Mathematics may be described as the fundamental science. It is that branch of science that uses numbers and symbols. Numbers and symbols are arranged using systematic mathematical rules.Mathematics may be broadly described as the science of space, time, measurement, quantities, shapes and numbers and their relationships with each other.
The study of mathematics is based on reasons. The universe exists in space and time, and is constituted of units of matter. To calculate the extension or composition of matter in space and time and to compute the units that make up the total mass of the material universe is the object of Mathematics. For the space-time quantum is everywhere full of matter and we have to know matter mathematically in the first instance.
Pure mathematics is mainly concerned with concepts that are based on the rules of mathematics. Pure Mathematicians chiefly deal with establishing mathematical proofs. These concepts are not necessarily aimed at meeting the needs of the physical world.
Applied mathematics, on the other hand, is that branch of Mathematics that is applied to other branches such as chemistry, physics, chemistry, etc. It relies on a problem-solving approach. It tries to find a practical solutions to solve the day-to-day problems of life.
In practical world, pure mathematics and applied mathematics overlap each other. The concepts of pure mathematics are often used by applied mathematicians to find out practical solutions.
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