1. What is mathematical modeling
2. What you need to learn
3. The software tools you need
4. Paper templates, search literature, search data
1. What is mathematical modeling
The National College Student Mathematical Modeling Contest is a national college student competition in China, which aims to improve the mathematical modeling ability and innovative thinking of college students, and cultivate students' comprehensive quality and teamwork ability . The competition is usually supervised by the Ministry of Education of China, co-sponsored by the Chinese Society of Higher Education and related units. The competition is held once a year and is open to undergraduate, graduate and doctoral students from universities across the country. The participating teams are usually composed of 3-5 members . They need to propose scientific and effective solutions by modeling, analyzing and solving the given problems within the specified time . The topics of the competition usually cover multiple subject areas, including mathematics, physics, economics, management, etc., aiming at simulating and solving practical problems. The participating teams need to demonstrate strong mathematical modeling capabilities, including skills in problem analysis, model building, data processing, model solving, and result verification . The National Undergraduate Digital Modeling Competition is widely recognized as an important platform for cultivating college students' innovative thinking and practical ability, and has a positive effect on the academic research and comprehensive quality improvement of participating students. The competition also provides an opportunity for exchanges and cooperation between universities and promotes the sharing and opening of educational resources. Participating in the National Undergraduate Digital Modeling Competition is a good opportunity for students to learn and grow. It can exercise their problem-solving ability, teamwork awareness and innovative thinking, and lay a solid foundation for future academic research and career development.
There are several other mathematical modeling competitions: China Postgraduate Mathematical Modeling Competition, American College Student Digital Modeling Competition, Shenzhen Cup Digital Modeling Challenge (Shenzhen Cup), National Electrician Cup Digital Modeling Competition, etc.
2. The knowledge and skills that need to be learned (for the catalog)
Participating in the China Postgraduate Mathematical Modeling Contest requires a certain foundation of mathematical modeling and related knowledge. The following are some knowledge that usually need to be mastered in advance:
1. Mathematical analysis : understand basic concepts and methods such as calculus, differential equations and integrals, and be able to use calculus knowledge to model and analyze problems.
2. Probability and statistics : master the basic concepts of probability theory and mathematical statistics, distribution, parameter estimation and hypothesis testing, and be able to use probability and statistical methods to deal with random and uncertain problems.
3. Linear algebra : Familiar with matrix operations, linear equations, matrix eigenvalues and eigenvectors, etc., and be able to use linear algebra knowledge for data processing and model solving.
4. Numerical calculation : Understand the basic methods of numerical calculation, such as interpolation, numerical integration, numerical solution of ordinary differential equations, etc., and be able to use numerical calculation methods to solve practical problems.
5. Optimization methods : Familiar with optimization theories and methods, such as linear programming, integer programming, nonlinear programming, etc., and be able to use optimization methods to model and solve problems.
6. Data processing and analysis : Possess the ability of data processing and analysis, including data cleaning, data visualization, data fitting and statistical analysis.
7. Programming skills : master at least one programming language, such as Python, MATLAB, etc., and be able to write programs for calculation, simulation and data processing in the process of modeling and problem solving.
At the end of the article, there is a catalog of specific learning knowledge
3. Required software tools
1. Mathematical modeling software : Commonly used mathematical modeling software includes MATLAB , Mathematica and Maple, etc. These software provide a rich library of mathematical functions and tools that can be used to build mathematical models, solve equations, perform data analysis and visualization, and more.
2. Statistical analysis software : In terms of data processing and statistical analysis, commonly used software includes SPSS , R, and statistical libraries in Python (such as NumPy and pandas). These software provide various statistical methods and tools for data cleaning, descriptive statistics, hypothesis testing, regression analysis, etc.
3. Optimization software : For optimization problems, commonly used software includes LINGO , Gurobi, CPLEX, and optimization toolboxes in MATLAB. These software provide a variety of optimization algorithms and tools for modeling and solving optimization problems such as linear programming, integer programming, and nonlinear programming.
4. Programming language and environment : Proficiency in at least one programming language is very helpful, such as Python, MATLAB and R, etc. These programming languages provide rich mathematical and scientific computing libraries, which can be used for mathematical modeling, data processing, algorithm implementation, etc.
5. Data visualization tools : Data visualization is an important means of displaying analysis results and model outputs. Commonly used data visualization tools include MATLAB's plotting functions, matplotlib and seaborn libraries in Python, and visualization software such as Tableau.
6. Equation editing software
4. Thesis template, search literature, search data
1. Thesis templates should be read in advance to see more first-prize works over the years.
2. Use some resource websites at home and abroad
. 3. Some topics will provide data, and crawl if there are no topics. The source of the search must be reliable.
Next, the knowledge catalog will be explained according to the principle and code operation
一 线性规划（运输问题、 指派问题、对偶理论与灵敏度分析、投资的收益和风险）
二 整数规划（概论、分枝定界法、0 −1整数规划、蒙特卡洛法（随即取样法）、指派问题的计算机求解、生产与销售计划问）
三 非线性规划（非线性规划、无约束问题、约束极值问题、飞行管理问题）
四 动态规划
五 图与网络模型及方法（最短路问题、 树、匹配问题、Euler 图和 Hamilton 图、最大流问题、最小费用流及其求法）
六 排队论模型
七 对策论
八 层次分析法
九 插值与拟合（插值方法、曲线拟合的线性最小二乘法、最小二乘优化、曲线拟合与函数逼近）
十 数据的统计描述和分析
十一 方差分析
十二 回归分析（一元线性回归、多元线性回归、非线性回归）
十三 微分方程建模
十四 稳定状态模型
十五 常微分方程的解法
十六 差分方程模型（蛛网模型、商品销售量预测、遗传模型、遗传模型）
十七 马氏链模型
十八 动态优化模型
十九 神经网络模型
二十 偏微分方程的数值解
二十一 目标规划
二十二 模糊数学模型
二十三 现代优化算法（模拟退火算法、遗传算法、禁忌搜索算法、改进的遗传算法、蚁群算法）
二十四 时间序列模型（移动平均法、指数平滑法、差分指数平滑法、自适应滤波法、趋势外推预测方法、平稳时间序列）
二十五 灰色系统理论（关联分析、优势分析、灰色模型 GM、灰色预测）
二十六 多元分析（聚类分析、主成分分析、因子分析、判别分析、典型相关分析、对应分析、多维标度法）
二十七 偏最小二乘回归分析
二十八 存贮论
二十九 经济与金融中的优化问题（经济均衡问题及其应用、投资组合问题、市场营销问题）
三十 生产与服务运作管理中的优化问题
三十一 支持向量机
三十二 作业计划