Nature of Mathematics

Nature of Mathematics

Introduction

         Mathematics results from the discovery, the formulation, the systematic development and the application of patterns of inductive and deductive thinking. It consists of related ideas and patterns of thought. It is the queen of all sciences. It has continuously been developed and changed with changing needs of the contemporary society. The individual, community, association, organization, institution and government use mathematics in their own ways. Mathematical knowledge is necessary to study science, humanities and education. Mathematics is applicable to every aspect to individual life, social work, economic, politics etc. it is like a heart in human life.

What is Mathematics?

The problems of the man or society that is in turn of our existing world, is increasing day by day.

People need to solve such existing and facing complex and critical problems to live a happier life. To solve such tremendously expensed and exploded problems, people used many tools, among them mathematics is the renowned and well one.

The term ‘Mathematics’ is etymologically derived from an ancient Greek word “Mathancian” which means “to learn”. Golt and Futterman (1982) stated “knowledge of mathematics is indispensable to our daily life, counting object, reading and writing numbers, performing arithmetic calculation, as well as reasoning with numbers are tasks most people perform in their life. A strong background in mathematics is necessary for almost all technical careers in society. Competences in mathematics have been identified as a critical skill directly related to education and occupational choice.”

Once looked back, it is not possible to know such accurate date from when mathematics has begin. Nevertheless, the study of many mathematicians reveals and it is crystal clear that the mathematics became parts of human life from the birth of human life.

Meaning and Definitions of Mathematics:

Mathematics is a term that means many things to many people. Some enjoy it, others do not. For many people arithmetic and mathematics are synonymous. However, arithmetic is a part of mathematics. For general public mathematics is the arithmetical operation among the numbers such as addition, subtraction, multiplication, division and solution of other such problems on their daily life situation. This is indeed a vital and a correct use of the term for them. It is one of the greatest heritages of the mankind. Those who love it climbed intellectual maintains.

              Mathematics, the study of quantity, structure, space and change has been interpreted and explained in various ways. It developed with abstraction and logical reasoning, from counting, calculation, measurement and the study of the shapes and motions of physical objects. It results from the discovery, the formulation, the systematic development and the application of pattern of inductive and deductive thinking of related ideas and patterns of thoughts lies in the mathematics. Mathematics is applicable to every aspects of individual life such as social work, economy, politics, research, planning etc. Mathematical knowledge is necessary to study of science, humanities, and education. So it is called the queen of science, not only for science it is like a heart of human activities.

                     Mathematics helps in the field of physical science and social science, which gives much information like table charts diagrams, graphs, geometrical and technical drawing. In boarder sense mathematics use as language tool and to develop thinking skills, subject and deductive science.

Some definitions of Mathematics

1)    Mathematics is a way of thinking, i.e. way of organizing, analyzing and synthesizing a body of data.

2)    Mathematics is study of patterns. It is through mathematical description that regularities and similarities in nature can often be classified.

3)    Mathematics is an art. As in other arts, mathematics is characterized by order and internal consistency. Mathematics is queen of all science.

4)    Mathematics is the language of science and as such uses carefully defined terms and symbolic representation that enhance our ability to communicate.

We study about mathematics we see mainly categories of mathematics into two part:- one is pure mathematics, and other is applied mathematics.

Pure mathematics:-

The part of mathematics which is related to theoretical concepts is called pure mathematics and which studies patterns of thought without regard to their application.

Applied mathematics:

The part of mathematics which is related to practical affairs is called applied mathematics.  It is branch of mathematics that concerns itself with the mathematical techniques typically used in the application of mathematical knowledge to other domains.

All pure mathematics arose from applied mathematics the need to develop new method to solve problems of everyday life. The developments in pure mathematics often were carried far beyond their original application and led to future developments quite, remote from practical experience. Later, what initially developed as pure mathematics often proved to be extremely useful in do not know its wide application at the time of invention. For example – complex numbers were developed from the point of view of pure mathematics, but now it finds intensive applications in electricity, ratio, related fields of physics and engineering. The reverse is also true mathematicians developed these methods with no provision of their use in modern electrical engineering Discoveries by pure mathematician are continuously being put to use in applied science, and problems in applied science in turn inspire investigations in pure science. In view of the close relationship between pure and applied mathematics. Applied mathematician applies the discoveries made by pure mathematics in daily life situation. When applied mathematician faces problems while applying the inventions made by pure mathematicians they again turned towards pure mathematician. This process continues forever.

Applied mathematicians use mathematical models to better understand, and possibly solve, real-life problems.

Nature of Mathematics Knowledge

The word of mathematics is essentially man made word and has been designed by man to meet his ideas of intellectual perfection. The beginning of mathematics was advanced with the ancient period of human civilization; Mathematics is useful and necessary day to day life of human beings. It is more applicable due to the invention of science and technology. It is used to solve the daily life problems at the beginning period. However, it is out of track from the knowledge of human behavior. It is dynamic and revolutionary in nature. It is creative nature. To know how the mathematics is related to other disciplined, we have to identify the nature of mathematics.

It is useful and essential for personal life, social life, science and technology and any research field with the following dynamic nature:

                    i.            Inductive nature of mathematics: Mathematics begins from the induction. Most of the mathematical discoveries are based on induction.

                  ii.            Mathematics is a way of thinking: Logical thinking, decision making are the mathematical process.

                iii.            Mathematics is an organized structure of knowledge: In mathematics each knowledge or principles are based on previous knowledge.

               iv.            Mathematics is both science and arts: Mathematics is based on the fast. Principles and relations. Hence, it is well planned organized and structure of knowledge.

                 v.            Mathematics is a language: Mathematics has its own language, definitions, symbols and principles.

               vi.            Mathematics is a creative science

            vii.            Mathematics is the study of patterns.

           viii.            Mathematics is a practical science: It is based on the experiment of day to day work.

                ix.            The deductive and logical nature of Mathematics: Here the concern is with the question of what follows by force of logic from known truth.

                  x.            Mathematics generates from the phenomena/events in the nature and applicable in the nature for problem solving and future development.

               xi.            Telescopic and microscopic nature of mathematics.

              xii.            Mathematics has its own terms and terminology to express / explain phenomena, axioms/postulates and theorems and the process of creation of mathematics is almost universal.