Fall 2021 - MATH 817 G100
Groups and Rings (4)
Class Number: 2562
Delivery Method: In Person
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.
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
- 6 assignments - every 2 weeks with equal weighting 60%
- Take-home Exam 40%
Algebra: A Graduate Course, I.
American Mathematical Society, 2009
Representation Theory: A First Course
W. Fulton and J. Harris
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.
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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).
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