The Comprehensive Guide on 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 mathematical 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 between the different branches of mathematics.

Branches of Mathematics

Here are some of the crucial mathematics branches

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. 


Arithmetic is the most ancient branch of mathematics. It is used to deal with the 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 the basic calculations in our daily life. It is the foundation of pure mathematics.


It is one of the main branches of pure math. We use the English alphabets to donate the algebraic values. We use it to find the unknown missing value in the algebraic expression and equations. Besides in algebra, there are lots of rules of operations, relations and constructions, algebraic structures, and polynomial equations. 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.


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 is using geometry to fulfill their daily requirements. The Industrial manufacturing industry depends on geometry. Even when you walk on the road, you also use geometry to find your ways of using GPS.


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 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.


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.


The basic branch of analysis is calculus. We use it to deal with the study of the rate of change in different quantities. Apart from that, it is used to study the functions and limits. We use the analysis for the use of infinite processes that is the passage to a limit. It is used to solve the measuring lengths, areas, volume, and other quantities. 

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.


It is used as the foundation of underlying mathematical logic. We use it to formalize valid reasoning. 


It is used to study discrete objects. In this, we use to count the object to meet the specific criteria. We also construct and analyze objects to meet the specific criteria. In this, we find the smallest, largest, and optimal objects. We also test to find the algebraic structure of these objects.


Topology is extensive in geometry. It is used to find out those properties of the shapes that can’t be changed even if the figure dimension is changed completely.

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. 

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

Information theory and signal processing

Information theory is another crucial branch of applied mathematics. It is used for the quantification of information. It is used to find the best ways to send reliable data efficiently. 

On the other hand, signal processing is popular to analyze, interpret, and signal manipulations. It is used for many kinds of signals, such as biological signals, radar signals, and many others. To process all these types of signals, it involves filtering, storage and reconstruction, noise reduction compression, and other techniques.

Probability and statistics

Probability and statistics are interrelated with each other. Both of these are important part 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 the science. We use it to collecting the data, analyzing the data on the basis of some given criteria.


More branch will definitely add in mathematics. But here in this blog, we have mentioned the crucial one that can be used by the beginners as well as from the professional one. Math is everywhere; you can implement it anytime. So what are you waiting for? Start applying these basic mathematics branches 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 assignment help to the students. Grab the best deal on a mathematics assignment help to enhance your grades.

0 0 vote
Article Rating
Notify of
Inline Feedbacks
View all comments