Counting and Recursion: Permutations and Combinations, Principle of Inclusion & Exclusion, Pigeonhole Principle, Mathematical induction, Recurrence relation, Generating Functions.
Relation & Diagraphs : Product sets & Partitions, Relations & diagraphs, paths in relation & diagraphs, properties of relations, Equivalence relations, computer representation of relations & diagraphs, manipulation of relations.
Ordered Relations & Structures: Partially ordered sets, extermal elements of partially ordered sets, Bounding Elements, Well Ordered Set, Lattices, Principle of Duality, Bounded, Distributed, and Complemented Lattices, Finite Boolean algebra, functions on Boolean algebra.
Trees: Introduction, labeled trees, m-ary trees, undirected trees, properties of tree, Spanning tree, Minimal spanning tree, Binary search trees.
Graphs Theory: Basic Terminology, types of graph, paths & cycles, Euler graph & cycles, Hamiltonian graph & cycles, shortest path algorithm ( Djikstras algorithm), Graph Isomorphism, Planar Graph, Graph colorings and chromatic number.