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Syllabus for 640:551 Fall 2022
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The following sections in Brundan and Kleshchev:

 2.1- 2.5: Categories, functors, natural transformations.

 3.1- 3.6: Universal constructions (3.5 can be skipped as long as you
           know what a free object is).

 4.1- 4.4: Multilinear algebra.

 6.1- 6.8: Group theory (6.5 and 6.6 contain lots of important
           examples that you are encouraged to know, but the exam will
           not require that you know these examples.)

 7.1- 7.6: Group actions (except 7.4, and 7.2 has same status as 6.5
           and 6.6).

10.1-10.2: Basics on commutative rings.

16.1-16.4: General theory of modules.

17.1-17.2: Modules over PIDs.

Other topics:

Sesquilinear forms and symmetric, Hermitian, and normal endomorphisms.
Covered in sections 7-9 of the Algebra Bootcamp Notes posted on the
course website.

Hilbert's Basis Theorem, Noether's Normalization Theorem, Hilbert's
Nullstellensatz. Covered in the Algebraic Geometry Notes posted on the
course website.

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