According to the Mathematics dictionary; the definition of mathematics is the study of the sciences of numbers, quantities, geometry and forms. Mathematics is divided into two branches: Pure and Applied Mathematics.
Pure Mathematics is concerned with increasing knowledge of the subject rather than using knowledge in practical ways, i.e. its study is theoretical. For example, trigonometry, geometry, set theory, vector, etc. It is concerned with concepts and ideas that do not necessarily have any immediate practical application.
Applied mathematics is the application of mathematical methods by different fields such as science, engineering, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical science and specialized knowledge. Applied mathematics is like a flowing river having pure mathematics on its two banks playing like domain on the boundaries. The two branches are so interrelated and mixed that no sharp (or dividing) line can be drawn between them.