Counting: Permutation & Combination, Derangement, Pigeonhole Principle, Binomial Coefficient, Principle of Inclusion and Exclusion.
Set Theory: Operations on sets, Cartesian product of sets, General proofs of some fundamental identities on sets.
Group Theory: Functions: Definition, Classification of functions, Operations on functions, Algebraic Structures: Definition, Groups, Subgroups and order, Cyclic Groups, Cosets, Lagrange's theorem, Normal Subgroups, Permutation and Symmetric groups, Group Homeomorphisms, Definition and elementary properties of Rings and Fields, Integers Modulo n.
Relation Algebra: Relations and Digraphs, Properties of relations, Equivalence relations and equivalence classes, Operations on relations, Connection between relations and some data structures, Transitive Closure and Warshall’s algorithm. Partial order relations, Partial order sets: Definition, Partial order sets, Combination of partial order sets, Hasse diagram. Lattices: Definition, Properties of lattices – Bounded, Complemented and Complete lattice.
Graph Theory: Basic of Graph, Euler paths and circuits, Hamiltonian paths and circuits, isomorphic graphs, Connected Graph, Trees, Labeled trees, Tree searching, Undirected trees, Isomorphic trees, Minimal spanning trees, Prim’s algorithm, Planar Graph,
Matching problems, Coloring graphs, Transport networks.
Propositional Logic and Predicate Calculus: Propositions and Logical operations, Conditional statements, First order predicate, well-formed formula of predicate, quantifiers, Inference theory of predicate logic.
Methods of proof, Mathematical induction, Recursively defined functions, Growth of Functions, Recurrence relations.