THE IMPORTANCE OF DISCRETE MATHEMATICS IN COMPUTER TECHNOLOGY

Computer technology is a proof of today’s growing world; by the developing technology its effects -

advantages or disadvantages- are seen in many parts of daily life. At first, connections between computer

technology and the real world seem far, but computers are not used only for computing due to the

representations of many variables and conditions of real life. Abacus is called to be the first computer, but comparing Abacus with modern computers shows that

there have been many stages, up to coming to this level in computer technology. Many details in real life

can be simulated; for instance, colours can be represented by pixels or manner of thinking by artificial

intelligence.

Because of the common problems, theories of computing, logic and nature of life have to be tied

together to get the most effective solution. As a result of this combination, methods that are used for

representing situations and developing applications are based on the same structure, supported by Discrete

Mathematics. To deal with advanced subjects of computer technology many applications of Discrete

Mathematics are required.

Although Discrete Mathematics does not seem essential for computer technologies, it has many important advantages for developments such as converting problems of real world to computer

technology and creating algorithms, using Boolean Algebra, as well as supporting software applications.

I. First of all, making the connection between real world and computer technology leads to the developments of new areas and opportunities. As an axiom, a

function of different variables has to produce results both in life and theory.

1. Both numeric symbols and other variables in real life correspond to numbers in computer

technology 2. Representation of mathematical

expressions by electrical devices lead to new results in mathematics and computer systems

II. Due to the values of variables and results, domain and range sets differ.

1. A proposition can be only true or false, in other words, it is a dichotomy

2. “0 and 1” are the only elements of domain for variables in computer technology, which cover many hazards of real world by corresponding all

the elements of it to “0 and 1”

III. As a way of creating algorithms flow charts are useful for small programs or functions.

1. Being efficient, data structures occuring during the execution time of a program and using functions

2. A comprehensible and effective method for advancing algorithms is pseudocade

3. Correctness of a program besides debugging

IV. Boolean Algebra is a bridge that supports transition between computer technology and real life.

System of Boolean Algebra is quite easy; it consists of literals, operators and some basic theorems only.

1. Boolean Algebra is a form of equational reasoning

2. Boolean expressions can be

represented by truth tables

V. Applications of Boolean Algebra are generally on logical and electrical circuits

1. In general, the first design of a logical circuit is not systematic, the main problem for logical

circuits is making the cheaper one with including required features

2. Many different physical devices, both electrical and nonelectrical, have been used to

build logical gates

VI. Taking advantages of Discrete Mathematics in software applications makes things easier to deal with

problems.

Artificial intelligence structures are based on logical theorems.

VII. Taking advantages of Discrete Mathematics in software applications makes things easier to deal with

problems.

In conclusion; discrete mathematics and computer technology are unseperatable.

Since all computer technology is based on discrete mathematics.