**Mathematics** is the oldest academic discipline of the world and a foundation of natural sciences, social sciences, engineering and technology including physics, chemistry, medicines, statistics. It is concerned with the study of structure, quantity, space and their changes. The term “mathematics” is originated from the Greek word mathema means study, learning or mathematical study. Initially it was developed to count the quantities and measuring the space and time but later it was developed by Greek mathematicians and its first appearance can be found in Greek mathematician’s work including Euclid’s element in 600 BC, China in 300 BC, India in AD 100 and in Muslim countries in AD 800, which was developed and classified by modern mathematicians in various branches of mathematics. Mathematics is classified in two major categories— Pure mathematics and Applied mathematics

Pure Mathematics:

Pure mathematics deals with the quantity, structure, space and their changes and works as the base for complex mathematics. Pure mathematics is based on general elements of mathematics and includes numbers (natural number and integers), sets, operations or relations between sets, groups, fields, geometry, calculus, Functions, chaos theory, space. Pure mathematics has its own sub-branches such as continuity, limits, Calculus (differentiation and integration), Real analysis, Algebra, Discrete mathematics, Complex analysis, Functional analysis, Abstract algebra, Geometry (projective and inversive geometry), topology, Number theory.

Applied Mathematics:

Applied mathematics is concerned with the use of abstract mathematical tools to solve the problems of natural and social sciences and engineering. It encircles a vast area of the field and plays an important role to help the researchers to find out the solution of complex mathematical questions. Main streams of applied mathematics are Actuarial science (along with probability, statistics and economic theory), Management science, Numerical analysis, Operations research, scientific computing or computer science (uses logic, algebra, and combinations) and Statistics (including probability and decision theory). Applied mathematics is frequently used in physics, chemistry, biology, medicines, engineering, computer science, medicines, economics and mathematical physics.