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How to write a model essay on mathematical modeling
Mathematical modeling thesis writing

First, the importance of writing a mathematical model answer sheet

1. is the only basis for evaluating the performance, level, award-winning level and mathematical model answer sheet of the participating teams.

The answer sheet is the written form of the competition result.

3. The training of writing the answer sheet is the basic training of scientific writing.

Second, the basic content of the answer sheet and the problems that need attention.

1. marking principle

Rationality of hypothesis, creativity of modeling, rationality of result and clarity of expression.

2. The article structure of the answer sheet

Title (write a more accurate title; At the same time, be innovative and eye-catching)

Abstract (200-300 words, including the main features, modeling methods and main conclusions of the model)

Keywords (key terms and methods to solve problems)

1) restatement of the problem.

2) problem analysis.

3) Model assumptions.

4) Symbol description.

5) Model establishment (problem analysis, formula derivation, basic model, final or simplified model, etc.). ).

6) model solving (designing or selecting calculation methods; Algorithm design or selection, algorithm ideological basis, steps and implementation, calculation block diagram; The name of the software used; Quote or establish necessary mathematical propositions and theorems; Solutions and processes. )

7) Further discussion (result representation, analysis and test, error analysis, model test)

8) Model evaluation (characteristics, advantages and disadvantages, improvement methods and popularization. )

9) References.

10) appendix (calculation program, block diagram; Various processes of solving calculus and calculating intermediate results; All kinds of charts. )

3. Problems that should be paid attention to

1) summary.

Including:

A. Mathematical classification of the model (what type does it belong to mathematically);

B. the thinking of modeling (thinking);

C. algorithm idea (solution idea);

D modeling features (model advantages, modeling ideas or methods, algorithm features, result test, sensitivity analysis, model test, etc.). );

E. Main results (numerical results and conclusions; Answer all the "questions" asked by the topic.

▲ Pay attention to expression: accurate, concise, clear-cut, grammatical and in line with the article format. Be sure to proofread carefully.

2) Restatement of the problem.

3) Problem analysis.

The relationship between factors, the relationship between factors and environment, the changing law of factors themselves, and the types of research methods or models.

5) Model assumptions.

According to the scoring principle determined by the National Organizing Committee, the rationality of basic assumptions is very important.

A. make assumptions according to the conditions in the topic

B. Make assumptions according to the requirements in the topic

Key assumptions are indispensable; Suppose it meets the meaning of the question.

6) Establishment of the model.

A. basic model:

I) First of all, there must be a mathematical model: mathematical formula, scheme, etc.

Ⅱ) Basic model, complete, correct and concise;

B. simplify the model:

I) The idea and foundation of simplification need to be clearly explained;

Ii) Simplify the model and give it as completely as possible;

C. The model should be practical and effective, with the principle of effectively solving problems.

Mathematical modeling is faced with practical problems to be solved, rather than pursuing high (level), deep (carving) and difficult (degree) in mathematics.

I) If it can be solved by elementary methods, there is no need for advanced methods;

Ii) If it can be solved by simple methods, there is no need for complicated methods;

Iii) If you can use a method that is understood by more people, you don't need a method that can only be understood by a few people.

D. Encourage innovation, but be pragmatic, don't digress, and do something unconventional. Mathematical model innovation can appear in:

▲ In modeling, the model itself, good simplification methods and strategies, etc.

▲ The model is being solved;

▲ Results representation, analysis, testing and model testing;

▲ Promotion part.

E. Problems needing attention in the process of problem analysis and deduction:

I) analysis: pertinent and accurate;

Terminology: professional and expert;

3) Principles and basis: correct and clear;

Ⅳ) Description: concise and to the point, listing the key steps;

ⅴ) Taboo: layman's words, unclear terminology, confusing and lengthy expression.

7) model solving.

A. When a mathematical proposition needs to be established:

Proposition narrative should conform to the norms of mathematical propositions and be as rigorous as possible.

B need to explain the principle, thinking, basis and steps of the calculation method or algorithm.

If existing software is used, explain the reason for using the software and the name of the software.

C. In the calculation process, intermediate results are unnecessary and should not be listed.

D. Try to work out a reasonable numerical result.

8) result analysis and inspection; Model checking and model modification; The results show that.

A. the correctness or rationality of the final numerical results is the first;

B, carrying out necessary tests on numerical results or simulation results;

When the result is incorrect, unreasonable or has a large error, analyze the reasons and modify and improve the algorithm, calculation method or model.

C. The questions, numerical results and conclusions required to be answered in the topic should be listed one by one;

D listing data: consider whether it is necessary to list multiple groups of data, or compare and analyze the data with additional data, so as to provide a basis for proposing various schemes;

E. The result expression: centralized, clear at a glance, intuitive and convenient for comparative analysis.

▲ Numerical results show that the table is carefully designed; If possible, in the form of a chart.

▲ It is better to use a graphic solution.

9) When necessary, discuss the answers to questions qualitatively or regularly. The final conclusion should be clear.

10) model evaluation

Outstanding advantages and unavoidable disadvantages.

Change the original requirements, re-modeling can be done here.

Don't play with new mathematical terms when popularizing or improving the direction.

1 1)

12) appendix

Detailed results and detailed data tables can be listed here, but don't be wrong, and the wrong ones would rather not be listed. The main result data should be listed in the text, not afraid of repetition.

Check the main three points of the answer sheet and put the three levels:

A. correctness, rationality and innovation of the model

B. correctness and rationality of the results

C. the text is clear, the analysis is incisive, and the abstract is wonderful.

Third, thinking and work planning before writing the answer sheet

What questions need to be answered on the answer sheet-what problems need to be solved in modeling;

How to answer questions ―― how to express the results;

What key data should be listed for each question-what key data should be calculated for modeling;

For each quantity, list one or more sets of numbers-whether to calculate one or more sets of numbers.

Fourth, the principle requirements of the answer sheet

1. Accurate-scientific;

2. Organizational logic;

3. Simplicity-the beauty of mathematics;

4. Innovation-one of the goals of research and application is also the need of talent training;

5. Practicality-modeling and practical problem requirements.

Verb (abbreviation of verb) modeling concept

1. Application consciousness

To solve practical problems, the results and conclusions should be in line with reality;

The model, method and results should be easy to understand and convenient for practical application; Think and deal with problems from the standpoint of users.

2. Mathematical modeling

Solving problems by mathematical methods requires mathematical models;

The mathematical abstraction of the problem model is universal and scientific, and is not limited to the solution of this specific problem.

3. Innovative consciousness

Modeling has its own characteristics, which is more reasonable, scientific, effective and practical. More universal application significance; Not just for innovation.