Mathematics is applied in many different fields, including science, engineering, medicine and economics. The application of mathematics in these fields is generally called applied mathematics, which sometimes arouses new mathematical discoveries and promotes the development of new mathematical disciplines.
Mathematicians also study pure mathematics, that is, mathematics itself, without any practical application. Although many jobs begin with learning pure mathematics, they may find suitable applications in the future.
Specifically, there are sub-fields to explore the relationship between the core of mathematics and other fields: from logic and set theory (mathematical basis), to empirical mathematics in different sciences (applied mathematics), to more modern uncertainty research (chaos and fuzzy mathematics).
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The important branch of mathematics is:
I. Number theory
Number theory is a branch of pure mathematics, which mainly studies the properties of integers. Integer can be the solution of the equation (Diophantine equation). Some analytic functions (like Riemann zeta function) contain some properties of integers and prime numbers, and some problems of number theory can also be understood through these functions. The relationship between real numbers and rational numbers can also be established by number theory, and real numbers can be approximated by rational numbers (Diophantine approximation).
Second, algebra.
Algebra is a branch of mathematics, which studies the general solutions and properties of numbers, quantities, relationships, structures and algebraic equations (groups). Elementary algebra is generally taught in middle schools, introducing the basic ideas of algebra: studying what happens when we add or multiply numbers, understanding the concept of variables and how to establish polynomials and find their roots.
Third, geometry.
Geometry is the study of spatial structure and properties. It is one of the most basic research contents in mathematics, which has the same important position as analysis and algebra, and has a very close relationship. Geometry has a long history and rich contents. It is closely related to algebra, analysis and number theory. Geometric thought is the most important thought in mathematics.
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