Mathematics 4800-1 Symmetry & Groups Spring 2010
Instructor:
Sarah N. Kitchen
Email: kitchen@math.utah.edu
Homepage: http://www.math.utah.edu/∼kitchen
Office: JWB 307
Office Phone: 581-8338
Office Hour: By appointment only.
Text: Linear Representations of Finite Groups, Jean-Pierre Serre.
ISBN: 9780387901909. Used: $55.95,
New: $74.60. Other texts as necessary.
Course Description:
The focus of this course will be precisely the study of symmetry groups and
their representations, with a view towards applications. Students will be expected to work individually or
in small groups to research a special topic related to the course material and will present their research in
the second half of the semester. Topics covered by the lecturer beyond an introduction to the representation
theory of finite groups, and in particular the representation theory of symmetry groups, will depend on the
interests of the class. Prerequisites: Minimum, MATH 2270 or 2250 or other linear algebra introduction.
MATH 5310 is ideal, but will not be assumed.
Assignments and Grades:
Participation is of utmost importance in this class. Your grade will depend on two assignments:
• One 40-minute lecture on a section from the course text.
• An individual research project. You will need to submit a paper on your topic, as well as give a
one-hour lecture. The final draft of the paper is due on the last day of class.
Regular attendence plus satisfactory completion of both assignments will result in an A, of one assignment
gets you a B, and only attending the class will earn you a C. If you do not participate at all and do not
attend class regularly, you will receive a failing grade.
I will routinely suggest homework problems, but will not collect or grade them. There will be no exams.
Tentative Course Outline:
January
February
March
April
11-15
18-22
20
25
25-29
1-5
8-12
14-19
22-26
1-5
5
8-12
15-19
22-26
30
1-28
28
Ch. 1-2
Ch. 2-3
Ch. 4-5
Ch. 5
Ch. 6
Introduction to groups and linear algebra
Linear representations; Character theory
LAST DAY to drop classes
LAST DAY to register for classes
Character theory; Induced representations
(S) Compact groups; (S) Examples
(S) More Examples; Lattices
Sarah out of town: (S) TBD; Guest lecture
(S) TBD; Sarah returns 2/25: The group algebra
TBD
LAST DAY to withdraw
TBD
TBD
SPRING BREAK
Project presentation
Project presentations
University last day of classes
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committed to policies of nondiscrimination and equal opportunity, and vigorously pursues affirmative action
in all programs, activities, and employment with regard to race, color, national origin, sex, age, and status
as a person with a disability. Religion, sexual orientation, and status as a disabled veteran or veteran of the
Vietnam era also are protected under nondiscrimination and equal opportunity employment policies. The
University seeks to provide equal access to its programs, services and activities for people with disabilities.
Reasonable prior notice is needed to arrange accommodations. Students should call 801-581-5020 or 801585-1813 (both are TDD). Evidence of practices not consistent with these policies should be reported to
the Employee Relations/Dispute Resolution Office, 801-581-8365 (voice or TDD). If you require special
accommodations under the ADA please inform me through official channels early in the semester.
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