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 consist 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.

Meaning and Definitions of Mathematics:

                 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. 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 is the science of number of spaces"-Dictionary.

              "Mathematics is the gate and key to all science"-Roges Bacon.

            From above statement 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.

Meaning and definition of Mathematics

Mathematics is a term that mean 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, substraction, 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 heritage of the mankind. Those who love it climbed intellectual maintains.

Some definitions of Mathematics

1)    Mathematics is a way of thinking, i.e.,a 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.

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.

            Mathematics is a term that means many things to many people. Some enjoy it, others do not, for many people, Arithmetic and mathematics are the synonymous. To some, it is a basic computational skill where as to others it is the study of abstract systems. For still others, mathematics means misery and frustration as they recall unpleasant experiences in studying mathematics. It is one of the greatest heritage to the mankind. Those who love it climbed intellectual mountains.

            Entire books have been written to answer the question, and why short answer must in complement at best, no are who has not actually done mathematics can fully appreciate its beauty and power, and therefore people who have not done real mathematics at some level have difficulty a understanding what mathematics is just a people. Who have not both heard music and produced music themselves would have difficulty fully understanding what is music is.

         Mathematics involves the manipulations of symbols and abstract concept to produce information from given data in a form that is more useful in certain circum stance then the original data. Suppose, for example, there are 3 people in the room, subsequently 5 more people enter the room, and then another 6 people, No people exit the room. By using mathematics we can establish that there are 14 people in the room The statement “there are now 14 people in the  room” contains less information them then original data, but this conclusion was certainty in horrent in the original data. The final statement nevertheless is of sub satanically grater use to any one who wises to serve dimmer to all those in the room.

            Every teacher of mathematics has heard the complant I can do the mathematics: it’s just the

            problems ‘I can’t do’ this is analogous to saying. “I can do the English: it’s just that I can’t write anything worthwhile. “ The main purpose of the teaching mathematics is to solve real problem.

            Actually, mathematics is the study of quantity, structure, space and change. It developed, with abstraction and logical reasoning, from counting, calculation, measurement, and the study of the shapes and motions of physical objects.

          We study about mathematics we see mainly categories of mathematics into two part

            One is pure mathematics, and other is applied mathematics. First we know about these

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:

       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 every day 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.

       The language, tool and theorems of mathematics are applied in a vast range of disciplines within engineering and computer science, the physical sciences, the biomedical sciences, management and economics, psychology, etc. As a field of study and research applied mathematics lies at the boundary between mathematics and its applications. While not easily defined with any great precision, applied mathematics involves the application of interesting mathematical tools to significant applied problems and /or to the development of novel mathematics adapted to particular applications. Applied mathematicians use mathematical models to better understand, and possibly solve, real-life problems.

           

            At first the terms we are primarily concerned with applications as mathematical literacy implies  there will be a trend for all teachers whatever their main specially to use and teach mathematics whenever  they meed it. Good teachers of the future are most likely to be those who, as pupil’s, were shown useful application by their own mathematics teachers. This reason for mathematics teachers to present application in their lesson plans; mathematics teacher to teach mathematical knowledge skills generalize to a concern with the pupil’s future employment in different fields (industry, education, science, agriculture, management, etc.) . The following are regions for teaching applications of mathematics.

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.