Basic mathematics: the foundation in the foundation
Mathematics is a basic subject, and basic mathematics is the foundation of foundation. Its research field is broad and theoretical. Mainly refers to geometry, algebra (including number theory), topology, analysis, equations and some branches of mathematics developed on this basis. Specific branches include: projective differential geometry, Riemannian geometry, global differential geometry, harmonic analysis and its application, wavelet analysis, partial differential equations, applied differential equations, algebra and so on.
Research hotspot
Tobia (Ph.D. student in computer science in 2007, majoring in basic mathematics): There is no doubt that people who choose basic mathematics as their research direction will really take mathematics as their career, because their work is often ten or even a hundred years ahead of the applied mathematics of this era. Some people think it's incredible, but they don't hesitate. The hottest direction now is mathematical physics. In fact, various mathematical tools are used to solve difficult physical problems. Among these mathematical tools, algebraic geometry is the most popular. Because of its close connection with physics, it can be expected that this direction will always be a hot research field.
University recommendation
Mathematics Department of Zhejiang University was founded in 1928, with a long and glorious history. The "Chen Su School" founded by Chinese famous mathematicians Professor Chen and Professor Su once enjoyed a world-renowned reputation. In 2007, the mathematics discipline of Zhejiang University was recognized as a first-class national key discipline by the Ministry of Education, and the discipline leader was Professor Liu Kefeng, an internationally renowned mathematician. Basic mathematics is the first batch of master's degree awarding points and postdoctoral mobile stations in China. It is a part of the first batch of national key disciplines (combined with applied mathematics), and a national training base for science talents in mathematics has been established. Universities with strong basic mathematics disciplines include Fudan University, Nankai University, Peking University, Tsinghua University, Sun Yat-sen University, Nanjing University and Sichuan University.
Applied mathematics: a hot spot in the unpopular field
Professional contour
Applied mathematics is the most extensive of the five subjects of mathematics. Strictly speaking, calculation, operation and statistics are all disciplines of applied mathematics, but the meaning of applied mathematics we refer to now is much narrower, and it is basically divided into two major directions: computer graphics and images (CAGD) and wavelet analysis. CAGD mainly refers to the use of modern mathematical methods to study the theory and application of image graphics, specifically in the direction of image transformation and compression, deformation and generation of graphics, differential equations, computational geometry, scientific calculation and so on. Computer graphics images mainly include image processing, computer graphics, computer-aided geometric design, scientific calculation and medical image reconstruction. Wavelet analysis refers to fractal geometry, wavelet analysis and approximation theory.
Research hotspot
Lin Binbin (Ph.D. candidate in applied mathematics in 2007): Speaking of the research hotspots of applied mathematics, it should be said that there are many hotspots in every direction, such as the processing of three-dimensional graphics. In the future, the making software of image search and image database will be more popular, and the reconstruction of three-dimensional model with two-dimensional information and the connection between computer automatic processing and artistic creation should be the mainstream in graphics.
University recommendation
The School of Mathematics and System Science of Xinjiang University undertakes the national key discipline "Applied Mathematics" and the Xinjiang University "2 1 1 Engineering" key discipline "Applied Mathematics and System Engineering". Among the more than 200 universities in China that recruit master's degree students majoring in applied mathematics, Xinjiang University ranks seventh in applied mathematics discipline strength, following Peking University, Tsinghua University, Fudan University, Zhejiang University, Nankai University and Sichuan University. The reason why Xinjiang University is specially recommended is that Xinjiang University, together with the seven famous universities mentioned above, is a key advantage discipline unit of applied mathematics. However, as a non-autonomous three-district college, the admission score is much lower than that of a prestigious school, and the cost performance of applying for the exam is higher.
Computational mathematics: doing calculations for physics and engineering.
Professional contour
Since the 20th century, due to the wide application of computers, computational mathematics has made great progress, and the development of computational mathematics theory has promoted the progress of computer and information science. Although computational mathematics has not been paid enough attention in China, it is one of the hottest subjects abroad. The main research directions of computational mathematics include numerical functional analysis and continuous computational complexity theory, numerical differentiation and finite element, nonlinear numerical algebra and complex dynamic system, numerical solution of nonlinear equations, numerical approximation theory, computer simulation and information processing, and mathematical modeling and calculation of engineering problems. At present, the best development direction has been combined with the CAGD direction of applied mathematics, because the core of both is numerical calculation and computer programming is the means.
Research hotspot
Cai Xiaohao (Ph.D. student of computational mathematics in 2006): Computational mathematics is a very important subject at home and abroad, mainly studying scientific engineering calculation and other issues. Because interdisciplinary research brings many new research directions, there are many research directions of computational mathematics. Now the hottest direction should be numerical solutions of differential equations, numerical algebra, manifold learning, especially manifold learning, which has been hot for several years and is expected to continue to be hot.
University recommendation
Xi Jiaotong University is one of the first three universities in China to establish computational mathematics, which is a national key discipline. On the basis of maintaining the advantages of the main research directions of applied mathematics and computational mathematics, we attach importance to and strengthen the research on the mathematical basis of information science, scientific calculation, modern optimization, data analysis and statistical calculation, numerical simulation of electronic systems, mathematical modeling of biological systems, and have a group of experts and scholars such as Cheng Zhengxing, Hou, Ma and Zhang Ke. Universities with strong computational mathematics disciplines include Peking University, Jilin University, Dalian University of Technology, Shanghai University, Shandong University, Xiangtan University, Northwestern Polytechnical University and Hunan University.
Logistics and Control Science: Providing New Ideas and Methods for Modern Science and Technology
Professional contour
Logistics and control science is a very practical subject. Operation and control are two related aspects, both centered on system optimization. The research directions of operational research mainly include mathematical finance, financial risk management, control theory, algorithm design and analysis, mathematical planning and so on. Cybernetics is a discipline that studies the regulation laws of various systems. It is an interdisciplinary subject formed by the mutual penetration of automatic control, communication technology, computer science, mathematical logic, neurophysiology, statistical mechanics and behavioral science. Operational cybernetics embodies the overall development trend of modern science and provides new ideas and scientific methods for modern science and technology. China began to translate and introduce cybernetics works in the early 1960s, but in recent years it began to conduct extensive and in-depth research, and began to use cybernetics to establish mathematical models of economy, population, energy and production management, such as input-output model and population model, and achieved good results.
Research hotspot
Wang Songjing (Ph.D. student in operational research and cybernetics in 2007): I know the direction of operational research, such as engineering control model, financial model and logistics planning. Financial mathematics is the hottest now, and it will definitely be even hotter in the future. Portfolio optimization has not been taken seriously yet, but it will certainly be very popular in the future. The employment prospect of operational research is broad, but for ordinary companies, the majors of operational research and cybernetics far exceed the actual needs, so choosing a research center is a better way out.
University recommendation
In 2007, the mathematics discipline of Shandong University was rated as "the national first-class key discipline", and its operational research and control science discipline surpassed Tsinghua, Fudan, Zhejiang, Nankai and other famous schools in one fell swoop in the ranking of China Scientific Evaluation and Research Center (2006-2007), ranking first. Professor Peng Shige has made original achievements in the research of maximum principle of stochastic optimal control system, backward stochastic differential equation theory and nonlinear mathematical expectation theory, and has been highly praised by colleagues at home and abroad. Professor Wu Zhen is not only the main theoretical topic in stochastic analysis, but also has a strong application background in financial mathematics and stochastic control. The main research direction is the theory of forward and backward stochastic differential equations. Universities with strong disciplines in operational research and control science include Fudan University, Shanghai University, Chongqing University, Beijing Jiaotong University, Harbin Institute of Technology, Northeastern University and East China Normal University.
Probability theory and mathematical statistics: exploring the laws in random phenomena
Professional contour
In nature and human daily life, randomness is very common, such as the winning number of each welfare lottery. Probability theory is to make an objective and scientific judgment on the possibility of a certain result of random phenomena according to the statistical laws of a large number of similar random phenomena, and to make an objective and scientific judgment and quantitative description on the possibility of this occurrence; Compare these possibilities. Mathematical statistics is to apply probability theory to study the regularity of a large number of random phenomena, give strict theoretical proof to the statistical methods obtained through a certain number of scientifically arranged experiments, and judge the applicable conditions, methods, formulas and conclusions of various methods, so that people can judge whether a judgment can be guaranteed to be correct with considerable probability from a group of samples and can control the probability of error.
Research hotspot
Luo Yan (Ph.D. student in Probability Theory and Mathematical Statistics in 2007): Now the research of applied statistics is getting hotter and hotter, getting closer to life, and getting more and more attention from all walks of life. But let's not forget that the basis of statistics is probability. The research on probability is still worthy of attention.
Song Gaoyang (Ph.D. student in probability theory and mathematical statistics in 2007): The main directions of statistics are stochastic theory, data analysis and financial statistics. As far as the current situation is concerned, data analysis and data mining will be more popular because of their wider applications. If graduate students choose to work after graduation, applied subjects are the best choice.
University recommendation
After three generations, the research group of probability theory in Beijing Normal University has a 40-year tradition and accumulation, including famous experts and scholars such as Chen Mufa, Li Zenghu, Zhang Yuhui and Wang Fengyu. This research group is praised as "China School of Markov Process" or "Peking School" by two international mathematical review magazines. His main research interests are interactive particle systems, stochastic analysis, and measure-valued Markov processes. Universities with strong disciplines of probability theory and mathematical statistics include Nankai University, Central South University, Northeast Normal University, Wuhan University, Huazhong University of Science and Technology, and University of Science and Technology of China.
The big tree of mathematics has flourished after years of development. Generally, there are dozens or even hundreds of professors or lecturers in the mathematics department of key universities, and everyone's research direction is different. Their differences are like Leonardo da Vinci's eggs. With the crossing and development of various disciplines, more new branches have emerged. It is precisely because of this that mathematics is so colorful.