First, classified discussion.

When solving some mathematical problems, we sometimes encounter various situations, which need to be classified, solved one by one, and then integrated to get a solution. This is the reason why the idea of classified discussion leads to classified discussion, which is mainly manifested in the following aspects:

1, the mathematical contour involved in the problem is defined by classification, for example, the definition of a is divided into A >；; 0, a=0 and a<0.

2. The mathematical theorems, formulas, operational properties and laws involved in the problem are limited by scope or conditions, or the positional relationship between points and circles given by classification can be divided into three situations.

3. When solving problems with parameters, we must discuss them according to the range of parameters. For example, when studying the open direction of quadratic function image, it is divided into A >；; 0 and a; 0，△& gt； 0，△& lt； 0，delta = 0。

Second, functions and equations

Function thought refers to analyzing, reforming and solving problems with the concept and nature of function; The idea of equation is to start with the quantitative relationship of the problem, transform the conditions in the problem into a mathematical model with mathematical language, and then solve the equation (group) so that the function of the problem has a close relationship with the equation.

For example, a univariate linear function can be regarded as a binary equation about x and y; Binary equation can be regarded as a linear function with V as X. It can be said that the learning of function can not be separated from the characteristics of equation sequence, and solving and studying equations are all manifestations of the idea of applying equations.

Introduction to mathematics

Mathematics is a universal means for human beings to strictly describe and deduce 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.

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.