# BRANCHES OF MATHEMATICS, DEFINITIONS AND EXAMPLES

Math is essential in our daily lives. Math can be used in a variety of ways. Without mathematics, we can’t envision a well-organized universe. Mathematics was only studied infrequently in recent years. However, mathematics has expanded in recent years to include a variety of fields. The branches of mathematics are continuing to grow in order to make significant contributions to the realm of technology.

As a result, there are numerous mathematical disciplines in the actual world. Nowadays, mathematics is taught at all levels, from elementary to advanced, and it is used to aid in the development of cutting-edge computer technology. As a result, pupils’ understanding of the value of mathematics will be critical. As a result, it is critical for students to clear up any misconceptions they may have regarding various fields of mathematics.

## BRANCHES OF MATHEMATICS

Over time, mathematics has grown in scope. Pure mathematics and applied mathematics are two types of mathematics. The term “applied mathematics” refers to mathematics that can be used to solve problems in the actual world.

Algebra, Geometry, Arithmetic, Trigonometry, Calculus, and more fields of mathematics exist.

### ALGEBRA

Definition says,

“Algebra is a discipline of mathematics that deals with symbols and the rules that govern their manipulation. These symbols, which are now written as Latin and Greek letters in elementary algebra, indicate quantities with no set values, sometimes known as variables. The fields’ areas are represented by the letters x and y.”

Algebra is a large subject of mathematics that deals with solving and manipulating algebraic statements to arrive at results. The value of a variable is found by solving for unknown quantities denoted by alphabets that constitute a part of an equation. It’s a fascinating discipline of mathematics that uses intricate formulae and methods to solve issues.

Example,

Calculate the value of 20^2 – 5^2

Use the formula a2 – b2 = (a – b)(a + b)

here a = 20 and b = 5

(a – b)(a + b)

= (20 – 5)(20 + 5)

= 15 × 25

= 375

### GEOMETRY

Definition says,

“Geometry is a discipline of mathematics that explores how things are measured in terms of their sizes, forms, angles, and dimensions. 2D shapes are flat shapes such as squares, circles, and triangles that are part of flat geometry.”

You must investigate the branch of geometry. Geometry is a practical field of mathematics concerned with the proportions, shape, and volumes of figures. It concentrates on the study of shapes, polygons, and geometric objects in two and three dimensions. The congruence of objects is investigated while concentrating on their unique qualities and calculating their volume, area, and perimeter.

Example,

A circle has a radius of 10 cm. Find its diameter, circumference, and area.

r = 10 cm

The diameter of a circle will be

2r

= 2 × 10 cm

= 20 cm

Circumference of the circle will be

2 π r

= 2 × π × 10= 62.8 cm

The area of a circle will be

π r^2

= π × 10 x 10

= 314 cm2

### TRIGONOMETRY

Definition says,

“Trigonometry is a discipline of mathematics concerned with the application of certain functions of angles to calculations. In trigonometry, there are six functions of an angle that are often utilized. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their names and acronyms (CSC).”

Trigonometry is the study of triangle angles and sides in order to calculate distance and length. Trigonometry is a study of the relationship between the angles and sides of a triangle, and it is one of the most widely used fields of mathematics in the world of technology and science to produce items. It’s all about the properties of different triangles!

### CALCULUS

Definition says,

“the branch of mathematics that deals with the finding and properties of derivatives and integrals of functions, by methods originally based on the summation of infinitesimal differences. The two main types are differential calculus and integral calculus.”

It is a discipline of mathematics that analyses the rate of change and is one of the most advanced. With the introduction of calculus, the study of mathematics underwent a radical transformation. Mathematical concepts could previously only be applied to static things, but with the introduction of calculus, mathematical principles could be applied to moving objects.

### ARITHMETIC

Definition says,

“Arithmetic is a field of mathematics concerned with the study of numbers and the different operations that can be performed on them. Addition, subtraction, multiplication, and division are the four basic math operations.”

The oldest branch of mathematics is arithmetic. It’s used to work with numbers ranging from 0 to 9, even odd, prime, or anything else. It includes the basic operations of addition, multiplication, subtraction, and division. From students to working professionals, arithmetic is used by everyone. In addition, we use it in our daily lives to conduct fundamental calculations. Pure mathematics is built on this foundation.

1. What are the main branches of pure mathematics?

Ans. The main branches of pure mathematics are:

• Algebra
• Geometry
• Trigonometry
• Calculus
• Arithmetics

2. What are the Branches of Mathematics for higher classes?

Ans. Mathematics in higher classes involves the following types:

• Analysis
• Discrete Maths
• Applied Mathematics
• Cartesian Geometry
• Matrix Algebra
• Combinatorics
• Topology
• Order theory

3. What branch of mathematics is Calculus?

Calculus is a discipline of mathematics that deals with the study of change over time. Calculus is primarily concerned with the ideas of function limits, derivatives, and integrals.

## Prism and Lens

The light travelling from one medium to another of different optical densities gets refracted. Light of all wavelengths…