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Information and assists related to previous national competitions can be viewed
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Ideas for question D:
(Updated as soon as the game starts)
Summary of common algorithms for modeling in the national competition.
Before the start of the national competition, we summarized the common algorithms for mathematical modeling. You can refer to them and learn from them.
Frequently asked questions about mathematical modeling in the national competition are divided into:
1. Classification problem
2. Prediction problem
3. Optimization problem
4. Evaluation issues
4.1 Classification problem
Discriminant analysis
distance discrimination method
Fisher's criterion
Bayes criterion
step by step discrimination method
Cluster analysis
System clustering method (hierarchical clustering method)
Fast clustering method (K-means clustering method)
Two-step clustering method (intelligent clustering method)
fuzzy cluster analysis
Clustering methods combined with genetic algorithms, neural networks or gray theory
Neural network classification method
4.2 Prediction problem
Regression analysis method
time series analysis
Gray prediction method
BP neural network method
Combination forecasting method
4.3 Optimization problem
mathematical programming model
differential equation model
Graph theory and network optimization problems
probability model
Combinatorial optimization classic problem
Multidimensional Knapsack Problem (MKP)
Two-dimensional assignment problem (QAP)
Traveling Salesman Problem (TSP)
Vehicle Routing Problem (VRP)
Job Shop Scheduling Problem (JSP)
4.4 Evaluation Problem
Analytical Hierarchy Process (AHP)
Gray comprehensive evaluation method (gray correlation analysis)
fuzzy comprehensive evaluation method
BP neural network comprehensive evaluation method
Data envelopment method (DEA)
Portfolio Evaluation
How to become a master of mathematical modeling
1. Solid foundation
The so-called foundation here does not refer to the foundation of mathematics alone, but refers to some basic knowledge, which may be some common sense, including mathematics, physics, chemistry, biology, geography, etc. . Of course, this knowledge is not necessarily learned in the classroom, some of it comes from life. Everyone may be good at modeling, but not everyone can build excellent models. When you find that you have no ideas for some small problems in real life, it’s not that you don’t have the talent for mathematics, but that you lack the understanding of life. accumulation of knowledge. Don't ask what the use of learning calculus is at the beginning.
What you have to do is to learn it first, even if you just memorize it, so that you won't encounter problems like "Use the least money to do the most things." "This is the most common problem when you feel you don't know what to do. Therefore, what we have to do is to dabble in as much knowledge as possible, and don't just stick to our own major.
2. Rich imagination
Don’t stick to a fixed way of thinking. When you encounter a problem, think of several solutions to the problem and try methods that others have never thought of. Don't classify the problem as soon as you get it. Many people are willing to classify the problem as soon as they come up, such as optimization problems, combination problems, equation problems, etc. Then use some methods related to this classification to solve the problem. Many real-life problems are very complex, and simple classification is sometimes meaningless. Doing so not only limits your thinking, but also makes you more stubborn. A rich imagination will bring you closer to the problem, and a broad mind will allow you to see all aspects of the problem. Of course, rich imagination is based on rich knowledge.
3. The simplest is the best.
This may be a rule that all science follows. In Einstein’s eyes, the complex principle of mass-energy conversion is just an extremely simple formula: E=mc2. Simple methods are easier to understand, easier to implement, and easier to maintain. When encountering a problem, give priority to the simplest solution, and only consider complex solutions when the simple solution cannot meet the requirements. Of course, even if you want to apply a complex solution, you must adopt a step-by-step approach and gradually improve the previous solution. Do not try a very complex solution at the beginning.
4. Don’t get into trouble
When you encounter obstacles, you might as well stay away from the problem for a while, look at the scenery outside the window, listen to light music, chat with friends, or read a few novels. When I encounter a problem, I usually go to chat with friends. Some well-intentioned suggestions and even encouragement from friends can give my brain a full rest. When I start working again, I will find that those problems can now be easily solved.
5. Desire for answers
The history of the development of human natural science is a process of craving for answers. Even if we can only know a small part of the answer, it is worth our efforts. As long as you have firm belief and must find the answer to the question, you will devote energy to exploring. Even if you don't get the answer in the end, you will learn a lot in the process.
6. Communicate more with others
. There must be a teacher among the three of us. Maybe in a casual conversation with others, a spark of inspiration can burst out. Go online more and see what other people think about the same issue, which will give you a lot of inspiration. Of course, don't regard the purpose of communicating with others as getting answers to questions. Even the exchange of learning methods is beneficial to you.
7. Good programming literacy
With the continuous advancement of science, more and more disciplines have become inseparable from computers. Mathematical modeling, which is one of the main means of solving real-life problems, is of course inseparable from computers. Some people may think that those who engage in mathematical modeling only need to be able to write some simple programs. I hold a negative attitude towards this. For programming, no matter the size of the program, it is still a project. Since it is a project, it must be done according to quality standards. Isn't there an ISO9000 quality standard? That standard applies to programming as well. Only when the quality of programming is guaranteed can the computer tool truly become a useful weapon for modeling.
8. Tenacity and perseverance
This is perhaps the biggest difference between “masters” and ordinary people. Masters are not geniuses, they have been honed over countless days and nights. Success can bring us great joy, but the process is extremely boring. You might as well do a test and insist on going to the library to read books or materials related to mathematical modeling for one hour every day for half a year. If you can complete this work without interruption, you can meet this requirement.