Mathematics also 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.
The knowledge and application of basic mathematics is an indispensable part of individual and group life. The refinement of its basic concepts can be seen in ancient mathematical classics of ancient Egypt, Mesopotamia and ancient India. Since then, its development has made small progress. But algebra and geometry at that time were still independent for a long time.
Algebra can be said to be the most widely accepted "mathematics". It can be said that algebra was the first mathematics he came into contact with since everyone began to learn to count when he was a child. Algebra, as a discipline to study numbers, is also one of the most important parts of mathematics. Geometry is the earliest branch of mathematics that people began to study.
Extended data:
Many mathematical objects, such as numbers, functions, geometry, etc. A that reflects the internal structure that defines continuous operations or relationships. 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 from abstract systems such as groups, rings and fields.
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, such as some ancient ruler drawing problems, which are finally solved by Galois theory, involving field theory and group theory.
Another example of algebraic theory is linear algebra, which makes a general study of vector space 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 digital objects satisfying a given structure.
References:
Baidu encyclopedia-mathematics