Curriculum |
| Course | Introduce |
Core courses | The Course of Functional Analysis | 1. nonlinear operators in infinity dimensional normed linear spaces 2. the basic theory of topology linear spaces 3. Frechet-derivative and Gateaux-derivative of nonlinear operators. 4. topology degree theory and its applications 5. Variational methods and its applications |
Elements of Algebra | Chapter 1 Groups. It includes the related definitions and properties of groups, cyclic groups, normal subgroups, quotient groups, homomorphism theorems, direct sums, and decompositions, etc. Chapter 2 Rings. It includes the related definitions and properties of rings, ideas, quotient rings, and homomorphism theorems, etc. Chapter 3 Modules. It includes the related definitions and properties of modules, free modules, and projective modules, etc. |
Specialized courses | Artificial Neural Network | Artificial Neural Networks is a technology that involves many disciplines: neurosciences, mathematics, statistics, physics, computer science, and engineering. As such, neural networks find applications in such diverse fields as system modeling, time series analysis, pattern recognition, signal processing, and control. The primary purpose of this course is to provide a comprehensive introduction to ANN. Introduction of ANN, learning processes, perceptrons, radial basis function network, support vector machines, principal component analysis, and self-organizing maps are all included in the course. |
Numerical Linear Algebra | Elementary matrices; Matrix decompositions; direct methods for linear system of equations; iterative methods for linear system of equations; QR method for matrix eigenvalue problem; QZ method for generalized eigenvalue problem; Lanczos method; special topics. |
The Finite Difference Methods for Partial Differential Equations | The finite difference method for partial differential equation is one of the Master Degree Courses that represents the theory of finite difference methods for parabolic equation. Students can learn basic ideas and methods to solve partial differential equation. Grids, finite difference discretization, convergence, stability, numerical error analysis, and so on, are all included in the class. |
The Finite Element Method for Elliptic Problems | Theory of Sobolev Spaces，Variational formulation of elliptic boundary value problems，The construction of finite element spaces，Polynomial interpolation theory，Error analysis of finite element methods.. |
Optional courses | Matrix Computations | Numerical methods for polynomial eigenvalue problem, periodic matrix-pairs eigenvalue problem，multivariate eigenvalue problem, multiparameter eigenvalue problem, and structural matrix eigenproblem. Projection methods for linear system of equations. Special topics. |
Finite Element Method for Evolution Equations | Standard Galerkin method，Galerkin method based on more general approximation，Smooth data error estimates，Non-smooth data error estimates，Maximum norm error estimates，Negative norm error estimates，General full discrete schemes. |
Mathematical Models and Numerical Methods of Fluid Dynamics | The mathematical models and numerical methods of fluid dynamics is a selective course that represents the fundamental theory and methods for simulating of fluid dynamics by comprehensive introduction of mathematical models and its numerical methods of groundwater quality. Phenomena, mechanism, mathematical models, and numerical methods of hydrodynamic dispersion in porous media, are all included in the class. |
Least Squares Problems | The ordinary least squares, Constrained least squares, the total least squares, and generalized inverses. |
Modern Theory of Partial Differential Equations | The course introduces the Sobolev space Hs(W) and the partial differential equations in Hs(W), and the main course is the following: 1. Introduce the space Hs(W) and its main characteristic: completeness, reflexivity, imbedding theory etc. 2. the existence of solutions for partial differential equations under suitable conditions, and the regular estimate, where we will introduce variational methods, semi-group methods, Fourier transformation, Galerkin methods etc. |
Introduction to Artificial Intelligence | Artificial Intelligence is a subject on simulating human’s intelligence by the computer. It develops intelligent machines or intelligent systems and lets them simulate, extend and expand human’s intelligence by artificial methods and technologies in order to realize some intelligent actions. An introduction to artificial intelligence introduces basic concepts, principles, methods and simple applications of artificial intelligence. It lays a foundation for graduate students to further research on the related fields of artificial intelligence. |
Parallel Algorithms and Some New Numerical Methods | Fractional steps parallel finite difference methods， Domain decomposition methods for non-overlapping subdomains，Domain decomposition methods for overlapping subdomains，Multigrid method，Other parallel algorithms，Finite volume element method, Discontinuous Galerkin finite element method. |
Analysis and Control System Based on Data | The mathematical model of the control system, method of data collection, data analysis technology and software, automatic control system analysis and design, analysis and control of system stability. |
Inverse Problems in Fluid Modeling | The inverse problems in fluid modeling is a selective course that involves the application of computational mathematics, mathematics programming, and statistics in groundwater modeling. By the introduction of theory and methods of inverse problem in groundwater modeling, students can learn basic ideas and methods to solve the real problem in fluid dynamics. Concepts of inverse problems, solving inverse problems with indirect methods, or direct methods, or adjoint state method, or stochastic methods, and so on, are all included in the course. |
Mathematical Methods for Data Processing | Fourier transformation; Wavelet method; Empirical mode decomposition; Statistical methods. |
Elliptic Curve Cryptography | Structure of finite fields, Polynomials over finite fields, Factorization of polynomials, Exponential sums, linear recurring sequences, Theoretical applications of finite fields, Applications to coding and cryptology. |
Finite Fields and their Applications | Structure of finite fields, Polynomials over finite fields, Factorization of polynomials, Exponential sums, linear recurring sequences, Theoretical applications of finite fields, Applications to coding and cryptology. |
Iterative Methods for Solving Linear Systems | Background in linear algebra, Kyrlov subspace methods and preconditioned Krylov subspace methods. |