1. The importance of writing digital and essay papers 1. The evaluation of the team's performance is good or bad, high and low, the award level, and the digital and essay papers are the only basis.
2. The thesis is a written form of the results of the competition.
3. The training to write mathematical and essay papers is a basic training for scientific writing.
Second, the basic content of the mathematics thesis, the issues that need to be paid attention to
1 Review principles : the rationality of the assumption, the creativity of the modeling, the rationality of the results, and the clarity of the statement.
2 Article structure of digital papers
0) Abstract
1) Problem description, problem analysis, background analysis, etc.
2) Model assumptions, symbol description (table)
3) Model establishment (problem analysis, formula derivation, basic model , Final or simplified model, etc.)
4) Solving the model
▲ Calculation method design or selection;
algorithm design or selection, algorithm thinking basis, steps and implementation, calculation block diagram; the name of the software used;
▲ reference or establish the necessary mathematical propositions and Theorem;
▲ Solution and process
5) Results presentation, analysis and testing, error analysis, model testing ...
6) Model evaluation, characteristics, advantages and disadvantages, improvement methods, promotion ...
7) Reference
8) Appendix
calculation block diagram in
detail Chart
...
Details of each part:
Summary section:
The following parts should be included (a. Mathematical classification of models (what type in mathematics) b. Ideas of modeling c. Algorithm ideas (model solution ideas) d. Modeling characteristics (model advantages, modeling Ideas or methods, algorithm characteristics, result testing, sensitivity analysis, model testing….) E. Main results (numerical results, conclusions) (all “questions” answered in the question))
The assumption part of the model:
The assumptions of the model mainly have two aspects: (1) make assumptions based on the conditions in the topic; (2) make assumptions based on the requirements of the topic. Note: The key assumptions can't be missed; the assumptions should fit the topic.
Model building part:
(1) The basic model (mathematical formulas, plans, etc.) requires completeness, correctness, and conciseness;
(2) The simplified model should be clearly stated (simplified thinking, basis), and the simplified model should be given as completely as possible;
(3) The model should be practical and effective, with the principle of solving problems effectively.
What mathematical modeling faces is to solve practical problems, not to pursue mathematics: high (level), deep (engraved), difficult (large degree). If you can solve it with elementary methods, you don't need advanced methods; if you can solve with simple methods, you don't need complicated methods; if you can use methods that are understood and understood by more people, you don't need methods that can only be understood and understood by a few people.
(4) Encourage innovation, but be practical and do not digress
Digital and analog innovations can appear in
1) In modeling, the model itself, simplified good methods, good strategies, etc .;
2) In solving the model;
3) Results presentation, analysis, inspection, model inspection;
4) Promotion section
5 ) In the process of problem analysis and derivation, the problems that need to be paid attention to: analysis must be pertinent and accurate; terminology should be professional and expert; principles and requirements should be correct and clear; the requirements for expression should be concise and key steps should be listed. Avoid jargon, the terminology is not clear, the expression is confusing and lengthy.
Model solving part:
( 1 ) When it is necessary to establish a mathematical proposition: the propositional narrative must conform to the mathematical propositional expression specifications, and the argument should be as rigorous as possible.
( 2 ) It is necessary to explain the principles, ideas, basis and steps of the calculation method or algorithm. If using existing software, explain the reason for using the software and the name of the software.
( 3 ) During the calculation process, the intermediate results may or may not be listed.
( 4 ) Try to calculate a reasonable numerical result.
Results analysis and inspection part: (model inspection and model correction; result presentation)
( 1 ) The correctness or rationality of the final numerical result is the first;
( 2 ) Carry out necessary tests on numerical results or simulation results. When the result is incorrect, unreasonable, or the error is large, analyze the cause and revise or improve the algorithm, calculation method, or model;
( 3 ) The questions, numerical results and conclusions required to be answered in the questions must be listed one by one;
( 4 ) Column data problem: consider whether you need to list multiple sets of data, or additional data to compare and analyze the data, to provide a basis for the proposal of various schemes;
( 5 ) The results indicate that they should be concentrated, clear and intuitive, and easy to compare and analyze; the numerical results indicate that tables should be carefully designed; if possible, in the form of graphical charts; the solution scheme is better illustrated.
( 6 ) When necessary, answer questions and make qualitative or regular discussions. The final conclusion should be clear.
Model evaluation part:
The advantages are outstanding, and the disadvantages are not avoided. Change the requirements of the original question, re-modeling can be done here. When promoting or model improvement, try to use the terms that have been used.
The appendix lists the detailed results, detailed data tables (rather not wrong column). The main result data should be listed in the text, not afraid to repeat.
Check the main three points of the answer sheet, and check the three points: ( 1 ) the correctness, rationality and innovation of the model; ( 2 ) the correctness and rationality of the results; ( 3 ) the clear expression of the words, the incisive analysis and the wonderful summary
After getting the question, everyone needs to think about the following:
What type of problem is it: continuous, discrete?
What problems need to be solved; optimization scheme, prediction model, shortest path, etc .;
What relevant models, algorithms can be used to solve, and what mathematical tools are needed;
Thinking and work planning before writing modeling papers:
Which questions do the thesis need to answer:
What problems need to be solved in modeling
How are the questions answered and how are the results expressed?
What key data should be listed for each question-what key data should be calculated for modeling
For each quantity, list one group or multiple groups-whether to calculate one group or multiple groups
Principles required by the thesis:
Accurate-scientific
Organize-Logical
Concise-Mathematical Beauty
Innovation-one of the goals of research and application, talent training needs
Practical-modeling, practical problem requirements.
