MATHEMATICS AND COMPUTER SCIENCE RELATIONSHIP.
In today’s world mathematics is a must learned subject . In all the inventions and discovery , the main reason for their success of the practical’s are due to mathematics. So in order to make a career in today’s world require mathematics.
But this Is blog of computers science and information technology, then why should we read mathematics so it requires mathematics to understand the reason behind such technology. So I am going to write something about mathematics for its uses and technology in the computer world.
One of the main aims of logic is to provide rules by which one can determine whether any particular argument or reasoning is valid (correct)
Logic is concerned with all kinds of reasoning whether they be legal arguments or mathematical proofs or conclusions in a scientific theory based upon a set of hypothesis. Because of the diversity of their application these rules are called rules of inference, must be stated in general terms and must be independent of any particular language used in the arguments.
More precisely, in logic we are concerned with the forms of argument rather than arguments themselves. Like any other theory in science the theory of inference is formulated in such a way that we should be able to decide about the validity of an argument by following the rues mechanically and independently of our own feelings about the argument.
Of course to proceed in this manner requires that the rules mechanically and independently of our own feelings about the argument. Of course to proceed in this manner requires that the rules be stated unambiguously.
Any collection of rules or any theory needs a language in which these rules or theory can be stated. Natural languages are not always precise enough. They are also ambiguous and as such are not suitable for this purpose.
It is therefore necessary first to develop a formal language called the object language. A formal language is one in which the syntax is well defined. In fact, every scientific discipline develops its own object language which consists of certain well-defined terms and well specified uses of these terms.
The only difference between logic and other disciplined is that in other disciplines we are concerned with the use of the object language while in logic we are as interested in analyzing of an object language without considering its use in the theory of inference.
In order to avoid ambiguity we use symbols which have been clearly defined in the object languages. An additional reason to use symbols is that they are easy to write and manipulate. Because of use this symbols the logic that we shall study is also called symbolic logic, Our study of the object language requires the use of another language.
For this purpose we can choose any of the natural languages. In this case our choice is English and so the statements about the object language will be made in English. This natural language (English) will them be called or meta language. Certain inherent difficulties in this procedure could be anticipated. Because we wish to study a precise language while using another language which is not so precise.