What is Pure Mathematics ?

Pure mathematics is also a mathematical study of the basic concepts and structures that underline mathematics. It uses mathematics to explore abstract ideas, that generally not necessary to describe a real physical system.  

This can include developing fundamental tools used by different mathematicians, such as describing multi-dimensional space, calculus, and algebra, or better consideration of the philosophical meaning of numbers and mathematical themselves. Broadly speaking, pure mathematics is an entirely abstract concept and its main purpose is to search for deep understanding and dilate knowledge of maths itself. 



Traditionally, pure maths has been allocating into three general fields: algebra, which handles discrete aspects; analysis, which handles the continuous aspects of mathematics; and geometry. The undergraduate program is specially planned so that students become amicable with each of these areas. Students may also wish to search for different topics such as logic, number theory, subjects within applied mathematics and, complex analysis. 


Generality and Abstraction in Pure Mathematics 

There is one main concept in pure mathematics and that is the idea of generality, pure maths often manifest a trend towards increased generality. Advantages and uses of generality incorporate the followings: 


  1. Generality can clarify the presentation of materials, means the resulting in shorter proofs or disagreement and arguments that are much easy to follow .


  1. Generalizing mathematical structures and theorems can lead to an intense understanding of original structures or theorems.  


  1. Generality can provide ease to connections between various branches of mathematics. And category theory is one area of maths committed to exploring the commonality of the structure as it plays a vital role in some of the areas of mathematics.  



Wrapping Up 

Pure mathematics means to make a deep dive into math only for the sake of advancing and studying mathematics and only for the sake of mathematics. Pure mathematics is not only studied for the sake of academic purpose but to study for the basic structures and concepts. Cryptography and Finance are the perfect examples of the area to which pure maths is applied in different ways. 


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