03110015-8 mathematical analysis 348 19
Teaching target: students majoring in mathematics and applied mathematics
Abstract: This course is a basic course for mathematics majors. This paper mainly introduces the systematic knowledge of limit theory, unary calculus, infinite series and multivariate calculus. Through learning, students can correctly understand and master the basic concepts and theories of mathematical analysis, initially master the demonstration methods of mathematical analysis, skillfully calculate the integral, and gain the ability of preliminary application, thus laying the necessary foundation for further studying the follow-up courses of this major and understanding and mastering the mathematics textbooks in middle schools.
Assessment method: closed-book examination
Textbook: Mathematical Analysis, edited by East China Normal University, Higher Education Press.
Bibliography: Mathematical Analysis compiled by Mathematics Department of Fudan University; Liu Yulian edited the lecture notes on mathematical analysis; Peking University edited mathematical analysis.
Course number, course name, class hours, math scores.
03 1 10054 analytic geometry 80 4
Teaching target: students majoring in mathematics and applied mathematics
Analytic geometry is an algebraic method to study the properties of geometric figures, including vectors and coordinates, trajectories and equations, plane and space straight lines, cylinders, cones, surfaces of revolution and quadrics, quadrics and quadrics, and so on. It is one of the main basic courses of mathematics and applied mathematics, and it is a necessary prerequisite for mathematical analysis and advanced mathematics courses.
Assessment method: closed-book examination
Textbook: Analytic Geometry, edited by Lv Lingen and Xu Zidao, Higher Education Press.
Bibliography: A Guide to Analytic Geometry Learning, edited by Lu Lingen; Zhu Dingxun's Spatial Analytic Geometry
Course number, course name, class hours, math scores.
03 1 10066-7 Higher Algebra 198 1 1
Teaching target: students majoring in mathematics and applied mathematics
Abstract: This course is an important basic course for mathematics majors, and it is also the first required course for learning other mathematics majors. This paper mainly introduces the basic theories of univariate polynomial and multivariate polynomial theory, determinant and linear equations, matrix, quadratic form, linear space, linear transformation, characteristic root and characteristic subspace, Euclidean space, so that students can master the basic theories of polynomial and linear algebra and cultivate their ability to solve practical problems by algebraic methods.
Assessment method: closed-book examination
Textbook: Advanced Algebra, edited by Peking University, Higher Education Press.
Bibliography: Advanced Algebra, edited by Zhang et al., Higher Education Press; Advanced Algebra edited by Fudan University Shanghai Science and Technology Press
Course number, course name, class hours, math scores.
03 1 10084 ordinary differential equation
Teaching target: students majoring in mathematics and applied mathematics
Preparatory course: mathematical analysis, advanced algebra
Abstract: Ordinary differential equation is a subject that studies the theory and solution of differential equation (mainly ordinary differential equation). It is a classic and dynamic subject with both application and theory. The main contents include the existence and uniqueness theory of solutions of first order ordinary differential equations; Solutions of first-order differential equations; Solutions of higher order differential equations; Theory and solution of linear differential equations (groups). Students are required to correctly understand the basic concepts of ordinary differential equations, master the basic theories and main methods, and have certain problem-solving ability, so as to lay a foundation for further study of modern theories and follow-up courses in this discipline.
Assessment method: closed-book examination
Textbook: Ordinary Differential Equations, edited by Wang Gaoxiong and Zhou Zhiming, Higher Education Press.
Bibliography: Ordinary Differential Equations edited by Ye, Nanjing University; Ordinary Differential Equations compiled by Fudan University
Course number, course name, class hours, math scores.
03 1 10094 complex variable function 72 4
Teaching target: students majoring in mathematics and applied mathematics
Preparatory course: mathematical analysis
Abstract: This course is an important specialized course for mathematics majors. This paper mainly introduces the basic contents of analytic theory and geometric theory of simple complex variable function. Including complex number, complex variable function, analytic function, complex variable function integration, series expansion, residue theory, conformal transformation and analytical continuation. Through study, students can master the basic theory and method of complex variable function and gain preliminary application ability.
Assessment method: closed-book examination
Textbook: Complex Variable Function, written by Zhong Yuquan, Higher Education Press.
Bibliography: Yu Jiarong's Complex Function
Course number, course name, class hours, math scores.
03 1 10 106 probability theory 72 4
Teaching target: students majoring in mathematics and applied mathematics
Preparatory course: mathematical analysis, advanced algebra
Abstract: Probability theory is a mathematical discipline that studies the statistical laws of random phenomena, and it is an important basic course for mathematics majors. This paper mainly introduces events and their operations, classical probability, probability space, conditional probability, experimental independence, Bernoulli experiment and so on.
Assessment method: closed-book examination
Textbook: Probability Theory, edited by Fudan University, Higher Education Press.
Bibliography: Probability Theory and Mathematical Statistics compiled by Department of Mathematical Mechanics, Sun Yat-sen University (Volume I and Volume II), Higher Education Press.
Course number, course name, class hours, math scores.
0311014 Modern Algebra 72 4
Teaching target: students majoring in mathematics and applied mathematics
Preparatory course: Advanced Algebra
Abstract: This course is an important elective course for mathematics majors, and it is also an essential foundation for learning many important fields of modern mathematics. It focuses on the study of algebraic structure, and systematically introduces the basic structures of mapping and algebraic operation, homomorphism and isomorphism, groups, rings and fields. Cultivate students' abstract thinking ability and the ability to understand the nature and structure of some algebraic objects from the algebraic system of groups, rings and fields.
Assessment method: closed-book examination
Textbook: Modern Algebra, edited by Zhang, Higher Education Press.
Bibliography: Modern Algebra, edited by Wu Pinsan, Higher Education Press; Xiong edited Modern Algebra.
Course number, course name, class hours, math scores.
03 1 10 134 real variable function 72 4
Teaching target: students majoring in mathematics and applied mathematics
Preparatory course: mathematical analysis
Abstract: This course is an important specialized course for mathematics majors. Lebesgue integral theory is systematically introduced, including set theory, point set measure theory, measurable function theory and Lebesgue integral theory. Through study, students can master the basic ideas of modern abstract analysis, deepen their understanding of mathematical analysis and mathematics teaching in middle schools, and lay a preliminary foundation for further study of modern mathematical theory.
Assessment method: closed-book examination
Textbook: Introduction to Real Variable Function and Functional Analysis (I), edited by Zheng, and, Higher Education Press.
Bibliography: A Preliminary Study of Real Variable Function and Functional Analysis edited by East China Normal University (I)
Course number, course name, class hours, math scores.
03 1 10 173 functional analysis 48 3
Teaching target: students majoring in mathematics and applied mathematics
Preparatory course: mathematical analysis, real variable function
Abstract: This course is a restricted course for mathematics and applied mathematics majors. This paper mainly describes the concepts of distance space, normed linear space and Hilbert space, several basic theorems of linear analysis, Riess-Schodel theory of completely continuous operators, and the preliminary spectral theory of bounded self-adjoint operators in complete inner product spaces. Through the study of this course, students can have a basic understanding of modern analysis and lay a solid foundation for continuing scientific research in the future.
Assessment method: closed-book examination
Textbook: Introduction to Real Variable Function and Functional Analysis (Volume II), edited by Zheng, and, Higher Education Press.
Bibliography: A Preliminary Study of Real Variable Function and Functional Analysis (Volume II) edited by East China Normal University.
Course number, course name, class hours, math scores.
03 1 10 123 advanced geometry 543
Teaching target: students majoring in mathematics and applied mathematics
Foundation: Analytic Geometry, Advanced Algebra
Abstract: This course is one of the important basic courses for mathematics majors. This paper mainly discusses one-dimensional and two-dimensional projective geometry, systematically introduces the basic concepts of projective geometry, projective correspondence between lines, direct correspondence and affine correspondence between projective planes, basic invariant cross ratio of projective transformation, transformation group and geometry, affine theory of projective theory and conic curve, projective geometry foundation and non-Euclidean geometry outline.
Assessment method: closed-book examination
Textbook: Advanced Geometry, edited by Mei Xiangming, Liu Zengxian and Lin, Higher Education Press.
Bibliography: Advanced Geometry edited by Zhu Dexiang
Course number, course name, class hours, math scores.
03 1 10 154 differential geometry 72 4
Teaching target: students majoring in mathematics and applied mathematics
Preparatory course: analytic geometry and mathematical analysis
Abstract: This course is an important elective course for mathematics majors. This paper mainly introduces simple curve, curvature and torsion, Frenet formula, adjacent structure of spatial curve, plane curve, basic theorem of curve theory, first and second basic forms of surface, principal curvature, Gaussian curvature, developable surface, basic theorem of surface theory, geodesic, etc. Through learning, students are required to master the local properties of curves and surfaces in three-dimensional Euclidean space, and use vector analysis as a tool and research method to develop their spatial imagination and further improve their mathematical literacy.
Assessment method: closed-book examination
Textbook: Differential Geometry edited by Mei Xiangming and Huang Jingzhi, Higher Education Press.
Bibliography: Lectures on Differential Geometry edited by Wu Daren.
Course number, course name, class hours, math scores.
03 1 10 144 calculation method
Teaching target: students majoring in mathematics and applied mathematics
Pre-courses: advanced algebra, mathematical analysis, analytic geometry, differential equations.
Abstract: Some common problems in mathematics are discussed, such as solving linear equations, finding the roots of equations, eigenvalues and eigenvectors of matrices, interpolation, initial values of definite integrals and differential equations, etc. The calculation methods, basic principles and characteristics of these methods are introduced. Through study, students can master the necessary theory and skills of calculation methods and skillfully write algorithm programs of calculation methods.
Assessment method: closed-book examination
Textbook: Calculation Method, edited by Zhang Derong, People's Education Press.
Bibliography: Theory and Application of Numerical Analysis, edited by G.M. Phillips; Introduction to Matrix Computing, edited by G.W. Stewart; Introduction to Numerical Analysis edited by Atkinson