Background and proposal of the problem, analysis of the problem, hypothesis of the model, symbolic interpretation, establishment and solution of the model, evaluation and popularization of the model, and references.
Formal mathematical modeling papers are generally more than 20 pages long. Considering that you are in the third grade, your teacher's requirements are not so high, and your ability should be lacking. My suggestion is that you choose a challenging topic according to your actual situation. The nature of the topic is similar to that of the application topic, but it is different from the general application topic. You don't have to be sure of the answer. Do some analysis and discussion on the problem itself, and it is best to combine it with reality.
It should be noted that the assumption should be reasonable and there should be a mathematical model (including some equations and inequalities, etc.). ), we should have analytical thinking, evaluate the advantages and disadvantages of our own model, and it is best to promote it in a targeted way.
Question 2: 1. What is a mathematical model? What are the general steps of mathematical modeling? 2. What abilities and knowledge are needed for mathematical modeling? Good answer, reward 100. Mathematical modeling is a practice of solving practical problems by mathematical methods, that is, through the processes of abstraction, simplification, assumption and introduction of variables, the practical problems are expressed mathematically, a mathematical model is established, and then advanced mathematical methods and computer technology are used to solve them.
Mathematical modeling comprehensively applies all kinds of knowledge to solve practical problems, which is one of the necessary means to cultivate and improve students' ability to apply what they have learned to analyze and solve problems.
General methods and steps of mathematical modeling
There is no certain pattern in the methods and steps of establishing mathematical model, but an ideal model should reflect all the important characteristics of the system: the reliability and availability of the model. General methods of modeling:
Mechanism analysis: according to the understanding of the physical characteristics, analyze the causal relationship and find out the laws reflecting the internal mechanism. The established model usually has clear physical or practical significance.
Test and analysis method: the research object is regarded as a "black box" system, and the internal mechanism cannot be directly sought. By measuring the input and output data of the system, and on this basis, using the statistical analysis method, the model with the best data fitting is selected from a certain type of model according to the predetermined standard. Test analysis method is also called system identification.
Combining these two methods is also a common modeling method, that is, the structure of the model is established through mechanism analysis, and the parameters of the model are determined through system testing.
In the actual process, which method to use for modeling mainly depends on our understanding of the research object and the purpose of modeling. The concrete steps of mechanism analysis and modeling are roughly as follows:
1, the variables and parameters are determined by abstraction, simplification and assumption in practical problems;
2. Establish a mathematical model, solve it mathematically and numerically, and determine the parameters;
3. Test the mathematical model with the measured data of practical problems.
4, in line with the reality, delivered to use, can produce economic and social benefits; Not realistic, re-model.
Classification of mathematical models:
1. According to the research methods and mathematical characteristics of the object, it can be divided into elementary model, geometric model, optimization model, differential equation model, graph theory model, logic model, stability model and statistical model.
2. According to the actual field (or discipline) of the research object, it is divided into population model, traffic model, environment model, ecological model, physiological model, urban planning model, water resource model, pollution model, economic model and social model.
Mathematical modeling needs rich mathematical knowledge, involving advanced mathematics, discrete mathematics, linear algebra, probability statistics, complex variable functions and other basic mathematical knowledge. At the same time, you need a wide range of interests, strong logical thinking ability and strong language expression ability.
What do you need to know to participate in the mathematical modeling competition?
I. National Mathematical Modeling Competition for College Students
Second, the methods and general steps of mathematical modeling
Third, important mathematical models and corresponding case studies.
1, case analysis of linear programming model and economic model
2. Case analysis of 2.AHP model and management model.
3. Statistical regression model and case analysis.
4. Graph theory model and case analysis.
5. Differential equation model and case analysis.
Fourth, related software.
1, Matlab software and programming; 2.Lingo software; 3.Lindo software.
Five, ten commonly used digital and analog algorithms
1. Monte Carlo algorithm 2. Data processing algorithms, such as data fitting, parameter estimation and interpolation. 3. Programming algorithms, such as linear programming, integer programming, multivariate programming and quadratic programming. 4. Graph theory algorithm. 5. Computer algorithms, such as dynamic programming, backtracking search, divide and conquer algorithm, branch and bound. 6. Three nonclassical algorithms of optimization theory. 7. Grid algorithm and exhaustive method. 8. Several discretization methods of continuous data. 9. Numerical analysis algorithm. 10. Image processing algorithm.
VI. How to obtain information
Seven, how to write a paper
Eight, how to organize the team: team spirit, good at cooperation, constantly ask questions and solve problems.
Nine, how to win the prize: relatively complete, there are several innovations.
X. how to deal with information: WORD, LaTeX, fly ball, QQ.
In fact, just look at the examples and understand some basic models. I also have many examples here. If there are important lectures in various schools, just ask me ... >>
Question 3: How to build a good mathematical model? A good mathematical model should be able to solve problems first, and only a model that can solve problems is a good model. Secondly, it lies in the creativity of the model. Creativity does not mean that you have to find a new method or algorithm by yourself, but that even if you use a long-term algorithm, you can solve the problem in a new field and have good adaptability. This is a good mathematical model. Note that the mathematical model can be a formula, an algorithm or something like a chart.
Question 4: What are the general steps of mathematical modeling?
Understand the actual background of the problem, clarify its practical significance, and master all kinds of information of the object. The essence of the problem is contained in mathematical thought and runs through the whole process of the problem, and then the problem is described in mathematical language. Requirements in line with mathematical theory, in line with mathematical habits, clear and accurate.
Model hypothesis
According to the characteristics of the actual object and the purpose of modeling, the problem is simplified with accurate language and some appropriate assumptions are put forward.
Model structure
On the basis of assumptions, use appropriate mathematical tools to describe the mathematical relationship between variables and constants, and establish the corresponding mathematical structure (try to use simple mathematical tools).
Model solving
Using the obtained data, all parameters of the model are calculated (or approximately calculated).
model analysis
The idea of establishing the model is expounded, and the results are analyzed mathematically.
model testing
The model analysis results are compared 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.
Application and popularization of the model
The application pattern varies with the nature of the problem and the purpose of modeling. The generalization of the model is to have a more comprehensive model based on the existing model, which is more suitable for the actual situation.
Question 5: What is Zhibei? Five points is a dirty word in Fuzhou dialect. ..
Describe women ....
Question 6: What are the common methods for establishing mathematical models? Generally speaking, the methods of establishing mathematical models can be divided into two categories: one is mechanism analysis and the other is experimental analysis. Mechanism analysis is based on the understanding of the characteristics of real objects to find out the laws reflecting the internal mechanism, and the established models often have clear physical or practical significance.