Introduction to Basic Mathematics of Hunan Normal University

1, the history and present situation of this discipline.

Basic mathematics is a basic research discipline (Qian Xuesen) related to the development of the whole science and technology. Since its establishment, Hunan Normal University has been devoted to the construction and development of this discipline. Over the past 50 years, this discipline has trained a large number of mathematics talents for the country, especially for our province, mainly mathematics teachers, including a number of top-notch teaching and scientific research talents. A large number of graduate students who graduated from our school have become specialized and senior teachers in middle schools. In recent years, we have also sent a large number of high-level talents to universities at home and abroad. Many of them have become professors and researchers in famous universities and scientific research institutions at home and abroad. In 2000, researcher Sun Xiaotao, winner of the Prime Minister's Fund, was a 79-grade student in our school and has stayed in school to work.

In the past twenty years, the development speed of this subject has obviously accelerated. Under the guidance of school policy, scientific research is regarded as an important part of discipline construction, and the scientific research level and overall quality of teachers have been improved through vigorous introduction and active training. The structure of professional titles, academic qualifications and age has improved significantly, and scientific research and teaching have made great progress. It has formed a high-level discipline group with basic teaching as the core, covering the main subjects of mathematics and infiltrating theoretical physics and computer science.

This discipline began to recruit master students from 1982, and 1995 was granted the master's degree. 1996 became the key construction discipline in Hunan Province, and was granted the doctor's degree in 2000 and enrolled doctoral students in 2000. There are 30 professors and 32 associate professors in this discipline, including 2 national "young and middle-aged experts with outstanding contributions", 9 doctoral supervisors and 24 teachers with doctoral degrees. Become a training center for higher mathematics talents, focusing on training mathematics educators.

2. Characteristics and development prospects of main research directions.

(1) Ordinary differential equations and bifurcation theory: mainly study bifurcation and chaos theory of ordinary differential equations, stability of functional differential equations and bifurcation theory of singularities. This is a research field with rapid development, rich content and wide application at home and abroad in recent twenty years. The scientific research achievements in this direction have attracted the attention of colleagues at home and abroad and have been reported at international conferences many times.

(2) Algebra: mainly study algebraic representation theory and its application, algebraic structure of quantum groups, algebraic K theory and algebraic homology theory. The scientific research achievements in this field have been published in international conferences for many times and have been applied by peers at home and abroad, which has contributed to the establishment of algebraic representation theory of China School, and has taken the lead in studying koszal regular algebra with algebraic representation theory, which has a good research prospect for noncommutative algebraic geometry.

(3) Direction of function theory: mainly study harmonic analysis, function approximation, wavelet theory, analytic function space, complex variable culvert geometry, etc. Some famous conjectures have been solved many times, which has aroused widespread concern of domestic counterparts. There are also gratifying achievements in wavelet application research, and the application and industrialization of the achievements have been realized.

(4) Direction of mathematical equation: Mainly study the numerical method and finite element method of nonlinear partial differential equation. This research direction has achieved good results. The superconvergence method of finite element was first discovered in China, which played a very important role in the emergence and development of China's superconvergence school.

(5) Basic theory of probability and statistics: mainly study the theory and application of Markov process, super process, random flow, path space, high-dimensional statistics, diffusion process and random field. The research in this direction has attracted the attention of colleagues at home and abroad, and has been well received at home and abroad. The existence of super-regular Q process is solved, and the properties of Markov process after explosion are studied. The research on superprocess, stochastic flow and path space has attracted the attention of internationally renowned experts.

In addition, in recent years, a number of remarkable achievements have been made in the direction of combinatorial mathematics, and the research of Orsay mathematics has made a good start.

3. Advantages and disadvantages of similar disciplines in China at present.

This discipline has formed an academic team with famous domestic professors as the core, young and middle-aged professors and doctors as the main body, and an active atmosphere for scientific research and creation. It has formed a number of stable research directions, undertaken more than one key project of the National Natural Science Foundation and general project 10, and two research projects have entered the national "973" research project, and achieved a number of internationally advanced and influential work at home and abroad, some of which are in the international leading position. Compared with similar disciplines in China, the academic leaders have a high level and active scientific research work. In particular, there are a group of stable young academic leaders and academic backbones with great potential for scientific research and development. The main research direction of basic mathematics is a high-level and distinctive research team. Since 1996, about 40 papers have been published in key academic journals at home and abroad every year, and about 10 papers have been included in sci.