When we finish the whole mathematical modeling process, we should summarize the work and write a paper. Writing a paper on mathematical modeling is similar to completing the answer sheet when participating in mathematical modeling for college students in many ways. In fact, the mathematical modeling competition also includes the test of students' writing ability, so the writing of papers is a very important issue.

First of all, we should make clear the writing purpose of the paper. Mathematical modeling is usually put forward by some departments according to actual needs, and perhaps those departments have provided financial support. At this time, the paper has the purpose of reporting to specific departments, but even in other cases, it is necessary to make a comprehensive and systematic summary of the whole process of modeling, so that relevant technicians (marking staff during the competition) can believe the rationality of the model assumptions and understand the applicability of the mathematical methods used in the process of model establishment, thus affirming the data and conclusions of the model. Of course, a good paper is based on the scientific nature of the mathematical model established by the author. Secondly, we should pay attention to the organization of the paper.

The following paper should pay attention to the specific place to do some analysis.

(A) the rationality of the problems and assumptions

When writing a paper, you should imagine the reader as a group that knows nothing or little about the problem you are studying. So, first of all, you should briefly explain the situation of the problem, that is to say, explain the ins and outs of the matter. List the necessary data, put forward the problems to be solved, and give the contents of the key information of the research object. Its purpose is to make readers have an impression on the problems to be solved, so that thoughtful readers can try to solve the problems themselves. The test questions of previous mathematical modeling competitions can be regarded as examples of scenario description.

It is impossible and unnecessary to provide every detail of the problem in the situation description. So it is not enough to build a mathematical model, but also to add some assumptions. Model hypothesis is a key step in establishing mathematical model, which is related to the success or failure of the model. Therefore, it is necessary to carefully analyze the actual problems, screen out the variables that best represent the essence of the problems from a large number of variables, and simplify the relationship between them. This part should be in the paper? Hypothesis of the problem? Reflected in the part. Since assumptions are generally not directly provided by actual problems and vary from person to person, we should pay attention to the following aspects when writing this part:

(1) The assumptions in the paper should be expressed in strict and exact mathematical language, so that readers will not misinterpret them.

(2) The assumptions put forward are indeed necessary for establishing a mathematical model, and the assumptions unrelated to establishing the model will only disturb the reader's thinking.

(3) Assumptions need to be verified. The rationality of assumptions can be obtained from the process of analyzing problems, such as making common-sense assumptions from the nature of problems; Or by observing the image of the given data, the functional form of the variable can be obtained; You can also refer to other materials and derive from the class. For the latter, the relevant contents of references should be pointed out.

(B) the establishment of the model

After making assumptions, we can introduce variables and their symbols into the paper, express the relationship between them abstractly and accurately, and finally successfully establish equations or summarize them into other forms of mathematical problems through certain mathematical methods. Here, we must use the method of analysis and demonstration, that is, the method of reasoning, so that readers can clearly understand that in the process of logical reasoning, the process of getting the model should not jump too much, which will affect the persuasiveness of the paper. Where reasoning is needed, there should be a deduction and rigorous process. When quoting a ready-made theorem, we must first verify the conditions that satisfy the theorem. All kinds of mathematical symbols used in this paper must be explained when they first appear. In short, the process of getting the mathematical model should be clearly expressed, so that readers can get a basis for judging the scientific nature of the model.

(3) Calculation and analysis of the model

After the actual problem comes down to a mathematical problem, it needs to be solved or analyzed. In numerical solution, the calculation method should be explained, and the name of the software or calculation program used should be given (usually in the form of appendix). You can also use computer software to draw curves and surfaces, and vividly express the numerical calculation results. According to the calculation results, some conclusions helpful to practice are obtained by analytical method.

Some models (such as nonlinear differential equations) need stability or other qualitative analysis. At this time, it is necessary to point out the mathematical theory on which it is based and draw a clear conclusion on the basis of reasoning or calculation.

In the process of model establishment and analysis, conclusions with universal significance can be expressed in the form of clear theorems or propositions. Conclusion the problems that should be paid attention to in use can be listed in the form of mnemonics. Theorems and propositions must clearly state the conditions for the conclusion to be established.

(d) discussion of the model.

This mathematical model can be discussed from many aspects. For example, we can explore how the model will change for different scenarios. Or according to the actual situation, we can change some assumptions made at the beginning of the article and point out the changes in the mathematical model. Different numerical methods can also be used to calculate and compare the results. Sometimes we should broaden our thinking and consider the changes brought about by different modeling methods.

Generally, the advantages and disadvantages of established models should be discussed and compared, and the applicable scope of the model should be pointed out realistically.

In addition to the main text, the answers to papers and competitions should also be summarized. We should not neglect the writing of abstract. Because it will give readers and commentators a first impression. The main ideas, conclusions and characteristics of the paper model should be clearly explained so that people can see the new ideas of the paper.

Language is the basic element of a thesis. The language of mathematical modeling papers, like other scientific papers, needs expressiveness and competence. Don't write a sentence so long that people can't read it quickly. In language, we should use more objective statements and avoid using pronouns such as you, me and him and sentences with subjective intentions. English paper writing should use passive voice, and scientific propositions and judgments generally use the present tense.

Finally, the writing and drawing of the paper are also very important. The figures in the attached drawings should be clearly explained and the handwriting should be correct.

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