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关于2019年浙江大学求是数学暑期学校的通知

编辑:fy 时间:2019年06月14日 访问次数:1150

浙江大学求是科学班是教育部基础学科拔尖学生培养计划的重要组成部分,求是数学班由浙江大学竺可桢学院和数学科学学院共同负责建设。为了帮助青年学生了解数学学科发展前沿问题,促进各高校优秀学生的交流,达到资源共享的目的,浙江大学数学科学学院将于201978-19日在浙江大学紫金港校区举办“2019年浙江大学求是数学暑期学校”。暑期学校共安排三门课程,每门课约20课时,邀请了Wei-Ping LI(香港科技大学,讲授Introduction to Algebraic Geometry)、Jue YanIowa State University,讲授Numerical Methods for Ordinary Differential Equations/Systems)、Zhengfang Zhou Michigan State University,讲授Lectures on Fixed Point Theory and Its Applications)、。

授课对象:本期课程面向数学专业大学本科二年级及以上学生。本校学生:包括求是班学生和非求是班学生,通过选课网报名。选择旁听而不需要学分的同学可以直接参与听课。

上课安排:紫金港西1-102




课程介绍:

Introduction to Algebraic Geometry

Wei-Ping LI(香港科技大学)

This is an introductory course of algebraic geometry. We start with geometric aspect of algebraic geometry. Here we introduce the concept of complex manifolds, divisors, line bundles, the canonical divisor, adjunction formula, sheaves and cohomology of sheaves. Some concrete examples such as Riemann surfaces, called algebraic curves, and algebraic surfaces will be discussed. Riemann-Hurwitz formula and Riemann-Roch formula will be studied if time permits. This is in the spirit of Griffiths and Harris’ book "Principles of Algebraic Geometry”.

Numerical Methods for Ordinary Differential Equations/Systems

Jue YanIowa State University

In this course we will carry out a comprehensive study on finite difference numerical methods solving ODEs. We will start with first order Euler method and introduce the concept of local truncation error and consistency of a method. We then review function approximation with Lagrange interpolation polynomial and its error term. High order multi-step method will be studied with the assistance of Lagrange polynomial approximation. High order multi-stage Runge-Kutta method will be derived. Toward the end we will introduce zero-stability concept and finalize the discussion with absolute-stability for long time run for dynamic systems.

First order Euler method Matlab sample code will be given before the class. Two home works (high order multi-step method and high order Runge-Kutta method) are expected and will be carried out in two-body groups format. Daily Lab time attendance is expected and graduate student assistance will be available on MatLab code implementation.

Lectures on Fixed Point Theory and Its Applications

Zhengfang Zhou (Michigan State University)

Many mathematical problems can be formulated as solutions of an equation F(x) = 0 , or equivalently x = G(x) = x - F(x), namely fixed points for a function. The lectures will focus on the fixed point theory, starting from the simple contraction principle, famous Brouwer fixed point theorem, then going to topological degree theory for fnite dimensions and general Banach spaces. We will also study the index theory for symmetrical functions, and establish some existence theory for multiple solutions. Finally we will use the theory to study the existence and multiple or infinitely many solutions of some nonlinear partial differential equations. The depth and breadth of the application will depend on the background of students. Most of the lectures are in English, and students are encouraged to ask questions and actively participate the discussion during the classes.

《求是数学导论系列讲座》彭赛列闭合定理
 李时璋 助理教授(密西根大学安娜堡分校)
介绍彭赛列闭合定理,并且介绍简单的代数曲线以及一些相关的知识。


欢迎参加!