The following directions of graduate students in mathematics department may be helpful to you!
Basic mathematics: the foundation in the foundation
Professional contour
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.
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.
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.
Logistics and Control Science: Providing New Ideas and Methods for Modern Science and Technology
Professional contour
Operation and control science is a highly 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.