Unit 1 – Nature of Mathematics ( B.Ed. Mathematics)

 

Unit 1 – Nature of Mathematics

Mathematics - Meaning and Definition

The term mathematics is said to be traced from ‘mendh’ meaning ‘to learn’, related to the Greek word ‘manthenein’. Mathematics is an exact science which is related to measurements, calculations, discovering relationships and dealing with the problems of space. In dictionary meaning, mathematics is the science of number and space.

Definitions

·        Mathematics is the indispensable instrument of all physical researches- Kant

·        Mathematics is the gateway and key to all sciences- Bacon

·        Mathematics is the queen of sciences and arithmetic is the queen of all mathematics – Gauss

·        Mathematics is the language in which God has written the universe- Galileo

·        Mathematics is the study of quantity – Aristotle

Nature of mathematics / features/ characteristics

Science of space ,number, magnitude and measurements

Science of calculations

·        Science of discovery

·        Science of logical reasoning

·        Systematized , organized and exact branch of science

·        Mathematics has its own language

·        Mathematical rules, laws and formulae are universal

·        Inductive and experimental science

·        Abstract form of science

·        Intellectual game

·        Mathematics helps to develop self-confidence and self reliance

·        Helps to develop scientific attitude

·        Gives accurate and reliable knowledge

Mathematics as a science

Mathematics is the science and study of numbers. It is often considered as science because it is a logical study of numbers, quantities and shapes. It involves the use of evidence, reasoning and proof to develop and test hypotheses, and it seeks to understand and explain the underlying patterns and structures in the world around us. Mathematics can be considered as father of all sciences or tool which helps in solving problem of every other sciences.

 Mathematics as a game

In mathematics, we create a set of rules and regulations just like in a game, and proceed with logical reasoning. It is a game with figures and numbers.

Mathematics as a language

“Mathematics is the language in which God has written the universe”- Galileo Galilei

Mathematics is called the language of science. Math can act as a universal language. A phrase or formula has the same meaning, regardless of another language that accompanies it. As a language, mathematics is characterized by symbols to express size, shape and order. These symbols make mathematical expressions precise, concise and accurate.in this way, math helps people to learn and communicate, even if other communication barriers exist.

Mathematics as a tool

According to Kant, Mathematics is the indispensable instrument of all physical researches. That is, mathematics helps everyone to quickly understand the relationship between two concepts. It is the indispensable tool for calculating, organizing, simplifying and interpreting numerical data.

Difference between mathematical science and basic science

Math is differs from basics science. In science, truth means correspondence with observation whereas in mathematics truth is the logical consistency of the statements made and results obtained. Basic science is experimental in nature but mathematics is progressive in its nature. Science gives importance to observation whereas mathematics gives importance to logic. Mathematics is more related with calculations and science is more related with working, reasoning, concepts behind everything.

Pure and applied mathematics

Pure mathematics is the branch of mathematics most concerned with mathematical concepts. It involves systematics and deductive reasoning. It deals with exact statements, concepts and theories which are disconnected from perception. It treats only theories and principles without regard to their application to concrete things.

Eg: Algebra, geometry, Number theory..

Application of pure mathematics in the real world is called applied mathematics.it considers those parts of mathematical theories that have certain direct or practical application to objects or actions in the material world. It helps the development of other sciences or subjects.

Eg: Probability theory, Statistics, fluid mechanics..

Role of axioms and postulates

Axioms

Axiom comes from Greek word ‘axioma’ which means ‘to deem worth’. Every area in mathematics is based on some statements which are assumed to be true and not proved. These are self-evident truths which we take to be true without proof.

Examples:-

·        Things that are equal to the same thing are equal to one another

·        If equals are added to equals the result will be equal

·        If a>b, b>c, then a>c.

Postulates

Non logical axioms usually called postulates. It is self-evident truths which are taken for granted without any necessity of proof or explanation. Postulates are suppositions without proof. It aims to capture what is special about a particular structure.

Examples:

·        A straight line can be drawn from any point to any other point

·        Two straight lines cannot intersect in more than one point

·        Two circles intersect at two points.

Correlation of mathematics

·        Correlation of mathematics with other subjects

Correlation between mathematics and social science

In social sciences we come across graphs, charts, curves etc; thus we can say that social sciences draw a lot from mathematics.

Correlation between mathematics and general science

Science without mathematics is totally meaningless, because chemical reactions, scientific theories and detail of elements are only generated with the help of mathematics.

Correlation between mathematics and Agriculture

Agriculture has correlation with maths like area of crops, which season is suitable for which crop. We have to make various land measurements and for this purpose a knowledge of mathematics is essential. How much quantity of water may be used in irrigation is also calculated in concern of agriculture by the use of mathematics.

Correlation between mathematics and Economics

In economic we study the earning and spending factors of a society, population, production etc. statistics plays an important role in economics. The application of statistical methods is most helpful in economic forecasts. Trade cycles, trends of exports and imports all are represented statistically.

Correlation between mathematics and languages

No subject can be taught without the help of language. The principles of mathematics are expressed through the medium of language. If the language that is spoken in a mathematics class or written in a book is not correct, the exact idea of the subject matter shall not be conveyed.

Correlation between mathematics and history

The relationship between mathematics and history is reciprocal. History helps mathematics to know about various mathematicians who were pioneers in their field and enriched mathematics by their contributions. History also provides the information about the origin and development of mathematics.

·        Correlation of mathematics with real life

Mathematics is one subject which has extensive application in our daily life. We use math concepts, as well as the skills we learn from practicing math problems every day. Examples: Managing time, budget, cooking, driving, architecture, gardening, agriculture and stitching etc.