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 2: What knowledge does mathematical modeling mainly need? I recommend you to read the book on mathematical modeling written by Xie Jinxing. After eating a book, you have mastered the basic methods of various questions. When you do a problem, you should first look carefully. Then, sometimes you will find that if all the conditions are used, you may not be able to do anything at all. Therefore, you should learn to refine the conditions. Another is to find useful modeling methods from other people's literature through the collection of various materials on the Internet. If you want to get particularly good grades, you must have your own ideas. Modeling in the United States is still very different from that in China, with different difficulties and requirements. At least one person must be proficient in matlab programming. The paper must be written well, with fluent sentences and no typos.
Do you need to learn a lot to participate in the mathematical modeling competition?
There is no need to learn a lot of mathematical knowledge systematically, which is not allowed by time and energy. The genius of many excellent papers lies not in how much mathematical knowledge they use, but in their comprehensive, practical, problem-solving or innovative thinking. Sometimes, you may encounter some knowledge that you haven't learned in your paper. What should I do? The mathematical knowledge used in excellent papers is most likely to be used in mathematical modeling competitions, so it is of course necessary for you to look it up.
Specifically, there are about the following three aspects:
The first aspect: the application ability of mathematical knowledge.
To sum up, there are basically the following categories:
1) probability and mathematical statistics
2) Overall planning and spool planning
3) differential equation;
There is also knowledge that intersects with computer knowledge: computer simulation.
Some students have never learned the above content at all, and some students have only learned a little probability and mathematical statistics. What about differential equations? The word "self-study", I once heard Fan Yi, the teacher in charge of correcting mathematical models, say that "it is a better answer sheet to solve the answer sheet that others can solve with advanced theory by the simplest and easiest mathematical method".
The second aspect: the ability to use computers.
Generally speaking, all students who have participated in the mathematical model competition can skillfully use the Word processing software "Word" and master the use of the spreadsheet "Excel"; Using "Mathematica" software, language ability is preferred. Most of this knowledge is learned by students themselves in their spare time.
The third aspect: the writing ability of the paper
As mentioned above, the full text of the test paper is essays, and the writing of the article has a strict format. It is not easy to express your ideas clearly. Sometimes one question is not made clear before another. The marking teacher has * * * knowledge. If an article is still boring after reading 10 minutes, it is likely that this article will be ignored.
Finally, I wish you good grades.
Question 3: What knowledge do you need to master to participate in the mathematical modeling competition? I have participated in several model competitions. And they are all above the second prize.
First, we need to understand the process of modeling. It is suggested to find a paper on mathematical models over the years and clarify ideas and steps.
Secondly, look at the knowledge of mathematics. The emphasis is on optimization and statistics. There is a topic about optimization almost every year.
Third, look at the related algorithms. Repeat with the second item above, of course. And use MATLAB maple to realize the following.
Fourth, learn programming knowledge, such as C++, MATLAB, lingo and so on.
Fifth, find two people who complement you and form a team. Some people focus on programming, some people focus on papers, some people focus on mathematics and so on.
Finally, good luck.
Question 4: 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 5: What knowledge do you need to master in mathematical modeling? I have participated in two model competitions. And they are all above the second prize.
First, we need to understand the process of modeling. It is suggested to find a paper on mathematical models over the years and clarify ideas and steps.
Secondly, look at the knowledge of mathematics. The emphasis is on optimization and statistics. There is a topic about optimization almost every year.
Third, look at the related algorithms. Repeat with the second item above, of course. And use MATLAB maple to realize the following. Fourth, learn programming knowledge, such as C++, MATLAB, lingo and so on.
Fifth, find two people who complement you and form a team. Some people focus on programming, some people focus on papers, some people focus on mathematics and so on.
Finally, good luck.
Question 6: What knowledge do college students need for mathematical modeling? Zhihu Entry Level:
Modeling Jiang Qiyuan's Mathematical Modeling
Programming matlab, very simple.
Research on typesetting in writing
Deepen learning:
Learning machine algorithm for modeling and out-of-band programming
Programming learning r, CAD and other auxiliary tools.
Research on price reduction typesetting of characters
Finally, it depends on what you are.
Mathematical modeling is divided into modeling, writing and programming.
You can specialize in which one you take.