1. Pure Mathematics: Study the basic concepts, principles and methods of mathematics itself, such as number theory, algebra, geometry, topology, etc.

2. Applied mathematics: applying mathematical theories and methods to solve practical problems, such as numerical analysis, operational research, probability theory and mathematical statistics, and optimization methods.

3. Computational Mathematics: Study the cross fields of computer science and mathematics, such as algorithm design, computational complexity theory, computer graphics, etc.

4. Statistics: Study the collection, analysis, interpretation and display of data, and the methods of inferring general features from data, such as descriptive statistics, inferential statistics and regression analysis.

5. Financial Mathematics: Studying mathematical models and methods in financial markets, such as option pricing, risk management, portfolio optimization, etc.

6. Engineering mathematics: apply mathematical theories and methods to practical problems in engineering field, such as cybernetics, signal processing, optimal design, etc.

7. Physics: Studying the basic laws of matter and energy depends on mathematics, such as quantum mechanics, classical mechanics, electromagnetism and so on.

8. Chemistry: To study the nature, composition and changing process of matter, many experiments and theoretical analysis need mathematical tools, such as quantum chemistry, thermodynamics and dynamics.

9. Biology: Students study the structure, function and evolution of objects, many of which can be described by mathematical models, such as genetics, ecology and molecular biology.

10. Economics: To study the allocation and utilization of resources and the operation of market mechanism, many theoretical and policy analyses need mathematical methods, such as microeconomics, macroeconomics and econometrics.