Introduction of mathematical model:
It is a scientific or engineering model constructed by using mathematical logic method and mathematical language. The history of mathematical models can be traced back to the time when humans began to use numbers. With the application of numbers, various mathematical models are constantly established to solve various practical problems.
A mathematical model can be established to establish an optimal scheme for daily activities such as college students' comprehensive quality evaluation, teachers' work performance evaluation, and visiting friends and purchasing. The establishment of mathematical model is a necessary bridge to communicate the relationship between practical problems and mathematical tools.
Mathematical model refers to a mathematical structure expressed in a general or approximate way with reference to the characteristics or quantitative dependence of a certain thing system. This mathematical structure is a pure relational structure of a system characterized by mathematical symbols. The generalized mathematical model includes various concepts, formulas and theories in mathematics.
Because they are all abstracted from the prototype of the real world, in this sense, the whole mathematics can also be said to be a science about mathematical models. In a narrow sense, mathematical model only refers to the mathematical relationship structure that reflects a specific problem or a specific thing system. In this sense, it can also be understood as a mathematical expression, which describes the relationship between variables in the system.
The content expressed by mathematical model can be quantitative or qualitative, but it must be reflected in a quantitative way. Therefore, the operation mode of mathematical model method is biased towards quantitative form.
Concise and practical:
In the process of modeling, we should reflect the essential things and their relationships, and eliminate the non-essential things that have little influence on reflecting the objective truth, so that the model can be as simple and operable as possible and the data can be easily collected while ensuring a certain accuracy.
True and complete:
True, systematic, complete and vivid reflection of objective phenomena; Must be representative; Extrapolation, that is, the information of the prototype object can be obtained, and the reasons about the prototype object can be obtained in the process of model research and experiment; It must reflect all kinds of achievements made in completing basic tasks, and it must conform to the actual situation.