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Detailed Analysis Of Branches Of Mathematics – Relationship And Differences

Mathematics is all around the world, you can’t skip mathematics even in a day. Whatever we do in a day involves maths. This is why mathematics is very essential in our day to day life and we can’t even imagine a day without maths. The word mathematics has originated from the term ‘Mathema’ which means Science or knowledge. Generally mathematics is written as Math or Maths. Initially there were limited branches of mathematics but with time maths and it’s branches have evolved.

Mathematics has made considerable contributions especially in the field of technology. Thus, there are several important branches of mathematics starting from basic to the advanced level. But many students face difficulty in understanding the difference between the different branches of maths. 

Learn The Different Important Branches Of Mathematics

Pure Mathematics

It is the basic branch of maths which basically deals with the basic mathematical concepts. It is generally independent of any kind of application outside the maths. Pure math applies the maths concepts in the real world situations. 

Arithmetic Mathematics 

The next branch of maths is the most ancient branch that is Arithmetic maths. It is the study of numbers from 0 to 9 and other numbers, even odd numbers, prime numbers, factors, LCM etc. You learn the basic operations that we study since our childhood such as addition, subtraction, division, multiplication, BODMAS etc. It is the most commonly used maths as it is used by from a child to adult to professionals to non working persons etc. We perform the basic operations using this branch. This is why it is considered as the foundation of Pure Maths.

Algebra Maths 

It is the most favourite mathematics branch for students as mostly all the students enjoy working on algebraic expressions. It is basically one of the crucial branches of pure mathematics. In algebraic expressions, we use English alphabets to denote the algebraic values. 

We use the algebra to find out the missing or unknown value in algebraic expressions or equations. Algebra does not only include algebraic equations rather it has many more like other rules of operations, polynomial equations etc. 

It also has subparts and elementary algebra is very famous for them. Generally we use elementary algebra for numbers representation. We can apply algebra in several structures like ringa or fields etc. We can say that it deals with symbols and states the rules of operating such symbols.

It has a number of algebraic formulas to solve the algebraic equations. 

In algebraic expression we have variables which are represented in English letters and whose values we need to find out such as x, y, z etc. 

Example of an algebra equation is 2x + 3y = 5.


The next branch of mathematics is Geometry. It would not be wrong to say that it is the most practical mathematical branch in the world. You can check the applicability of geometry in real life and that too in day to day operations. It includes different shapes, sizes, figures and their properties and importance. 

You will learn functioning of points, lines, angles, different types of surfaces, shapes and other solids etc. The best practical application of geometry you can see is that we all use geometry in GPS for finding ways. It is also used by manufacturing industries. 


Similar to geometry there is one more branch with the name topology and it is an extensive form of geometry only. We use this branch to study the properties of shapes which cannot be changed even though their figure dimensions change absolutely. 


If you have ever studied physics then you must be knowing the usage of maths in physics. You can solve numerous physics problems with the help of mathematics. Widely used concepts of mathematics in physics ate derivatives, integration, differentiation etc. Thus a number of maths and physics concepts are similar and their foundations are also the same. 


If you ask any mathematical student about trigonometry then they will say it is very tough. The word trigonometry is made up with two Greek words that are trigon which means triangle and second word is metron which means to measure. When the other branches of maths failed to solve the mathematical problems then we developed Trigonometry for the same.

It is the study of angles and triangles and it states the relation between such angles and sides of triangles. 

It also studies geometry.

You will read different types of triangles like acute, right angle etc. 


The next branch of mathematics is Calculus. Issac Newton and Gottfried Leibniz developed the Calculus in the 17th century. It studies the instant rate of change in calculations. You can easily sum the small factors and thus can find the whole number. 

You must have heard of limits, functions, integrals, derivatives, integration etc. All these concepts come under the purview of Calculus. Calculus has two types that are differential calculus and integral calculus. 

You can use the calculus concepts in science, engineering and in economics also. 


The next  branch of mathematics is Logic and it deals with the valid reasoning using different mathematical logics. 

Number Theory

The next branch is Number theory and it is used with the positive integers and its properties. You can also study the relationship between different integers. 


We are always afraid of mathematics and thus we do not value it although it is the most important part of our daily life as we use the practicality of mathematics in daily life. The number of branches of mathematics is n and we are always confused between them. We hope this article has dispelled your doubts. If you face any difficulty in understanding these concepts or the difference between them, you can contact our experts at any time through Math homework help.

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