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**Math: -**Math is the study of space, relation, structure, change, and many other topics which seek pattern. Mathematics is the language of science and engineering formingan essential and important tool in most of the fields, including engineering, social science, medicine, natural science etc. Mathematics has evolved from mere number crunching such as counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects to more advanced applications in real life.

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**Quantity**: - As the name suggests it deals with various ways of quantifying measurable things, properties and phenomenon. Natural numbers, Integers, Rational numbers, Real numbers and Complex numbers are various types of numbers. Number theory has its basis in these forms of numbers and their properties.

**Structure**: - Mathematics can be applied to study various properties of sets, functions and effect of operations or relations on them. Combinatorics, Number theory, Group Theory, Graph Theory and Order Theory are used for such purposes.

**Space**: - One of the most fascinating aspects of mathematics is the understanding of patterns which govern the space around us. This starts with Euclidean geometry and advances with co-ordinate geometry. Quantity and space both are vital in different fields of mathematics. Geometry, Trigonometry, Differential geometry, Topology, Fractal geometry and Measure Theory come under this ambit.

Change: - Calculus, is one of the most versatile tools of mathematics. This deals with change, rate and time concepts. Differential Calculus, Integral Calculus, Differential equations, etc. cover this. Besides pure calculus, vector calculus, chaos theory and complex analysis also come under the study of change.

Other branches of Mathematics include:

**Mathematical logic**

Model theory

Proof theory

Recursion theory

Set theory

Discrete Mathematics

Applied mathematics

Mathematical physics

Analytical mechanics

Mathematical fluid dynamics

Numerical analysis

Optimization

Probability

Statistics

Mathematical economics

Financial mathematics

Game theory

Mathematical biology

Cryptography

Operations research

Information theory

Control theory

Dynamical systems

Model theory

Proof theory

Recursion theory

Set theory

Discrete Mathematics

Applied mathematics

Mathematical physics

Analytical mechanics

Mathematical fluid dynamics

Numerical analysis

Optimization

Probability

Statistics

Mathematical economics

Financial mathematics

Game theory

Mathematical biology

Cryptography

Operations research

Information theory

Control theory

Dynamical systems

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