Ten algorithms that mathematical modeling should master \x0d\ 1, Monte Carlo algorithm (this algorithm is also called random simulation algorithm, which is a method to solve problems through computer simulation, and at the same time, it can test the correctness of its own model through simulation, which is a necessary method in the competition) 2. Data fitting, parameter estimation, interpolation and other data processing algorithms (there are usually a lot of data to be processed in the competition, and the key to processing data lies in these algorithms, usually using Matlab as a tool) 3. Linear programming, integer programming, multivariate programming, quadratic programming and other planning problems (most of the problems in modeling competitions belong to optimization problems, and many times these problems can be described by mathematical programming algorithms, usually realized by Lindo and Lingo software) 4. Graph theory algorithms (these algorithms can be divided into many kinds, including shortest path, network flow, bipartite graph and other algorithms. Problems involving graph theory can be solved by these methods and need careful preparation. Computer algorithms such as dynamic programming, backtracking, divide-and-conquer algorithm, branch and bound (these algorithms are commonly used in algorithm design and can be used in competitions in many occasions) 6. Three non-classical algorithms of optimization theory: simulated annealing method, neural network and genetic algorithm (these problems are algorithms used to solve some difficult optimization problems, which are very helpful to some problems, but the algorithms are difficult to implement and need to be used carefully) 7. Grid algorithm and exhaustive method (grid algorithm and exhaustive method are the best algorithms for violent search, and they have applications in many competition questions. When focusing on the model itself and ignoring the algorithm, this violent scheme can be used, and it is best to use some high-level languages as programming tools. 8. Some continuous discretization methods (many problems are practical, data can be continuous, and computers only recognize discrete data. Therefore, it is very important to discretize it and implement the idea of replacing differential with difference and integral with sum. 9. Numerical analysis algorithm (if high-level language programming is used in the competition, some commonly used algorithms in numerical analysis, such as solving equations, matrix operation, function integration, etc., need to write additional library functions to adjust) 10, image processing algorithm (there is a kind of problem related to graphics in the competition, even if it has nothing to do with graphics, there should be many pictures in the paper, and how to display and process these graphics is the problem that needs to be solved. Matlab is usually used for processing) \x0d\ mathematical modeling materials \x0d\ competition reference books \x0d\ l, Chinese college students' mathematical modeling competition, edited by Li Daqian, Higher Education Press (1998) .2. Tutoring materials for college students' mathematical modeling competition, (1) (2) (3). 1997, 1998).3. Mathematical modeling education and international mathematical modeling competition "Engineering Mathematics" album, edited by Ye, "Engineering Mathematics" magazine, 1994). \ x0d \ domestic textbooks and series \x0d\ 1. The first edition won the "National Excellent Textbook Award" 1992 in the second national excellent textbook selection organized by the State Education Commission. 2. Mathematical Model and Computer Simulation, edited by Jiang and Xin Peiqing, University of Electronic Science and Technology of China Press, (1989). 3. Hua, author of Essays on Mathematical Models (from Mathematics to Books). (199 1).4. Mathematical modeling-methods and examples, edited by Shou Jilin et al. Xi Jiaotong University Press (1993). 5. Mathematical model, edited by Pu Dingguo and Tian Weiwen, Southeast University Press (1994)...( 1995) 7. Mathematical model, edited by Chen Yihua, Chongqing University Press, (1995) 8. Mathematical Model Modeling and Analysis, edited by Cai Changfeng, Science Press, (1995). 9. Course of Mathematical Modeling Competition, edited by Li Shangzhi, Jiangsu Education Press, (1995). Xu and Yang Jinhao, edited by Chengdu University of Electronic Technology Press, (1996). 1 1, Mathematical Modeling, edited by Shen, Shi Jiuyu and Gao Zhenbin, Harbin Engineering University Press, (1996) .000666666 (1996). 13. Mathematical Modeling Methods, edited by Qi Huan, Huazhong University of Science and Technology Press, (1996). 14. Mathematical Modeling and Experiment, edited by the Symposium on Mathematical Modeling and Industrial Mathematics in Nanjing Institute of Technology, edited by Hohai University Press, (1996) edited by Liu and Zeng, and published by Beijing Normal University Du (1997). 16. Mathematical Modeling, edited by Yuan Zhendong, Lin Wuzhong and Jiang, published by East China Normal University Press. 17, Mathematical Model, edited by Tan Yongji and Yu Wenpi, published by Fudan University Press, (6544) edited by Fei Peizhi and Cheng Zhongying, edited by Sichuan University Press, (1998). 19, Selected Excellent Cases of Mathematical Modeling (Engineering Mathematics Base Construction Series), edited by Wang Guoqiang. (1999) .2 1, Lecture Notes on Mathematical Models, edited by Lei, Peking University Press (1999) .22, Excellent Cases of Mathematical Modeling, edited by Zhu Daoyuan, Southeast University Press, (1999) .22. (1999) .24. Theory and Practice of Mathematical Modeling, edited by Wu Xiang, Cheng Lizhi, Mathematical Experiment by National Defense University Press, edited by Fu Peng, Gong Li, Liu Qiongsun and Zhongshi He, Science Press, 2000. 28. Mathematical Modeling and Mathematical Experiments, edited by Zhao Jing and Qi Dan, Higher Education Press, (2000). \x0d\ foreign reference books (Chinese version) \ x0d \ Bender, translated by Zhu, Science Popularization Press (1982). 2. Mathematical model, Guan, translated, Machinery Industry Press, (1985). 3. Differential equation model, (Applied Mathematical Model SeriesNo. 1 Volume). (1988) .4. Politics and Related Models, (Volume II of Applied Mathematical Models Series), [edited by W.F. Lucas, translated by Wang Guoqiu, etc. , National University of Defense Technology Press, (1996) .5, Discrete and System Models, (Volume 3 of Applied Mathematical Models Series), [W. USA .( 1996).6. Life Science Models, (Volume 4 of Applied Mathematical Models Series), [US1W. , National University of Defense Technology Press, (1996). 7. Model Mathematics-Continuous Dynamic System and Discrete Dynamic System, [written by UK 1H]. B.Grif6ths and a. 0 1 dnow, edited by Xiao Li Zhang Zhijun, Science Press, (1996) .8. Mathematical modeling-a case study of four industries in Britain, (Translation Series of Applied Mathematics No.4), English] D.burg. (1997)\x0d\ professional reference books \x0d\ (There are many books in this field, only a few are listed for reference): 1, Mathematical model of water environment, by W. Kinze 1bach, edited by Yang Rujun and Liu, China Building Industry Press, Railway Press. 4. Mathematical model and application of crop pest management, edited by Pu Zhelong, Guangdong Science and Technology Press (1990). 5. Mathematical Models in System Science, edited by Ouyang Liang, (1995). 6. Mathematical Modeling and Research of Population Ecology, edited by Ma Zhien, Anhui Education Press, (1996). 7. New Progress in Modeling, Transformation and Optimization-Structural Synthesis Method, Sui, Dalian University of Technology Press, (1986). 8. Genetic model. China Agricultural Publishing House (1997). (edited by Wang Shousong, Department of Mathematics, Sun Yat-sen University, April 5438+0, 2006) \x0d\ Process \x0d\ Model preparation \ x0d \ Understand the actual background of the problem, clarify its practical significance, and master all kinds of information of the object. Describe the problem in mathematical language. \x0d\ model hypothesis \x0d\ According to the characteristics of the actual object and the purpose of modeling, simplify the problem and put forward some appropriate assumptions in accurate language. \x0d\ Modeling \x0d\ On the basis of assumptions, use appropriate mathematical tools to describe the mathematical relationship between variables and establish the corresponding mathematical structure (try to use simple mathematical tools). \x0d\ Model solving \x0d\ Calculate (or approximately calculate) all parameters of the model by using the obtained data. \x0d\ Model analysis \x0d\ Analyze the results by mathematical methods. \x0d\ Model verification \x0d\ Compare the analysis results of the model 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. \x0d\ Model application \x0d\ Application methods vary according to the nature of the problem and the purpose of modeling. \ x0d \ x0d \ 1。 Study mathematics knowledge hard and improve your own knowledge system, especially knowledge related to mathematics, such as advanced mathematics, engineering mathematics, applied mathematics, etc. \x0d\2。 Expanding knowledge, we can see that many competition topics are very realistic social hot issues, and relevant background knowledge is very necessary; \x0d\3。 Read more case study tutorials. When studying case analysis, we should pay attention to the following points: how to consider various factors in practical problems, comprehensively use what we have learned and establish a suitable model; How to optimize the model; How to solve the model; How to explain the solution of the model? \x0d\ The three most difficult problems in mathematical modeling, 1, need to be understood gradually. How to express the problems we face with the learned mathematical ideas is called modeling. 2. Apply the learned mathematical knowledge to solve and optimize the newly established mathematical model. 3. Explain the mathematical solution just obtained as a phenomenon or method in real problems. These three processes embody a "reality->; Mathematics->; A realistic process. This is actually the hardest part. This requires you to understand the actual problems you face first, then turn from reality to mathematics, then jump out of mathematics and return to reality. \x0d\4。 Speaking of matlab, I suggest you borrow a matlab manual as a reference book! After all, matlab is only the foundation to realize your mathematical model. This is not to say that matlab is not important, but it is also important! \x0d\ I wish you happiness!