THE NATURE AND SCOPE OF MATHEMATICS.pptx

nature and scope in mathematics

1. THE NATURE AND SCOPE OF MATHEMATICS Historical Perspectives Meaning and definition of Mathematics Nature of Mathematics Scope of Mathematics Aims of teaching Mathematics Relationship with other subjects

2. Plutonian schools of thoughts Aristotelian schools of thoughts LATE 19 TH AND EARLY 20 TH CENTURY VIEWS Logicism : the contents were the elements of the body of classical mathematics, its definitions, its postulates, and theorems. Intuitionism: the contents were the theorems that had been constructed from first principles via patterns of reasoning. Formalism: mathematics was made up of the formal axiomatic structures developed to rid classical mathematics of its shortcomings. HISTORICAL PERSPECTIVES

3. Mathematics was tend to carry strong Platonic views about the existence of mathematical concepts outside the human mind. The conceptions of mathematics was based on Aristotelian schools of thought of mathematics as a game play with symbols but the mathematician rejects this notion and describes it as a meaningless game played with symbols. According to Hersh , the working mathematician is not controlled by constant attention to validating every step with an accepted formal argument. MODREN VIEWS AND MATHEMATICS

4. Mathematics must be accepted as a human activity, an activity not strictly governed by any school of thoughts. Mathematics objectives are invented or created by humans. They are created, not arbitrarily, but arise from activity with already existing mathematical objects, and from the needs of science and daily life. Once created, mathematical objects have properties which are well determined, which we my have great difficulty in discovering, but which are possessed independently of our knowledge of them. Continuo…..

5. The study of the history mathematics does not answer the question “what is mathematics?” However, it provides a valuable perspective to understand the nature of mathematics. Historically mathematics has grown largely as a result of… Social needs, as shown in everyday life, commerce, science and technology. The intellectual need to connect together existing mathematics into a single logical framework or proof structure. PURE AND APPLIED MATHEMATICS

6. The word mathematics can used as… The truths that are discovered The methods used to discover truths. Applied mathematics: In a classroom much of the mathematics we teach is applied mathematics in the sense that it relates directly to life’s activities connected with buying, selling, trade, business, consumer, applications, weighing, measuring etc. Applied mathematics growth has been in areas of operational research, linear programming, system analysis, statistics, al involving processes to handle numerical information in an increasingly technologically advanced world. Continuo….

7. The mathematical ideas we teach in schools develop over many years of study and become associated in our minds with all the applications and illustrations presented to explain them. Pure Mathematics: In pure mathematics we start from certain rules of inference, by which we call infer that if one proposition is true, then some other proposition is also true. These rule or inference constitute major part of the principles of formal logics. Continuo…

8. According to Bretrund Russell, “the subject in which we never know what we are talking about, nor whether what we are saying is me.” There is a very thin line dividing pure and applied concepts. On the one hand concepts of pure mathematics are formulated because of the need to apply them and on the other, every discovery of formulation has some application somewhere. Continuo….

9. The term ‘mathematics’ has been interpreted and explained in various ways. This is due to our empirical knowledge and various types of experiences. But ultimately all types of explanations conclusively end at some kinds of relationship with number and space. Thus, mathematics deals with quantitative facts and relationships as well as with problem involving space and form. Meaning of mathematics

10. The word mathematics have be derived from the Greek word “ Mathema ” which means “Science, knowledge or learning.” Mathematics is a science which deals with the quantitative aspects of our life and knowledge. Mathematics is also called the science of logical reasoning. Continuo…

11. According to Locke: “mathematics is a way to settle in the mind of children a habit of reasoning.” According to Marhsal H. Stone: mathematics is the study of abstract system built of abstract element. These elements are not described in concrete fashion.” According to Bertrand Russell: mathematics may be defined as the subject in which we never know what we are talking about, not whether what we are saying is true.” Definitions of Mathematics

12. Mathematics is a science of space, numbers, magnitude and measurement. Mathematics has its own language. Language consists of mathematical terms, mathematical concepts, formulas, theories, principles, and signs etc. It gives accurate and reliable knowledge. Mathematics knowledge is exact, systematic, logical, and clear so that once it is captured it can never be forgotten, Nature of Mathematics

13. Mathematical rules, laws and formulas, are universal and that can be verified at any space and time. It develops the ability of induction, deduction, and generalization. Mathematics helps in developing scientific attitude among children. The study of mathematics gives the training of scientific method to the children. Mathematics is a systematized, organized and exact branch of science. Continuo…

14. Mathematics involves conversation of abstract concepts into concrete form. Mathematics is science of logical reasoning. Mathematics does not leave any doubt in the mind of learner about theories, principles concepts etc. Mathematics helps to develop that habit of self-confidence and self-reliance in children. Mathematics helps in the developments of sense of appreciation among children. Continuo…

15. Mathematics language is well defined, useful and clear. It draws numerical inferences on the basis of given information and data. Mathematical knowledge is applied in the study of science and in this different branches; for example physics, chemistry, biology, and other sciences. It is not only useful for different branches of science but also helps in its progress and organization. Continuo…

16. Mathematics is the science of discovery: it discovers express relationships in symbolic form- in words, in numbers, in letters etc. Mathematics deals with the art of drawing conclusion: it helps children in drawing right conclusions and inferences. Mathematics is a tool subject: mathematics is a powerful tool of wide applicable. Mathematics is subject of logical sequence: it’s learning always proceeds from simple to complex and from concrete to abstract. Scope of Mathematics

17. Mathematics is the science of precision and accuracy: mathematics is known as an exact science because of its precision. Mathematics is a science of logical reasoning: it governs the patterns of deductive proof through which mathematics is developed. Continuo…

18. Data Scientist: Data scientist are specialists who use mathematical and statistical methods, computer modeling and software to extract knowledge and information from structured( such as database in MS-Excel or SQL) or structured data. Mathematician: Mathematicians can be of two types: theoretical and applied ones. Theoretical mathematicians develop new principles of mathematics and try to find new development in the existing ones. Applied mathematicians apply the concepts of mathematics to solve bigger problems in economics, scientific, and engineering domains. Continuo…

19. Astronomer: Astronomer primarily use principles of physics and mathematics to understand the working of universe and contribute to research and breakthrough experiments. A students who wants to pursue a career in this field and is interested in exploring the scope of mathematics can consider becoming an Astronomer. Economist: Economics is increasingly becoming a numerical science, given that the job of an economist is to identify problems and solutions within the requisite distribution and production of goods and services such as land, labor and raw materials. They have to research, analyze and monitor prevailing economic conditions and predict likely economic conditions. Continuo..

20. Engineer: Engineers are creators of novel and better products and services, be it electronics, software or computer products. They have to be aware and upbeat about technological advancements taking place across the globe. Engineering comes within the scope of mathematics as a field of careers. Continue…

21. The following are the aims of teaching mathematics: To enable the students to have clear ideas about number concept. To give the individual an understanding of ideas and operations in numbers and quantity needed in daily life. To enable the individual to become proficient in the four fundamental operations of addition, subtraction, multiplication and division. To provide the basis of mathematical skills and processes which will be needed for vocational purposes. Aims of Teaching Mathematics

22. To enable the learner to acquire and develop mathematical skills and attitude to meet the demands of Daily life Future mathematical work Work in the related fields of knowledge To enable the students to make appropriate approximations. To enable to learners to understand the concept of ratio and scale drawing, read and interpret graphs, diagrams and tables. To enable the individual to apply his mathematics to a wide range of problems that occur in daily life. Continuo…

23. Mathematics and social: in social science study material has been taken mainly from four subject History, Geography, Economics and Civics. For each subject mathematics is a basic knowledge. Mathematics and Geography: study of Mathematics is fully dependent on mathematics. Comparative study of the rivers, heights of mountains, minerals, vegetation, population, and inertial capacity is possible with the helps of mathematics. Relationship of Mathematics with other Subjects

24. Mathematics and Economics: study of mathematics has become necessary for gaining knowledge of Economic. Economics of country, position of currency, import-export, import national development and saving scheme are only possible with the help of mathematics. Mathematics and physics: in physics, at every step, mathematics calculations is required. Only mathematics mind can study physics confidently. Continuo….

25. Mathematics and Chemistry: all the chemical combinations and their equations are based on mathematical calculations. Mathematics and Science of Medicine: science of medic is fully dependent on mathematics. To know the temperature of person, to know the blood pressure, to know the parts of food etc. is possible with the help of mathematics. Mathematics and Engineering: as oxygen is essential for all living beings, mathematics is the oxygen of engineering. It is base of all engineers. Continuo…