## 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 October 27 **

Rings and Fields. Integral extensions. Localization. Dedekind domains.

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. Frobenius elements, inertia and decomposition
groups. Galois theory of infinite extensions.

Practice Final due on Monday, November 27.

** Monday November 27 to Wednesday December 6 **

End of Galois Theory. Some review.