本课程期末考试采用口试的方法。在给出的一些没讲过的课题中，每个学生选一个，查阅参考文献自学以后报告，同学给他打分。 通过这种方法增加同学的参与程度，提高自学能力，增强表达交流能力。
以下是计划采用的选题：
1. Sard Theorem
2. Homotopy invariance of degrees of maps
3. Browder Fixed Point Theorem
4. Manifolds with boundary and cobordism ring
5. Morse Inequalities
6. Poincare-Hopf Theorem
7. Fundamental Groups
8. Covering Spaces
9. Higher homotopy groups are abelian
10. Vector bundles and their sections
11. Tubular neighborhood theorem
12. De Rham theorem and Poincare duality theorem
13. Laplace operator and Hodge theory
14. Exceptional Lie Groups
15. Gauss-Bonnet-Chern theorem and Chern classes
16. Introduction to Yang-Mills theory
17. Brief history of Poincare conjecture
18. Hawking-Penrose singularity theorem
19. Exotic $7$-spheres
20. Introduction to Donaldson's work and exotic R^4
21. Darboux theorem
22. Hamiltonian action and moment maps
23. Maxwell's equations in terms of exterior differential forms
Last modified: Thursday, June 5, 2003 12:45 PM