### Lecturers:

- Prof. Xiaojun Chen. E-mail: xjchen[at]scu[dot]edu[dot]cn.
- Prof. Raphael Ponge. E-mail: ponge[dot]math[at]icloud[dot]com.

- Prof. Bohui Chen is substituting for Prof. Xiaojun Chen effective October 7.
- Effective November 16 the lectures will be given by Prof. Ponge.
- Effective
**December 16**the lectures move online exclusively. Slides will be posted on this website.

### Time and Place:

Mondays and Wednesdays, sections 3-4 (10:00-11:40), 3rd Teaching Building, Room 315.

### Textbook:

*An Introduction to Manifolds* by Loring W. Tu, 2nd edition, Universitext, Springer, 2011 (Springer Link). Click here and use the password provided in class to get an e-copy of the book. Please send an e-mail to Prof. Ponge if you haven’t got the password.

### Grading Scheme:

- Your grade will be based on your scores on homework assignments and Final exam.
- There will 5 take-home homework assignments.
- The
**Final Exam**will take place on**December 30**.

### Final Exam Info

- The Final Exam will take place on December 30 from 10:00-11:40.
- The exam will cover Sections 1 through 23 (inclusive) (as covered during the lectures).
- The exam is closed book.

### Homework Assignment:

**Homework 1**(due October 12)**:**- Problems #1.4, 2.4, 3.4, 3.5, 3.8, 4.6.
- For #3.4 look at transpositions and use Lemma 3.11.
- For #3.5 use #3.4.

**Homework 2**(due November 2)**:**- Problems # 5.5, 6.2, 6.4, 7.6, 7.7, 8.2, 8.4.
- For #7.6, 7.7 show that the quotient space is homeomorphic to the unit circle.

**Homework 3**(due November 25)**:**- Problems # 9.7, 9.8, 10.4, 10.5, 11.2, 12.3.

**Homework 4**(due December 14; postponed to December 16)**:**- Problems # 13.4, 13.6, 14.5, 14.12, 15.6, 15.12, 16.3, 16.11, 16.12.

**Homework 5**(due December 30)**:**- Problems # 17.3, 19.4, 20.9, 21.9, 22.5.

### Schedule:

- Sep. 7: Appendix A (sections A1–A7).
- Sep. 9: Appendix A (sections A8–A13) + Appendix D.
- Sep. 14: Section 1 (slides) & Section 2 (slides). Recommended problems: #1.2, 1.3, 1.5, 1.6, 1.8, 2.1, 2.2, 2.3.
- Sep. 16: Section 3 (slides). Recommended problems: #3.7, 3.9, 3.10, 3.11.
- Sep. 21: Section 4 (slides). Recommended problems: #4.1, 4.2, 4.3, 4.4.
- Sep. 23: Section 4 (continued) + problems on Sections 1~4.
- Sep. 27: Problems on sections 1~4.
- Sep. 28: Section 5 ( slides). Recommended problems: #5.1, 5.2, 5.3, 5.4.
- Sep. 30: Section 5 (continued) + problems on Section 5.
- Oct. 5 & 7: No classes, National Day Holiday.
- Oct. 12: Section 6 ( slides). Recommended problems: # 6.1, 6.3.
- Oct. 14: Section 7 ( slides). Recommended problems: # 7.1, 7.2, 7.3, 7.4, 7.5, 7.8, 7.9.
- Oct. 19: Section 8 ( slides). Recommended problems: # 8.1, 8.3, 8.5, 8.6, 8.7, 8.8, 8.9, 8.10.
- Oct. 21: Section 8 (continued) + problems on Sections 5~8 (if time is permitted).
- Oct. 26: Section 8 (continued) + Section 9 ( slides). Recommended problems: # 9.1, 9.2, 9.3, 9.4, 9.5, 9.6, 9.7, 9.8, 9.9, 9.10.
- Oct. 28: Section 9 (continued).
- Nov. 2: Section 10 (slides) + Section 11 (slides). Recommended Problems: # 10.4, 10.5, 10.7, 11.1, 11.2, 11.4, 11.5.
- Nov. 4: Section 11 (continued) + Section 12 (slides). Recommended problems #12.1, 12.2, 12.3, 12.4.
- Nov. 9: Section 12 (continued).
- Nov. 11: Section 13 (slides). Recommended problems #13.2, 13.3(a), 13.4, 13.5, 13.6, 13.7.
- Nov. 16: Section 13 (continued) + Section 14 (slides). Recommended problems #14.1, 14.2, 14.3, 14.4, 14.5, 14.7, 14.8, 14.10, 14.11, 14.12, 14.13.
- Nov. 18: Section 14 (continued) +
- Nov. 23: Section 15 (slides). Recommended problems: #15.3, 15.4, 15.5, 15.7, 15.8, 15.10, 15.11, 15.12, 15.13, 15.14, 15.5, 15.16.
- Nov. 25: Section 15 (continued) + Section 16 (slides). Recommended problems: #16.1, 16.2, 16.3, 16.4, 16.5, 16.6, 16.7, 16.8, 16.9, 16.11, 16.12.
- Nov. 30: Section 16 (continued).
- Dec. 2: Section 17 (slides). Recommended problems: #17.1, 17.2, 17.3, 17.4, 17.5, 17.6,
- Dec. 7: Section 18 (slides). Recommended problems: # 18.3, 18.4, 18.5, 18.6, 18.7, 18.8.
- Dec. 9: Section 19 (slides). Recommended problems: # 19.1, 19.2, 19.3, 19.4, 19.5, 19.7, 19.11, 19.12, 19.13.
- Dec. 14: Section 20 (slides). Recommended problems: #20.4, 20.7, 20.8, 20.9, 20.10.
- Dec. 16: Section 21 (Orientations) (slides). Recommended problems: # 21.2, 21.4, 21.5, 21.6, 21.7, 21.8, 21.9.
- Dec. 21: Section 22 (Manifolds with Boundary) (slides). Recommended problems: # 22.3, 22.4, 22.5, 22.7, 22.8, 22.9, 22.10, 22.11.
- Dec. 23: Section 23 (Integration on Manifolds. Stokes’ Theorem) (slides). Recommended problems: # 23.1, 23.3, 23.4, 23.5.
- Dec. 30:
**Final Exam**.