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 1/29Chapter 1.
Thu 1/31Chapter 2.
Tue 2/5Chapter 3.HW due: 1-1,1-3,1-5,1-7,2-4,2-6,2-10 (from the first edition)
Thu 2/7Chapter 3.
Tue 2/12Chapter 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 2/14Chapter 5.
Tue 2/19Chapters 5,6.HW due: 3-4,3-5,3-7,4-5,4-6,4-13 (from the second edition, from now on)
Thu 2/21Chapter 6.
Tue 2/26Chapters 6,8.HW due: 5-1,5-3,5-7,5-9,5-11,5-15,5-17
Thu 2/28Chapter 9.
Tue 3/5 No class
Thu 3/7Chapter 9.HW due: 6-2,6-3,6-5,6-9,6-12,6-14
Tue 3/12Chapter 10.
Thu 3/14Chapter 10.HW due: 8-2,8-6,8-15,9-4,9-8,9-14,9-17
Tue 3/26Midterm review
Thu 3/28 Midterm: Practice .Covers chapters 1-6,8-10.
Tue 4/2Chapter 11.
Thu 4/4Chapter 12.HW due: 10-3,10-9,10-15,10-16,11-2,11-4,11-7
Tue 4/9Chapter 13.
Thu 4/11Chapter 14.HW due: 11-11,11-13,11-16,12-3,12-7,12-8
Tue 4/16Chapter 14.
Thu 4/18Chapter 15.HW due: 13-4,13-8,13-9,13-17,13-18,14-2,14-5
Tue 4/23Chapter 15.
Thu 4/25Chapter 16.HW due: 14-6,14-9,15-3,15-5,15-8,15-13
Tue 4/30Chapter 16.
Thu 5/2Chapter 17.HW due: 15-14, 15-16, 16-2, 16-6, 16-9, 16-10, 16-22
Tue 5/7Chapter 18.
Thu 5/9Chapter 18.HW due: 16-13, 16-14, 16-15, 17-2, 17-6, 17-10, 17-13
Mon 5/20 Final examMath P-131,

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 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

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.

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