1, basic mathematics

Basic mathematics, also called pure mathematics, is the core of mathematics. Its ideas, methods and conclusions are the foundation of the whole mathematical science and the think tank of natural science, social science and engineering technology. Basic mathematics includes mathematical logic, number theory, algebra, geometry, topology, function theory, functional analysis, differential equations and many other branches. , but also in the production of new research areas, the scope is extremely wide. Generally speaking, it is far beyond a research category in the general sense.

2. Computational mathematics

Computational mathematics is the theory and algorithm to study the numerical solutions of mathematical problems in the field of science and technology, especially the numerical solutions of electronic computers, with special emphasis on the research of efficient and stable algorithms. The research on efficient computing methods is as important as the development of high-speed computers. In addition, numerical simulation can be used to reduce or even replace some large-scale experiments that are expensive or even difficult to realize. In recent years, with the rapid development of electronic computers, new branches of disciplines such as symbolic calculus, machine proof, computer-aided design and mathematical software have emerged, and combined with other fields, interdisciplinary disciplines such as computational mechanics, computational physics, computational chemistry and computational biology have been formed.

3. Probability theory and mathematical statistics

Probability theory and mathematical statistics are subjects that study the inherent regularity of random phenomena. Probability theory aims to study the quantitative laws of random phenomena in theory and is the basis of mathematical statistics. Mathematical statistics is a subject that studies how to collect, analyze and use random data effectively from the mathematical point of view, which provides a broad world for the practical application of probability theory. Probability theory and mathematical statistics promote each other and play an important role in science and technology, industrial and agricultural production, economy and finance, population health and environmental protection with the help of computer technology. The penetration of probability and statistics into various disciplines has become one of the remarkable characteristics of the development of modern science.

4. Applied Mathematics

Applied mathematics is an important bridge between mathematics and the real world, which mainly studies mathematical problems in natural science, engineering technology and humanities and social sciences, including important fields such as information, economy, finance and management, and the reaction of mathematics to the research and solution of problems in these fields; Including the establishment of corresponding mathematical models, the use of mathematical methods to solve practical problems, and the study of mathematical theories with practical background and application prospects. Since the Second World War, applied mathematics has developed rapidly, and its ideas and methods have profoundly influenced the development of other sciences, and promoted the birth and growth of some important comprehensive disciplines (such as nonlinear science). At the same time, in the process of studying and solving practical problems, new and important mathematical problems are constantly emerging, which effectively promotes the development of mathematics itself.

5. Operations Research and Cybernetics

Operations research and cybernetics take mathematics as the main tool to study and solve the problems of modeling, analysis, planning, design, control and optimization of social, economic, financial, military, production management, planning and decision-making systems from the viewpoint of system and information processing. It is a subject that includes many branches. Operations research combines mathematics, computer science and management science, and provides theoretical basis for the planning, design, management, operation and optimal decision-making of various systems through the study of modeling methods and optimization methods. At present, control theory is at the forefront of the cross development of mathematics, computer science, engineering science and life science, and it is the theoretical basis of modern technology represented by automation, informationization, robotics, computer and aerospace technology.