## What is math?The word ## Definitions of MathCommonly, there is no accepted definition of math. Aristotle defined mathematics as, The study of According to the German philosophers Modern philosophers do not consider mathematics as a science because science is based on The study of math includes the following: **Numbers:**The study of numbers involves how can we count the things.**Structure:**The study of structures involves how things can be organized. The subfield of structure is called algebra.**Place:**The study of place involves the arrangements for the things. The subfield of place is called geometry.**Change:**The study of change involves how things become different. The subfield of change is called analysis.
## Why math is important?Math is very important in our daily lives. In reality, it is implemented everywhere. It is useful for solving problems that occur in the real world. This is the reason that so many people besides mathematicians study and use mathematics. There are too many fields such as There are the following reasons that makes the mathematics as a powerful tool. - Math is involved around us. So, it is an essential and powerful discipline in today's world. Our perspective of the important issues facing us as individuals, families, businesses, and nations.
- It provides an effective way of building
**mental discipline**. - It improves
**mental rigor**for developing**logical, analytical, and problem-solving skills.** - The knowledge of mathematics plays a crucial role in understanding other subjects such as physics, art, music, etc.
## Fields of MathematicsIn mathematics there are - Pure Mathematics
- Applied Mathematics
## Pure MathematicsIn pure mathematics, we study the mathematical concept independently of any application outside mathematics. It includes **Proof Theory:**It includes set theory and model theory.**Number Theory:**It includes arithmetic, elementary number theory, analytic number theory, algebraic number theory, and other number theories such as computational number theory, geometric number theory, etc.**Algebra:**It includes order theory, general algebraic system, field theory and polynomials, commutative rings and algebras.**Combinatorics:**It includes graph theory.**Geometry:**It includes convex geometry, discrete geometry, differential geometry, and algebraic geometry. The algebraic geometry further includes arithmetic geometry, Diophantine geometry, and real algebraic geometry.**Topology:**It includes general, algebraic, and differential topology.**Analysis:**It is a branch of mathematics that is rapidly expanding. It includes other subdivision of the mathematics. It finds both, direct and indirect applications in subjects as diverse as number theory, cryptography, and abstract algebra.
## Applied MathematicsThe combination of mathematics and specialized knowledge is known as applied mathematics. It is used in different fields such as science, engineering, computer science, and business. It includes **Probability:**It includes the random theory of random-phenomena.**Statistics:**It includes the study of surveys and experiments.**Computational Sciences:**It includes numerical analysis and computer algebra.**Physical Sciences:**It includes mechanics, mechanics of structure, mechanics of deformable solids, fluid mechanics, particle mechanics.
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