Brief survey and importance of Discrete mathematics

The mathematics is a basic tool to understand science and engineering. Generally mathematics can be divided into two categories discrete mathematics and continuous mathematics. The branch of mathematics in which we deal mostly with only those real numbers which are multiple of some basic units, if the basic unit is 1 then the discrete variable can assume only integral values, is known as discrete mathematics. Therefore the variables which we use in discrete mathematics, are known as discrete variables, thus in continuous mathematics number system is usually real numbers while for discrete mathematics it is an integer. As a result a discrete variable can not become infinitely small, and as such concept like instantaneous rate of change is not available in discrete mathematics, but this is the basic concept in continuous mathematics. Hence discrete mathematics is the branch of mathematics devoted to the study of discrete objects whose main concern is with continuous functions. Of course neither the discrete nor the continuous mathematics is a watertight compartment. Some branches of mathematics, like numerical analysis and linear algebra, have both continuous and discrete functions. some typical example of discrete mathematics includes.

1. A drawer contains ten black and ten white balls. What is the least number of balls one must pull out to be sure to get a matched pair?

2. How can a circuit that adds two integers and a circuit that compares two integers be designed ?.

3. A variable name in a programming language must be either a letter or a letter followed by a decimal digit. How many different variable names are there in this language?

4. A computer system consists of five subsystems. Each subsystem might fail independently with probability of 0.2. The failure of any subsystem will lead to a failure of the whole computer system. Given that the computer system fails, what is the probability that the subsystem 1 and only subsystem 1 fails.

Importance of discrete mathematics.

The discrete mathematics has played an important role to deal some practical problems in daily life. For example the topic of relation and functions, helps us to discuss the general relations of our lives. If we test relation “fatherhood” by discrete mathematics this is an equivalence relation. Or generally in daily lives a father can not be equivalence to his son and vice versa. Discrete mathematics shows the relation of brotherhood is an equivalence relation, so is true in daily lives. Because a brother could be equivalence to his brother. Therefore discrete mathematics is rapidly growing an increasingly used area of mathematics with many practical and relevant applications.It is an excellent tool for improving problem solving and reasoning skills, and is appropriate for all at al levels and of all abilities. The knowledge of discrete mathematics is the key for advanced work in many branches of mathematics and computer science, which includes data structure, database theory, automata theory, compiler design, operating system, and many others. Thus the idea of discrete mathematics are the fundamental to the science and technology specific to the computer age.

Dr. Hakimuddin Khan

Associate Professor

Deptt. of Management Studies