McGill University

Department of Mathematics & Statistics

Higher Algebra I

189-570A

Detailed Syllabus

Wednesday September 6 to Friday September 15
Overview of the course. Generalities on algebraic structures. Groups, rings, vector spaces, modules. Categories and Functors. Groups and permutations.

Assignment 1 due on Monday, September 18.
Corrections.

Monday September 18 to Friday September 29
Representation theory of finite groups.

Assignment 2 due on Monday, October 2.
Corrections.

Monday October 2 to Friday October 13
Representation theory of finite groups, continued.

Assignment 3 due on Monday, October 16.
Corrections.

Monday October 16 to Friday October 27
Rings and Fields. Integral extensions. Localization. Dedekind domains.

Assignment 4 due on Monday, October 30.
Corrections.

Monday October 30 to Friday November 10
Galois Theory.

Assignment 5 due on Monday, November 13.
Corrections.

Monday November 13 to Friday November 24
Galois Theory, continued. Frobenius elements, inertia and decomposition groups. Galois theory of infinite extensions.

Practice Final due on Monday, November 27.
Corrections.

Monday November 27 to Wednesday December 6
End of Galois Theory. Some review.