[Maths Class Notes] on What is Mathematics? Pdf for Exam

Mathematics is a subject of rationality, the science of structural relation and order that has originated from elemental practices of counting, measuring, and explaining the shapes of objects. In addition, it deals with quantitative calculation and logical reasoning. Mathematics thus simply means to study, to learn or gain knowledge. The theories given in mathematics help us understand and solve different kinds of problems in academic as well as in real life situations. Solving mathematical problems is perhaps the best brain exercise.

History of Mathematics

Now that you are aware of what mathematics is, let’s get to know about the evolution of this historical subject. The development of mathematics has involved an increasing intensity of idealization and abstraction of its subject matter. The subject has been explored by a number of mathematicians around the world since centuries, in distinct civilizations. Archimedes (287-212 BC), from the BC century is remembered as the Father of Mathematics. He introduced formulas to calculate the volume and surface area of solids. On the other hand, Aryabhatt, born in 476 CE, is renowned as the Father of Indian Mathematics.

Since the 17th century, maths has been a vital supplement to the physical sciences and technology, and in more recent times it has presumed to play a similar role in the quantitative aspects of the life sciences.

The study of mathematics started with the Pythagoreans, as a “demonstrative discipline” during the 6th century BC. The term mathematics evolved from the Greek word “mathema”, which implies “subject of instruction”.

Another mathematician, named Euclid, introduced the axiom, theorems, proofs and postulates, which are also widely used in current mathematics.

History of Mathematics is a primitive study and is defined by each part of the world, in a differential method. Various mathematicians have provided different theories for many concepts, which we are now applying in modern mathematics.

Numbers that we use for calculations had variations during the medieval period. The Romans bring into being the Roman numerals which use English alphabets in order to represent a number, such as:

 

Branches of Mathematics

The main branches of mathematics include:

1. Algebra

2. Number System

3. Geometry

4. Trigonometry

5. Topology

6. Calculus

7. Probability and Statistics

Rules In Mathematics

A common rule used in maths is the BODMAS rule. According to this rule, the arithmetic operations are carried out based on the brackets and order of operations. The full form of BODMAS can be easily understood with the given description:

BODMAS –

B: Brackets

O: Orders

D: Division

M: Multiplication

A: Addition

S: Subtraction

Thus, the 1st priority given here to the brackets then;

Division> multiplication > addition > subtraction

For instance, if we need to solve [10+ (4 x 10) ÷2], then applying the BODMAS rule, first multiply 4 and 10, within the brackets.

→ 10 + (4 x 10) ÷2

= 10 + 40 ÷ 2

Now divide 40 by 2

→ 10 + 20

→ 30

Class Wise Important Topics in Mathematics

Below are some important topics for each Class (from 1 to 12) which is covered under maths.

Class 1

1. Numbers In Words

2. Shapes

3. Addition And Subtraction Of Integers

Class 2

1. Place Value

2. Counting Numbers

Class 3

1. Introduction To Data

2. Comparing Fractions

3. Multiplication Tables

4. Multiplication And Division Of Integers

Class 4

1. Introduction to Large Numbers

2. Factors And Multiples

3. Multiplying Fractions

4. Multiplication And Division Of Decimals

Class 5

1. Introduction to Lines and Angles

2. Introduction To Area

3. Area Of A Square  

4. Dividing Fractions

5. Addition and Subtraction of Decimals

Class 6

1. Introduction To Algebra

2. Integers and Fractions

3. Whole Numbers

Class 7 

1. Introduction To Lines, Angles and Triangles

2. Means Of Comparing Quantities: Percentage

3. Concept of Visualising Solid Shapes

Class 8

1. Introduction To Rational Numbers, Squares and Square Roots

2. Exponents And Powers

3. Mensuration

Class 9

1. Introduction to Number System

2. Theory of Polynomials

3. Quadrilateral and finding Volume and Surface Areas

Class 10

1. Introduction to Circles and Quadratics

2. Constructions and Co-ordinate Geometry

3. Arithmetic Progression, Probability And Statistics

Class 11

1. Sets, Relations and Functions

2. Trigonometric Functions and Linear Inequalities

3. Permutation, Combination and Conic Sections

4. Limits and Derivatives

Class 12

1. Matrices and Determinants

2. Inverse Trigonometric Functions

3. Application of Integrals

4. Vector algebra and Linear Programming

5. Continuity And Differentiability