The Comprehensive Guide on Branches of Mathematics

branches of mathematics

Mathematics is crucial for our daily life. There are lots of application of math. We can’t imagine a well-organized world without the use of mathematics. In recent times there was a limited study of mathematics. 

But over the last few years, mathematics has developed with diverse branches. Mathematics branches are kept developing to make considerable contributions to the technology field. Therefore there are plenty of mathematics branches that exist in the real world. 

Nowadays, mathematics starts from the basic to the advanced level that is helping in the latest computer technology. That is why the importance of mathematics is going to be crucial for the students. 

Thus it becomes crucial for the students to clear their doubts about the different branches of mathematics. However, in this blog, we will learn some important 10 branches of mathematics. So, scroll down to learn different branches of mathematics.

What Is Mathematics?

Mathematics is the study of numerical relationships, geometrical formations, and repeating patterns. It is a broad and complex subject with many different branches. In addition, mathematics is a beautiful and fascinating subject. It is a language that allows us to communicate ideas about the world precisely and concisely. It is also a powerful tool that can be used to solve problems and make the world a better place.

Importance of Mathematics in Daily Life In 2023

Mathematics is essential in our daily lives. It is used in a wide variety of tasks, from simple everyday activities to complex scientific calculations. Here are some of the ways that mathematics is important in our daily lives:

1. Cooking

We use mathematics to measure ingredients, calculate cooking times, and determine how much food to buy.

2. Shopping

We use mathematics to compare prices, calculate discounts, and budget our spending.

3. Time Management

We use mathematics to set deadlines, track our progress, and estimate how long tasks will take.

4. Problem-Solving

We use mathematics to solve problems in our personal and professional lives. For example, we might use mathematics to determine the best route to a destination, to calculate the cost of a project, or to optimize our finances.

5. Decision-Making

We use mathematics to make informed decisions. For example, we might use mathematics to evaluate investment options, to compare insurance policies, or to choose the best college.

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6. Communication

We use mathematics to communicate our ideas clearly and concisely. For example, we might use mathematics to write a budget, to create a presentation, or to explain a scientific concept.

Branches Of Mathematics

Mathematics is a complicated field of study. It includes interlinked topics and overlapping concepts. A comprehensive analysis of the branches of mathematics helps students in organizing their concepts clearly and generate a strong foundation. Being aware of each branch’s differences and importance helps students methodically study various concepts of mathematics. 

Following are the main branches of mathematics. These branches are essential for setting a solid foundation for mathematics.

10 Branches Of Mathematics

Pure Mathematics

It is the basic study of mathematical concepts. We use it to study many concepts outside mathematics. It originated to solve real-world problems. The real obtained for the pure math calculation is used for practical applications. 

1. Arithmetic

Arithmetic is the most ancient branch of mathematics. It is used to deal with numbers, i.e., 0 to 9, even odd, prime, or anything. It contains the basic operation to add, subtract, multiply, and divide. Arithmetic is used by everyone, from students to working professionals. Besides, we use it to perform basic calculations in our daily life. It is the foundation of pure mathematics.

Let’s take an example of a basic arithmetic formula along with the relevant example. The below-mentioned formula is used to calculate the average of the given number.

The marks scored by 5 students in a test are 25,30,40,25,20. Calculate the average marks obtained by the 5 students.

The average marks can be calculated by using the formula mentioned above. 

X = (25+30+40+25+20)/5

= 140/5 =28

Therefore, the average marks obtained by the 5 students are 28.

2. Algebra

It is one of the main branches of pure math. We use the English alphabet to donate the algebraic values. We use it to find the unknown missing value in the algebraic expression and equations. 

Besides, there are many rules of operations, relations and constructions, algebraic structures, and polynomial equations in algebra. The essential part of algebra is known as elementary algebra. 

We use it to represent the numbers. Algebra is more than elementary algebra. It is also applicable to different structures such as groups, rings, and fields.

Some of the basic formulas for algebra are:

(a + b)^2 = a^2 + 2ab + b^2a^2 – b^2 = (a – b)(a + b)a^2 + b^2 = (a + b)^2 – 2ab(a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca(a – b)^2 = a^2 – 2ab + b^2(a – b – c)^2 = a^2 + b^2 + c^2 – 2ab + 2bc – 2ca(a – b)^3 = a^3 – 3a^2b + 3ab^2 – b^3 = a^3 – b^3 – 3ab(a – b)(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 or (a + b)^3 = a^3 + b^3 + 3ab(a + b)a^3 + b^3 = (a + b)(a^2 – ab + b^2)a^3 – b^3 = (a – b)(a^2 + ab + b^2)a^4 – b^4 = (a – b)(a + b)(a^2 + b^2)(a – b)^4 = a^4 – 4*a^3*b + 6*a^2*b^2 – 4ab^3 + b^4(a + b)^4 = a^4 + 4*a^3*b + 6*a^2*b^2 + 4a*b^3 + b^4a^5 – b^5 = (a – b)(a^4 + a^3*b + a^2b^2 + ab^3 + b^4)

Calculate the value of 19^2 – 5^2

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

here a = 19 and b = 5

(a – b)(a + b)

= (19 – 5)(19 + 5)

= 14 × 24

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= 336

3. Geometry

Geometry is one of the high and practical branches of mathematics. In other words, we can easily have a reasonable understanding of geometry from the real world. It deals with the shapes and sizes of figures and their properties. 

Geometry involves points, lines, angles, surfaces, solids, and shapes. Every industry uses geometry to fulfill its daily requirements. The Industrial manufacturing industry depends on geometry. Even when you walk on the road, you also use geometry to find your way of using GPS.

Some of the basic formulas for geometry are:

Perimeter of a Rectangle = P = 2(l+b)Perimeter of a Square = P = 4aArea of a Rectangle = A = l×bArea of a Square = A = a^2Area of a Triangle = A = ½×b×hArea of a Circle = A = π×r^2Circumference of a Circle = A = 2πrArea of a Trapezoid = A = ½×(b1 + b2)×hSurface Area of a Cube = S = 6a^2The curved surface area of a Cylinder = 2πrhVolume of a Cylinder = V = π*r^2*hTotal surface area of a Cylinder = 2πr(r + h)

A circle has a radius of 5 cm. Find its diameter, circumference, and area.

Given Radius is,

r = 5 cm

The diameter of a circle will be


= 2 × 5 cm

= 10 cm

Circumference of the circle will be

2 π r

= 2 × π × 5

= 31.4 cm

The area of a circle will be

π r^2

= π × 5 x5

= 78.5 cm2

4. Trigonometry

Trigonometry deals with the higher class of mathematics. It is derived from two Greek words, i.e., trignon (meaning a triangle) and metron (meaning a measure). We use it to study relationships between angles and sides of triangles. 

In other words, it is directly connected with geometry. Besides, when the world was looking for a solution that couldn’t be solved by the use of arithmetic, algebra, and geometry, then trigonometry came into existence.

Some of the basic formulas for trigonometry are:

FunctionPropertyMathematical value
Sin aopposite/hypotenuse
Cos aadjacent/hypotenuse
Tan aopposite/adjacentSin a/ Cos a
Cosec a1/opposite/hypotenuse1/ Sin a
Sec a1/adjacent/hypotenuse1/ Cos a
Cot a1/opposite/adjacent1/ Tan a

5. Calculus

Calculus was developed by Issac Newton and Gottfried Leibniz in the 17th century. It is used to deal with the instantaneous rates of change calculations. We also use it for the summation of small factors to determine the whole number. 

It is used for limits, functions, derivatives, integrals, and infinite series. There are two types of calculus, i.e., differential calculus and integral calculus. Calculus is used in science, economics, and engineering.

Some of the basic formulas for calculus are:

Differential CalculusIntegral Calculus

6. Number Theory

We use it to deal with the number of positive integers property and relationships. It is one of the crucial branches of pure math. It is used to study the integers and integer-valued functions. Apart from that, we also use it to study the natural, whole numbers, and prime numbers.

Two primes are the prime numbers that differ exactly by 2. The following are some of the twin primes:

5, 7

3, 5

11, 13

29, 31

17, 19

41, 43

Applied Mathematics

The term applied mathematics is also known as advanced math. It involves numerical computations in computer science. It is used to express mathematical problems. 

Nowadays, it is used in some of the most excellent technologies, such as modeling and simulation. For example, we use it to test the train engine prototypes. Most of the computer testing software is based on applied math. Applied math uses mathematics physics.

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Probability and statistics

Probability and statistics are interrelated with each other. Both of these are important parts of applied math. Probability is used to study uncertain events and knowledge. 

Whenever we are going to have the conclusion for the unknown data, then we use probability. Probability is used in the field of predictions. On the other hand, statistics is science. We use it to collect the data, analyzing the data on the basis of some given criteria.

Dynamical systems and differential equations

When we want to study the unknown functions and their derivatives, then we use the differential equation. On the other hand, the dynamic system has a fixed rule. We use it to describe the clock pendulum swinging, the water flow in a pipe, and any other thing which is dynamic in nature.

Mathematical physics

Mathematics is widely used in the field of physics. Mathematical physics is evolved to solve problems in physics. Nowadays, it is widely used in some of the applications which are based on physical theories. Besides, integration, differentiation, integrals, and derivatives are widely used in physics. 


Mathematics is widely used in computer science. This branch of mathematics is known as computation. It involves the study of algorithms, data structure, and scientific computing science and engineering. Apart from that, it involves the methods, i.e., used to solve computer science problems with the help of mathematics.

The fields of mathematics and computing intersect in computer science, the study of algorithms and data structures, and in scientific computing, the study of algorithmic methods for solving mathematics, science, and engineering problems.

Wait! Here’s something you will regret to skip.

Magical math tricks for kids to do lengthy calculations within seconds!!!

Let’s find some of the interesting tricks. These tricks help you to solve your problems within seconds.

Now let’s discuss some interesting questions related to Mathematics.

Answers To Some Of The Interesting Questions

1. Which Maths Is Good For Management Related Fields, Applied Maths Or Pure Maths?

Both branches of mathematics have their own usage. But, degrees like Business Administration, HR Management, Accounting, and Economics degrees all need calculus and statistics. These two branches of mathematics are involved in Pure mathematics. Therefore, it would be better if you have effective knowledge about Pure Maths. 

2. Which Branch Of Diploma Engg Has Minimum Use Of Math?

Well, engineering is all about mathematics. Students need to deal with mathematics somehow and somewhere. But, it has been noticed that CS (Computer Science) Diploma Engineering has the least and easy math compared to other engineering branches like mechanical Engg. Therefore, we can say that CS Diploma Engg is the only branch with the least mathematics usage.

3. Which Branch Has More Maths And Science, Computer Or Electronics Engineering?

Undoubtedly, electronic engineering includes the most usage of maths and science. There are several subjects like Signal And System (SAS), Electromagnetic, and so on that simultaneously deal with science and maths. 

But it also varies as per the university/college/institute’s syllabus. But it is quite clear that electronic engineering has the most maths and science-related subjects to study. 

Benefits Of Learning Mathematics

Here are some of the benefits of learning mathematics:

1. Improved Problem-Solving Skills

Mathematics teaches you how to break down problems into smaller, more manageable pieces. This helps you to develop better problem-solving skills, which can be applied to a wide range of tasks in your personal and professional life.

2. Increased Critical Thinking Skills

Mathematics requires you to think logically and critically. This helps you to better understand the world around you and to make better decisions.

3. Enhanced Analytical Skills

Mathematics helps you to develop better analytical skills. This means that you are better able to identify patterns and trends, and to draw conclusions from data.

4. Improved Communication Skills

Mathematics requires you to communicate your ideas clearly and concisely. This helps you to express yourself better, both verbally and in writing.

5. Greater Career Opportunities

A strong understanding of mathematics can open up a wide range of career opportunities. Many jobs in science, engineering, finance, and other fields require strong mathematical skills.


Now let’s bind up our words on branches of mathematics. More branches will definitely add to mathematics. But here in this blog, we have mentioned the crucial ones that can be used by beginners as well as from professional ones. Math is everywhere; you can implement it anytime. So what are you waiting for? 

Start applying these basic branches of mathematics and start getting a good command over them. But if you still find it difficult to understand these branches, then you can get help from math experts. We are offering the best math homework help to the students. Grab the best deal on math homework help online to enhance your grades.

Frequently Asked Questions

Who is the father of mathematics?

Archimedes is recognized as the Father Of Mathematics. His birthplace was Syracuse, the Greek island of Sicily. He lived from 287 BC – 212 BC

What is the hardest branch of math?

Abstract Algebra is considered the most complicated mathematics branch that is not easy to learn. N-space algebra offers some amazingly difficult help to polish your ability to view infinite mathematics dimensions.