Discrete mathematics is the study of discrete objects, which are to be distinguished primarily from continuous objects. A discrete object is any object that has a clearly defined limit and that is countable. Such an object can be mathematical (for example, integers and rational numbers) or they can be physical objects like tables and bicycles. One easy way to remember the scope of discrete mathematics is that it covers virtually all of the mathematical branches with the notable exception of calculus.
Discrete mathematics includes set theory, logic, number theory, algebra and many other subdivisions of mathematics as a discipline. Today, the most prevalent applications of discrete mathematics are found in computer theory and engineering, which relies heavily on the use of algorithms and computational formulas that are at the heart of software development. In fact, algorithms form the core of discrete mathematics, which is heavily driven by a focus on inductive procedure and proofs.
Technically speaking, finite mathematics is a subdivision of discrete mathematics. The two are so closely intertwined that it is often the case that the two are spoken of interchangeably. However, finite mathematics usually denotes a very specific set of applications of discrete mathematics now associated with business or public policy. Finite mathematics deals with finite objects and so is a central feature of linear processes, statistics, game theory and probability. It never deals with infinite processes of the kind one finds in calculus.
There are some helpful hints to remember when drawing a distinction between discrete mathematics and finite mathematics. Discrete math tends to be more rigorous and theoretical, driven by certain demonstrations. Finite mathematics is more practical and less rigorous, and is more experimental than strictly deductive. Still, the easiest way to distinguish the two is by virtue of their uses. Today, discrete mathematics is the principal instrument of computer science. Finite mathematics, however, is the preferred methodological tool for businessmen looking to make predictions.