Mathematical modeling is a practice of using mathematical methods to solve practical problems. That is, through the process of abstraction, simplification, assumption and introduction of variables, the actual problem is expressed mathematically, the mathematical model is established, and then advanced mathematical methods and computer technology are used to solve it. Mathematical modeling comprehensively uses all kinds of knowledge to solve practical problems. It is one of the necessary means to cultivate and improve students' ability to apply what they have learned to analyze and solve problems. There is no definite model for the general methods and steps of mathematical modeling, but an ideal model should reflect all the important characteristics of the system: the reliability and availability of the model. The general method of modeling: mechanism analysis: according to the understanding of the characteristics of real objects, analyze their causal relationship and find out the laws that reflect the internal mechanism. The established model usually has clear physical or practical significance. Test and analysis method: the research object is regarded as a "black box" system, and the internal mechanism cannot be directly sought. By measuring the input and output data of the system, and on this basis, using statistical analysis methods, according to predetermined standards, the best model is selected from some models. Test analysis method is also called system identification. Combining these two methods, that is to say, it is also a common modeling method to establish the structure of the model by mechanism analysis and determine the parameters of the model by system testing. In the actual process, which method to use for modeling mainly depends on our understanding of the research object and the purpose of modeling. The concrete steps of mechanism analysis and modeling are roughly as follows: 1. In practical problems, variables and parameters are determined by abstraction, simplification and assumption; 2. Establish a mathematical model, solve it mathematically and numerically, and determine the parameters; 3. Test the mathematical model with the measured data of practical problems. 4, in line with the reality, delivered to use, can produce economic and social benefits; Unrealistic, re-modeling. Mathematical model classification: 1. According to the research methods and mathematical characteristics of the object, it can be divided into elementary model, geometric model, optimization model, differential equation model, graph theory model, logic model, stability model and statistical model. 2. According to the actual field (or discipline) of the research object, it is divided into population model, traffic model, environmental model, ecological model, physiological model and so on. Social model, etc. Mathematical modeling needs rich mathematical knowledge, involving advanced mathematics, discrete mathematics, linear algebra, probability statistics, complex variable functions and other basic mathematical knowledge. At the same time, it also needs a wide range of interests and strong logical thinking ability. And language expression ability. What you need to know to participate in the mathematical modeling contest 1. National Mathematical Modeling Competition for College Students II. Methods and general steps of mathematical modeling. Important mathematical models and corresponding case analysis 1, linear programming model and economic model case analysis II. Case analysis of analytic hierarchy process model and management model III. Statistical regression model and case analysis. Graph theory model and case analysis 5. Differential equation model and case analysis iv. Related software 1. 2.Lingo software; 3.Lindo software. Five, digital and analog ten commonly used algorithms 1. Monte Carlo algorithm. 2. Data processing algorithms, such as data fitting, parameter estimation and interpolation. 3. Programming algorithms, such as linear programming, integer programming, multivariate programming and quadratic programming. 4. Graph theory algorithm. 5. Computer algorithms, such as dynamic programming, backtracking search, divide and conquer algorithm, branch and bound. 6. Three nonclassical algorithms of optimization theory. 7. Grid algorithm and exhaustive method. 8. Several discretization methods of continuous data. 9. Numerical analysis algorithm. 10. Image processing algorithm. 6. How to get information? How to write a paper? How to organize a team: team spirit, good at cooperation, constantly asking questions and solving problems. Nine, how to win the prize: relatively complete, there are several innovations. X. How to deal with information: WORD, LaTeX, Flyball, QQ. In fact, just look at the examples and understand some basic models. I also have many examples here. If there are important lectures in various schools, just ask me.