This class will be an introduction to differential forms, a central tool in modern topology, geometry, and physics. The course begins where Math 222 ends, with Green's theorem, the divergence theorem, and Stokes' theorem. All of these theorems are special cases of one theorem, known as the general Stokes' theorem, about integration of differential forms. The objective of the first part of the course will be to understand and prove this theorem. We will then discuss manifolds and what can be learned about them using differential forms.
Homework is an important part of any math class. It is important that you practice doing the problems. This will help you to understand the material better and will prepare you for the exams. You are encouraged to discuss the homework, and to work together on the problems. However each student is responsible for the final preparation of his or her own homework papers.
Homework will be due weekly, generally on Tuesdays. The homework will be posted here.
There will be a take-home midterm and a take-home final exam. The midterm will be handed out on Thursday, March 3 and will be due Thursday, March 24. The final will be handed out on the last day of class, Tuesday, May 3, and will be due Thursday, May 12.
The course grade will be computed as follows:
I will hold office hours Mondays and Wednesdays, 2:30-3:30pm, but am often available in my office. You can also always email me at firstname.lastname@example.org to make an appointment.
It is the policy of Wesleyan University to provide reasonable accommodations to students with documented disabilities. Students, however, are responsible for registering with Disabilities Services, in addition to making requests known to me in a timely manner. If you require accommodations in this class, please make an appointment with me during the first two weeks of class, so that appropriate arrangements can be made. All discussions will remain confidential. Students with disabilities should also contact Dean Lazare. Please see http://www.wesleyan.edu/deans/disability-students.html for more information.