Question 2: How to do mathematical modeling? I just participated in the National Mathematical Modeling Competition for College Students in September. A basic mathematical modeling paper should include the following aspects:
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 3: How to learn mathematical modeling? All right! Just write down the names of three people when filling out the registration form, and the registration fee will be paid by yourself. What instructors and so on are all empty. This year's competition time is from 8:00 on September 9 to 8: 00 on September 12, so make preparations early!
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 learn mathematical model and what knowledge do you need to know to participate in 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 6: What is mathematical modeling? I won't elaborate on the detailed definition of online mathematical modeling, but say something else ~ ~
The main development direction of mathematics is the combination of mathematics and calculation. Combining mathematical algorithms with computer technology to solve practical problems, you will learn by going up one flight of stairs from computer in the future, because your algorithm is more advanced than theirs. This is the main survey of the mathematical modeling competition.
The gold content of mathematical model competition is also relatively high. You won the ranking in the competition, which can completely prove that you have certain strength ~ ~
You don't need to worry about your poor math scores. I have participated in several competitions, and my knowledge of mathematics is not very advanced. High school mathematics can solve many problems, mainly optimization and simulation. I think it is more important to test one's thinking ability. Besides, you only need one specialty in math, computer and writing ~ ~
If you take part in the competition, you will really gain a lot and learn a lot of new knowledge. In this way, you can know that what you have learned can be used in your life, thus stimulating your interest in learning. Really, I strongly recommend you to learn some ~ ~ to participate in the competition ~ ~ If you have any other questions to ask, hehe ~ ~ I have done modeling and writing, and my programming is similar ~ ~
Question 7: Learn mathematical modeling and see which book is the best.
To commemorate the passing of university mathematical modeling: two school competitions, two national competitions, two American competitions and an electrician's cup. From the first semester of freshman year to now, the next semester of junior year, time flies, and the career of college modeling has come to an end. Thanks to the seniors and sisters who helped me on the modeling road, the grace of dripping water should be rewarded by the spring. Write down this feeling, hoping to give my brothers and sisters some inspiration and complete their own ideas. The writing is poor. If you don't know what to write, just write in order.
How did I choose to be a model?
When I was a freshman, I first heard about mathematical modeling. Actually, I was a freshman last semester, but I'm not a freshman next semester. I came across it when I was browsing the web, because of my reverence for mathematics, philosophy and history since I was a child (although universities dare not choose any of them, especially mathematics and philosophy, for fear that it is too difficult to learn well), so I firmly decided to study mathematical modeling. By reading the student handbook or other materials issued by the school, we found that there is a mathematical modeling competition in our school. In view of the fact that I didn't have any math knowledge in my freshman year, I didn't start preparing. The focus was on finding my teammates. Once I played table tennis, I met two handsome telecom guys, and we will play together in the future. One of them (M) has great potential to learn bullying. Later, after the final exam, I inquired about his high score in mathematics. Sure enough, I tentatively asked, do you want to participate in modeling together? Well, success!
The second teammate met her in the first semester of freshman year (asked her a lot of questions about changing majors), but was asked to form a team in the second semester. As usual, I was shocked when I asked about my grades. It's a girl F, whose English is super good and her calculus is close to full mark (I transferred to her college in the second semester). Send an invitation decisively, do you want to form a team together, well, success.
About finding teammates: in the case of asymmetric information, priority is given to the professional collocation of three people. For example, telecom partners are responsible for programming and modeling of science and engineering topics, economic and financial statistics are responsible for papers and statistical modeling, and mathematical computing majors are responsible for all-round modeling and helping papers. Personally, I think this is better. Because modeling can be roughly divided into three parts: modeling, programming and thesis, one person is responsible for one part as a whole, but we must not go to extremes, and everyone is responsible for one part alone. This combination lacks communication and interaction. It should be run-in in training and combined with everyone's personal characteristics. Which are mainly responsible and which are auxiliary.
Then there was the first inter-school competition: the first time was quite exciting, because we asked several seniors and sisters before, and the models were all up all night, so we were going to stay up all night. The first topic I got was about the relationship between people with different eating habits and health levels in different departments of a unit. In retrospect, this is actually a relatively simple statistical analysis problem. But I didn't have such consciousness at that time. All the problems are done by office, and I don't know what to do after thinking about them for a long time. The process of doing it is painful, but it is also exciting. The result of the third prize in the school competition proves that it is not enough to have passion, but also to make up a lot of knowledge.
Recommended introductory bibliography for beginners:
Mathematical model (Jiang Qiyuan, Xie Jinxing)
Mathematical modeling method and analysis. Mark Mersat (New Zealand)
The first book was written by Mr Lao Jiang, which is very suitable for beginners. It is also a domestic style in content arrangement. According to the knowledge points of the model, they are classified and synthesized one by one. The second book is from New Zealand. I read this book when I was a sophomore. I only read the first part. I find this book quite suitable for beginners. It is a typical foreign textbook style. Starting with a model example, I will tell you all aspects of mathematical modeling. One of the repeated five-step mathematical modeling methods is really reasonable after careful understanding. After reading most of this book, I can understand and use this method. The first school competition was because the first step of the five-step method was not done. By the way, there is also a book recommended by Mrding. It is the First Lesson of Mathematical Modeling written by Giordano, chairman of the American Mathematical Modeling Competition Committee. There is a Chinese version translated by Jiang Qiyuan, which I haven't seen in the library. I can have a look when I have the chance.
How to model
During the first National Day, I started school training. I borrowed a lot of books in advance and borrowed all my cards. For me, the training before the first national competition is the most rewarding period, which is bigger than any other time period.
During this time, all three of us have worked hard. You have to learn a lot during daytime training, and then you can only rest ... >>