Spring 2014 Course Syllabus - Mathematics 8062.002

Course: Mathematics 8062.002.
Course Title: Differential Geometry & Topology II.
Time: Tuesday, Thursday 3:30 pm - 4:50 pm.
Place: Wachman Hall 617.
Instructor: Mendoza, Gerardo A.
Instructor Office: Wachman Hall 618.
Instructor Email: gerardo.mendoza@temple.edu
Instructor Phone: 1-5053.
Office Hours: by appointment.
Prerequisites: Math 8061 or permission from instructor.
Textbook: 1) Allen Hatcher, Algebraic Topology, Cambridge University Press, 2001.
2) Bott, R., Tu and L. W., Differential forms in algebraic topology, Springer Verlag, 1982.
Course Goals: In addition to gaining a deep working understanding of the subject, the student is expected to be able to write clear, clean, complete proofs in the subject.
Topics Covered: This is the second semester of a year-long course on the geometry and topology of smooth manifolds. The principal focus will be on the construction of algebraic objects encoding aspects of the topology of a given manifold: the fundamental group, the higher homotopy groups, and homology and cohomology (singular, Čech, de Rham), as tools to attempt to understand the topology of the manifold. We will then apply these ideas to the classification--to the extent that this is possible--of manifolds and of vector bundles. A full discussion of the latter and the related principal G-bundles will be included as part of the course.
Course Grading: The final grade will be based on the homework (weekly, total 25%), the midterm exams (2, each 25%) and a final examination (25%).
Exam Dates: Partial exams on February 20 and March 27. Final exam May 13, 1:00-3:00.
Attendance Policy: Attendance is required. Missing four classes implies a failing grade.

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 a withdrawal form is processed by a registration office of the University by the Drop/Add deadline date given below. For this semester, the crucial dates are as follows:

• The first day of classes is Tuesday, January 21.
• The last day to drop/add (tuition refund available) is Monday, February 3.
• Spring recess is the week of Sunday, March 2 - Sunday, March 9.
• The last day to withdraw (no refund) is Tuesday, March 25.
• The last day of classes is Monday, May 5.

During the first two weeks of the fall or spring semester or summer sessions, 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.