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.
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.