Spring 2014 Course Syllabus - Mathematics 4061.001

Course: Mathematics 4061.001.
Course Title: Differential Geometry.
Time: Tuesday, Thursday 11:00 am - 12:20 pm.
Place: Barton Hall 201.
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 2043 (Minimum grade of C) and Math 2101, 2103 or 3051 (minimum grade of C-).
Textbook: Elementary Topics in Differential Geometry, by J. A. Thorpe. Publisher: Springer Verlag. ISBN: 978-1-4612-6155-1.
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 course is an introduction to differential geometry starting with concepts learned in Calculus III. A particular emphasis will be placed on the study of curves and surfaces in 3-space and their generalizations. The course will revolve around Riemannian geometry, but, time permitting, it will also include a brief introduction to one or more of the following: symplectic geometry and its relation to classical mechanics, general connections and their relation with field theory and pseudoriemannian manifolds, and general relativity.
Course Grading: The final grade will be based on the homework (weekly, total 20%), the midterm exams (2, each 20%) and a final examination (40%).
Exam Dates: Partial exams on February 20 and March 27. Final exam May 13, 10:30-12:30.
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.