Transcript Computer techonology

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.