Spring 2011 Course Syllabus

Course: Mathematics 9110.001.
Course Title: Topics in Algebra: Representation Theory II.
Time: TR 9:30 AM - 10:50 AM.
Place: Wachman Hall CC527.
Instructor: Lorenz, Martin W.
Instructor Office: Wachman Hall CC528.
Instructor Email:
Instructor Phone: 215-205-5013.
Office Hours: TR 11:00-12:00 or by appointment.
Prerequisites: Math 8011 & 8012 or equivalent or permission of instructor.
Textbook: William Fulton and Joe Harris: Representation Theory, A First Course. Graduate Texts in Mathematics Vol. 129, Springer-Verlag, New York ISBN: 978-0-387-97495-8.
Course Goals: This is a continuation of the course "Topics in Algebra: Representation Theory" (Math 9100) given in the Fall 2010 semester. While the emphasis in the first semester was on representations of finite groups, the second semester will be devoted entirely to Lie theory: Lie groups, Lie algebras, and their representations.
Topics Covered: The plan is to cover a selection of the topics in Parts II - IV of the textbook. On occasion, I will supplement the presentation in Fulton-Harris by adding material from the following highly recommended book: James E. Humphreys: Introduction to Lie Algebras and Representation Theory Graduate Texts in Mathematics, Vol. 9, Springer-Verlag, New York, 1972.
Course Grading: The course grade will be based on homework assignments (60%) and an in-class final exam (40%).
Exam Dates: According to the official exam schedule, the final exam is to be given on Thursday 05/05, 8:00-10:00, in CC527. If this is inconvenient, we can change the date by common agreement.
Attendance Policy: Attendance will not be monitored, but you are strongly encouraged to attend class regularly and to take complete class notes.
Homework: Homework will be assigned and collected regularly. You may work together on the assignments, but I expect everybody to write up their own solutions; obvious copies will not be accepted.

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 18.
• The last day to drop/add (tuition refund available) is Monday, January 31.
• Spring recess is the week of Sunday, March 6.
• The last day to withdraw (no refund) is Monday, March 28.
• The last day of classes is Monday, May 2.

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.