Mathematics is a tool, logical and can train people's thinking ability; It pays attention to ways and means, which can make your thinking more acute; Furthermore, it can help you solve some practical problems. Master the law of numbers and train logical thinking. Mathematics is a basic subject, and all other subjects will be applied except Chinese.

Extended data:

I. Mathematical structure

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.

Second, rigor.

Mathematical language is also difficult for beginners. How to make these words have more accurate meanings than everyday language also puzzles beginners. Words such as open and domain have special meanings in mathematics.

Mathematical terms also include proper nouns such as embryo and integrability, but there is a reason for using these special symbols and proper nouns: mathematics needs accuracy more than everyday language. Mathematicians call this requirement for linguistic and logical accuracy "rigor".

Stiffness is a very important and basic part of mathematical proof. Mathematicians want their theorems to be derived from axioms through systematic reasoning. This is to avoid relying on unreliable intuition to get the wrong "theorem" or "proof", which has happened in many examples in history.

The degree of rigor expected in mathematics changes with time: the Greeks expected careful argumentation, but in Newton's time, the methods used were not so rigorous. Newton's definition of solving problems was not properly handled by mathematicians through rigorous analysis and formal proof until19th century.

Mathematicians have been arguing about the rigor of computer-aided proof. When a large number of calculations are difficult to verify, it is hard to say that they are effective and rigorous.