A mathematical problem is expressed by function, and the general law of this problem is explored by function. This is the most basic and commonly used mathematical method.

2. The combination of numbers and shapes:

Combining algebra with geometry, such as solving geometric problems by algebraic method and solving algebraic problems by geometric method, is the most commonly used method in analytic geometry. For example, find the root number ((A- 1)2+(B- 1)2)+ root number (A 2+(B- 1)2)+ root number ((A- 1) 2+B).

3. Discuss ideas by category:

When a problem may lead to different results because of different situations of a certain quantity, it is necessary to classify and discuss the various situations of this quantity. Such as solving inequality | a-1| >; 4. It is necessary to discuss the value of A.

4. Equation concept:

When a problem may be related to an equation, we can solve it by constructing the equation and studying its properties. For example, when proving Cauchy inequality, Cauchy inequality can be transformed into a discriminant of quadratic equation.

In addition, there are mathematical ideas such as induction and analogy, transformation and induction, probability and statistics. For example, we can study some similar problems by inductive analogy, get their similarities, and then get the general methods to solve these problems. The idea of transformation induction is to transform a complex problem into another simple problem and summarize its methods. The idea of probability statistics refers to solving some practical problems through probability statistics, such as the winning rate of lottery tickets, the comprehensive analysis of an exam and so on. In addition, some area problems can be solved by probability method.