Mathematics is one of the most important subjects. Mathematics is a subject of numbers, shapes, data, measurements and also logical activities. It has a huge scope in every field of our life, such as medicine, engineering, finance, natural science, economics, etc. We are all surrounded by a mathematical world.

The concepts, theories and formulas that we learn in Maths books have huge applications in real-life. To find the solutions for various problems we need to learn the formulas and concepts. Therefore, it is important to learn this subject to understand its various applications and significance.

What Is The Definition of Mathematics?

Mathematics simply means to learn or to study or gain knowledge. The theories and concepts given in mathematics help us understand and solve various types of problems in academic as well as in real life situations.

Mathematics is a subject of logic. Learning mathematics will help students to grow their problem-solving and logical reasoning skills. Solving mathematical problems is one of the best brain exercises.

Basic Mathematics

The fundamentals of mathematics begin with arithmetic operations such as addition, subtraction, multiplication and division. These are the basics that every student learns in their elementary school. Here is a brief of these operations.

• Addition: Sum of numbers (Eg. 1 + 2 = 3)
• Subtraction: Difference between two or more numbers (Eg. 5 – 4 = 1)
• Multiplication: Product of two or more numbers (Eg. 3 x 9 = 27)
• Division: Dividing a number into equal parts (Eg. 10 ÷ 2 = 5, 10 is divided in 2 equal parts)

History of Mathematics

Mathematics is a historical subject. It has been explored by various mathematicians across the world since centuries, in different civilizations. Archimedes, from the BC century is known to be the Father of Mathematics. He introduced formulas to calculate surface area and volume of solids. Whereas, Aryabhatt, born in 476 CE, is known as the Father of Indian Mathematics.

In the 6th century BC, the study of mathematics began with the Pythagoreans, as a “demonstrative discipline”. The word mathematics originated from the Greek word “mathema”, which means “subject of instruction”.

Another mathematician, named Euclid, introduced the axiom, postulates, theorems and proofs, which are also used in today’s mathematics.

History of Mathematics has been an ancient study and is described by each part of the world, in a varying method. There were many mathematicians who have given different theories for many concepts, which we are applying in modern mathematics.

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

Branches of Mathematics

The main branches of mathematics are:

• Number System
• Algebra
• Geometry
• Calculus
• Topology
• Trigonometry
• Probability and Statistics

These mathematical concepts fall under pure mathematics. These form the base of mathematics. In our academics we will come across all these theories and fundamentals to solve questions based on them.

Applied mathematics is another form, where mathematicians, scientists or technicians use mathematical concepts to solve practical problems. It describes the professional use of mathematics.

Symbols in Mathematics

Some of the basic and most important symbols, used in mathematics, are listed below in the table.

These are the most common symbols used in basic mathematical calculations. To get more maths symbols click here.

Properties in Mathematics

In mathematics, we learn about four major properties of numbers. They are:

• Commutative Property
• Associative property
• Distributive Property
• Identity Property

These are the four basic properties of numbers. These properties are also applicable to some other mathematical concepts such as algebra.

Rules in Mathematics

The most common rule used in mathematics is the BODMAS rule. As per this rule, the arithmetic operations are performed based on the brackets and order of operations. By the full form of BODMAS, we can easily understand this logic.

BODMAS – Brackets Orders Division Multiplication Addition and Subtraction

Therefore, the first priority here is given to the brackets then division>multiplication>addition>subtraction.

For example, if we have to solve [5+(3 x 5)÷2], then using the BODMAS rule, first multiply 3 and 5, within the brackets.

→ 5+(3 x 5)÷2 = 5 + 15÷2

Now divide 15 by 2

→ 5 + 7.5

→ 12.5

Formulas in Mathematics

Here are some common formulas used in mathematics to solve multiple problems.

• Area and Perimeter Formula
• Coordinate Geometry Formulas
• Heron’s Formula
• Quadratic Formula
• Differentiation Formulas
• Distance Formula
• Section Formula & Conic Sections
• Standard Deviation Formula
• Trigonometry Formulas

Topics in Mathematics

Let us see some important topics for each Class (from 1 to 12) that are covered under mathematics.

Class 1 Mathematics

• Numbers In Words
• Addition And Subtraction Of Integers
• Shapes

Class 2 Mathematics

• Counting Numbers
• Place Value

Class 3 Mathematics

• Multiplication Tables
• Multiplication And Division Of Integers
• Comparing Fractions
• Introduction To Data

Class 4 Mathematics

• Factors And Multiples
• Multiplication And Division Of Decimals
• Multiplying Fractions
• Introduction to Large Numbers

Class 5 Mathematics

• Dividing Fractions
• Addition and Subtraction of Decimals
• Lines and Angles Introduction
• Area Of A Square – Introduction To Area

Class 6 Mathematics

• Whole Numbers
• Algebra
• Integers
• Fractions

Class 7 Mathematics

• Lines And Angles
• Triangles
• Percentage: Means Of Comparing Quantities
• Visualising Solid Shapes

Class 8 Mathematics

• Rational Numbers
• Mensuration
• Squares and Square Roots
• Exponents And Powers

Class 9 Mathematics

• Number System
• Polynomials
• Quadrilateral
• Surface Areas and Volume

Class 10 Mathematics

• Quadratics
• Circles
• Arithmetic Progression
• Co-ordinate Geometry
• Constructions
• Probability And Statistics

Class 11 Mathematics

• Sets
• Relations and Functions
• Trigonometric Functions
• Linear Inequalities
• Permutation And Combination
• Conic Sections
• Limits and Derivatives

Class 12 Mathematics

• Matrices
• Inverse Trigonometric Functions
• Determinants
• Application of Integrals
• Vector algebra
• Linear Programming
• Continuity And Differentiability