2016 Fall Course Syllabus - Mathematics 8061.001
Course: Mathematics 8061.001.
Course Title: Differential Geometry and Topology I.
Time: Monday and Wednesday, 9-10:20am.
Place: Wachman Hall, Room 527.
Instructor: Vasily Dolgushev.
Instructor Office: Wachman Hall, Room 530.
Instructor Email: vasily.dolgushev@temple.edu
Instructor Phone: 215-204-7287.
Office Hours: Tuesday 1-2:30pm and by appointment.
Prerequisites: Math 3141, 3142, 4063 or permission of instructor.
Textbook: V. Guillemin and A. Pollack, Differential topology; M.W. Hirsch, Differential topology.
Course Goals: To master the fundamental concepts of differential geometry.
Topics Covered: This semester will be devoted to geometry and topology of manifolds and smooth maps. We will talk about the (co)tangent bundle, vector (and tensor) fields, exterior forms. We will talk about local behavior of smooth maps. We will learn Sard's theorem and Whitney's embedding theorem. We will also learn oriented intersection theory and integration on manifolds. If time will permit, we will talk complex manifolds and Hodge theory.
Course Grading: Homeworks: 73%, the midterm: 12%, the final exam: 15%.
Exam Dates: The midterm: October 5 (Wed). The final exam: TBA.
Attendance Policy: Attendance will not be monitored, but you are strongly encouraged to attend class regularly and to take complete class notes.
Written assignments: You have to justify all your steps in your written assignments. Also, please, write legibly! Not justifying steps or not writing legibly may reduce your score.
Homeworks: Weekly assignments of homeworks are posted on the blackboard. You may work together on homework assignments, but I expect everybody to write up their own solutions; obvious copies will not be accepted. The writ- ing component is an essential part of this course. Two lowest grades for the homework assignments will be dropped.
Any student who has a need for accommodation based on the impact of a disability should contact me privately to discuss the specific situation as soon as possible. Contact Disability Resources and Services at (215) 204-1280, 100 Ritter Annex, to coordinate reasonable accommodations for students with documented disabilities.
Freedom to teach and freedom to learn are inseparable facets of academic freedom. The University has adopted a policy on Student and Faculty Academic Rights and Responsibilities (Policy # 03.70.02) which can be accessed here.
Students will be charged for a course unless dropped by the Drop/Add deadline date. Check the University calendar for exact dates.
During the first two weeks of the fall or spring semester, students may withdraw from a course with no record of the class appearing on the transcript. In weeks three through nine of the fall or spring semester, or during weeks three and four of summer sessions, the student may withdraw with the advisor's permission. The course will be recorded on the transcript with the instructor's notation of "W," indicating that the student withdrew. After week nine of the fall or spring semester, or week four of summer sessions, students may not withdraw from courses. No student may withdraw from more than five courses during the duration of his/her studies to earn a bachelor's degree. A student may not withdraw from the same course more than once. Students who miss the final exam and do not make alternative arrangements before the grades are turned in will be graded F.
The grade I (an "incomplete") is reserved for extreme circumstances. It is necessary to have completed almost all of the course with a passing average and to file an incomplete contract specifying what is left for you to do. To be eligible for an I grade you need a good reason and you should have missed not more than 25% of the first nine weeks of classes. If approved by the Mathematics Department chair and the CST Dean's office, the incomplete contract must include a default grade that will be used in case the I grade is not resolved within 12 months.