Broadly, Mathematics can be sub-divided into the study of quantity, structure, space and change; i.e. arithmetic, algebra, geometry and analysis. There are sub-divisions committed to researching the relationships amongst the heart of mathematics to the other fields including logic, set theory (foundations), experimental mathematics of a variety of sciences (applied mathematics) and thorough study of uncertainty. The study of quantity begins with the numbers, firstly, the common natural numbers and integers and arithmetical operations on them that are qualified in arithmetic.

Geometry studies space, specifically, Euclidean geometry. Trigonometry is the field of mathematics that is concerned with the relationships between the angles and the sides of triangles and with the trigonometric functions. It integrates the numbers and space and covers the recognized Pythagorean Theorem. Also, mathematics studies change. Understanding and explaining change is a frequent theme in the natural sciences and calculus was formed as a very effective technique of investigating it. The functions occur here, as a fundamental theory unfolding a varying quantity.

            Several mathematical objects, like the sets of numbers and functions, show internal structure. The structural characteristics of these objects are examined in the study of fields, groups, rings and other abstract systems that are themselves such objects. This is referred to as the area of abstract algebra. Mathematics can be classified into two areas; discrete mathematics and applied mathematics. Discrete mathematics is the familiar name for the areas of mathematics most usually relevant in the computer science theory.    

This takes in the computational complexity theory, computability theory and information theory. Computability theory scrutinizes the restrictions of diverse theoretical models of the computer, together with the most influential known model - Turing machine. Complexity theory studies the tractability by computer. Applied mathematics regards the employment of abstract mathematical tools in figuring out the material problems in the business, sciences and other areas. Applied mathematics considerably overlaps with the discipline of statistics, whose theory is prepared mathematically, particularly with probability theory. Also, there are some common misconceptions about Mathematics. It is not a closed intellectual system, in which, the whole thing has already been done. There is no dearth of open problems. Mathematics is not numerology and it is not related with supernatural attributes of numbers. It is not accountancy and it is not limited to arithmetic.