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MA951 - Graduate Algebra

Lecturer: Marco Schlichting

Term(s): Term 1

Commitment: 30 lectures

Assessment: 100% Oral Exam

Prerequisites: Familiarity with topics from 2nd year undergraduate algebra modules such as MA251 and MA249.

Content: The goal of the module is to provide an opportunity to (re-)visit undergraduate material in algebra from a graduate perspective allowing the students to fill in gaps and broaden their knowledge. We will cover material from commutative and non-commutative ring theory, module theory, category theory, Galois theory, representation theory, multi-linear algebra, and homological algebra. See also format below.

Format: Lectures are 10-12 on Wednesdays, and 10-11 on Fridays in B3.02. Depending on background and interest of participants, I intend to split the module in two streams, a Main Stream (taught 2h on Wednesdays weeks 1-9/10) and an Advanced Stream (taught 1h on Fridays weeks 1-10, possibly also Wednesday week 10).

On Wednesdays we will cover the main points of MA377 Rings and Modules, MA3E1 Groups and Representations, and MA3D5 Galois Theory. On Fridays I will give an introduction to Homology and Cohomology of groups which will cover the basics of homological algebra, Tor and Ext, Hochschild-Serre spectral sequence with the goal of computing all homology groups of various groups of small order.

Both streams will have complete lecture notes and exercises.

Students can choose which stream they want to be examined in.

References: -Main Stream: Lang "Algebra", Hungerford "Algebra", and Dummit and Foote "Abstract Algebra" - Advanced Stream: Brown "Cohomology of groups"

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