I.The Basic Information of the Course
Course Number:202012420002
The EnglishName of theCourse：ProfessionalFrontier
The ChineseName of theCourse：学科前沿
In-classHours andAllocation(total class hours:16, classroom teaching:16classhours.)
Credit(s):1
Semester:1
AppliedDiscipline(ProfessionalDegreeCategory)：Mathematics
CourseObjectOriented：Masteranddoctoral studentof Mathematics
EvaluationMode:ProcessEvaluation
TeachingMethod:HeuristicTeaching
CourseOpening Department:Collegeof Mathematical Sciences
II.Prerequisite Course
Mathematical analysis,Advanced algebra, Real variable functions,Ordinary differential equations
III. The Objectives and Requirements of the Course
Through the study of this course, students can understand and master the research frontiers, academic achievements, current hot issues and technical difficulties of each branch of mathematics. Cultivate students' theoretical thinking ability, develop their research ideas, improve their practical ability, and lay a solid theoretical foundation for further study of mathematical knowledge and mathematical research.
IV. The Content of the Course
1,Algebra. It includes the basic framework of advanced algebra, group ring domain theory, and introduces the latest achievements of homology algebra, lie groups namely representation theory, and its application in other disciplines.
2,Combination and graph theory. It includes the existing achievements and research ideas of discrete mathematics, especially the research and development of combinational tensors.
3,Differential equation theory. It includes the classification of differential equations, relevant concepts, basic research ideas, and the latest research progress. It also introduces the application progress and practical problems of differential equations in other disciplines.
4.Biological mathematics. Including biological mathematics modeling, parameter interpretation, current progress, future direction of development.
5.Intelligent data analysis. Including fuzzy set theory, morphology theory, and their methods and applications in image processing.
6. Mathematical methods in mechanics. It includes the basic concepts and research methods of elastic mechanics and fluid mechanics, as well as the realization process and technical problems of various methods in computer simulation.
7.Artificial intelligence and system Modeling: including optimization theory and methods, systems analysis, and the application of these mathematical skills to practical problems.
8. Numerical calculation and simulation: including theory and method of error analysis, interpolation and approximation of functions, numerical solution of linear and nonlinear equations, numerical integration and differentiation, etc.
V. Reference Books, Reference Literatures, and Reference Materials
It is chosen by the teacher.
Outline Writer (Signature):冯国峰
Leader in charge of teaching at the College (Signature)：
Date：
中文
