Two pathways are available in Fundamental Mathematics
Pathway A: Master of Science in Functional Analysis and Application
This pathway focuses on differential inclusion theory and neural network optimization computation theory, which projects new-type set-valued integral operators to settle the existence of solution for random multi-value periodic problem and applies its results to periodic feedback control system. This pathway also offers research on controllability of control system presented by integro-differential evolution inclusion equation which resolves new-style neural network model for non-smooth optimization by differential inclusion theory.
Pathway B: Master of Science in Qualitative Theory of Differential Equation
This pathway covers research on some mathematical problems of compressible fluid, incompressible fluid and other relevant flow patterns, including existence, uniqueness and regularity of solution. It also studies well-posedness of solution of Boussinesq equation when initial curl equaling to initial value of vortex layer or in L-space. It offers researches on second order and high-order nonlinearity boundary value problems to provide theoretical basis for concrete solutions by topological functional theories, i.e., topological degree theory, screw theory, operator theory, and critical point theory.
Two pathways are available for Computational Mathematics
Pathway A: Master of Science in Numerical Algebra and Information Encoding
This pathway offers research on linear and non-linear equations of different types of constrained matrices set problems in model updating and signal restoration, solution of structured matrix equation problems, relevant theory and effective numerical methods for algebraic inverse eigenvalue problems. Based on the research achievements of numerical algebra and computational complexity theory, it covers research on structure of cryptographic function and its security analysis, design method, security analysis, formal proof of digital signature, and cryptographic protocol. On the basis of trust chain, it aims at studies on construction of trust service method for cloud computing, design of secure multi-party computation solution for particular application.
Pathway B: Master of Science in Constrained Matrix Equation and Numerical Solution of Partial Differential Equation
This pathway covers research on the solution of constraint set matrix equation, structure of solution of constrained matrix equation, existence of solution, existence condition, expression of solution, variational inequality problem for numerical solution of differential equation, constrained optimization problem of FEM simulation of solution to ground state and excited state of GP equation and numerical simulation for mechanical problem.
Three pathways are available for Probability Theory and Mathematical Statistics Computational Mathematics:
Pathway A: Master of Science in Data Analysis
This pathway covers analysis and research of qualitative and quantitative data, excavation for potential information of data, exploration to internal structure of data, establishment of relevant mathematical model and development of application software on the basic of series of theories and methods, i.e., multivariate statistical analysis, multi-criteria neural network optimization, fractal and geostatistics, etc. It also launches applied studies on geological survey and mineral exploration according to the research results in mathematical statistics.
Pathway B: Master of Science in Financial Mathematics
This pathway offers research on extreme value distribution and risk value of financial Return On Assets (ROA). It aims at estimations on tail of nonlinear Auto-Regressive Conditional Heteroscedastic (ARCH) model with fat-tail information against financial risks. Based on multi-criteria neural net work optimization and fractal theory, this pathway also aims at analysis and research of economic data, establishment of relevant mathematical model, exploration, and analysis for microstructure of the future market.
Pathway C: Master of Science in Biostatistics
This pathway focuses on analysis and explanation for varieties of biological phenomena and experimental data. It also covers modeling, covariate selection, parameter estimation and nonparametric estimation of recurrent event data as well as analysis and research of asymptotic behavior.
Sub-discipline: Applied Mathematics
This sub-discipline is one of key disciplines sponsored by Beijing Municipality.
Four pathways are available for this sub-discipline:
Pathway A: Master of Science in Differential Equation and High Performance Scientific Computing
This pathway covers research on high-performance scientific computing algorithm based on physical background of concrete conditions; solution structure of differential equation, equilibrium solution of radiation hydrodynamics equations and blow-up problem of solution; complex flow field and quantum effect through theoretical analysis and numerical simulation technique; application of image restoration on the basis of differential equation theory and numerical method just like level set method.
Pathway B: Master of Science in Nonlinear Analysis and Application
This pathway, based on soliton theory and relevant theories in algebra and group theory, offers research on integrability condition of nonlinear evolution equation with variable coefficients, solution structure of Wronski and Gramm determinant, relevant solution structure of Pfaffian coupling-mode equation by constructing nonlinear coupled-mode evolution equation with variable coefficients. This pathway also focuses on studies on analytical solution of nonlinear evolution equation with variable coefficients and its relevant coupling-mode equation in the field of optical fiber communication, hydrodynamics, biology, oceanography and atmospheric dynamics.
Pathway C: Master of Science in Economics Game Theory
This pathway focuses on game theory problem of phenomena and behavior in modern economics. It involves in existence and stabilization of Nash equilibrium and its solution. This pathway, combining topology with analysis, offers studies on continuous selection and fixed point for necessary and sufficient existence conditions of Nash equilibrium in topological space, and then conducts further research on existence of Nash equilibrium.
Path D: Master of Science in Image and Information Processing
In the field of image reconstruction, this pathway covers research on symmetrical structure, its block grouping iterative correction schemes and deep structure based on projection data. According to fundamental solution theory of linear equation, it offers qualitative research on dependency relationship between calculating point and projection data. This pathway aims to construct new algebra iterative method and fast iterative algorithm with direct imaging. In the field of computer stereo vision, this pathway addresses relationship between unique geometric characteristic on two-dimensional awareness surface and depth perception in vision system in real environment. It covers introduction of visual model with whole light field, digitized virtual aperture focus and discrete model for 3D reconstruction with field of view; exploration and utilization of reconstruction to characterize 3D depth-of –field information in narrow viewing angle; establishment of expression method of planar stereo scene.