Principle objective of this lecture is to presentation on Discrete Mathematics and its Applications. The study of topics in discrete mathematics usually includes the analysis of algorithms, their implementations, along with efficiencies. Discrete mathematics will be the mathematical language of computer science, and as this kind of, its importance has improved dramatically in recent ages. Discrete mathematics is the analysis of mathematical structures which can be fundamentally discrete rather compared to continuous. In contrast to real numbers who have the property of various “smoothly”, the objects studied in this topic – such as integers, graphs, and statements in logic – do not vary smoothly in this way, but have distinct, separated values.