusion principle,
relations, representation of relations by graphs, properties of relations, equivalence relations and partitions, partial orderings,
Functions: mappings, injection and surjections, composition of function, inverse functions, special functions, recursive function theory.
Elementary combinatorics: Counting techniques, pigeonhole principle, recurrence relation, generating functions.
Graph theory: Elements of graph theory, Euler graph, Hamiltonian path, trees, tree traversals, spanning trees.
Algebra: groups, Lagrange’s theorem, homomorphism theorem, rings and fields, structure of the ring Zn and the unit group Zn, lattice.