National Undergraduate Mathematical Contest in Modeling (hereinafter referred to as "Mathematical Contest in Modeling") is a national college student subject competition sponsored by the China Higher Education Association, which aims to promote students' learning and research in mathematics and related subjects, and cultivate innovative spirit and comprehensive quality Activity. The competition is generally held in October every year, and it is currently one of the largest and most influential subject competitions for college students in China.
Participants in the Mathematical Modeling Competition need to form a group of 3 people to participate in the modeling and problem solving of real problems provided by the sponsor. Participants need to conduct in-depth analysis of the problems and give solutions through research, model building, solution and result analysis within the specified time. At the same time, the contestants also need to present their research results to the judges through written reports and oral defenses.
The topics of the Mathematical Modeling Contest come from a wide range of sources, covering economics, management, natural sciences, engineering technology, social sciences and other fields, and the topics involve mathematics, statistics, computer science, operations research and other disciplines. Participants need to have strong mathematical literacy, rich knowledge reserve, independent thinking and teamwork ability, and improve their subject application ability and comprehensive quality through practice.
This article refers to the sharing of mathematical modeling learning materials:
Link: https://pan.baidu.com/s/1Z2xSG0gvwX8NnzxBRagWRA?pwd=zvdi
Extraction code: zvdi
Algorithms commonly used in the National Undergraduate Mathematical Contest in Modeling include the following :
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Basic algorithms: such as search algorithms (depth-first search, breadth-first search), sorting algorithms (quick sort, merge sort, heap sort, etc.), greedy algorithms, dynamic programming, etc.
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Numerical calculation methods: such as numerical solutions of ordinary differential equations (Eulerian method, Runge-Kutta method, etc.), numerical solutions of partial differential equations (finite difference method, finite element method, etc.), interpolation and fitting, etc.
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Optimization algorithms: such as linear programming, nonlinear programming, integer programming, stochastic simulated annealing algorithm, genetic algorithm, simulated annealing algorithm, etc.
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Statistical analysis methods: such as regression analysis, variance analysis, time series analysis, cluster analysis, principal component analysis, etc.
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Graph theory algorithms: such as shortest path algorithm (Dijkstra algorithm, Floyd algorithm, etc.), minimum spanning tree algorithm (Prim algorithm, Kruskal algorithm, etc.), network flow algorithm (maximum flow, minimum cut, etc.), etc.
The method of the National Undergraduate Mathematical Contest in Modeling can generally be divided into the following steps:
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Understand the problem: First, you need to carefully read the problem description and data provided by the competition, understand the background, goals and constraints of the problem, and ensure a comprehensive understanding of the problem.
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Analyzing the problem: analyze the structure and characteristics of the problem, and choose a suitable model and method to solve it. A variety of models, such as mathematical models, computational models, and statistical models, are usually required.
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Model building: convert the problem into a mathematical model, determine the assumptions and variables of the model, and formulate corresponding solving strategies and algorithms.
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Programming solution: use computer programming language to convert the model into a program, and obtain the result through computer solution.
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Analysis results: analyze the solution results, evaluate the rationality and practicability of the model, and visualize the results.
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Writing a thesis: Write a thesis on the problem-solving process, model building, program design, result analysis, etc., and clearly describe the problem-solving process and results.