Fall 2012 Course Syllabus - Mathematics 9100.001

Course: Mathematics 9100.001.
Course Title: Topics in Algebra: Representation Theory.
Time: TR 0930-1050.
Place: Wachman Hall CC527.
Instructor: Lorenz, Martin W.
Instructor Office: Wachman Hall CC528.
Instructor Email: martin.lorenz@temple.edu
Instructor Phone: 215-204-5013.
Office Hours: TR 11:00-12:00 or by appointment.
Prerequisites: Math 8011 & 8012 or equivalent or permission of instructor.
Textbook: The course will not follow any particular textbook. As background references, I recommend the following books: (1) Pavel Etingof et al.: Introduction to Representation Theory, American Mathematical Society (2011). (2) Jean-Pierre Serre: Linear Representations of Finite Groups. Graduate Texts in Mathematics Vol. 42, Springer-Verlag, New York (1977). (3) William Fulton and Joe Harris: Representation Theory, A First Course. Graduate Texts in Mathematics Vol. 129, Springer-Verlag, New York (1991). All these texts contain material outside the scope of this course. While Serre's book deals exclusively with finite groups, the one by Fulton & Harris considers both groups and Lie algebras, the main focus being on the latter. Etingof's book also treats representations of quivers and other topics from representation theory.
Course Goals: This course will give an introduction to algebraic representation theory. The emphasis this semester will be on representations of finite groups over the complex numbers, where the fundamental ideas of representation theory are most accessible. My approach will largely be example based, with the symmetric groups featuring prominently.
Topics Covered: I will start by introducing the fundamental notions of representation theory in the general setting of algebras. Then I will specialize to the case of group algebras or, equivalently, representations of groups. We will focus on finite groups and representations over the complex numbers this semester. In this case, everything can be calculated explicitly by means of "characters".
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 12/13, 8:00-10:00. I am happy to change this if so desired by the class.
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 Monday, August 27.
• Labor Day is Monday, September 3.
• The last day to drop/add (tuition refund available) is Monday, September 10.
• Thanksgiving is Thursday, November 22.
• The last day to withdraw (no refund) is Tuesday, October 23.
• The last day of classes is Wednesday, December 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.