Simon Fraser University
Engaging the World

Course Outlines

Fall 2019 - MATH 817 G100

Groups and Rings (4)

Class Number: 4121

Delivery Method: In Person

Overview

  • Course Times + Location:

    Sep 3 – Dec 2, 2019: Tue, 10:30 a.m.–12:20 p.m.
    Burnaby

    Sep 3 – Dec 2, 2019: Thu, 10:30 a.m.–12:20 p.m.
    Burnaby

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, p-groups, nilpotent and solvable groups, aspects of simple groups, representation theory, group algebras, chain conditions, Jacobson radical, Chevalley-Jacobson density theorem, Wedderburn-Artin 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 p-groups
  • 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%
  • Take-home 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: 978-0821847992

Representation Theory: A First Course
W. Fulton and J. Harris
Springer, 2004
ISBN: 978-0387975276

Graduate Studies Notes:

Important dates and deadlines for graduate students are found here: http://www.sfu.ca/dean-gradstudies/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/s10-01.html

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS