國立清華大學數學系

代數拓樸

Math 5525-00 (Fall 2026) Algebraic Topology 

Course Description:

Algebraic topology has wide applications in many areas of mathematics. This introductory course covers some essential elements of algebraic topology, and briefly introduces some applications in differential equations and geometry. In particular, the course includes brief introduction to homotopy theory, homology theory, and cohomology theory. This course is intended for graduate and advanced undergraduate students who have taken standard undergraduate courses for topology, differential geometry, differential equations, and algebra. Students without background in basic group theory, point set topology, should NOT take this course.

Syllabus: 

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Textbook: 

William S. Massy: A Basic Course in Algebraic Topology, Springer, GTM volume 127, 1991.  

References:

James R. Munkres: Elements of Algebraic Topology, Addison-Wesley, 1984.