I.The Basic Information of the Course(Time New Rome, 12 points, bold font)
Course Number: 202012420005
The EnglishName of theCourse：Topology
The ChineseName of theCourse：拓扑学
In-classHours andAllocationtotal class hours:48, classroom teaching:48
Credit(s):3
Semester:1
AppliedDiscipline(Professional Degree Category)：Master degrees in Mathematics
CourseObjectOriented：AcademicMaster
EvaluationMode:Closed-book Examination,
TeachingMethod:Seminar-style Teaching
CourseOpening Department: MathematicalDisciplines
II.Prerequisite Course
Calculus, Complex Analysis, Set Topology
III. The Objectives and Requirements of the Course(Time New Rome 12 points, total words: about 200 words)
The course is a basic course for graduate students for Master degree in mathematical science. The aim of the course is to help students to grasp the basic ideas, theories and methods inTopology and have the ability to apply the knowledge of Topology to solve problems.
Topology is one of the core subjects in Mathematical Science. Some problems in Topology,such as classification of low dimensional manifold is a fundamental problem in mathematics. We hope student to enlarge their mathematical sight by taking the course.By learning this course, the students should reach the following basic requirements: get familiar with some basic Topology terminologies,concepts, ideals; understood the current developments in geometry and Topology.
IV. The Content of the Course(Time New Rome, 12 points, bold font, 1000-2000 words)
Description:
Chapter 1 Preliminaries (12classhours)
1.1Topological spaces and continuous /homeomorphic maps
1.2 Basic properties of Topological spaces: compactness, connectivity and separateness
Chapter 2 Metric topology (12classhours)
2.1Basic properties
2.2Nagata—Sirminov Metrization and completion
2.3 Convergences
2.4 Bair spaces and dimension theory
Chapter 3 Quotient space and classification of compact surfaces (12classhours)
3.1 Quotient spaces and Homogenous spaces
3.2 Triangulazatios/cutting /gluing and classification of compact surface
Chapter 4 Differential topology (12classhours)
4.1 A brief introduction to the differential manifolds
4.2Whiteny/Nashembedding Theorems
4.3 More theory
Political education:
1, Wenjun Wu, was a Chinese Topologist. Professor Wu made a great contribution a
In the theory of characteristic classes. He also has done many works in ancient Chinese mathematical history and mechanic proofs.
2, Boju, Jiang, was a Chinese Topologist. He was the author of very popular book “ Topology of Strings”. We should learn Prof Boju on how to spread mathematics among teenagers, which is a
great patriotism.
V. Reference Books, Reference Literatures, and Reference Materials
1. 江泽涵《拓扑学引论》，上海科学技术出版社，1986.
2. KellyJ.L General Topology. GTM27，1955.
3. S.Lang, Introduction to Differential Manifolds, New York John Wiley & Sons. Inc 1962., 1968。
4. J. Milnor, On Manifolds homeomorphic to 7-Sphere, Ann of Math., 64(1956) , 399-405
5. J. Milnor, Morsetheory世界图书出版社，2002.
6. J.R. Munkres, Topology.机械工业出版社，2004，
7. Frank W. Warner.Foundations of Differentiable Manifolds and Lie Groups.GTM94,世界图书出版社,2000。
8. 熊金成，点集拓扑学讲义，人民教育出版社，1981。
9. 尤承业.拓扑学讲义.北京大学出版社，2008
10．张筑生.微分拓扑学新讲.北京大学出版社，2002。
B. Learning Resources (Time New Rome 12 points)
1.http://www.arxiv.org
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