1. Model establishment and analysis: Mathematical model is the basis of economic research. By establishing mathematical models, economists can abstract and simplify economic phenomena, so as to better understand and explain economic behavior. For example,

2. Optimization: Many problems in economics involve the allocation and utilization of resources, and the optimization problem needs to be solved. Mathematical methods such as linear programming, nonlinear programming and dynamic programming play an important role in these problems.

3. Probability theory and statistics: In economics, many phenomena are random. Probability theory and statistics provide economists with tools to analyze and deal with these random phenomena. For example, regression analysis, time series analysis and Bayesian inference are all applications of statistics in economics.

4. Calculus and difference equations: Calculus and difference equations are widely used in economics, such as marginal effect analysis, elasticity analysis and equilibrium analysis. In addition, the difference equation is also used to study dynamic economic systems, such as economic growth model and monetary policy transmission mechanism.

5. Econometrics: Econometrics is an important branch of economics, which mainly studies how to use mathematical and statistical methods to analyze and model economic data. Econometric methods include regression analysis, panel data analysis and instrumental variable method.

6. Game theory: Game theory is a mathematical theory to study the mutual restriction and cooperation among multiple decision makers. In economics, game theory is widely used in market competition, cooperation and conflict, system design and other fields.

7. Financial mathematics: Financial mathematics is a mathematical theory that studies the pricing of financial markets and financial products. Option pricing, risk management, portfolio optimization and other issues all need to use financial mathematics methods.

8. Micro-econometrics: Micro-econometrics mainly studies the relationship between individual economic behavior and economic phenomena. It uses microscopic data (such as household survey data and enterprise data). ) to estimate the economic model, thus revealing the causal relationship behind economic phenomena.