First of all, a brief introduction.
Mathematics is a universal means for human beings to strictly describe the abstract structure and mode of things, and can be applied to any problem in the real world. All mathematical objects are artificially defined in essence. In this sense, mathematics belongs to formal science, not natural science. Different mathematicians and philosophers have a series of views on the exact scope and definition of mathematics.
Second, mathematics.
1, mathematics [English: Mathematics, from ancient Greece μ? θξμα(máthēma)； Often abbreviated as math or maths], it is a discipline that studies concepts such as quantity, structure, change, space and information. Mathematics is a general means for human beings to strictly describe and deduce abstract structures and patterns of things, and can be applied to any problems in the real world.
2. All mathematical objects are artificially defined in essence. In this sense, mathematics belongs to formal science, not natural science. Different mathematicians and philosophers have a series of views on the exact scope and definition of mathematics. Mathematics plays an irreplaceable role in the development of human history and social life, and it is also an indispensable basic tool for studying and studying modern science and technology.
Third, the structure
1, many mathematical objects such as numbers, functions, geometry, etc. Reflect the internal structure of continuous operation or the relationship defined therein. Mathematics studies the properties of these structures, for example, number theory studies how integers are represented under arithmetic operations. In addition, similar things often happen in different structures, which is further abstract.
2. Then it is possible to describe the state of a class of structures with axioms. What needs to be studied is to find the structure that satisfies these axioms among all the 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.