1. Basic knowledge of mathematics:

Calculus: Calculus is the basis of mathematical modeling, including concepts such as derivative and integral. It is used to describe the rate of change, solve extreme value, integral area and other problems.

Linear algebra: Matrix operation and solving linear equations in linear algebra are very important for data processing and solving in modeling problems.

Probability theory and mathematical statistics: used to describe uncertainty and randomness, including probability distribution, expectation, variance, maximum likelihood estimation, etc.

2. Mathematical modeling method:

Ordinary differential equation (ODE) and partial differential equation (PDE): They are used to describe the evolution law of dynamic systems and are often used in ecological models and physical models.

Optimization theory: used to solve optimization problems, including linear programming, integer programming, nonlinear programming and other methods.

Graph theory and network flow: used to solve problems such as network optimization and path planning, including algorithms such as shortest path, minimum spanning tree and maximum flow.

Discrete mathematics: including set theory, graph theory, logic, etc. , which is used to deal with discrete problems, such as coloring of graphs, traveling salesman problem, etc.

3. Computing tools and programming languages:

Mathematical software: such as MATLAB, Mathematica, etc. , used for symbolic calculation and numerical simulation.

Programming languages: Python, R, etc. , used for data processing, numerical calculation and modeling.

4. Background knowledge of practical problems:

Domain knowledge: you need to know the specific domain knowledge involved in modeling problems, such as ecology, physics, economics, etc.

Data analysis and processing: Learn to use statistical methods and data processing skills to clean, transform and analyze real data.

5. Teamwork and document writing:

Teamwork: Mathematical modeling is usually teamwork, which requires learning to cooperate with teammates, work together and solve problems together.

Document writing: Learn to write a report on mathematical modeling, clearly presenting the problem analysis, modeling process, result analysis and conclusion.

6. Practical experience and problem-solving ability:

Practice project: Participate in actual mathematical modeling competitions, projects or research, and accumulate practical experience.

Problem-solving ability: exercise your ability to analyze and solve problems, and cultivate your ability to find, ask and solve problems.