MAT 531: Topology and Geometry II

Spring 2018

Department of Mathematics
SUNY at Stony Brook

Course Description: This course is an introduction to the basic structures and concepts of smooth manifolds. Topics to be covered include: foundations of differentiable manifolds, differentiable maps, vector fields and flows, differential forms and integration on manifolds, Stokes' theorem, Froebenius' theorem, Lie derivatives, immersions and submersions, de Rham cohomology, cochain complexes, degree of a map, Mayer-Vietoris Theorem.

Textbook: Introduction to Smooth Manifolds, by John M. Lee, 2nd Edition, Springer, 2012.

Instructor: Marcus Khuri, Math Tower 3-122. Office Hours: Tuesdays and Thursdays from 2:30-4:00pm. Email:

Course Assistants: Aleksander Doan, Math Tower 2-106. Office Hours: Wednesdays from 12:00-1:00pm in office, and Wednesdays from 10:00am-12:00pm in MLC. Email:

Class schedule: TuTh 10:00-11:20am, Mathematics 4-130

Homework: Homework is a fundamental part of this course, and you will have to work hard on the assigned problems in order to succeed. Assignments will be posted on the course website at the beginning of each week, and will be due on Wednesday of the following week at 3pm. A box or envelop will be placed outside the office of the course assistant, where you may turn in your homework. Late homework will not be accepted. Homework will account for 50% of the total grade.

Homework 1 (Due 1/31) - §1: 5, 6, 7; §2: 5, 7, 10, 14;

Homework 2 (Due 2/7) - §3: 3, 4, 6; §4: 5, 6, 8;

Homework 3 (Due 2/14) - §4: 10, 13; §5: 4, 6, 7, 10, 11;

Homework 4 (Due 2/21) - §8: 4, 10, 11, 12, 13, 14, 16;

Homework 5 (Due 2/28) - §9: 2, 5, 17, 18; §19: 4, 5, 12;

Midterm Examination in class on 3/1 -- it covers sections 1-5, 8, 9, 19.

Exams: There will be an in class midterm as well as a final, each respectively accounting for 20% and 30% of the total grade. The midterm exam will be in class on Thursday, March 1, and the final exam will take place on Friday, May 11, 11:15am-1:45pm in our classroom Mathematics 4-130. By enrolling in this course, you are attesting to the fact that you will be available for the exams at these times.

Disability Support Services (DSS)
If you have a physical, psychological, medical or learning disability that may impact your course work, please contact Disability Support Services, ECC (Educational Communications Center) Building, room 128, (631) 632-6748. They will determine with you what accommodations, if any, are necessary and appropriate. All information and documentation is confidential. Students who require assistance during emergency evacuation are encouraged to discuss their needs with their professors and Disability Support Services. For procedures and information go to the following website:

Academic Integrity
Representing another person's work as your own is always wrong. Faculty are required to report any suspected instances of academic dishonesty to the Academic Judiciary. Faculty in the Health Sciences Center (School of Health Technology & Management, Nursing, Social Welfare, Dental Medicine) and School of Medicine are required to follow their school-specific procedures. 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, or inhibits students' ability to learn. Faculty in the HSC Schools and the School of Medicine are required to follow their school-specific procedures.