1. Pure mathematics: This is the basis of mathematics, including algebra, geometry, analysis, number theory and other branches. The goal of pure mathematics is to understand the basic structure and concepts of mathematics and the relationship between them.
2. Applied Mathematics: This is the field of applying mathematical theory to practical problems. The research fields of applied mathematics are very extensive, including physics, engineering, economics, biology, computer science and so on.
3. Computational Mathematics: This is the field of studying how to use computers to solve mathematical problems. The methods and techniques of computational mathematics are widely used in various scientific and engineering problems.
4. Probability statistics: This is the field of studying the regularity of random phenomena. Probability and statistics methods are widely used in natural science, social science, engineering technology and other fields.
5. Financial Mathematics: This is the field of applying mathematical methods to study financial markets and financial products. The methods and techniques of financial mathematics are widely used in risk management, investment decision-making, derivative pricing and other issues.
6. Operational Research: This is the field that studies how to make the most effective use of resources to solve complex problems. The methods and techniques of operational research are widely used in logistics, production, scheduling, network optimization and other issues.
7. Data science: This is the field of studying how to extract useful information from a large number of data. The methods and technologies of data science are widely used in machine learning, artificial intelligence, big data processing and other issues.
The above is only part of the research direction of mathematics. In fact, with the development of science and technology, the application field of mathematics is constantly expanding, and new research directions are constantly emerging.