There is a carpenter, an electrician and a painter who agree to decorate their own house. Before the renovation, they reached the following agreements: (1) each person works 10 days (including working for his own family); (2) According to the general market price, the daily salary of each person is between 60 and 80 yuan; (3) Everyone's daily salary should make everyone's total income equal to total expenditure. The following table is the working day distribution plan they worked out after consultation. How to calculate the salary that each of them deserves?
Choose one of the above two topics and write a paper on mathematical modeling.
Answer:
Ask a question (that is, the topic, here is a question for you, you can correct it if it is not good)
A carpenter, an electrician and a painter agreed to decorate their own house. Before the renovation, both parties reached the following agreement:
(1) Everyone works 10 days (including working for his own family);
(2) According to the general market price, the daily salary of each person is between 60 and 80 yuan; (3) Everyone's daily salary should make everyone's total income equal to total expenditure. Table 5-3 is the working day distribution plan they made after consultation. How to calculate the salary that each of them deserves? (4)n people decorate each other, give their due salary model, and write a program that can be realized on the computer.
Woodworking electrician painter
Working days in carpenter's house 2 1 6
Working days in electrician's house 4 5 1
Working days in the painter's house 4 4 3
Then the symbol description (that is to say, what exactly does the symbol you use mean, explain it)
Then the model is established (that is, what relationship you get from the problem, this should be written separately)
Finally, the model is solved (that is, the answer to the question is written down)
Text format or something, your teacher should not ask for it.
Almost. I hope you like my answer.
Basic format of mathematical modeling papers
(200-300 words, including the main features of the model, modeling methods and main results. When there are many keywords (important terms and methods used in solving problems), it is best to have a directory of 1. Restatement of the problem II. Problem analysis 3. Model assumptions and conventions. Symbol description and noun definition 5. Model establishment and solution ① Supplementary assumptions, clear concepts and introduction of parameters; ② Model form (there can be multiple models); 6。 Further discussion (the influence of parameter change and hypothesis change on the model) 7. Model test (using data to calculate results, analyze and test) 8. Advantages and disadvantages of the model (improvement direction and popularization of new ideas)
9。 References and reference books and websites 10. Appendix (calculation program, block diagram; Various processes of solving calculus and calculating intermediate results; Various graphs and tables. )
Little experience: 1. Write down your assumptions at any time. Sometimes when we start the next step under a very reasonable assumption, we should write this assumption down conveniently, otherwise we may forget it in the end, which will make our answer more rigorous. 2。 Record your thoughts at any time and express them completely without leaving any room. 3。 It has its own characteristics and shines brilliantly.
How to write a paper on mathematical modeling
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 reflected in the "hypothesis of the problem" part of the paper. 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 readers' 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.
Ten secrets of participating in mathematical modeling competition
1 Integrity is the most important.
Mathematical modeling competition is a comprehensive competition to test students' research ability and practical ability. There are many aspects of knowledge and ability in the exam, but I think the most important thing is honesty. I feel that China's education in this field is far from enough. I know that many students do not write papers realistically, but fabricate data and modify conclusions. Although they can't program, they insist that they did it, and they sorted out some data. These behaviors may fool the judges and win prizes for them, but they will be bad for them in the future. I hope they can attract enough attention.
Teamwork is the key to winning the prize.
In the three-day competition, team communication may take up more than half of the time. In a group, it is very normal to disagree. If a team completely agrees, I don't think they will win the prize. How to resolve differences is very important, and even directly determines whether you can win the prize. My suggestion is "compromise", which seems to be a derogatory term, but what I mean is not to always think that your point of view is correct, but to listen to other people's points of view and seek similarities between the two. If three people are arrogant, maybe everyone is strong, but once they cooperate, their differences can't be solved, which means "three Zhuge Liang are not as good as one cobbler." I advise you not to form a team in that situation. Before the competition, we should cultivate cooperation, such as doing simulation questions together and making full use of everyone's advantages. It is also possible that Zhang San prepares graph theory and Li Si prepares optimization methods, and then we can communicate together in a few days, so that we can run in the relationship between teams. Usually in the competition, the three people have a clear division of labor. One is the leader, who mainly constructs the framework of the whole problem and puts forward creative ideas. Naturally, he can also participate in other parts such as paper writing, programming, calculation, etc., and should be regarded as an omnipotent figure; The second is a calculator, as the name implies, which mainly deals with calculation problems, such as programming to calculate a calculus or manually calculating an optimal path. Excellent team calculators are generally proficient (proficient or not) in the application of a software, such as C such as MATLAB such as LINGO；; The last one is a writer, whose main job is to write papers and polish them. A good paper should make people understand the meaning at first sight, so the writer's works still need some skills. Of course, the most important thing is the discussion and communication among the three players. Qi Xin will work together to form a good communication atmosphere during the whole game.
3 the problem of time and physical strength
Time allocation is also very important in the competition. If the assignment is not good, you may not finish the paper, so you should make some general arrangements at the beginning. Don't divide it too carefully, for example, do the first small question on the first day and the second small question on the second day, so there will be pressure and everything will go with the flow. If you are not busy writing at first, you can record some key points of group discussion. Don't be too neat, just write casually, and it's not too late to start writing papers on the third day. It didn't start until the third night. One more thing to say is to keep up with your physical strength. Generally, I sleep less than 10 hour for three days, and my physical strength is not good. I suggest you stay up late to program several times before the game, which not only exercises your modeling ability, but also achieves the purpose of exercising your physical strength. I don't think it is useful to exercise before the game. Stay up as long as you can, but you can't stay up the day before the game.
Step 4 pay attention to the summary
Abstract is the facade of the paper. If the abstract is not well written, the judges will not read it later, so naturally they can only give a prize for successful entry. First of all, don't write nonsense, don't copy some words from the topic, go straight to the point and write down how you analyzed the problem and how you solved it. The most important thing is to know what the conclusion is. In China, if the conclusion is correct, winning the prize is inevitable. If it is not correct, the judges may continue to look down or throw it aside, but if they don't write the conclusion, they will definitely not win the prize, which is no different from the American competition, so they should write it carefully. It will take at least two hours to ponder, so don't underestimate its importance. How to write the abstract of excellent papers, and read more, should be one of the contents prepared before the game.
Thesis writing should be formal.
The paper must be written in the following ways: abstract, problem restatement, model hypothesis, symbol explanation, problem analysis, (establishing, analyzing and solving the model), model test, references, appendix and so on. If a paper fails in structure, the competition will certainly not succeed. Generally, some articles with structural failure will be eliminated first in the initial evaluation. If the paper has no good structure, no matter how good the content is, it will be useless. Generally, the structure of the front side of the paper will not change, and the back side can be arranged according to the actual situation. The omitted parts can include result explanation, sensitivity analysis, other models, model expansion, advantages and disadvantages analysis, etc. Read more excellent papers and you will know what other forms there are. Appendices can be attached with some algorithm flowcharts or larger results or charts.
6 carefully analyze the problem
I have never seen a general competition topic myself, and I found that none of the competition topics in recent years can be successfully set in books directly, and many of them have no fixed model to refer to, so analyzing problems is not a process of finding books, relying on books is bound by thoughts. You can do it according to your own analysis. Learn a method when practicing at ordinary times, and you can solve it with the method you learned before, instead of applying books. What should you do without a model set? You have to analyze it yourself. I estimate that one-third of the teams can do the five points mentioned above and do it well, but at this point, they need real skills. If they usually work hard and play the game normally, no problem.
7 programming is an important means.
During the American competition, many papers written by American students are descriptions of programming data. For example, topic A of 1999, when a planet hits the earth, they can also simulate the consequences of the impact, which is incredible to us. American students have strong hands-on ability, while China students are good at theoretical analysis, so I put programming after analysis, which is the characteristic of China. Mathematical modeling competition especially emphasizes the ability of computer programming to solve practical problems. In recent years, it has been emphasized that the ability of programming can not be practiced overnight and needs long-term hard training. Commonly used tools are MATLAB, Mathematica, C/C++ and so on. A person only needs to know one language, but he needs to be proficient in it. For example, how to draw histogram and how to use Floyd algorithm, you can't use it well without pre-competition preparation in the game, so every commonly used algorithm is programmed by yourself.
8 model hypothesis and model establishment
After reading the abstract, the judges immediately read the model hypothesis. A common method is to copy a few hypothetical sentences in the title, which will leave a good impression on people. After all, it means that you have already examined the questions. But you can't copy them all. You should add some assumptions. It is generally assumed that it is enough to describe it in words, and it is best not to be too specific. Some important parameters should not be fixed, only some values can be taken, otherwise people will feel that the thesis is very limited. The model is based on your analysis of the problem. It is best to put forward mathematical symbols and establish models on the same page, which is convenient for the judges to compare symbols. The mathematical formula should be rigorous and the derivation should be rigorous, which reflects the mathematical quality and ability of the contestants. Even if you make a mistake, others will mistake you for being right when they see your battle. With so many papers, the judges can't keep pushing them down according to your formula. You have to write them mathematically.
9 the combination of graphics and text can add color.
I heard that inaccurate information is a paper that judges like to program with MATLAB. I don't know if this is the case, but it shows that teachers need to read a paper with charts or tables. If the paper is written like a political book, it is estimated that no one will be interested, especially scientific papers. MATLAB programming is favored because of its powerful graphics processing ability. Charts are particularly illustrative. If there is a lot of data in the conclusion, it is best to make a chart to illustrate it, which will make your paper more convincing and easier to get praise from the judges.
/kloc-0 0 Other
There are many other contents, and I can't finish them. Pick some important ones. For example, don't discuss it online. There are different levels of people online, and you don't know who is right or wrong. And many people want to win the prize, not to tell you what is right, but to cheat you into saying the opposite. Sometimes the truth is often in the hands of a few people. Also, don't write too much about sensitivity analysis, just make a general explanation, and don't pretend to be the host. The last thing that comes to mind is to write a paper with mathtype, without any subscripts, the font of the paper should be small four, the subtitle should be bold four, and so on.