? The undergraduate team chooses a question from questions A and B, and the specialist team chooses a question from questions C and D. ..
? Paper is printed on one side of white A4 paper; Leave a margin of at least 2.5 cm at the top, bottom, left and right; Tie it from the left.
? The first page of the paper is a letter of commitment, and the specific content and format are shown on the second page of this specification.
? The second page of the test paper is a special page for numbering, which is used for numbering the test papers before and after the division and national review. See the third page of this specification for the specific content and format.
? The title and abstract of the paper are written on the third page of the paper, and the text of the paper begins on the fourth page.
? The paper starts from the third page, and the page number must be located in the middle of the footer of each page, and numbered consecutively with Arabic numerals starting from "1".
? Papers can't have headers, and there can't be any signs that may show the identity of the respondent.
? The title of the paper is in bold No.3, and the first-level title is in bold No.4, centered; The second-level and third-level titles are small and bold, and the left end is aligned (not centered). All other Chinese characters in this paper use small four-character fonts, and the line spacing is single-spaced. When printing, try to avoid color printing.
? Note: The abstract should be concise and detailed (including keywords), which plays an important role in the evaluation of the whole paper. Please write carefully (note that the length can't exceed one page and it doesn't need to be translated into English). During the national review, the quality of the papers will be preliminarily screened according to their abstracts, overall structure and general situation.
? Citation of other people's achievements or other public information (including information found on the Internet) must be clearly listed in the text citation and references in accordance with the prescribed expression of references. The number of references in the text is indicated by square brackets, such as [1][3] and so on. You must also indicate the page number when quoting books. The references are listed in the order cited in the article, and the book expression is as follows:
[No.] Author, title, place of publication: publishing house, year of publication.
The periodical papers in the references are expressed as follows:
[No.] Author, paper name, magazine name, issue number: page number, publication year.
The expression of online resources in references is:
[No.] Author, resource title, website, visit time (year, month, day).
? Under the premise of not violating this specification, each division can add other requirements to the paper (such as adding other pages and other information before the first page required by this specification, or adding blank pages at the end of the paper, etc.). ); From the beginning of the letter of commitment to the end of the paper, there shall be no other requirements outside this specification in each competition area (otherwise it will be invalid).
? The right to interpret this specification belongs to the Organizing Committee of the National Mathematical Modeling Competition for College Students.
[attention]
Write down the first page of the paper and keep it before the department reviews it. At the same time, the division review number shall be established on the first page and the second page (the numbering method shall be specified by each division), and the Division Review Record Form can be used for division review (each division decides whether to use this form during review). After the review, the Division will establish a "National Uniform Number" for the papers submitted to the national review on the second page (the numbering method is stipulated by the National Organizing Committee and the format is the same as last year), and then send them to the national review. The second page (numbered page) of the examination paper shall be taken down and kept by the National Organizing Committee before marking, and a "National Marking Number" shall be established on the second page.
Organizing Committee of National College Students Mathematical Modeling Competition
Revised on March 6, 2009/kloc-0.
General structure of mathematical modeling papers
1 summary (separate page)
Main understanding, main methods, main results, main characteristics (no graph, no table)
Function: Understand the importance of archives and have a general understanding of archives.
Best page pair: 2/3 pages.
2. Restatement and analysis of the problem
3. Question hypothesis
Assumption is the basis of modeling, which is oriented and easy to be ignored. Common mistakes are lack of assumptions or unrealistic assumptions. Conditions or arguments that are critical or have a significant impact on the results should be clearly defined in the assumptions.
Two principles for making assumptions:
(1) Simplification principle: Grasp the main contradiction and discard the secondary factors, which is convenient for mathematical processing.
② The principle of being close to reality.
The above two principles are mutually restrictive, so we should master the "degree". Usually, model first and then make assumptions.
4, symbol description (can be combined with 3.4)
5. Model establishment and solution (importance: more than 60%)
6, model test (error generally refers to the mean square error)
7, the result analysis (6.7 can be combined)
8. Further discussion or extension of the model.
9. Advantages and disadvantages of this model
10, references
1 1, attachment (the result must not be placed in the attachment)
The best number of pages in the paper: 15-2 1 page.
? Paper structure 1
subject
abstract
1. Restatement of the problem
2. Reasonable assumptions
3. Symbolic practice
4. Problem analysis
5. Establishment and solution of the model
6. Evaluation and popularization of the model
1, error analysis
2. Improvement and popularization of the model.
Practical suggestions and opinions on XXXX:
1.……
2.……
……
7. Reference
8. Appendix
? General format of mathematical modeling papers
? abstract
(main understanding, main methods, main achievements and main features)
Or (background, objectives, methods, results, conclusions and suggestions)
? Restatement and analysis of problems
? Problem hypothesis
? Symbolic description
? Model establishment and solution
? model testing
? result analysis
? Further discussion on the model
? Advantages and disadvantages of the model
Key points of excellent papers:
1. The language is concise, logical and well written.
2. The combination of words and graphics makes the content intuitive, clear, clear and easy to understand.
3. Don't just use words to explain, use more graphics or tables, and make a concise analysis of them. After all, words are so boring that no one has the patience to read such a lengthy article.
4. The knowledge and software cited or used in the paper should be clearly explained.
5. Attach some necessary data (figures or tables) to the appendix, and attach the program written in the paper.
An explanation of each step.
Main understanding, main methods, main achievements and main characteristics (no diagram, no table).
Function: Understand the importance of archives and have a general understanding of archives.
Best page pair: 2/3 pages
Restatement and analysis of problems: guide, understanding of the meaning of problems,
? Modeling creativity
Creativity is the soul, and articles should have bright spots.
Good ideas and good ideas should be both unexpected and human.
Not expected.
There are both novelty (uniqueness) and rationality.
One of the misunderstandings: The deeper you apply mathematics, the more creative you are.
Solving problems is the first principle, and the most appropriate method is the best method.
Myth 2: Creativity is mainly reflected in modeling and solving.
Creativity can be reflected in all aspects of modeling, with various forms of expression.
Myth 3: Good ideas come from inspiration, but they can't be satisfied.
Good creativity comes from mastering mathematical methods and thoroughly understanding problems.
? Clear expression
Good article = good content+good expression.
? Think of the reader. The explanation should include the understanding of the topic, the introduction of key indicators or arguments, the thinking of modeling, and the analysis of the results.
? Write a summary, including: the main methods of modeling, the main results, the main advantages of the model.
? Someone is in charge of writing and starts working as soon as possible. The thinking process of writing is also the process of conceiving the framework and clearing the train of thought, which is conducive to grasping the thinking of modeling as a whole and in turn promoting modeling.
? Use charts appropriately to increase readability.
What does the writing of mathematical modeling paper include: model preparation: understanding the actual background of the problem, clarifying its practical significance, and grasping all kinds of information of the object. Describe the problem in mathematical language.
Model hypothesis: according to the characteristics of the actual object and the purpose of modeling, simplify the problem and put forward some appropriate assumptions in accurate language.
Modeling: On the basis of hypothesis, use appropriate mathematical tools to describe the mathematical relationship between variables and establish the corresponding mathematical structure. (Try to use simple math tools)
Model solution: calculate (estimate) all the independent variables of the model by using the obtained data.
Model analysis: analyze the results by mathematical methods.
Model test: compare the results of model analysis with the actual situation to verify the accuracy, rationality and applicability of the model. If the model is in good agreement with the actual situation, the practical significance of the calculation results should be given and explained. If the model is not consistent with the actual situation, it is necessary to modify the assumptions and repeat the modeling process.
Model application: the application method varies with the nature of the problem and the purpose of modeling.
This website has the answers you want. Dussiau. I can also write for you.
As an advanced mathematics teacher, especially an instructor who has coached and led a team to participate in the national college students' mathematical modeling competition all the year round, I can deeply understand that the mathematical modeling competition paper is different from the general mathematics paper, mainly because of its comprehensiveness. The test paper of mathematical modeling competition is closely related to reality, aiming at the objectivity and practicality of the problem. There is a process of analysis, arrangement and synthesis, including reading the meaning of the problem, choosing appropriate mathematical tools, establishing a reasonable mathematical model, using appropriate calculation methods, rigorous argumentation and deduction, clear conclusions, practical test of the results, appropriate evaluation and summary, and popular and concise language. A good article should have the following characteristics: realistic analysis, reasonable and convincing assumptions, selection of appropriate mathematical knowledge, strict logical reasoning and argumentation. Reasonable use of calculation methods and software to get the correct answer, test the correctness of the results and seek truth from facts, which is not only concise and clear, but also can explain the summary of the problem. First, the actual analysis and understanding of the topic of the mathematical modeling competition is an objective and practical problem. The content is all-encompassing Accurately understanding the background and requirements of the topic is the first step to solve the problem. This requires us to analyze all the factors involved in the topic. It is necessary to analyze which factors have an impact on the problems we are discussing, which are the main factors, which are the secondary factors, which are the decisive factors, which are irrelevant, and the master-slave relationship between the factors. It is necessary to fully and correctly understand the requirements of the topic. That is, what problems the topic requires us to solve. Never misinterpret the meaning of the topic, otherwise all previous efforts will be in vain. It is necessary to analyze what kind of data is needed to solve the problem, whether these data topics are given enough, and if not, collect them yourself. It is necessary to analyze which mathematical tools are suitable for solving problems, and which mathematical knowledge is not helpful or not suitable for solving this problem. On the basis of analysis, it is best to work out the steps and methods of solving problems and the tools needed (here mainly refer to mathematical knowledge, calculation methods and software). Only in this way can we solve and write in an orderly and leisurely way. Second, the establishment of a convincing and reasonable hypothetical mathematical model is based on assumptions. According to the requirements of the topic, we must first collect relevant information. This information must be reliable. It is authoritative to a certain extent. Rationality means that it conforms to objective reality and cannot violate the theorems and laws that have been proved to be correct. Hypothesis is a crucial step in mathematical modeling, which is related to the success or failure of modeling and the quality of the model. Hypothesis is also the difficulty of mathematical modeling. The assumption of mathematical modeling is to give full play to everyone's imagination and creativity and put forward appropriate and reasonable opinions. If this step is successful, your whole modeling process will be half successful. The rationality of this question is convincing. That is to say, what area, what school and what major is your model aimed at? All sources of these materials should be reliable and authoritative. The motivation of the model should be sufficient and convincing. Third, choose the right mathematics knowledge. In mathematical modeling, the same problem can be solved in many ways, so many different mathematical knowledge can often be used. Of all the available mathematical methods, the simpler the mathematical knowledge used, the better. Because our model is for people to see and is built to solve practical problems. Only the simpler model (including calculation) can be understood and applied by people, and the application value of the model will be higher. If used improperly, it will not only complicate the problem, but sometimes even lead to absurd results. This is a problem that we need to consider carefully and solve seriously. Fourth, strict logical reasoning and argumentation should establish corresponding models according to different regions and professions. In the process of analysis and demonstration, there should be sufficient basis, the source of data should be explained, and there should be sufficient basis. You can't rely on your own feelings to estimate, but you should be convincing. Fifth, pay attention to the popularity of language and concise mathematical modeling. Like other scientific papers, language is the first impression. Just like people's clothes, they should be decent, simple, neat and beautiful, not too gorgeous or too fancy, which makes people uncomfortable to look at. This requires us to practice more and read more good articles. We should be good at learning from others' strengths, and sometimes we can imitate others' practices. Imitation is not plagiarism. On the basis of predecessors' experience, learn from others' thinking methods, improve according to the objective reality of their own problems, and combine their own views. This is innovation, this is invention. Sixth, a good summary is the first threshold. Why do you say that? Because there are more and more teams, the number of marking experts is limited. You should read the abstract first when correcting the test paper. If you read the abstract, people feel that this article is not worth reading, and you may be eliminated in the first step. If you can't even get in the door, you won't have a chance to win the prize. At least it should include thinking method, main conclusions, advantages and disadvantages. It is suggested to read more well-written abstracts and do more work. More training. It is best to achieve the following effects: reading the abstract of your article will make people feel the need to read the content further. Seventh, talk about the novelty and innovation of the article. 1. Innovative ideas should be different from ordinary people. This can be reflected in the following points: (1) is reflected in the assumptions of the model; (2) reflected in the shape; (3) Embodied in demonstration and deduction; (4) Reflected in the solution and calculation; (5) Reflected in data collection.
What should be included in the appendix of a mathematical modeling paper? 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 results should be listed in the main text, not afraid of repetition.
Check the main three points of the answer sheet and put the three levels:
Correctness, rationality and innovation of n model
The correctness and rationality of the results
N words are clearly expressed, incisive and abstract.
What is the content of primary school mathematical modeling thesis? Mathematics of playing football.
What are the good materials for junior middle school mathematics modeling paper and physics modeling paper Abstract: Seat allocation is a common problem in daily life, which can solve practical problems for enterprises, companies and schools. Seats can be specific seats for congresses, shareholders' meetings, enterprise staff meetings, etc. Suppose there is a school to hold a representative meeting, with only 20 seats, and the total number of people in the three departments is ***200, that is, department A 100, department B 60 and department C 40. If you are the planner of the meeting, you should allocate 20 seats in the conference hall reasonably, so as to ensure that everyone in each department participates and be fair to everyone. Then this problem will be solved by mathematical modeling.
Keywords: Q-value method fair seats
Question restatement: There are ***200 students in three departments, (A Department 100, B Department 60 and C Department 40) representing ***20 seats, and the three departments are allocated to 10, 6 and 4 seats respectively. The old situation has become the following. How to distribute it is the fairest. The number of people who have transferred three books now is 103.63.34.
(1) How to allocate 20 seats?
(2) How to allocate the extra 2 1 seats.
Problem analysis:
First of all, the fairness of distribution results is usually measured by the equal or close number of people represented by each representative seat. At present, the customary distribution method is proportional distribution method, namely:
The number of seats allocated by a unit = the proportion of the total number of people in a unit' total seats'
If the number of seats allocated by some participating units according to the above formula is decimal, the seats will be allocated first according to the integer number of allocated seats, and the remaining seats will be allocated in turn according to the decimal size of all participating units. So the initial number of students and student representative seats are as follows
Total number of department names a, b and c
Number of students 100 60 40 200
The proportion of students is 100/200 60/200 40/200.
Seat allocation 10 6 4 20
When students change departments, the number of students in each department and the number of student representative seats become
Total number of department names a, b and c
Number of students 103 63 34 200
The proportion of students is 103/200 63/200 34/200.
Proportional allocation of seats 10.3 6.3 3.4 20
According to the usual seat allocation 10 6 4 20
(1) Such 20 seats should be A series 10 seats, B series 6 seats and C series 4 seats.
Second, the college decided to add another representative seat, and the total representative seat became 2 1. Reassign seats as usual, yes
Total number of department names a, b and c
Number of students 103 63 34 200
The proportion of students is 103/200 63/200 34/200.
Proportional allocation of seats10.8156.6153.57 438+0
According to the usual seat allocation, 1 1 7 3 2 1.
The result of this allocation is that there is one less seat in Part C than before, which makes people feel that the allocation of seats is obviously unfair. How can we be fair? At this time, it is necessary to solve it by mathematical modeling.
Establishment of the model:
Assuming that the seats are fairly distributed by two units, set up
Number of seats per unit Number of representatives per seat
Unit A p 1 n 1
Bpp2n2 unit
In all fairness, there should be =, but this is generally not true. Note that this equation does not exist.
If >, it means that unit A suffers (that is, it is unfair to unit A).
if
Therefore, we can consider using a formula to measure the degree of unfair distribution, but this formula has some shortcomings (the characteristics of absolute numbers), such as:
The number of people and seats in a certain two units is n 1 =n2 = 10, p 1 = 120, p2= 100, so p=2.
The number of people and seats in the other two units are n 1 =n2 = 10, p 1 = 1020, p2= 1000, so p=2.
Although both cases have p=2, it is obvious that the second case is fairer than the first case.
The following uses the relative standard to improve the formula, and defines the relative unfair standard formula for seat allocation:
If it is called a relatively unfair value to A, it is recorded as
If it is called a relatively unfair value to B, it is recorded as
According to the definition, the smaller the unfair value to one party, the more favorable it is for one party to allocate seats, so we can reduce the unfairness in allocation by making the unfair value as small as possible.
Determine the allocation scheme:
Using the unfair value to determine the distribution scheme, we might as well set >; In other words, this is unfair to unit A. When another seat is allocated, the relationship may be
1.& gt shows that this seat is unfair to A after it is given to A;
2.& lt, it means that this seat is unfair to B after being given to A, and the unfair value is
3.& gt, it means that this seat is unfair to A after being given to B, and the unfair value is
4.& lt, impossible.
The above allocation method can determine the allocation of new seats in case 1 and case 3, but it is not easy to determine the allocation of new seats in case 2. The unfair value formula is used to determine the allocation of seats. For the new seat allocation, if any,
Then the extra seat should be given to A, and vice versa. On the inequality Rb (n 1+ 1, N2)
Introduction formula
Therefore, we know that the increased seat allocation can be determined by the maximum value of Qk, and can be extended to the general situation of multiple groups. The method of determining seat allocation with the maximum value of Qk is called Q-value method.
The Q-value method of multi-group (M-group) seat allocation can be described as:
1. First calculate the q value of each group:
Qk，k= 1，2，…，m
2. Find the maximum Q value Qi (if there are multiple maximum values, choose one of them).
3. Assign the seat to the I group corresponding to the maximum Q value Qi.
Solution of the model:
Allocate according to the integer part that should be allocated first, and allocate the rest according to the Q value. The integer quota for this issue * * * allocates 19 seats, specifically:
a 10.8 15n 1 = 10。
B 6.6 15 n2 =6
C 3.570 n3 =3
For the allocation of the 20th seat, calculate the Q value.
q 1 = 1032/( 10’ 1 1)= 96.45； Q2 = 632/(6′7)= 94.5； Q3 = 342/(3′4)= 96.33
Because Q 1 is the largest, the 20th seat should be given to the first department; For the allocation of 2 1 seat, calculate the q value.
q 1 = 1032/( 1 1 ' 12)= 80.37； Q2 = 632/(6′7)= 94.5； Q3 = 342/(3′4)= 96.33
Because Q3 is the largest, we should give the seat of 2 1 to the C system.
(2) The final allocation of seats is: A 1 1 seat B 6, seat C 4.
Conclusion: 20 seats should be allocated as follows: A 10 seats, B 6 seats and C 4 seats.
If there are 2 1 seats, then there should be 1 1 seats in Part A, 6 seats in Part B and 4 seats in Part C.
Seeking excellent mathematical modeling papers. Sent, please check.
I urgently need to send a paper on mathematical modeling to the mailbox and send it to you at night. I have a paper (draft, draft is easy to understand) that we participated in the national college mathematics competition and won the second prize in the country. Hope useful to you