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1 Introduction
1.1 The role of mathematical modeling
(1) Extra points for guaranteed research; extra points for provincial government and national scholarships! ! ! ! !
(2) Cultivate the ability to solve problems. This kind of thinking can subtly affect a person's logical way of thinking about problems and the way of solving problems.
(3) Greater knowledge and far-sightedness. Being able to get to know many big names in colleges and universities across the country and stepping out of your comfort zone will give you a deep understanding that there are people outside the mountains and there are people outside the mountains, which motivates you to make many correct decisions and things.
1.2 Some heartfelt words
The first thing: Mathematical modeling is not just provincial and national competitions
There are about 20 relevant units at the provincial and national levels every year. Some of them can form teams across schools, while others cannot. If there is an opportunity to form a cross-school team, be sure to try to find teammates from other schools. The gold content of each competition is different, generally at the provincial level, and a few at the school level and the national level. Before participating in a national competition with a relatively high gold content, you must use one or two competitions to practice your hands. You don't have to wait until the provincial and national competitions to learn how to use a gun for the first time. In a year's competition, some of the simulations last for a month. You don't have to devote yourself to the competition every day. You only need to finish it within this month, which is enough to have a hands-on competition. The following is the competition for the whole year of 2022. You can check the registration time, competition time, registration address, registration fee, and whether it can be cross-school from my article. Summary of all mathematical modeling times in 2022
The second thing: There are several conditions for mathematical modeling to win the award. One is the preparation for theoretical study in the early stage, the second is the theoretical strength of teammates, the third is the aesthetics of the paper, and the fourth is the accuracy of the model.
(1) If you prepare in the early stage, you need to master the common methods in mathematical modeling. The first thing to get the problem is to define the type of the problem. If you don't even know what type of problem is, you can't start by checking the information. You can learn from the following theoretical preparations. It is recommended to read books, so that you can learn quickly and macroscopically.
(2) The second is the importance of teammates. The time for digital and analog is generally 3 to 5 days. During these few days, as a captain, you must always maintain a macro understanding, the overall thinking of all questions and the dynamic assignment of teammates. . As the core of the team, the captain always keeps abreast of the progress of his teammates, and adjusts them in time according to the dynamics. Sometimes, the captain asks his teammates to find a clustering algorithm theory. The teammates spent the morning reading a bunch of classified algorithm theories. , wasted time. The captain must master the abilities of his teammates, and arrange the corresponding work according to the abilities of his teammates. If a teammate is not capable of coding, don't arrange for him to write code and use his own strengths. In addition, the captain must strictly control the time and set the deadline for each progress. For example, on the first day, the reference materials and algorithm models should be summarized, the theoretical modeling and implementation of the first question on the second day, the third day, the second The theoretical modeling and implementation of the question, strictly control the dealline, if the daily tasks are not completed, you need to pay attention to schedule the progress in the later time. As a team member, you must sharpen your guns in advance, and prepare all the skills you should master in Word rapid typesetting, Code skills, drawing software use skills, PS skills, information collection and literature skills. In the past few days, if you go to sharpen the gun again, it will directly drag the team down. How to study systematically, I will talk about it next.
(3) The third is the aesthetics of the paper, which means that when the judges are reviewing the paper, in addition to usually focusing on several points including abstracts, conclusions and modeling, another key point is the beauty of the layout and the beauty of the illustrations. The aesthetics of typesetting mainly refers to the title skeleton of the paper and the use of fonts, and try to keep it as smooth and beautiful as possible. In addition, the illustrations in the paper must be beautiful. For general data diagrams, we will export and draw them with Origin, and the flowcharts are drawn with Visio, and PS will be used to ensure the beauty of the illustrations.
(4) The fourth is the accuracy of the model, which refers to whether the model is a problem-solving model. In the paper, there should be three parts: model testing, model sensitivity analysis, and model evaluation and improvement. These three parts cannot be completed.
The second thing: a summary of what you need to learn to get started.
MATLAB is a must. It can simulate, draw, and solve. It is the best software in academia. Both WPS and Word need to know, the functions are similar, some places will be different, and the compatibility will be slightly different, but it will not affect, one is enough for the writing and typesetting of papers, and you can use Excel as well as possible. Excel can also draw many basic data graphs, as well as simple data processing. Visio is mainly used to draw various diagrams of various circles, boxes and lines. It can click and edit the original picture in the document to facilitate any changes and adjustments. Origin is mainly used to draw visual graphs of various data, such as line graphs, bar graphs, pie graphs, etc., which can be drawn very beautifully. Mathtype is a formula editor. Although WPS and Word have built-in editors, in a short period of time, facing a large number of formula editing and maintenance, an efficient editor must be used. The installation method is linked below.
Other Lingos mainly solve large linear, nonlinear and integer programming problems, which can be solved by a small MATLAB. SPSS may be used for a statistical problem and can be used for statistical analysis of data, such as correspondence analysis. PS is mainly used to refine the picture to make the picture more beautiful. The Python programming language is mainly aimed at machine learning algorithms and deep learning, and data analysis is very convenient. Mastering the programming language and skills in this area can quickly solve the model, because Python provides a very rich toolkit, and a lot of work can be saved by direct invocation.
Third thing: Teamwork skills and essay writing skills to compete in a short period of time.
(1) Teamwork
Document maintenance is the most troublesome thing for online teams to write. Word files are sent back and forth in WeChat groups. Sometimes, if you forget to iterate on a certain part, the whole paper and materials will be messed up. You can use an online knowledge base to maintain a unified document. Yuque is an online knowledge base. After you create a team, you can store word documents, PDFs, excel documents, and codes in a knowledge base. For text documents, multiple people can modify a document to ensure the consistency of the document, and finally the document can be exported as a word or other format file. It is very convenient to use this to summarize papers, share found materials and references. Download the APP, fill in my invitation code: EV4KFG , you can get a three-month membership. For the progress of the team, in addition to setting deadlines, try to discuss the progress at a fixed time to ensure the efficiency of the team. If you are remote, you can use software such as Tencent Conference to share the screen.
(2) For the writing of the thesis, the template of the thesis should be based on a standardized format, as shown in the figure below, including abstract, problem restatement, problem analysis, model assumptions, symbol description, model establishment and solution, model test or sensitivity Analysis, model evaluation and promotion, and summary are composed of nine parts.
Among them, the abstract and conclusion are the most important parts of a paper, and they are also the first content that the grading teacher looks at, and the main points are the points. Write the conclusion first. The main idea is what problem, what model is established, what results are obtained, the advantages and disadvantages of the model, and improvements. The abstract is a condensed version of the conclusion, which concisely describes what the problem is, what model is built, and what results are obtained. The format of writing can be as follows. The first paragraph is a background introduction, the second paragraph is a summary of question one, the third paragraph is a summary of question two, and so on.
It is very necessary to read excellent papers. If you want to play beautiful games, you must read excellent papers. The layout, drawing, and analysis ideas of excellent papers must be distinguishable by the public. You can check the summary of a blogger on github. https://github.com/BetterBench/Math_Model
2 Theoretical basis
For the learning of algorithms, it is recommended to learn to read books to learn systematically and quickly. The main algorithms are as follows.
(1) Linear programming
(2) Integer programming
(3) Nonlinear programming
(4) Dynamic programming
(5) Graph and network models and methods
(6) Queuing Theory Model
(7) Game Theory
(8) Analytic Hierarchy Process
(9) Interpolation and fitting
(10) Statistical description and analysis of data
(11) Analysis of variance
(12) Regression analysis
(13) Differential equation modeling
(14) Steady state model
(15) Solutions to differential equations
(16) Difference equation model
(17) Markov chain model
(18) Dynamic optimization model
(19) Neural network model
(20) Numerical solution of partial differential equations
(21) Goal planning
(22) Fuzzy mathematical concepts
(23) Modern optimization algorithms
(24) Time series model
(25) Grey System Theory and Application
(26) Multivariate analysis
(27) Partial least squares regression analysis
(28) Storage Theory
(29) Optimization problems in economics and finance
(30) Optimization problems in production and service operation management
(31) Machine Learning Algorithms
3 Recommended information
3.1 Books
"Mathematical Modeling Algorithms and Applications" Si Shoukui, link: https://pan.baidu.com/s/161wKCUIJ1dMOYGZCvScSpAPassword : 308z
"Application of Matlab in Mathematical Modeling" Zhuo Jinwu, link: https://pan.baidu.com/s/16mFpoDyd80iigaYTwXKkJg Password: q0l6
"SPSS Statistical Analysis Basic Course" Zhang Wentong, link: https://pan.baidu.com/s/1tCu6BiTKfox_QEBXnZz9wAPassword : 47il
"30 cases of Matlab intelligent algorithm" Shi Feng. Link: https://pan.baidu.com/s/14EY6yc11B1_sEc_550qp8w Password: 56fg
"Previous Excellent Papers of National Competitions": Learn the abstracts of excellent papers, analyze their logical ideas, writing ideas, and model analysis. Download
"Meisai's Excellent Papers": Look at other people's drawings and writing ideas. Link: https://pan.baidu.com/s/1Ciw2vcvlaO9Ps2do54xJdw Password: f55p
3.2 Online classes
3.3 Technical Blog
[Installation of Office Family Bucket on Windows 10]
[Install mathtype on Windows 10]
[Summary of websites for finding literature]
[Windows10 download and install Matlab]
[Linux download and install Matlab]
【Mac os download and install Matlab】
[Python environment configuration tutorial]
4 Supplements for teammates
Xiao Ming : (you can follow him on CSDN)
When many students first started to contact digital modeling, they often have this question: how to learn mathematical modeling, or how to get started? Will often fall into the following misunderstandings:
holding a book of advanced mathematics, linear algebra, probability theory. . . . I looked at it and gave up after reading two pages. I
just started to learn an algorithm, and I was stuck on the principle of the algorithm, and I deduced the algorithm formula there.
They all said that Latex is good, so I used Latex to layout the
three teammates. , programming is just coding...
I started to get in touch with digital and analog in 2018. I participated in more than 10 digital and analog competitions by myself, or brought friends to participate in various digital and analog competitions. In my experience, digital and analog must first be summarized, Imitation begins.
First of all, for the students who are just getting started in mathematics and modeling, how many points you have in the high school mathematics test, these are useless, or you don't need to deduce the formulas at all. The formulas of these models have been deduced long ago. For everyone Just need to be able to understand what this model does, and then be able to use it.
Secondly, Latex has become more and more popular in the field of digital and analog in recent years, but in my personal experience, I do not recommend that novices learn this. You should focus on the content with limited time. Going to adjust the Latex template will bring a lot of pressure to the other two teammates. And Latex I always feel that his forms are very inconvenient to type (although there are tools like Excel2Latex), illustrations and forms will run around if they are not done properly. You have found a bug that you can't solve in a short time, and you have never encountered it. This may directly lead to a few days of hard work. In the few days in the digital model, it is good that Xiaobai can last until he doesn't fall asleep. Don't talk about changing the bugs you wrote yourself (I will talk about the above problems in detail when I have time in the future)
The last question, when most of the classmates went to their teammates, they said that they could do the writing job. In my opinion, if you can only write essays, you must not write essays. If you can't understand the principle and code of each model, and you can't understand what your teammates do, then what you write, emm can only be called composition at best.
Next, let’s share a few small steps for getting started
with digital and analog. (1) Familiarize yourself with the composition of digital and analog papers.
From the abstract to the conclusion, what should be written in each part, and how to write it, you can watch a video explained by the scientific research exchange brother at station B. After reading this, I will look at the excellent papers and find out whether these excellent papers have these structures. There will also be some problems in the excellent papers. Everyone must have the ability to think independently. In fact, I always feel that the mathematical model of scientific research exchange is doing well, and the courses are not expensive every year, and the content will be updated. One or two hundred yuan is the money for three people to go out for a meal. To be honest, if you have to pay attention to this amount of money in your studies, then I highly do not recommend you to participate in the competition.
(2) Learn three commonly used basic algorithms
. Friends, please be optimistic. Here are 3 basic algorithms, that is, 3 (several) algorithms that appear repeatedly in a class of questions. It is recommended to start with the evaluation class. Algorithms look (analytic hierarchy process, Topsis method, entropy weight method). The three people in the group must have a very good understanding of these algorithms. Programming students must ensure that their code can run through before the competition, and can make some modifications according to the actual situation.
(3) There is a need for a run-in before the competition.
If you are an undergraduate, especially a sophomore, there is only one chance left for the national competition. So be sure to cooperate with each other before participating. Here's a quick way to develop tacit understanding.
First of all, you need to choose a question in a question type, and then 3 people read the question and find information. After 2 hours, discuss online and share your thoughts. Then find 1-2 excellent papers, read each one for 1 hour, and try to "reproduce" it. The specific method is as follows:
Recurrence does not mean that everyone should implement every step in these papers. In fact, even if you follow the steps in the paper, you may not get the same results as in the paper. The three of you, choose an excellent paper and try to sort it out yourself. You don't understand copying to others, let alone writing it yourself. In this process, you will have a deep understanding of typesetting, drawing, tabulation, etc. Through this method, you can quickly simulate actual combat and cultivate tacit understanding. No matter how many tutorials you watch, it is better to practice it yourself, Over!
5 Advanced
To be perfected. . .
Remember to click Follow and Favorites. In the future, I will continue to publish articles to explain how to accurately and quickly collect data, mathematical modeling, and re-implementation after getting the competition questions, and finally the writing and typesetting of papers, as well as how the team can collaborate and be efficient. output.