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I.The Basic Information of the Course

Course Number:202012420003

The EnglishName of theCourse：MathematicsResearchMethods

The ChineseName of theCourse：数学研究方法

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 methods and derivation skills of each branch of mathematics, as well as the current hot issues and technical difficulties. 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.Research methods in algebra. It includes elementary transformation, orthogonal transformation and unitary transformation.

2. Research methods of combination and graph theory: including breaking method, avoiding method, topology transformation and other ideas and methods.

3.Research methods of differential equation theory: including separation of variables, regularization, potential well theory and other ideas and methods.

4. Research methods of biological mathematics: including the ideas and methods of preserving the main factors, ignoring the secondary factors, model dimensionality reduction, etc.

5.Research methods of intelligent data analysis: including the determination of membership degree, expert examination, mean classification and other ideas and methods.

6. Mathematical research methods in mechanics: including linearization, variable substitution, spectral analysis and other ideas and methods.

7.Research methods of artificial intelligence and system modeling: including system modeling, data verification, Bayesian estimation and other ideas and methods.

8. Research methods of numerical calculation and simulation: including fitting standards and methods of functions under different measurements, decomposition and synthesis of matrices, and ideas and methods of discretizing continuous problems.

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)：

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