Concepts In Discrete Mathematics

Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbersthat have the property of varying ';smoothly', the objects studied in discrete mathematics such as integers, graphs, and statements in logic do not vary smoothly in this way, but have distinct, separated values. Discrete mathematics therefore excludes topics in ';continuous mathematics' such as calculus and analysis. Discrete objects can often be enumerated by integers. More formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable sets (sets that have the same cardinality as subsets of the natural numbers, including rational numbers but not real numbers). However, there is no exact, universally agreed, definition of the term ';discrete mathematics.' Indeed, discrete mathematics is described less by what is included than by what is excluded: continuously varying quantities and related notions. The subject matter has been discussed in such a simple way that the students will find no difficulty to understand it. The proofs of various principles and examples has been given with minute details.