MATH GU4044 Representations of Finite Groups

MATH GU4044 Representations of Finite Groups
Spring 2018

Time and place: MW 2:40--3:55, location 520 Mathematics.
Instructor: Robert Friedman (x4-4355). Office: 605 Mathematics.
Office hours: My office hours are Tuesdays and Thursdays, 1:30--2:30 PM in 605 Math, but feel free to drop by at any time.
Email: rf@math.columbia.edu
Teaching Assistant: Shuai Wang sw3028@columbia.edu. Office hours: Mondays 4:30--5:30 PM, in the Help Room (406 Mathematics).

This course is an introduction to the theory of finite-dimensional representations of finite groups, along with applications. Linear Algebra (Math UN2010) or Honors Math (Math UN1207--1208) and Modern Algebra I (Math GU4041) or the equivalent are prerequisites for this course. A knowledge of some of the basic material of Modern Algebra II (Math GU4042) is helpful.

Text: There is no required text.

Recommended texts. Here are some standard texts on representation theory:

Jean-Pierre Serre, Linear Representations of Finite Groups (Second Edition), Graduate Texts in Mathematics 42, New York, Springer, 1977.
William Fulton and Joe Harris, Representation Theory: A first course, Graduate Texts in Mathematics 129, New York, Springer, 1991.
Benjamin Steinberg, Representation Theory of Finite Groups: An Introductory Approach, New York, Springer, 2012.
Gordon James and Martin Liebeck, Linear Representations and Characters of Groups (Second Edition), Cambridge, Cambridge University Press, 2001.

Homework: There will be weekly problem sets, due at the beginning of class on Mondays. The first problem set will be due on Monday, January 29. You should attempt every homework problem and eventually understand how to do every problem correctly. Collaboration and discussion with your classmates is encouraged, but you must write up assignments individually.

Exams: There will be one 75-minute midterm exam and a final.

Midterm Exam: Monday, March 5, in class (tentative date)
Final: this is centrally scheduled by the University. The tentative time is Wednesday, May 9, 2018, 1:10--4:00, in the usual classroom. It must be taken at the scheduled time.

If you have two final examinations scheduled at the same time, it is the responsibility of the other department to provide an alternate exam. Examinations will not be rescheduled because of travel arrangements -- it is your responsibility to schedule travel appropriately. Makeup exams will be given only under exceptional circumstances, usually only for the final along with a grade of incomplete.

Grading: The final course grade will be determined by:

Homework: 25%;
Midterm exam: 25%;
Final exam: 50%.

Help: My office hours are Tuesdays and Thursdays, 1:30--2:30 PM in 605 Math, and you should always feel free to make an appointment or just drop by. Help is also available without appointment in the Mathematics Help Room (406 Mathematics) whenever it is open.

Academic Dishonesty: The vast majority of students do not cheat. Anyone who does so devalues the hard work of the rest of the class and creates a bad atmosphere for all. Anyone found to have cheated on an exam will receive a failing grade for the course and be subject to administrative discipline. If you are struggling with the material or have a problem about an upcoming exam, please discuss it with me instead of resorting to cheating.

Important dates:

January 17: First day of class
February 20: Drop date (most schools)
March 5: Midterm exam
March 12--18: Spring break
April 30: Last day of class
May 9: Final exam (tentative)

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