McGill University

Department of Mathematics & Statistics

Higher Algebra I


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.

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

Assignment 2 due on Monday, October 2.

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

Assignment 3 due on Monday, October 16.

Monday October 16 to Friday November 3
Representations of PSL2(Fp). Galois theory.

Assignment 4 due on Monday, October 30.

Monday October 30 to Friday November 10
Galois Theory.

Assignment 5 due on Monday, November 13.

Monday November 13 to Friday November 24
Galois Theory, continued. Galois theory of infinite extensions.

Practice Final.

Monday November 27 to Wednesday December 6
End of Galois Theory. Frobenius elements, inertia and decomposition groups. Some review.

Thursday, December 7, from 1:00 to 4:00 PM, in BH 1205. Final in-class exam.