Dear Vikas,
Here is a definition of discrete mathematics from Wolfram Math World:
Discrete mathematics is the branch of mathematics dealing with objects that can assume only distinct, separated values. The term "discrete mathematics" is therefore used in contrast with "continuous mathematics," which is the branch of mathematics dealing with objects that can vary smoothly (and which includes, for example, calculus). Whereas discrete objects can often be characterized by integers, continuous objects require real numbers.
The study of how discrete objects combine with one another and the probabilities of various outcomes is known as combinatorics. Other fields of mathematics that are considered to be part of discrete mathematics include graph theory and the theory of computation. Topics in number theory such as congruences and recurrence relations are also considered part of discrete mathematics.
The study of topics in discrete mathematics usually includes the study of algorithms, their implementations, and efficiencies. Discrete mathematics is the mathematical language of computer science, and as such, its importance has increased dramatically in recent decades.
As a potential, real life, example, consider Marissa who makes and sells framed pictures for $70 each (after expenses are met). At first glance, you might think that the graph of net profit versus units sold would simply be a line with slope 70 passing through the origin. But think again: such a line would predict that, if Marissa made and sold 1 and 1/2 pictures her net profit would be $105. But who in their right mind would buy half a framed picture? Would Marissa (being a sound business person) even be stupid enough to make half a picture? Probably not. The only way Marissa is going to make any money is by selling n pictures, where n = 1, 2, 3, 4, .... This is a situation where only integral values of the independent variable make sense.
