國立清華大學數學系

拓撲學導論

Math 3510-00 (Fall 2018) Introduction to Topology 

Course Description:

Topology is a vital part of modern mathematical language, and is indispensable to every graduate level math course related to analysis or geometry. It allows us to discuss continuity and convergence under abstract settings, to study obscure geometric concepts and objects in a clear and precise manner. In this introductory course for topology, we will briefly review some elements of set theory and logic, then cover the following topics:

1. Topology of metric spaces

2. Set-theoretic topology 

3. Systems of continuous functions

4. Basic algebraic topology

This course in intended for undergraduate students with ample background knowledges in mathematical analysis and algebra. More precisely, students are expected to be familiar with topology of R^n, continuous functions on R^n, uniform convergence, and basic concepts of group theory. All of these perquisites are covered in standard undergraduate courses for advanced calculus and abstract algebra.

Registered students are recommended to use the iLMS e-learning system (http://www.nthu.edu.tw/elearning.php), where updates of the course will be posted. Contact your teaching assistant if you have any question. 

Textbook: 

V. Runde: A Taste of Topology, Universetext, Springer, 2005. 

This book is available in pdf format at the NTHU library. NTHU students are allowed to download it for personal use.

References:

[1]. K.  Jänich: Topology, Undergraduate Texts in Mathematics, Springer, 1994.

[2]. J. R. Munkres: Topology, 2nd edition, Prentice Hall, 2000. 

Grading:

Homework assignments: 20%. Click Here

Midterm Exam: 40% -- November 8 (Thursday) from 1:20-3:10pm.

Final exam: 40% -- January 10 (Thursday) from 1:20-3:10pm.