Fall 2019  MATH 817 G100
Groups and Rings (4)
Class Number: 4121
Delivery Method: In Person
Overview

Course Times + Location:
Tu 10:30 AM – 12:20 PM
AQ 5015, BurnabyTh 10:30 AM – 12:20 PM
AQ 5015, Burnaby

Instructor:
Imin Chen
ichen@sfu.ca
1 778 7823339
Description
CALENDAR DESCRIPTION:
A survey of graduate group and/or ring theory. Possible topics include generators and relations, composition series, Sylow theory, permutation groups, abelian groups, pgroups, nilpotent and solvable groups, aspects of simple groups, representation theory, group algebras, chain conditions, Jacobson radical, ChevalleyJacobson density theorem, WedderburnArtin theorems.
COURSE DETAILS:
Prerequisites: MATH 340 and MATH 341 or their equivalents.
This course will be a survey of group and ring theory leading up to and including representation theory.
 Group actions, Sylow theorems and pgroups
 Permutation groups, New groups from old
 Solvable and nilpotent groups
 Operator groups and unique decompositions
 Module theory without rings
 Rings, ideals, and modules
 Simple modules and primitive rings
 Artinian rings and projective modules
 An introduction to character theory
 Burnside's theorem
 Representation theory of GL_2 over a finite field
 Representation theory of S_n
 Additional topics
Grading
 6 assignments  every 2 weeks with equal weighting 60%
 Takehome Exam 40%
NOTES:
MATH 817 classes will start in Week 2 of the semester.
Materials
RECOMMENDED READING:
Algebra: A Graduate Course, I.
Martin Isaacs
American Mathematical Society, 2009
ISBN: 9780821847992
Representation Theory: A First Course
W. Fulton and J. Harris
Springer, 2004
ISBN: 9780387975276
Graduate Studies Notes:
Important dates and deadlines for graduate students are found here: http://www.sfu.ca/deangradstudies/current/important_dates/guidelines.html. The deadline to drop a course with a 100% refund is the end of week 2. The deadline to drop with no notation on your transcript is the end of week 3.
Registrar Notes:
SFU’s Academic Integrity web site http://www.sfu.ca/students/academicintegrity.html is filled with information on what is meant by academic dishonesty, where you can find resources to help with your studies and the consequences of cheating. Check out the site for more information and videos that help explain the issues in plain English.
Each student is responsible for his or her conduct as it affects the University community. Academic dishonesty, in whatever form, is ultimately destructive of the values of the University. Furthermore, it is unfair and discouraging to the majority of students who pursue their studies honestly. Scholarly integrity is required of all members of the University. http://www.sfu.ca/policies/gazette/student/s1001.html
ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS