1. Introduction to the Mathematical Modeling National Competition
1.1 What is the Mathematical Modeling National Competition? How to judge
The National Undergraduate Mathematical Contest in Modeling is one of the largest extracurricular science and technology activities in colleges and universities across the country. The competition is held in September every year (usually from Friday of a certain weekend in the first half of the month to Monday of the next week, a total of 3 days, 72 hours). The competition is open to students from colleges and universities across the country, regardless of major. All undergraduate competitions are open to participation. Students can consult with the school's educational affairs department, and if necessary, they can also directly contact the National Competition Organizing Committee or the organizing committees of each competition area.
The National Undergraduate Mathematical Contest in Modeling was founded in 1992 and is held once a year. It is the fifth place in the "University Discipline Competition Ranking List" (the top four are Internet+, the Big Challenge Cup, the Small Challenge Cup, and the World ACM Competition). It is said that the competition is an "Olympic competition" in data analysis and mathematical modeling competitions.
2022 Ranking List of National College Discipline Competition (issued by the Ministry of Education) In 2022
, there will be 1,606 colleges/campus, 54,257 teams (49,424 undergraduate teams, 4,833 junior college teams) from all over the country, Australia, Malaysia and other countries, more than 16 Thousands of people signed up for the competition. The form of the competition is that 16W participating students will write a paper of about 25 pages within 3 days and 4 nights, and submit it online for selection.
Number of parameters from 1992 to 2022
Competition time: Mid-September of each year
Comprehensive award rate: about 30-40% for provincial awards, about 7% for
national
awards Generally no more than one-third
of the national award:
(1) According to the competition area
, for the part with no more than 200 teams, the base number of papers sent to the national review accounted for 12% of the number of teams
; For the part with 500 teams, the base number of papers sent for national review accounted for 10% of the number of registered teams. For the
part with more than 500 but not more than 800 teams, the base number of papers sent for national review accounted for 8% of the number of registered teams; For those with more than 800 teams, the base number of papers sent for national review accounts for 5% of the number of registered teams.
(2) According to the school
, any school can win up to 5 national first and 5 national second national competitions each year
1.2 The significance of participating in the national competition
1.2.1 Significance of being in school (1) The four-point grade point for applying for national awards for research or studying abroad can be increased by about 0.2 to 0.4 according to the group. Some schools can also directly guarantee research. During the interview, the contact tutor
will
It has a role in fueling the flames!
(2) The
National Scholarship Competition is a genuine national competition. No school does not recognize this competition. Whether it is the comprehensive evaluation or other scholarship selections, there will be bonus points. Some schools have established competition scholarships, which can be directly applied for. Individual rewards.
(3) Conducive to scientific research
On the one hand, by solving practical problems, it improves the ability of problem analysis, modeling and solving, and provides strong support for complex problems in scientific research; Ability to come up with novel ideas and innovative approaches.
In addition, knowledge involving multidisciplinary fields expands the participants' subject breadth and interdisciplinary application ability, and has a positive impact on the comprehensive application in scientific research. In short, you can produce a decent paper in three days. It’s not easy to do a scientific research. The top journals dare not say it. It’s not a rattle to kill other core journals.
1.2.2 Significance after employment
(1) I have personally experienced the cultivation of mathematical modeling thinking
. In essence, mathematical modeling is to exercise us to express a real problem with a mathematical model, and to use it in real work. As we have more and more opportunities and frequencies to deal with data, the application of data in our work can make our work ability stand out, such as operation + mathematical modeling = data operation, product manager + mathematical modeling equals data product manager, business analyst +Mathematical modeling is equal to data scientists, knowing mathematical modeling is simply the existence of weapon strengthening plus 10
(2) Cultivated teamwork ability
Mathematical modeling is a team competition. Let alone the difficulty of writing a paper within three days, it is definitely not enough to rely on the ability of one person if you want to make all kinds of graphs in the paper within three days. Cooperating with partners and solving problems with teammates can improve the teamwork and communication skills of the contestants. This division of labor and organizational skills will have a certain impact on the cultivation of leadership in future work.
1.3 How to form a team
| Role | modeler | programming hands | Thesis hand |
| feature | Infer other things from one instance and be well-informed (proficient in models and scenes) and be able to learn quickly | Proficient in programming, good at moving bricks, can learn quickly | Literary skills, UI design or aesthetic word proficiency |
| Task | Responsible for determining the thinking of the questions, consulting relevant literature, and grasping the complete progress of the competition | Discuss ideas with modeling classmates and solve the model through programming | Write a thesis, and need to do proper drawing, typesetting, formula editing |
| hard skills required | none | Proficiency in python or matlab | Good at PS, word, Visio |
One particularly important point: choose those who are serious and responsible, not those who do miscellaneous work, even if you have a little ability, it’s okay and you can exercise.
1.4 The essence of mathematical modeling
Model building and solution: Algorithm matching competition, model precipitation is the only way to speed up
Paper presentation: People are all pursuing beauty and art, and visual feasts can score PRO scores
1.5 What is more important in the national competition?
(1) Pay attention to the results
. There is a review standard for the national competition, such as prediction questions. The review standard has answers listed. If the answer is not correct, or it is not within the range, no matter how you model your language, you will not win the second prize or above;
(2) Pay attention to the process.
Each result must have a corresponding explanation, and the explanation must be straightforward. The more reasonable the matching of the model and the source of the explanation, the more comprehensive the display and analysis of the results, and the higher the score
1.6 How to choose a topic before preparing for the battle
Mechanism analysis category: derived from practical problems, it is necessary to understand certain physical mechanisms and transform them into optimization problems.
Differential equation model, numerical simulation and other
optimization classes: pure optimization problems, aiming to find the optimal solution to achieve the maximum or minimum value of a certain objective function. The requirements for the mechanism are not high, and the focus is on the solution.
Linear programming: interior point method, simplex method, modified simplex method,
nonlinear programming: downhill simplex method, improved BFGS quasi-Newton method, improved conjugate direction method, (boundary) truncated Newton method, linear approximation beam optimization Method, sequential least squares programming algorithm, trust region algorithm,
integer programming: branch and bound method, 0-1 programming, enumeration method,
heuristic algorithm: genetic algorithm (GA), particle swarm algorithm (PSO), simulated annealing Algorithms (SA), Monte Carlo
evaluation: pure evaluation problems, by constructing appropriate indicators and evaluation methods, the evaluation model can compare and analyze the pros and cons of different schemes.
Analytic Hierarchy Process, Factor Analysis (Exploratory), Data Envelope Analysis (DEA), Fuzzy Comprehensive Evaluation, Pros and Cons Solution Distance Method (TOPSIS), Rank Sum Ratio Comprehensive Evaluation Method (RSR), Coupling Coordination Degree, Entropy Value Method, CRITIC weight method, independence weight coefficient method, variation coefficient method, gray relational analysis, multi-criteria compromise solution ranking method (VIKOR), interpretive structure model (ISM
) Statistical analysis of a given data set, inferring data distribution, correlation, hypothesis testing, etc., to provide support and solutions for problems.
Arima, machine learning, gray forecasting, questionnaire analysis, correlation analysis, difference analysis, etc. For
pure beginners, it is recommended to start with evaluation and mathematical statistics models . Mechanism and optimization algorithms are not easy to learn quickly, and it takes longer to accumulate and accumulate
2. Seven-day study plan for modeling hand & thesis hand
2.1 Learning plan for the first day: model precipitation
2.2 Learning plan for the second day: sorting out model categories + deepening memory
2.3 Study plan for the third day: see the summary and table of contents
Link: https://pan.baidu.com/s/1s0_Vq5tM0pZ5JBRSyF-YLw?pwd=fr33 Extraction code: fr33
2.4 Study plan for the fourth day: reading papers
2.5 Learning Plan for the Fifth, Sixth and Seventh Days of Digital Modeling Hands: Actual Combat
The idea of doing 2 questions on the first day, then compare the study papers, and write a paper on the 2nd and 3rd days
2.6 Study plan for the 5th, 6th and 7th day of thesis writing: reading papers + actual combat
On the first day, I frantically read the typesetting of excellent papers, summed up the advantages, and improved the "typesetting sense". In the next 2 days, I cooperated with the modeling hand to write the papers
3. Seven-day learning plan for programming hands
3.1 Python & Malab & R
1. Python
a. Difference: Python is a general-purpose high-level programming language applicable to a variety of fields, including mathematical modeling. It provides a wealth of third-party libraries and modules for scientific computing, data analysis, machine learning, and more.
b. Advantages: The syntax is concise and easy to learn, suitable for beginners and rapid prototyping.
i. Has a large number of open source libraries (such as NumPy, SciPy, Pandas, etc.), supporting scientific computing and data processing.
ii. Supported by powerful machine learning libraries (such as Scikit-learn).
iii. Active community, rich documentation, easy to find answers to questions.
iv. Good portability, support cross-platform.
2. MATLAB:
a. Difference: MATLAB is a high-level language and interactive environment dedicated to mathematical computing and scientific engineering. It is widely used in numerical computing, data visualization, simulation and other fields.
b. Advantages: Rich built-in mathematical functions and toolboxes, suitable for numerical calculation and signal processing and other fields.
i. It is specially designed for engineering and scientific computing, and supports matrix operations.
ii. An interactive environment facilitates data exploration and visualization.
iii. Widely used in control system, signal processing and other fields.
iv. The Simulink environment is used to model and simulate the system.
3. R:
a. Difference: R is a programming language and environment for statistical computing and data analysis. It is mainly used for tasks such as statistical learning, data mining, and visualization.
b. Advantages: Rich statistical and machine learning libraries, including the famous ggplot2 data visualization library.
i. Great for data cleaning, analysis and visualization.
ii. Extensive support for statistical methods for handling complex statistical models.
iii. Features such as R Markdown support reproducible research and report writing.
iv. Wide applications in academia and data science.
Strongly recommend python, free, easy to install, quick to use, full-featured, easy to find code templates, and most importantly, you can use it for later work.
Recommended compiler: jupyter notebook or spsspro notebook
3.2 Learning plan for the first and second days: python basics (basic data Structural Cognition and Environment)
9 hours, divided into 2 days
https://www.bilibili.com/video/BV1YT4y1X7jT/
3.3 Study plan for the third day: pandas +Numpy+matplotlib and seaborn
https://www.bilibili.com/video/BV1eM4y1V7Mv
3.4 Study plan for the fourth day: Scipy application tutorial
https://www.bilibili.com/video/BV1i44y1M7Mz
3.5 Study plan for the fifth day: Sklearn application tutorial & SPSSPRO application tutorial
https://www.bilibili.com/video/BV1QP4y1t76A
3.7 Study plan for the sixth and seventh days: actual combat
In the next 2 days, we will cooperate with modeling hands in actual combat
4. The winning skills of the Mathematical Modeling National Competition
4.1 Problem-solving skills - dismantling method
Let me throw three questions to you first, and try to answer them:
1. How to become a big cow?
2. How to earn the first million in life?
3. How to say goodbye to being single?
Is it difficult to answer such a question? Yes, it is difficult. It's not because the national army is incompetent, it's because the problem is too big and the background is too broad. Of course, these questions themselves are not good questions. How to ask a good question is a topic worthy of an entire article, so I won’t go into details here.
However, in reality, we often encounter such big problems that we have to solve. At this time, the wisdom of dealing with problems needs to appear. The answer is also very simple, that is, first try to disassemble the big problem into small problems step by step, preferably into B%A, that is, problems that cannot be disassembled further, and then start looking for solutions.
(1) Disassemble big problems step by step.
First, make it clear that in the process of solving problems, locating and disassembling problems is the most important part. Regarding this point, you can remember the 80% rule and use 80% of your energy To locate and disassemble the problem, the rest only needs 20% of the energy to solve the problem. This time allocation may not be the same as many people's intuition, but it is very practical, just like repairing an item, it takes more time to find out which component is broken than to replace it.
With this awareness, after understanding that dismantling the problem is the most critical step to solve the problem, the thinking will be clear. In many cases, after the dismantling of the problem is completed, the answer will come out by itself. Of course, even if there is no answer and no self-discovery, the solution is not far away.
So how to disassemble a complex problem specifically, first analyze several key points of this problem, and list one, two, three.
An article clarifies [structured thinking]
Finding the key points of a problem is a test of your understanding of the problem. The first principle proposed by Musk is also based on finding the most essential core of a thing.
After trying to read and understand these problems, then think about the main points of solving these problems divergently. After trying to extract a few key points of this problem, try to use a formula to connect these points in series. Formulation is very important. Most problems can be formulated, just like the equations when we were in school. With the formula composed of this key point, you can break it down one by one according to the elements that make up the formula.
(2) Give an example
Having said so much, let's give an example to deepen our understanding. Now there is a question "how to increase the reading volume of the official account", this is also a big problem, it is a problem that needs to be disassembled, we try to disassemble it as follows: 1. Total reading volume = primary reading +
secondary reading
2 .First reading = total number of fans * reading conversion rate
3. Second reading = number of shares * number of readings brought by a single sharing
4. Number of shares = number of reposts + number of views Through this deduction, it is not difficult to get:
total reading = total number of fans * reading conversion rate + (number of reposts + number of views) * number of readings brought by a single sharing By observing the 5 elements that make up this formula, the big problem of improving the reading volume can be started from these 5 aspects 1.
Increase the number of total fans
2. Increase the conversion rate of reading
3. Increase the number of retweets
4. Increase the number of views
5. Increase the number of readings brought by a single sharing The method can already tell some ideas. Of course, these five elements can continue to be disassembled. After dismantling each layer, the solution to the problem will gradually appear in the mind. come out? At this time, I will ask my friends for advice. Compared with the three questions at the beginning, the question you asked is likely to be a good one.
(3) Benefits of dismantling the problem
● First of all, of course, it will help you solve the problem better, and it will definitely make you get twice the result with half the effort, especially in the face of relatively complex problems, how great it is to disassemble the problem until the answer is almost on paper ● A sense of
accomplishment, through the formula of dismantling big problems into elements, each completed item is equivalent to reaching a small milestone, and this achievement is more motivating to myself. Otherwise, when faced with a big problem that is difficult to solve, it is easy to feel hopeless and give up naturally;
● As the team leader, dismantling problems is also an important prerequisite for rational assignment of tasks. For example, in the above example, your team has 3 people, you can assign the 5 elements to 3 different people to be responsible, and it is easier to form a good synergy.
4.2 Essay Reading Skills - Alternatives
In the process of modeling learning, you may have discovered that modeling topics are often very abstract and complex, and the length is often very long. We may need to spend a lot of time to understand this topic. Then when we start to implement, because the topic contains a lot of unfamiliar vocabulary, we may need to read the topic multiple times, which will consume a lot of our time.
Therefore, the core of this technique is to use familiar words to replace the words in the original question.
Suppose we have a topic: "A certain satellite detected [deep-sea large organic organisms] using [ultra-high frequency microwave radiometer] and [optical imager]".
This topic looks very technical and is full of unfamiliar jargon. So we can use substitutions and replace complex terms with familiar words, for example, "glasses" for "UHF microwave radiometer", "camera" for "optical imager", "deep-sea macroorganisms" Replace with "fish".
Therefore, the title becomes: "A certain satellite detected fish with glasses and a camera".
In this way, the topic becomes easier to understand. We can understand immediately: Satellites use some kind of equipment to observe and study fish. After your modification, the problem becomes very simple to understand, and the subsequent operation will become much easier.
After completing the question, replace the familiar words "glasses", "camera", and "fish" with the professional terms in the original question. This is the use of substitution.
4.3 How to please the marking teacher - scoring routine
(1) Review
First trial: abstract, paper browsing, and rating, such as the second prize. See what method is used (if you don’t do model comparison and evaluation, you don’t know whether your method is good or bad), roughly the process, so actually look at the result, process or result diagram.
The second trial: Look at the main body of the paper and the specific method of the model for the abstract. If it is not as good as the expected value of the first trial, it will be awarded the third prize; if it fully meets the expectations, it may be promoted to the first prize. So how important is the summary?
Be sure to be concise in three parts: how to analyze the problem, what method to use, and what result to get.
(2) Characteristics of excellent papers:
● There must be results: No matter how complex the model is or how unique the idea is, it is useless if there is no result! The model that can produce results, but can't produce results and feels good is placed in "model optimization".
● As many pictures as possible and tall: pictures can help the judges understand your paper quickly, such as: modeling diagrams, output results diagrams, walking paths; ●
Model comparison: prove the advanced nature of your model and tell others about your model It is the best! It can be a comparison of different methods for this question, or it can be compared with the accuracy of other paper models.
4.4 Problem Analysis High Score Routine - Flowchart
Problem analysis can allow the judges to intuitively understand the author's modeling intention and main problem-solving ideas, so it must be taken seriously; in order to facilitate the review of the judges, it is recommended to add a flowchart in the problem analysis part. The flowchart can use VIS10 software or the built-in WPS The flow chart making module also needs to be described below the flow chart, and it is forbidden to provide only a flow chart without corresponding text description.
4.6 Model inspection and sensitivity analysis
● Model inspection is different from the evaluation of the advantages and disadvantages of the model. The model inspection mainly includes two modules: error analysis and sensitivity analysis. The error analysis can verify the correctness of the model, and the sensitivity analysis mainly verifies the universality of the model. Adding model checking can give the judges a more comprehensive understanding of the correctness of the established model, and more recognition of the results achieved by the modeling.
● Error analysis - generally applicable to prediction topics, to judge or analyze whether the calculation results of the model are accurate
● Sensitivity analysis is generally applicable to certain fixed parameters in the model, mainly to determine whether the model is applicable to more scenarios
4.5 Competition time and arrangement in 2023
The 2023 National Undergraduate Mathematical Contest in Modeling will be held from
18:00 on September 7 (Thursday) to 20:00 on September 10 (Sunday) ( 1) The afternoon of the first day
(evening on the 7th)
The question will be opened at six o'clock, so be sure to finish dinner before then, and then the whole team is ready to download the question together. The core task of the first day is the choice of topic (this usually only takes one night), so please confirm your choice on this day. Use the ones you have done in your daily practice, it is not necessary to study all of them.
There are five types of topics: ABCDE, among which, undergraduate students can only choose ABC, while junior college students can only choose DE. Select one of these topics that meets your requirements, and then discuss the idea of the topic with your teammates to see if there is a feasible solution or basic idea.
After the topic is determined, your task for tonight is completed. Of course, the stronger team can answer the first question tonight. But please be careful, don’t choose immediately just because the first two questions of a certain question are simple. This kind of question is often easy first and then difficult, and there is another kind of question that is difficult first and then easy. Carefully choose the topic that suits you. Many teams will change the topic halfway through.
Please keep a good rest on the first day and don't stay up late.
(2) The next day (No. 8)
On the second day, you need to start a specific analysis of the topic. There is no need to get up early, gather around eight or nine o'clock, remember to eat breakfast, and don't go hungry for the game. It is not recommended to stay up late at night, and it is best to return to the dormitory before eleven o'clock.
Today's main tasks are as follows:
● Analyze the topic and establish a basic mathematical model;
● Write code and solve the model;
● Complete the first and second questions.
In the evening, the students who are responsible for writing the thesis can start to build the basic framework of the thesis.
(3) The third day (Number 9)
Next, complete the third and fourth questions. If there is a fifth question, please try your best to complete it today, and you can consider staying up late (it is recommended to take a four-hour break between 1 am and 5 am to ensure that you will be energetic the next day, and staying up all night may reduce the efficiency of the next day).
Students who are responsible for writing the thesis should ensure that the first two questions have been completed.
(4) On the fourth day (closed at 20:00 on the 10th),
check whether the model or code needs to be corrected. In the morning, cooperate with the students who are responsible for writing the thesis to complete the preliminary and complete thesis. In the afternoon, the team will spend another hour or two to study whether there are any deficiencies in the paper and whether the results need to be improved. After writing, you can ask the instructor to review it to determine whether it can be submitted.
Be sure to submit the thesis. Every year, the papers are not submitted because of staying up late the previous day.
Planning Summary
The above arrangements are relatively compact. In fact, many teams cannot complete the last question even on the night of the 9th. In the face of such problems, you can consider moderate "language modeling" (the specific content needs to be understood by you, which is also a strategy worth learning). Finally, at least ensure that each topic of the thesis is completed, with rich pictures and texts, clear logical description, and beautiful layout.
Congratulations, you have at least won the provincial first prize.
4.6 What to do if you can't get the title
You can pay attention to Xiao P, an unknown mathematician who is the up owner of station B, and will release the topic ideas as soon as possible!