MAT 531 - Geometry/Topology II
Instructor: Samuel Grushevsky
Office hours: Wed 1.30-2.30, Thu 2.30-3.30 in Math 3-109, and by appt.
Grader: Steve Dalton
Office hours: Tue 12-2 in MLC, Thu 5.30-6.30 in Math 2-119
Schedule: TuTh 11.30am-12.50pm
Classroom: Physics P125
Overview: The course is an introduction to smooth manifolds. The material will be on smooth manifolds and maps between them, tangent bundle, vector fields, and differential forms, including Frobenius integrability, Stokes' theorem, De Rham cohomology, and Mayer-Vietoris theorem. See here for a sample list of topics.
Textbook: John M. Lee: Introduction to Smooth Manifolds. Reading the assigned chapter of the textbook before lecture will greatly help you!
Homework: Problem sets will be assigned, roughly weekly, and collected in class on days indicated.
Late homework will never be accepted, but under documented extenuating circumstances the grade may be dropped.
Grading: Homework: 50%, Midterm: 25%, Final: 25%.
Syllabus/schedule (subject to change)
| Tue 1/29 | Chapter 1. | |
| Thu 1/31 | Chapter 2. | |
| Tue 2/5 | Chapter 3. | HW due: 1-1,1-3,1-5,1-7,2-4,2-6,2-10 (from the first edition) |
| Thu 2/7 | Chapter 3. | |
| Tue 2/12 | Chapter 4. | HW due: 2-14,2-16,2-18,3-1,3-3,3-5,3-8 (from the first edition, a copy here) |
| Thu 2/14 | Chapter 5. | |
| Tue 2/19 | Chapters 5,6. | HW due: 3-4,3-5,3-7,4-5,4-6,4-13 (from the second edition, from now on) |
| Thu 2/21 | Chapter 6. | |
| Tue 2/26 | Chapters 6,8. | HW due: 5-1,5-3,5-7,5-9,5-11,5-15,5-17 |
| Thu 2/28 | Chapter 9. | |
| Tue 3/5 | No class | |
| Thu 3/7 | Chapter 9. | HW due: 6-2,6-3,6-5,6-9,6-12,6-14 |
| Tue 3/12 | Chapter 10. | |
| Thu 3/14 | Chapter 10. | HW due: 8-2,8-6,8-15,9-4,9-8,9-14,9-17 |
| Tue 3/26 | Midterm review | |
| Thu 3/28 | Midterm: Practice . | Covers chapters 1-6,8-10. |
| Tue 4/2 | Chapter 11. | |
| Thu 4/4 | Chapter 12. | HW due: 10-3,10-9,10-15,10-16,11-2,11-4,11-7 |
| Tue 4/9 | Chapter 13. | |
| Thu 4/11 | Chapter 14. | HW due: 11-11,11-13,11-16,12-3,12-7,12-8 |
| Tue 4/16 | Chapter 14. | |
| Thu 4/18 | Chapter 15. | HW due: 13-4,13-8,13-9,13-17,13-18,14-2,14-5 |
| Tue 4/23 | Chapter 15. | |
| Thu 4/25 | Chapter 16. | HW due: 14-6,14-9,15-3,15-5,15-8,15-13 |
| Tue 4/30 | Chapter 16. | |
| Thu 5/2 | Chapter 17. | HW due: 15-14, 15-16, 16-2, 16-6, 16-9, 16-10, 16-22 |
| Tue 5/7 | Chapter 18. | |
| Thu 5/9 | Chapter 18. | HW due: 16-13, 16-14, 16-15, 17-2, 17-6, 17-10, 17-13 |
| Mon 5/20 | Final exam | Math P-131, 2.15pm-5.pm |
Disability Support Services: If you have a physical, psychological, medical, or learning disability that may affect your course work, please contact Disability Support Services (DSS) office: ECC (Educational Communications Center) Building, room 128, telephone (631) 632-6748/TDD. DSS will determine with you what accommodations are necessary and appropriate. Arrangements should be made early in the semester (before the first exam) so that your needs can be accommodated. All information and documentation of disability is confidential. Students requiring emergency evacuation are encouraged to discuss their needs with their professors and DSS. For procedures and information, go to the following web site http://www.ehs.sunysb.edu and search Fire safety and Evacuation and Disabilities.
Academic Integrity: Each student must pursue his or her academic goals honestly and be personally accountable for all submitted work. Representing another person's work as your own is always wrong. Faculty are required to report any suspected instance of academic dishonesty to the Academic Judiciary. For more comprehensive information on academic integrity, including categories of academic dishonesty, please refer to the academic judiciary website at http://www.stonybrook.edu/uaa/academicjudiciary/.
Critical Incident Management: Stony Brook University expects students to respect the rights, privileges, and property of other people. Faculty are required to report to the Office of Judicial Affairs any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, and/or inhibits students' ability to learn.