B.C.A. Part I
Semester II
DISCRETE MATHEMATICS
– II
This is the official Discrete Mathematics-II Syllabus from the RTM Nagpur University (RTMNU)
UNIT - I: Set Theory: Set, Subsets operations on set, Venn
diagram
, algebra on sets, Cartesian product of sets, Binary relations,
Properties of binary relation, Relation matrix and the graph of a relation,
Partial order relations, Equivalence relations, Equivalence Classes,
Composition of ties.
UNIT - II: Functions - definition, types of function,
Invertible functions composition of functions. Counting - Permutation,
Combinations, The pigeonhole principle, recurrence relation, Mathematical
Induction.
UNIT - III: Algebraic Structures Semi groups & groups:
Binary operations, Semi groups, isomorphism and Homomorphism, Product and
Quotient of semi groups, Groups, subgroups, products and Quotient of groups.
Lattices: - Lattice concepts, isomorphic Lattices, Properties of lattices,
Finite Boolean algebras.
UNIT - IV: Graph Theory: Basic concepts, types of graphs,
Representation of graph in memory, Euler path and circuits, Hamiltonian Path, and circuits. Trees:- Basic concepts, Libeled trees, Undirected trees.
Discrete Mathematics-II Notes