Generalized Functional Analysis

The course mainly introduces the basics of generalized function analysis such as distance spaces, bounded linear operators on Banach spaces and bounded linear operators on Hilbert spaces, and sets up several classes of function spaces and special function spaces on these spaces. The course also includes several classes of function spaces and a selection of special classes of operators on these spaces. The content of this course takes into account the requirements of each research direction of this degree program on the knowledge of generalized functional analysis. Through the study of this course, the students will have the knowledge of generalized functional analysis necessary for the study and research of their majors, and will lay the basic foundation for their professional study.

Matrix Theory

On the basis of solid knowledge of linear algebra, the course further introduces the paradigm of vectors and matrices, matrix decomposition, eigenvalue estimation and regression, matrix analysis, generalized inverse matrix and other contents. The course is designed to provide students with a solid foundation in linear algebra. Through the study of this course, students master the basic concepts, basic theories and basic operations related to matrices, cultivate students' abstract thinking and logical reasoning ability, improve mathematical literacy, emphasize the practical background of physics and mechanics of mathematical concepts while paying attention to mathematical argumentation, and cultivate students' ability of applying mathematical knowledge to solve practical engineering and technological problems. This will lay a solid foundation for further study and research in the direction of mathematics, especially applied mathematics and computational mathematics.

Fundamentals of Nonlinear Optimization

The course focuses on convex analysis as the basis, comprehensively and systematically introduces the basic theory of nonlinear optimization, not only thoroughly explaining (smooth and non-smooth optimization problems, semidefinite planning problems, etc.) the optimality theory of various types of optimization problems, the stability theory, sensitivity analysis, duality theory, and the relevant basis of convex analysis, etc., but also introducing the variational inequality problem, nonlinear complementary problems, and equilibrium constraints, mathematical planning problems and other equilibrium problems. Recent results on equilibrium problems such as variational inequality problems, nonlinear complementarity problems, and equilibrium constraints and mathematical programming problems are also presented. its applications, and other research advances. The course is problem-driven, goal-oriented and international, requiring students to master the basic knowledge and theories necessary for dealing with optimization problems, to understand the challenges and opportunities of the discipline, the current status of the research on related scientific issues and research progress at home and abroad, to make a solid foundation for the subsequent professional direction, and to cultivate the students' rigorous style of scientific research, the ability to analyze the problems or solve the practical problems by applying the professional knowledge. The program also cultivates students' rigorous scientific research style, ability to analyze problems or apply specialized knowledge to solve practical problems.

Advanced Mathematical Statistics

This course is the advanced version of the undergraduate mathematical statistics, which expounds the basic concepts of classical statistics, such as statistical structure, R-N derivatives, statistical quantities, etc., and focuses on the profound mathematics of estimation, testing and statistical decision-making from the point of view of measurement theory.

Thesis Writing Guidance

The course focuses on scientific ethics and scientific research integrity, academic norms and misconduct, in accordance with the requirements of the Circular of the General Office of the Ministry of Education on Further Standardization and Strengthening of Graduate Student Cultivation Management.

The course focuses on scientific ethics and scientific research integrity, academic norms and misconduct, scientific research methods and thinking methods, Chinese (English) dissertation format and writing standards, international layout software LaTex.LaTex, international journal submission, literature search and review, thesis evaluation, scientific and technological achievements and project/program application.

The course focuses on case studies and practical training. The teaching of this course enables students to understand the responsibility of academic paper authors and academic ethics, correct the attitude of writing, and effectively improve the writing level of academic papers, master the international typesetting software LaTex, and understand the selection of domestic and foreign academic and professional journals, the basic procedures for submission and publication, and contact between authors and journals, etc., so as to improve the ability of students' professional academic English writing and international academic exchanges.

Operator Theory on Function Spaces

This course mainly deals with the space theory of classical Hardy space, Bergman space, Bloch space, Besov space, and the basic theory of Toeplitz operator, Hankel operator and composite operator on Hardy space and Bergman space. Through the study of this course, students master the basic knowledge of the theory of function spaces and operators on functions, understand the research background of the theory of function spaces and operators on function spaces, and lay the foundation for carrying out studies and research in this field.