Fall 2021 - MATH 817 G100

Groups and Rings (4)

Class Number: 2562

Delivery Method: In Person

Overview

  • Course Times + Location:

    Tu, Th 10:30 AM – 12:20 PM
    AQ 5005, 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%

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:

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS

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

TEACHING AT SFU IN FALL 2021

Teaching at SFU in fall 2021 will involve primarily in-person instruction, with approximately 70 to 80 per cent of classes in person/on campus, with safety plans in place.  Whether your course will be in-person or through remote methods will be clearly identified in the schedule of classes.  You will also know at enrollment whether remote course components will be “live” (synchronous) or at your own pace (asynchronous).

Enrolling in a course acknowledges that you are able to attend in whatever format is required.  You should not enroll in a course that is in-person if you are not able to return to campus, and should be aware that remote study may entail different modes of learning, interaction with your instructor, and ways of getting feedback on your work than may be the case for in-person classes.

Students with hidden or visible disabilities who may need class or exam accommodations, including in the context of remote learning, are advised to register with the SFU Centre for Accessible Learning (caladmin@sfu.ca or 778-782-3112) as early as possible in order to prepare for the fall 2021 term.