Shanghai Jiao Tong University, formerly known as Nan Yang Public School, was founded in 1896. Ever since the recruitment of the first class of students in April 1898, mathematics courses have been offered at SJTU. The Department of Mathematics was established in 1928. Since its establishment, the department has made important contributions to modern mathematics in China. The first annual meeting of the Chinese Mathematical Society was held at SJTU. In 1952, among the nationwide reconstruction of universities, most faculty and students from SJTU were relocated to either Fudan University or East China Normal University. In 1956, most part of SJTU moved w...
The course is an introduction to the theory of generalized functions (distributions) as functionals defined on certain classes of test functions. Starting with examples such as the Dirac delta-function I will talk about the basic properties of generalized functions including local properties and regularization of divergent integrals. Then I will also talk about differentiation ...
Introduction to graph theory and to network theory.
We start with the introduction to general graph theory, and in addition
we discuss algebraic graph theory. We will also discuss the
introduction to the network theory from the view point of graph theory.
We put an emphasis on how linear algebraic technique is applied
for the study of graphs and networks.
Calculus is one of the greatest achievements of the human intellect. Calculus is the foundation of modern mathematics and almost all other branches of modern science.
Inspired by problems in astronomy, Newton and Leibniz developed the ideas of calculus three hundred years ago. Since then, each century has demonstrated the power of calculus to illuminate questions in mathema...
This course covers linear equations, matrix theory and vector space, emphasizing topics useful in other disciplines. Linear algebra is a branch of mathematics that studies systems of linear equations and the properties of matrices. The concepts of linear algebra are extremely useful in physics, economics and social sciences, natural sciences, and engineering. Due to its broad r...
Although the concept of “manifold” comes from geometry, it is used in many other areas of mathematics, such as dynamical systems, harmonic analysis, and differential topology. This course is an elementary introduction to the theory of differentiable manifolds. Topics to be covered include (but not limited to): topological manifolds, definition and examples of differentiable man...
The course is an introduction to numerical methods with emphasis on algorithms, analysis of algorithms, and computer implementation issues. We will focus on the topics such as solution of nonlinear equations; interpolation and curve fitting; numerical differentiation and integration; solving ordinary differential equation; solving linear systems by direct methods and iterative ...
Probability and statistics is a mathematical discipline which studies stochastic phenomena. Now it is widely used in industrial and agricultural production, science and technologies. This course is one of the important basic courses for engineering majors in comprehensive universities, through which students shall know the general conceptions and methods about probability and s...
This course is an introduction to the theory of complex valued functions of a complex variable. Fundamental ideas and rigorous proofs will be emphasized. Topics to be covered include (but not limited to): complex numbers, analytic functions, maximum principle, Cauchy’s theorem, Liouville’s theorem, power series, isolated singularities, residues, Rouche’s theorem, Schwarz lemma,...
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