Mathematics is a discipline that studies the concepts of quantity, structure, change, space and information, and belongs to a formal science from a certain point of view. Mathematicians and philosophers have a series of views on the exact scope and definition of mathematics.

In the development of human history and social life, mathematics also plays an irreplaceable role, and it is also an indispensable basic tool for studying and studying modern science and technology.

Many mathematical objects, such as numbers, functions and geometry, reflect the internal structure of continuous operations or the relationships defined in them. Mathematics studies the properties of these structures, for example, number theory studies how integers are represented under arithmetic operations.

In addition, things with similar properties often occur in different structures, which makes it possible for a class of structures to describe their state through further abstraction and then axioms. What needs to be studied is to find out the structures that satisfy these axioms among all structures.

Extended data:

Structure of mathematics:

Many mathematical objects, such as numbers, functions and geometry, reflect the internal structure of continuous operations or the relationships defined in them. Mathematics studies the properties of these structures,

For example, number theory studies how integers are represented under arithmetic operations. In addition, things with similar properties often occur in different structures, which makes it possible for a class of structures to describe their state through further abstraction and then axioms. What needs to be studied is to find out the structures that satisfy these axioms among all structures.

Therefore, we can learn abstract systems such as groups, rings and domains. These studies (structures defined by algebraic operations) can form the field of abstract algebra. Because abstract algebra has great universality, it can often be applied to some seemingly unrelated problems. For example, some problems of drawing rulers and rulers in ancient times were finally solved by Galois theory, which involved the theory of presence and group theory.

Another example of algebraic theory is linear algebra, which makes a general study of vector spaces with quantitative and directional elements. These phenomena show that geometry and algebra, which were originally considered irrelevant, actually have a strong correlation. Combinatorial mathematics studies the method of enumerating several objects satisfying a given structure.